HP MLIB User's Guide Vol. 1 7th Ed.

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HP MLIB User’s Guide

Seventh Edition

HP Part No. B6061-96027 and B6061-96028

HP MLIB

December 2004

Printed in USA

Summary of content (584 pages)

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HP MLIB User’s Guide Seventh Edition HP Part No.
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Edition: Seventh Document Numbers: B6061-96027 and B6061-96028 Remarks: Released Dcember 2004 with HP MLIB software version9.0. User’s Guide split into two volumes with this release. Edition: Sixth Document Number: B6061-96023 Remarks: Released September 2003 with HP MLIB software version 8.50. Edition: Fifth Document Number: B6061-96020 Remarks: Released September 2002 with HP MLIB software version 8.30.
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Notice  Copyright 1979-2004 Hewlett-Packard Development Company. All Rights Reserved. Reproduction, adaptation, or translation without prior written permission is prohibited, except as allowed under the copyright laws. The information contained in this document is subject to change without notice. Hewlett-Packard makes no warranty of any kind with regard to this material, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose.
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Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv VECLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv LAPACK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi ScaLAPACK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Message passing-based nested parallelism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Default CPS library stack is too small for MLIB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Default Pthread library stack is too small for MLIB . . . . . . . . . . . . . . . . . . . . . . . . . 22 Roundoff effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Data types and precision . . . . . . . . . . . . . . . .
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SASUM/DASUM/IASUM/SCASUM/DZASUM Sum of magnitudes . . . . . . . . . . . . 62 SAXPY/DAXPY/CAXPY/CAXPYC/ZAXPY/ZAXPYC Elementary vector operation 65 SAXPYI/DAXPYI/CAXPYI/ZAXPYI Sparse elementary vector operation . . . . . . . 68 SCLIP/DCLIP/ICLIP Two sided vector clip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 SCLIPL/DCLIPL/ICLIPL Left sided vector clip . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 SCLIPR/DCLIPR/ICLIPR Right sided vector clip . . . . . . . . . . . . . . . . .
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plane rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 F_SAXPBY/F_DAXPBY/F_CAXPBY/F_ZAXPBY Scaled vector accumulation . . . 161 F_SAXPY_DOT/F_DAXPY_DOT/F_CAXPY_DOT/F_ZAXPY_DOT Combine AXPY and DOT routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 F_SCOPY/F_DCOPY/F_CCOPY/F_ZCOPY Copy vector. . . . . . . . . . . . . . . . . . . . .
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DGEMMS/ZGEMMS Strassen matrix-matrix multiply . . . . . . . . . . . . . . . . . . . . . 227 SGEMV/DGEMV/CGEMV/ZGEMV Matrix-vector multiply . . . . . . . . . . . . . . . . . 232 SGER/DGER/CGERC/CGERU/ZGERC/ZGERU Rank-1 update . . . . . . . . . . . . . . 237 SGETRA/DGETRA/CGETRA/ZGETRA In-place transpose of a general square matrix 241 SSBMV/DSBMV/CHBMV/ZHBMV Matrix-vector multiply. . . . . . . . . . . . . . . . . . 244 SSPMV/DSPMV/CHPMV/ZHPMV Matrix-vector multiply . . . . . . . . . . . . . . . . . .
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F_SGEMM/F_DGEMM/F_CGEMM/F_ZGEMM General matrix-matrix multiply 362 F_SGEMV/F_DGEMV/F_CGEMV/F_ZGEMV General matrix-vector multiply . . 365 F_SGEMVER/F_DGEMVER/F_CGEMVER/F_ZGEMVER Multiple matrix-vector multiply, rank 2 update. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 F_SGEMVT/F_DGEMVT/F_CGEMVT/F_ZGEMVT Multiple matrix-vector multiply 372 F_SGER/F_DGER/F_CGER/F_ZGER General rank-1 update . . . . . . . . . . . . . . . .
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Common arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 SM arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 Order of arguments for args(A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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SVBRSM/DVBRSM/CVBRSM/ZVBRSM 533 xii Variable block row format triangular solve Table of Contents
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Figures List of Figures xiii
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xiv List of Figures
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Tables Table 1-1 VECLIB and VECLIB8 Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Table 1-2 Compiler Defaults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Table 1-3 VECLIB Naming Convention—Data Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Table 1-4 BLAS Standard Operator Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Table 2-1 FPINFO return values . . .
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Table 4-19 BSR Format Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Table 4-20 6 x 6 Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Table 4-21 VBR Format Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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VECLIB Preface Hewlett-Packard’s high-performance math libraries (HP MLIB) help you speed development of applications and shorten execution time of long-running technical applications. HP MLIB is a collection of subprograms optimized for use on HP servers and workstations, providing mathematical software and computational kernels for engineering and scientific applications. HP MLIB can be used on systems ranging from single-processor workstations to multiprocessor high-end servers.
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LAPACK LAPACK HP Linear Algebra Package (LAPACK) is a collection of subprograms that provide mathematical software for applications involving linear equations, least squares, eigenvalue problems, and the singular value decomposition. LAPACK is designed to supersede the linear equation and eigenvalue packages, LINPACK and EISPACK.
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SuperLU Refer to Part 3 of this manual for information specific to HP ScaLAPACK. To supplement the HP specific information provided in Part 3 of this document, refer to the standard ScaLAPACK Users’ Guide. You can access the latest edition of the ScaLAPACK Users’ Guide at the Netlib repository at the following URL: http://www.netlib.org/scalapack/slug/index..html SuperLU This implementation provides the Distributed SuperLU library designed for distributed memory parallel computers.
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VMATH • Sparse symmetric and structurally-symmetric linear equation solutions. • Sparse symmetric ordinary and generalized eigensystem solutions. • Out-of-core symmetric and structurally-symmetric linear equation and eigensystems solutions. • Full METIS functionality This implementation provides the METIS Version 4.0.1 library. It is based on the public-domain METIS, which was developed at the University of Minnesota, Department of Computer Science, and the Army HPC Research Center.
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Purpose and audience Purpose and audience This guide describes the MLIB software library and shows how to use it. This library provides mathematical software and computational kernels for applications.
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Organization Organization The HP MLIB User’s Guide describes HP MLIB VECLIB in Part 1, HP MLIB LAPACK in Part 2, HP MLIB ScaLAPACK in Part 3, and HP MLIB Distributed SuperLU in Part 4. To learn fundamental information necessary for using the VECLIB library, read Chapter 1 and the introductory sections of the other chapters. These sections of background information will help you efficiently use the library subprograms.
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Organization Part 6 of this document is organized as follows: • Chapter 13 explains sparse symmetric linear equation subprograms • Chapter 14 describes METIS subprograms • Chapter 15 describes sparse symmetric eigenvalue subprograms • Chapter 16 describes BCSLIB-EXT functionality Supplemental material is provided as follows: • Appendix A describes how to call VECLIB and LAPACK subprograms from within C programs • Appendix B describes LINPACK subprograms available in HP MLIB • Appendix C lists parallelized
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Notational conventions Notational conventions The following conventions are used in this manual: Italics Italics within text indicate mathematical entities used or manipulated by the program: for example, solve the n-by-n system of linear equations Ax = b. Italics within command lines indicate generic commands, file names, or subprogram names. Substitute actual commands, file names, or subprograms for the italicized words. For example, the command line f90 prog_name.
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Documentation resources UPPERCASE MONOSPACE UPPERCASE MONOSPACE indicates Fortran programs. Brackets ( [ ] ) Square brackets in command examples designate optional entries. NOTE A NOTE highlights important supplemental information. Documentation resources The HP MLIB User’s Guide, the LAPACK Users’ Guide, and the ScaLAPACK Users’ Guide are available in hardcopy and online formats. For the HP MLIB User’s Guide, refer to: http:// www.hp.
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Documentation resources • HP-UX Floating-Point Guide. Describes how floating-point arithmetic is implemented on HP 9000 systems and discusses how floating-point behavior affects the programmer. • HP Fortran 90 Programmer’s Guide. Provides extensive usage information (including how to compile and link), suggestions and tools for migrating to HP Fortran 90, and how to call C and HP-UX routines for HP Fortran 90. • HP Fortran 90 Programmer’s Reference.
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Part 1 HP VECLIB
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Overview 1 Introduction to VECLIB Overview VECLIB, a component of HP MLIB, is a collection of subprograms optimized for use on Hewlett-Packard servers and workstations, providing mathematical software and computational kernels for engineering and scientific applications.
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Chapter objectives Hewlett-Packard scientific libraries. Refer to the Appendix, “Converting from LINPACK or EISPACK” in the LAPACK Users’ Guide, for assistance converting programs that currently call LINPACK or EISPACK routines to call LAPACK or VECLIB routines instead.
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Standardization Standardization VECLIB conforms to a variety of existing standards. For example, it includes Basic Linear Algebra Subprograms (BLAS), levels 1, 2, and 3, and Sparse BLAS. These products are available with standardized user interfaces on computers ranging from microcomputers to supercomputers. Because VECLIB conforms to these standards, it is a software bridge from other computers to Hewlett-Packard servers and workstations.
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Accessing VECLIB Table 1-1 VECLIB and VECLIB8 Libraries Processor Type PA 2.0 Itanium 2 OS Version Address Width Installation Directory 32-bit /opt/mlib/lib/pa2.0 libveclib.a libveclib.sl 64-bit /opt/mlib/lib/pa20_64 libveclib.a libveclib.sl libveclib8.a libveclib8.sl 32-bit /opt/mlib/lib/hpux32 libveclib.a libveclib.so /opt/mlib/lib/hpux64 libveclib.a libveclib.so libveclib8.a libveclib8.so HP-UX 11i or later HP-UX 11i V1.
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Accessing VECLIB Processor Type OS Version Address Width Itanium 2 HP XC6000 Intel V7.1 Compiler 64-bit Itanium 2 HP XC4000 PGI V5.1 Compiler Itanium 2 Opteron PGI V5.1 Compiler Installation Directory Libraries libveclib.a /opt/mlib/intel_7.1/hpmpi_2.1/lib/64 libveclib.so libveclib8.a libveclib8.so 64-bit libveclib.a libveclib.so /opt/mlib/intel_5.1/hpmpi_2.1/lib/64 libveclib8.a libveclib8.so 64-bit libveclib.a libveclib.so /opt/mlib/intel_5.1/hpmpi_2.1/lib/64 libveclib8.a libveclib8.
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Accessing VECLIB When you use the –aarchive_shared flag on your compiler command line for HP-UX, it ensures that the compiler links the archive library. If the archive library is not available, then it links the shared library. If you omit –aarchive_shared and –ashared_archive, the linker defaults to linking the shared library. Link with –Bstatic on Linux systems.
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Accessing VECLIB For example, the command lines in Method 2 for PA could be written: f90 [options] file ... −Wl,–aarchive_shared,−L/opt/mlib/lib/[pa2.0|pa20_64] −lveclib cc [options] file ... −Wl,–aarchive_shared,−L/opt/mlib/lib/[pa2.0|pa20_64] −lveclib −lcl −lm aCC [options] file ... −Wl,–aarchive_shared,−L/opt/mlib/lib/[pa2.0|pa20_64] −lveclib −lcl −lm 4. Set the LDOPTS environment variable to include: –aarchive_shared,−L/opt/mlib/lib/[pa2.
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Accessing VECLIB Linking with libisamstub.a C language codes that call Fortran77 routines from the BLAS Standard, the sparse linear equation system, or the sparse eigenvalue system, must explicitly link the ISAM (Indexed Sequential Access Method) stubs library into the program. For example, cc [options] file ... –Wl,–aarchive_shared,–L/opt/fortran/lib/libisamstub.a −lveclib −lcl −lm This only applies if you are linking with the VECLIB archive library. This option is only valid for 32-bit PA systems.
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Accessing VECLIB –aarchive_shared,−L/opt/mlib/lib/[hpux32|hpux64] For example: setenv LDOPTS “–aarchive_shared,–L/opt/mlib/lib/hpux32” Then use the −lveclib option on the compiler command line that links your program: f90 [options] file ... −lveclib cc [options] file ... −lveclib −lcl −lm aCC [options] file ... −lveclib −lcl −lm NOTE An LDOPTS specification takes precedence over using -Wl on the compiler command line.
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Accessing VECLIB NOTE When you use the Intel V8.0 C compiler to link the SOLVERS library, you may require one or more of -lifcore, -lifport, or -ldl. 2. Specify the entire path of the library file on the compiler command line that links your program. For example, to link your program with VECLIB for use with 32- or 64-bit addressing on a Linux system, use one of the following: ifort [options] file ... /opt/mlib/intel_8.0/hpmpi_2.1/lib/[32|64]/libveclib.a −openmp icc [options] file ... /opt/mlib/intel_8.
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Accessing VECLIB variable to specify a library path, you cannot override that specification with a -Wl option on your compiler command line. 5. Use the following commands to link your programs for use with the VECLIB8 library on a Red Hat Linux system. ifort −i8 [options] file ... -L/opt/mlib/intel_8.0/hpmpi_2.1/lib/[32|64]/lveclib8 −openmp icc [options] file ... −L/opt/mlib/intel_8.0/hpmpi_2.
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Accessing VECLIB For example: setenv LDOPTS “–Bstatic,–L/opt/mlib/lib/intel_8.0/hpmpi_2.1/lib/64” Then use the −lveclib option on the compiler command line that links your program: ifort [options] file ... −lveclib −openmp icc [options] file ... −lveclib −openmp NOTE An LDOPTS specification takes precedence over using -Wl on the compiler command line.
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Accessing VECLIB –Bstatic,−L/opt/mlib/lib/intel_7.1/hpmpi_2.1/lib/64 For example: setenv LDOPTS “–Bstatic,–L/opt/mlib/lib/intel_7.1/hpmpi_2.1/lib/64” Then use the −lveclib option on the compiler command line that links your program: efc [options] file ... −lveclib −openmp icc [options] file ... −lveclib −openmp NOTE An LDOPTS specification takes precedence over using -Wl on the compiler command line.
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Accessing VECLIB 4. Set the LDOPTS environment variable to include: –Bstatic,−L/opt/mlib/lib/pgi_5.1/hpmpi_2.1/lib/64 For example: setenv LDOPTS “–Bstatic,–L/opt/mlib/lib/pgi5.1/hpmpi_2.1/lib/64” Then use the −lveclib option on the compiler command line that links your program: pgf90 [options] file ... −lveclib −mp pgcc [options] file ... −lveclib −mp −lpgf90 −lpgf90_rpml −lpgf902 −lpgf90rtl −lpgftnrtl NOTE An LDOPTS specification takes precedence over using -Wl on the compiler command line.
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Accessing VECLIB This file includes both entry points xerbla and xerbla_, and xerbla_ conflicts with your XERBLA subroutine. Use one of the following workarounds on PA-RISC if you are compiling your own Fortran version of XERBLA: • Compile your XERBLA with +noppu. This implies that you also compile any of your program that calls XERBLA with +noppu, and that you apply this rule recursively.
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Accessing VECLIB SUBROUTINE XERBLA(SRNAME,INFO) ENTRY XERBLA_SRNAME,INFO) ... • Use f90 ALIAS directives and provide both xerbla and xerbla_ entry points: !$HP$ ALIAS xerbla='xerbla' !$HP$ ALIAS xerbla_='xerbla_' SUBROUTINE XERBLA(SRNAME,INFO) ENTRY XERBLA_(SRNAME,INFO) ... The ALIAS directives prevent the compiler from postpending the underbar onto the entry points and external references to XERBLA.
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Optimization SUBROUTINE mlib_routine(...) ENTRY mlib_routine_(...) ... And a C version might be: #undef mlib_routine #undif mlib_routine_ void mlib_routine (...){ ... } void mlib_routine_(...){ mlib_routine(...); } Optimization The key computational kernels in VECLIB have been optimized to take full advantage of both PA-RISC and Itanium tightly integrated architectures.
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Parallel processing You can enable or disable parallel processing at link time or at runtime. A program does not use parallelism in VECLIB unless parallel processing is enabled at both link time and at runtime. Linking for parallel or non parallel processing To enable parallel processing at link time, your link step must produce a multithreaded executable.
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Parallel processing For Korn shell: export MLIB_NUMBER_OF_THREADS=8 MLIB_NUMBER_OF_THREADS is examined on the first call to a parallelized VECLIB subprogram to establish the default parallel action within VECLIB. Use the subroutine MLIB_SETNUMTHREADS to restore VECLIB parallel processing to its run-time default that was specified by MLIB_NUMBER_OF_THREADS. Refer to the mlib_setnumthreads(3m) man page for usage information. • Use the subroutine MLIB_SETNUMTHREADS.
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Parallel processing • Call VECLIB subprograms in a parallelized loop or region. VECLIB supports nested parallelism where the outer parallelism is implemented through OpenMP while the inner parallelism is implemented with VECLIB SMP parallelism. To use this mechanism, you must be familiar with the techniques of parallel processing. Refer to the Parallel Programming Guide for HP-UX Systems for details. • Use the Message Passing Interface (MPI) explicit parallel model.
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Parallel processing endif c$omp end parallel call omp_set_nested(.false.) ... Using MLIB_NUMBER_OF_THREADS set to 1, the code would run two-way parallel: one OpenMP thread for C = αAB + βC and another for F = αDE + βF Setting MLIB_NUMBER_OF_THREADS to 2 would allow nested parallelism and run the code four-way parallel. If a parallel VECLIB subprogram is called from a parallelized loop or region, VECLIB will automatically avoid over-subscription of the CPUs.
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Parallel processing Assume the application started on two MPI processes. Using MLIB_NUMBER_OF_THREADS set to 1, the code would run two-way parallel: one MPI process for C = αAB + βC and another for F = αDE + βF Setting MLIB_NUMBER_OF_THREADS to 2 would allow nested parallelism and run the code four-way parallel. Default CPS library stack is too small for MLIB In libcps, the HP Compiler Parallel Support library, a CPS thread has a default stack size of 8M bytes.
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Roundoff effects Currently, 8 MB*(the number of threads) should be sufficient for all MLIB subprograms. If your application launchs threads directly from pthread library calls, set the minimum allocated stack size to match HP MLIB needs on each new thread. Setting the stack size on HP-UX as follows would be sufficient for programs that execute on two threads: int stacksize = 8388608; (...
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VECLIB naming convention Matching subprograms for real and complex data have been coded to maintain a close correspondence between the two. However, in some areas, the correspondence is necessarily weaker, and this has not been possible. Subprograms in VECLIB are provided in both 32-bit and 64-bit addressing versions, except in the VECLIB8 library where only 64-bit addressing is supported.
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Data type and byte length Data type and byte length There is a relationship between the data type of a subprogram, designated by the first character of its name (refer to T in Table 1-3), and the byte lengths of its arguments.
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Operator arguments uplo trans Refers to triangular matrices. There are two valid values to specify whether a matrix is upper or lower triangular. Used by routines applying a matrix, say A, to another vector or another matrix. There are three valid values to specify whether the matrix (A), its transpose (AT), or its conjugate transpose (A*) should be applied. op(A) refers to A, AT, or A* depending on the input value of the trans operator argument. Some BLAS routines have more than one trans operator.
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Operator arguments Table 1-4 BLAS Standard Operator Arguments Operator Argument norm sort side uplo transx Named Constant blas_one_norm blas_real_one_norm blas_two_norm blas_frobenius_norm blas_inf_norm blas_real_inf_norm blas_max_norm blas_real_max_norm blas_increasing_order blas_decreasing_order blas_left_side blas_right_side blas_upper blas_lower blas_trans Meaning 1-norm real 1-norm 2-norm Frobenius-norm infinity-norm real infinity-norm max-norm real-norm sort in increasing order sort in decreasin
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Error handling Error handling VECLIB subprograms are divided into two classes according to the way they detect and report usage errors: • Low-level subprograms • High-level subprograms Low-level subprograms Low-level subprograms are only minimally capable of detecting or handling errors. These subprograms attempt to do what is reasonable when a usage error occurs, but they do not warn you that something is wrong.
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Troubleshooting • ier > 0: Failure during the computation Some VECLIB subprograms do not have a success/error code in their argument lists, but instead call another VECLIB subprogram to process the error condition. MLIB provides the following error handlers: • XERBLA • XERVEC • F_BLASERROR Refer to the documentation for individual VECLIB subprogram to determine if one of these error handlers is used. For example, all BLAS Standard subprograms (those subprograms whose names begin with F_) use F_BLASERROR.
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HP MLIB man pages the original program into the small one. In this way, you eliminate extraneous code from suspicion. If the problem area is large, try to pare it to a manageable size. For example, if a 50-by-50 linear system fails, try to produce a 2-by-2 system that fails in the same way. HP MLIB man pages The HP MLIB man pages contain online documentation that includes information from the HP MLIB User’s Guide. The HP MLIB man pages are installed in the directory /opt/mlib/share/man.
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Overview 2 Basic Vector Operations Overview This chapter explains how to use the VECLIB vector subprograms that serve as building blocks for many user programs. It describes subprograms for performing dense and sparse vector operations.
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Chapter objectives Chapter objectives After reading this chapter you will: • Understand BLAS storage conventions • Know how to specify array sections • Know how to handle backward storage • Know how to use increment (also called stride) arguments • Understand the vector subprograms included with HP VECLIB, both Legacy BLAS and BLAS Standard subprograms Associated documentation The following documents provide supplemental material for this chapter: Dodson, D.S., R.G. Grimes, and J.G. Lewis.
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What you need to know to use vector subprograms What you need to know to use vector subprograms The following sections describe overall considerations for using vector subprograms: • BLAS storage conventions ❏ Fortran storage of arrays ❏ Fortran array argument association • BLAS indexing conventions ❏ Forward storage ❏ Backward storage ❏ Increment arguments • Operator arguments in the BLAS Standard • Representation of a permutation matrix • Representation of a Householder matrix BLAS storage conventions T
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What you need to know to use vector subprograms Fortran storage of arrays Two-dimensional arrays in Fortran are stored by columns. Consider the following specifications: DIMENSION A(N1,N2),B(N3) EQUIVALENCE (A,B) where N3 = N1 X N2. Then A(I,J) is associated with the same memory location as B(K) where K = I + (J−1) × N1 Successive elements of a column of A are adjacent in memory, while successive elements of a row of A are stored with a difference of N1 storage units between them.
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What you need to know to use vector subprograms BLAS indexing conventions This section describes handling stride arguments and forward and backward storage. A vector in the BLAS is defined by three quantities: • Vector length • Array or starting element within an array • Increment, sometimes called stride—defines the number of storage units between successive vector elements Forward storage Suppose that X is a real array. Let N be the vector length and let INCX be the increment.
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What you need to know to use vector subprograms Increment arguments The following examples illustrate how to use increment arguments to perform different operations with the same subprogram. These examples use the function F_SDOT with the following usage: SUBROUTINE F_SDOT (CONJ, N, ALPHA, X, INCX, BETA, Y, INCY, R) INTEGER CONJ, INCX, INCY, N REAL*4 ALPHA, BETA, R, X(*), Y(*) This usage adds the scaled dot product of the vectors X( * ) and Y( * ) to a scaled scalar R.
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What you need to know to use vector subprograms In BLAS Standard routines, you specify an operator argument with a named constant value. The actual numeric value assigned to the named constant is defined in the appropriate language’s include file. Operator arguments are represented in the Fortran 77 interface as INTEGERs. This specification is different from the legacy BLAS, where operator arguments are defined as CHARACTER*1.
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What you need to know to use vector subprograms Representation of a Householder matrix This section explains how the BLAS Standard represents a Householder matrix. An elementary reflector (or elementary Householder matrix) H of order n is a unitary matrix of the form H = I – τυυ H where τ is a scalar, and υ is an n-vector, with τ 2 υ 2 2 = 2 Re ( τ ) υ is often referred to as the Householder vector.
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Subprograms for basic vector operations Subprograms for basic vector operations The following sections in this chapter describe the vector subprograms included with VECLIB: • Legacy BLAS routines • BLAS Standard routines Note that the specification for operator arguments is different in legacy BLAS routines than in BLAS Standard routines. Operator arguments are represented in the BLAS Standard Fortran 77 interface as INTEGERs; in the legacy BLAS they are defined as CHARACTER*1.
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ISAMAX/IDAMAX/IIAMAX/ICAMAX/IZAMAX Index of maximum of magnitudes Legacy BLAS routines Name ISAMAX/IDAMAX/IIAMAX/ICAMAX/IZAMAX Index of maximum of magnitudes Purpose Given a real or integer vector x of length n, ISAMAX, IDAMAX, or IIAMAX determines the index of the element of the vector of maximum magnitude.
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Index of maximum of magnitudes ISAMAX/IDAMAX/IIAMAX/ICAMAX/IZAMAX INTEGER*4 i, ICAMAX, n, incx COMPLEX*8 x(lenx) i = ICAMAX(n, x, incx) INTEGER*4 i, IZAMAX, n, incx COMPLEX*16 x(lenx) i = IZAMAX(n, x, incx) VECLIB8: INTEGER*8 i, ISAMAX, n, incx REAL*4 x(lenx) i = ISAMAX(n, x, incx) INTEGER*8 i, IDAMAX, n, incx REAL*8 x(lenx) i = IDAMAX(n, x, incx) INTEGER*8 i, IIAMAX, n, incx, x(lenx) i = IIAMAX(n, x, incx) INTEGER*8 i, ICAMAX, n, incx COMPLEX*8 x(lenx) i = ICAMAX(n, x, incx) INTEGER*8 i, IZAMAX, n, incx
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ISAMAX/IDAMAX/IIAMAX/ICAMAX/IZAMAX Fortran Equivalent Example Index of maximum of magnitudes INTEGER*4 FUNCTION ISAMAX (N,X,INCX) REAL*4 X(*),TEMP,XMAX ISAMAX = 1 IF ( N .GT. 1 ) THEN XMAX = ABS ( X(1) ) INCXA = ABS ( INCX ) IX = 1 + INCXA DO 10 I = 2, N TEMP = ABS ( X(IX) ) IF ( TEMP .GT. XMAX ) THEN ISAMAX = I XMAX = TEMP END IF IX = IX + INCXA 10 CONTINUE ELSE IF ( N .LT.
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Index of minimum of magnitudes ISAMIN/IDAMIN/IIAMIN/ICAMIN/IZAMIN Name ISAMIN/IDAMIN/IIAMIN/ICAMIN/IZAMIN Index of minimum of magnitudes Purpose Given a real or integer vector x of length n, ISAMIN, IDAMIN, or IIAMIN determines the index of element of the vector of minimum magnitude.
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ISAMIN/IDAMIN/IIAMIN/ICAMIN/IZAMIN Index of minimum of magnitudes VECLIB8: INTEGER*8 i, ISAMIN, n, incx REAL*4 x(lenx) i = ISAMIN(n, x, incx) INTEGER*8 i, IDAMIN, n, incx REAL*8 x(lenx) i = IDAMIN(n, x, incx) INTEGER*8 i, IIAMIN, n, incx, x(lenx) i = IIAMIN(n, x, incx) INTEGER*8 i, ICAMIN, n, incx COMPLEX*8 x(lenx) i = ICAMIN(n, x, incx) INTEGER*8 i, IZAMIN, n, incx COMPLEX*16 x(lenx) i = IZAMIN(n, x, incx) Input n x incx Output i 44 HP MLIB User’s Guide Number of elements of vector x to be used.
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Index of minimum of magnitudes Fortran Equivalent Example ISAMIN/IDAMIN/IIAMIN/ICAMIN/IZAMIN INTEGER*4 FUNCTION ISAMIN (N,X,INCX) REAL*4 X(*),TEMP,XMIN ISAMIN = 1 IF ( N .GT. 1 ) THEN XMIN = ABS ( X(1) ) INCXA = ABS ( INCX ) IX = 1 + INCXA DO 10 I = 2, N TEMP = ABS ( X(IX) ) IF ( TEMP .LT. XMIN ) THEN ISAMIN = I XMIN = TEMP END IF IX = IX + INCXA 10 CONTINUE ELSE IF ( N .LT.
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ISCTxx/IDCTxx/IICTxx/ICCTxx/IZCTxx Count selected vector elements Name ISCTxx/IDCTxx/IICTxx/ICCTxx/IZCTxx Count selected vector elements Purpose Given a real, integer, or complex vector x of length n, these subprograms count the number of elements of the vector that satisfy a specified relationship to a given scalar a. The last two characters of the subprogram name specify the relation of interest between the elements of the vector and the scalar.
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Count selected vector elements ISCTxx/IDCTxx/IICTxx/ICCTxx/IZCTxx INTEGER*4 i, ICCTxx, n, incx COMPLEX*8 a, x(lenx) i = ICCTxx(n, x, incx, a) INTEGER*4 i, IZCTxx, n, incx COMPLEX*16 a, x(lenx) i = IZCTxx(n, x, incx, a) VECLIB8: INTEGER*8 i, ISCTxx, n, incx REAL*4 a, x(lenx) i = ISCTxx(n, x, incx, a) INTEGER*8 i, IDCTxx, n, incx REAL*8 a, x(lenx) i = IDCTxx(n, x, incx, a) INTEGER*8 i, IICTxx, n, incx, a, x(lenx) i = IICTxx(n, x, incx, a) INTEGER*8 i, ICCTxx, n, incx COMPLEX*8 a, x(lenx) i = ICCTxx(n, x, i
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ISCTxx/IDCTxx/IICTxx/ICCTxx/IZCTxx Output i Fortran Equivalent Example Count selected vector elements If n ≤ 0, then i = 0. Otherwise, i is the number of elements of x that satisfy the relationship with a specified by the subprogram name. INTEGER*4 FUNCTION ISCTEQ (N,X,INCX,A) REAL*4 A,X(*) ISCTEQ = 0 INCXA = ABS ( INCX ) IX = 1 DO 10 I = 1, N IF ( X(IX) .EQ.
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Index of maximum element of vector ISMAX/IDMAX/IIMAX Name ISMAX/IDMAX/IIMAX Index of maximum element of vector Purpose Given a real or integer vector x of length n, these subprograms determine the index of the maximum element of the vector. Specifically, the subprograms determine the smallest index i such that x i = max ( x j : j = 1, 2, …, n ) The vector can be stored in a one-dimensional array or in either a row or a column of a two-dimensional array.
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ISMAX/IDMAX/IIMAX Index of maximum element of vector Use incx = 1 if the vector x is stored contiguously in array x; that is, if xi is stored in x(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter. Output i Fortran Equivalent Example If n ≤ 0, then i = 0. Otherwise, i is the index of the maximum element of x. INTEGER*4 FUNCTION ISMAX (N,X,INCX) REAL*4 X(*),XMAX ISMAX = 1 IF ( N .GT. 1 ) THEN XMAX = X(1) INCXA = ABS ( INCX ) IX = 1 + INCXA DO 10 I = 2, N IF ( X(IX) .GT.
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Index of minimum element of vector ISMIN/IDMIN/IIMIN Name ISMIN/IDMIN/IIMIN Index of minimum element of vector Purpose Given a real or integer vector x of length n, these subprograms determine the index of minimum element of the vector. Specifically, the subprograms determine the smallest index i such that x i = min ( x j : j = 1, 2, …, n ) The vector can be stored in a one-dimensional array or in either a row or a column of a two-dimensional array.
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ISMIN/IDMIN/IIMIN Index of minimum element of vector Use incx = 1 if the vector x is stored contiguously in array x; that is, if xi is stored in x(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter. Output i Fortran Equivalent Example If n ≤ 0, then i = 0. Otherwise, i is the index of the minimum element of x. INTEGER*4 FUNCTION ISMIN (N,X,INCX) REAL*4 X(*),XMIN ISMIN = 1 IF ( N .GT. 1 ) THEN XMIN = X(1) INCXA = ABS ( INCX ) IX = 1 + INCXA DO 10 I = 2, N IF ( X(IX) .LT.
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Search vector for element ISSVxx/IDSVxx/IISVxx/ICSVxx/IZSVxx Name ISSVxx/IDSVxx/IISVxx/ICSVxx/IZSVxx Search vector for element Purpose Given a real, integer, or complex vector x of length n, these subprograms search sequentially through the vector for the first element xi that satisfies a specified relationship to a given scalar a and return the index i of that element. The last two characters of the subprogram name specify the relationship of interest between the element of the vector and the scalar.
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ISSVxx/IDSVxx/IISVxx/ICSVxx/IZSVxx Search vector for element INTEGER*4 i, IISVxx, n, incx, a, x(lenx) i = IISVxx(n, x, incx, a) INTEGER*4 i, ICSVxx, n, incx COMPLEX*8 a, x(lenx) i = ICSVxx(n, x, incx, a) INTEGER*4 i, IZSVxx, n, incx COMPLEX*16 a, x(lenx) i = IZSVxx(n, x, incx, a) VECLIB8: INTEGER*8 i, ISSVxx, n, incx REAL*4 a, x(lenx) i = ISSVxx(n, x, incx, a) INTEGER*8 i, IDSVxx, n, incx REAL*8 a, x(lenx) i = IDSVxx(n, x, incx, a) INTEGER*8 i, IISVxx, n, incx, a, x(lenx) i = IISVxx(n, x, incx, a) INTEGE
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Search vector for element Output Fortran Equivalent Example i ISSVxx/IDSVxx/IISVxx/ICSVxx/IZSVxx If n ≤ 0 or if no element of x satisfies the relationship with a specified by the subprogram name, then i = 0. Otherwise, i is the index i of the first element xi of x that satisfies the relationship with a specified by the subprogram name. Recall that xi is stored in x((i−1)×|incx|+1).
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SAMAX/DAMAX/IAMAX/SCAMAX/DZAMAX Maximum of magnitudes Name SAMAX/DAMAX/IAMAX/SCAMAX/DZAMAX Maximum of magnitudes Purpose Given a real or integer vector x of length n, SAMAX, DAMAX, or IAMAX computes the l∞ norm of x, that is, the maximum of the magnitudes of the elements of the vector s = x ∞ = max ( x i : i = 1, 2, …, n ). Given a complex vector x of length n, SCAMAX or DZAMAX computes s = max ( Re ( x i ) + Im ( x i ) : i = 1, 2, …, n ).
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Maximum of magnitudes SAMAX/DAMAX/IAMAX/SCAMAX/DZAMAX INTEGER*4 n, incx REAL*8 s, DZAMAX COMPLEX*16 x(lenx) s = DZAMAX(n, x, incx) VECLIB8: INTEGER*8 n, incx REAL*4 s, SAMAX, x(lenx) s = SAMAX(n, x, incx) INTEGER*8 n, incx REAL*8 s, DAMAX, x(lenx) s = DAMAX(n, x, incx) INTEGER*8 n, incx, s, IAMAX, x(lenx) s = IAMAX(n, x, incx) INTEGER*8 n, incx REAL*4 s, SCAMAX COMPLEX*8 x(lenx) s = SCAMAX(n, x, incx) INTEGER*8 n, incx REAL*8 s, DZAMAX COMPLEX*16 x(lenx) s = DZAMAX(n, x, incx) Input n x incx Output s
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SAMAX/DAMAX/IAMAX/SCAMAX/DZAMAX Fortran Equivalent Example Maximum of magnitudes REAL*4 FUNCTION SAMAX (N,X,INCX) REAL*4 X(*) SAMAX = 0.0 INCXA = ABS ( INCX ) IX = 1 DO 10 I = 1, N SAMAX = MAX ( SAMAX , ABS ( X(IX) ) ) IX = IX + INCXA 10 CONTINUE RETURN END Compute the maximum of the magnitudes of the elements of a REAL*8 vector x, where x is a vector 10 elements long stored in a one-dimensional array X of dimension 20.
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Minimum of magnitudes SAMIN/DAMIN/IAMIN/SCAMIN/DZAMIN Name SAMIN/DAMIN/IAMIN/SCAMIN/DZAMIN Minimum of magnitudes Purpose Given a real or integer vector x of length n, SAMIN, DAMIN, or IAMIN computes the minimum of the magnitudes of the elements of the vector s = min ( x i : i = 1, 2, …, n ). Given a complex vector x of length n, SCAMIN or DZAMIN computes s = min ( Re ( x i ) + Im ( x i ) : i = 1, 2, …, n ) where Re(xi) and Im(xi) are the real and imaginary parts of xi, respectively.
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SAMIN/DAMIN/IAMIN/SCAMIN/DZAMIN INTEGER*8 n, incx REAL*4 s, SAMIN, x(lenx) s = SAMIN(n, x, incx) INTEGER*8 n, incx REAL*8 s, DAMIN, x(lenx) s = DAMIN(n, x, incx) INTEGER*8 n, incx, s, IAMIN, x(lenx) s = IAMIN(n, x, incx) INTEGER*8 n, incx REAL*4 s, SCAMIN COMPLEX*8 x(lenx) s = SCAMIN(n, x, incx) INTEGER*8 n, incx REAL*8 s, DZAMIN COMPLEX*16 x(lenx) s = DZAMIN(n, x, incx) 60 HP MLIB User’s Guide Minimum of magnitudes
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Minimum of magnitudes Input SAMIN/DAMIN/IAMIN/SCAMIN/DZAMIN n x incx Output Fortran Equivalent Example s Number of elements of vector x to be used. If n ≤ 0, the subprograms do not reference x. Array of length lenx = (n−1)×|incx|+1 containing the n-vector x. Increment for array x. x is stored forward in array x with increment |incx|; that is, xi is stored in x((i−1)×|incx|+1). Use incx = 1 if the vector x is stored contiguously in array x; that is, if xi is stored in x(i).
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SASUM/DASUM/IASUM/SCASUM/DZASUM Sum of magnitudes Name SASUM/DASUM/IASUM/SCASUM/DZASUM Sum of magnitudes Purpose Given a real or integer vector x of length n, SASUM, DASUM, or IASUM computes the l1 norm of x, that is, the sum of magnitudes of the elements of the vector n s = x 1 = ∑ xi i=1 Given a complex vector x of length n, SCASUM or DZASUM computes n s = ∑ i=1 Re ( x i ) + Im ( x i ) where Re(xi) and Im(xi) are the real and imaginary parts of xi, respectively.
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Sum of magnitudes SASUM/DASUM/IASUM/SCASUM/DZASUM INTEGER*4 n, incx REAL*4 s, SCASUM COMPLEX*8 x(lenx) s = SCASUM(n, x, incx) INTEGER*4 n, incx REAL*8 s, DZASUM COMPLEX*16 x(lenx) s = DZASUM(n, x, incx) VECLIB8: INTEGER*8 n, incx REAL*4 s, SASUM, x(lenx) s = SASUM(n, x, incx) INTEGER*8 n, incx REAL*8 s, DASUM, x(lenx) s = DASUM(n, x, incx) INTEGER*8 n, incx, s, IASUM, x(lenx) s = IASUM(n, x, incx) INTEGER*8 n, incx REAL*4 s, SCASUM COMPLEX*8 x(lenx) s = SCASUM(n, x, incx) INTEGER*8 n, incx REAL*8 s, DZAS
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SASUM/DASUM/IASUM/SCASUM/DZASUM Sum of magnitudes Indexing Conventions” in the introduction to this chapter. Output s Fortran Equivalent Example If n ≤ 0, then s = 0. Otherwise, s is the sum of magnitudes of the elements of x. REAL*4 FUNCTION SASUM (N, X,INCX) REAL*4 X(*) SASUM = 0.0 IF ( N .LE.
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Elementary vector operation SAXPY/DAXPY/CAXPY/CAXPYC/ZAXPY/ZAXPYC Name SAXPY/DAXPY/CAXPY/CAXPYC/ZAXPY/ZAXPYC Elementary vector operation Purpose Given a real or complex scalar a and real or complex vectors x and y of length n, these subprograms perform the elementary vector operations y ← ax + y and y ← ax+ y where x is the complex conjugate of x.
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SAXPY/DAXPY/CAXPY/CAXPYC/ZAXPY/ZAXPYC Elementary vector operation INTEGER*8 n, incx, incy COMPLEX*8 a, x(lenx), y(leny) CALL CAXPY(n, a, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*8 a, x(lenx), y(leny) CALL CAXPYC(n, a, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*16 a, x(lenx), y(leny) CALL ZAXPY(n, a, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*16 a, x(lenx), y(leny) CALL ZAXPYC(n, a, x, incx, y, incy) Input n a x incx Number of elements of vectors x and y to be used in the elemen
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Elementary vector operation SAXPY/DAXPY/CAXPY/CAXPYC/ZAXPY/ZAXPYC Use incy = 1 if the vector y is stored contiguously in array y; that is, if yi is stored in y(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter. Output Notes If n ≤ 0 or a = 0, then y is unchanged. Otherwise, ax+y overwrites the input. y If incx = 0, then xi = x(1) for all i. The result is unspecified if incy = 0 or if x and y overlap such that any element of x shares a memory location with any element of y.
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SAXPYI/DAXPYI/CAXPYI/ZAXPYI Sparse elementary vector operation Name SAXPYI/DAXPYI/CAXPYI/ZAXPYI Sparse elementary vector operation Purpose Given a real or complex scalar a, a sparse vector x stored in compact form via a set of indices and a dense vector y stored in full storage form, these subprograms perform the elementary vector operation y ← ax + y. More precisely, let x be a sparse n-vector with m ≤ n interesting (usually nonzero) elements, and let {k1, k2, ...
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Sparse elementary vector operation SAXPYI/DAXPYI/CAXPYI/ZAXPYI INTEGER*8 m, indx(m) COMPLEX*8 a, x(m), y(n) CALL CAXPYI(m, a, x, indx, y) INTEGER*8 m, indx(m) COMPLEX*16 a, x(m), y(n) CALL ZAXPYI(m, a, x, indx, y) Input m a x Number of interesting elements of x, m ≤ n, where n is the length of y. If m ≤ 0, the subprograms do not reference x, indx, or y. The scalar a. Array of length m containing the interesting elements of x. x(j) = xi if indx(j) = i.
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SAXPYI/DAXPYI/CAXPYI/ZAXPYI indx Sparse elementary vector operation Array containing the indices {ki} of the interesting elements of x. The indices must satisfy 1 ≤ indx ( i ) ≤ n i = 1, 2, …, m and indx ( i ) ≠ indx ( j ) where n is the length of y. Array containing the elements of y, y(i) = yi. y Output Notes If m ≤ 0 or a = 0, then y is unchanged. Otherwise, ax+y overwrites the input. Only the elements of y whose indices are included in indx are changed.
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Two sided vector clip SCLIP/DCLIP/ICLIP Name SCLIP/DCLIP/ICLIP Two sided vector clip Purpose Given scalars a and b and a vector x of length n, these subprograms form the vector y by the clip operation a  yi =  xi  b if xi ≤ a if a < xi < b if b ≤ xi i = 1, 2, …, n The vectors can be stored in one-dimensional arrays or in either rows or columns of two-dimensional arrays. Indexing through the arrays can be either forward or backward.
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SCLIP/DCLIP/ICLIP Two sided vector clip x incx Array of length lenx = (n−1)×|incx|+1 containing the n-vector x. Increment for the array x: incx ≥ 0 x is stored forward in array x; that is, xi is stored in x((i−1)×incx+1). incx < 0 x is stored backward in array x; that is, xi is stored in x((i−n)×incx+1). Use incx = 1 if the vector x is stored contiguously in array x; that is, if xi is stored in x(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter.
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Two sided vector clip SCLIP/DCLIP/ICLIP incy Increment for the array y, incy ≠ 0: incy > 0 y is stored forward in array y; that is, yi is stored in y((i−1)×incy+1). incy < 0 y is stored backward in array y; that is, yi is stored in y((i−n)×incy+1). Use incy = 1 if the vector y is stored contiguously in array y; that is, if yi is stored in y(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter. Output Notes y Array of length leny = (n−1)×|incy|+1 containing the n-vector y.
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SCLIPL/DCLIPL/ICLIPL Left sided vector clip Name SCLIPL/DCLIPL/ICLIPL Left sided vector clip Purpose Given scalar a and a vector x of length n, these subprograms form the vector y by the left-sided clip operation a yi =   xi if xi ≤ a if xi > a i = 1, 2, …, n. The vectors can be stored in one-dimensional arrays or in either rows or columns of two-dimensional arrays. Indexing through the arrays can be either forward or backward.
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Left sided vector clip SCLIPL/DCLIPL/ICLIPL incx ≥ 0 x is stored forward in array x; that is, xi is stored in x((i−1)×incx+1). incx < 0 x is stored backward in array x; that is, xi is stored in x((i−n)×incx+1). Use incx = 1 if the vector x is stored contiguously in array x; that is, if xi is stored in x(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter.
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SCLIPL/DCLIPL/ICLIPL Left sided vector clip incy Increment for the array y, incy ≠ 0: incy > 0 y is stored forward in array y; that is, yi is stored in y((i−1)×incy+1). incy < 0 y is stored backward in array y; that is, yi is stored in y((i−n)×incy+1). Use incy = 1 if the vector y is stored contiguously in array y; that is, if yi is stored in y(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter. Output Notes y Array of length leny = (n−1)×|incy|+1 containing the n-vector y.
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Right sided vector clip SCLIPR/DCLIPR/ICLIPR Name SCLIPR/DCLIPR/ICLIPR Right sided vector clip Purpose Given scalar b and a vector x of length n, these subprograms form the vector y by the right-sided clip operation  xi yi =  b if xi < b if xi ≥ b i = 1, 2, …, n. The vectors can be stored in one-dimensional arrays or in either rows or columns of two-dimensional arrays, and the indexing through the arrays can be either forward or backward.
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SCLIPR/DCLIPR/ICLIPR Right sided vector clip incx ≥ 0 x is stored forward in array x; that is, xi is stored in x((i−1)×incx+1). incx < 0 x is stored backward in array x; that is, xi is stored in x((i−n)×incx+1). Use incx = 1 if the vector x is stored contiguously in array x; that is, if xi is stored in x(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter.
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Right sided vector clip SCLIPR/DCLIPR/ICLIPR incy Increment for the array y, incy ≠ 0: incy > 0 y is stored forward in array y; that is, yi is stored in y((i−1)×incy+1). incy < 0 y is stored backward in array y; that is, yi is stored in y((i−n)×incy+1). Use incy = 1 if the vector y is stored contiguously in array y; that is, if yi is stored in y(i). Refer to “BLAS Indexing Conventions” in the introduction to this chapter.
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SCOPY/DCOPY/ICOPY/CCOPY/CCOPYC/ZCOPY/ZCOPYC Copy vector Name SCOPY/DCOPY/ICOPY/CCOPY/CCOPYC/ZCOPY/ZCOPYC Copy vector Purpose Given real, integer, or complex vectors x and y of length n, these subprograms perform the vector copy operations y←x and y←x where x is the complex conjugate of x. The vectors can be stored in one-dimensional arrays or in either rows or columns of two-dimensional arrays. Indexing through the arrays can be either forward or backward.
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Copy vector SCOPY/DCOPY/ICOPY/CCOPY/CCOPYC/ZCOPY/ZCOPYC INTEGER*8 n, incx, incy REAL*8 x(lenx), y(leny) CALL DCOPY(n, x, incx, y, incy) INTEGER*8 n, incx, incy, x(lenx), y(leny) CALL ICOPY(n, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*8 x(lenx), y(leny) CALL CCOPY(n, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*8 x(lenx), y(leny) CALL CCOPYC(n, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*16 x(lenx), y(leny) CALL ZCOPY(n, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*16 x(lenx), y(len
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SCOPY/DCOPY/ICOPY/CCOPY/CCOPYC/ZCOPY/ZCOPYC Input n x incx Number of elements of vectors x and y to be used in the copy operation. If n ≤ 0, the subprograms do not reference x or y. Array of length lenx = (n−1)×|incx|+1 containing the n-vector x. x is used in conjugated form by CCOPYC and ZCOPYC and in unconjugated form by the other subprograms. Increment for the array x: incx ≥ 0 x is stored forward in array x; that is, xi is stored in x((i−1)×incx+1).
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Copy vector Fortran Equivalent Example 1 SCOPY/DCOPY/ICOPY/CCOPY/CCOPYC/ZCOPY/ZCOPYC SUBROUTINE SCOPY (N, X,INCX, Y,INCY) REAL*4 X(*),Y(*) IF ( N .LE. 0 ) RETURN IX = 1 IY = 1 IF ( INCX .LT. 0 ) IX = 1 - (N-1) * INCX IF ( INCY .LT. 0 ) IY = 1 - (N-1) * INCY DO 10 I = 1, N Y(IY) = X(IX) IX = IX + INCX IY = IY + INCY 10 CONTINUE RETURN END Copy the REAL*8 vector x into y, where x and y are vectors 10 elements long stored in one-dimensional arrays X and Y of dimension 20.
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SDOT/DDOT/CDOTC/CDOTU/ZDOTC/ZDOTU Dot product Name SDOT/DDOT/CDOTC/CDOTU/ZDOTC/ZDOTU Dot product Purpose Given real or complex data vectors x and y of length n, these subprograms compute the dot products n s = ∑ n xi yi i=1 and s = ∑ xi yi i=1 where x is the complex conjugate of x. The vectors can be stored in one-dimensional arrays or in either rows or columns of two-dimensional arrays. Indexing through the arrays can be either forward or backward.
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Dot product SDOT/DDOT/CDOTC/CDOTU/ZDOTC/ZDOTU INTEGER*8 n, incx, incy REAL*8 s, DDOT, x(lenx), y(leny) s = DDOT(n, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*8 s, CDOTC, x(lenx), y(leny) s = CDOTC(n, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*8 s, CDOTU, x(lenx), y(leny) s = CDOTU(n, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*16 s, ZDOTC, x(lenx), y(leny) s = ZDOTC(n, x, incx, y, incy) INTEGER*8 n, incx, incy COMPLEX*16 s, ZDOTU, x(lenx), y(leny) s = ZDOTU(n, x, incx, y, incy) INTELC
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SDOT/DDOT/CDOTC/CDOTU/ZDOTC/ZDOTU x incx Dot product Array of length lenx = (n−1)×|incx|+1 containing the n-vector x. x is used in conjugated form by CDOTC and ZDOTC and in unconjugated form by the other subprograms. Increment for the array x: incx ≥ 0 x is stored forward in array x; that is, xi is stored in x((i−1)×incx+1). incx < 0 y incy Use incx = 1 if the vector x is stored contiguously in array x; that is, if xi is stored in x(i).
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Dot product SDOT/DDOT/CDOTC/CDOTU/ZDOTC/ZDOTU Fortran Equivalent Example 1 REAL*4 FUNCTION SDOT (N, X,INCX, Y,INCY) REAL*4 X(*),Y(*) SDOT = 0.0 IF ( N .LE. 0 ) RETURN IX = 1 IY = 1 IF ( INCX .LT. 0 ) IX = 1 - (N-1) * INCX IF ( INCY .LT.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 117
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 118
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 119
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 120
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 121
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 122
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 123
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 124
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 125
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 126
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 127
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 128
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 129
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 130
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 131
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 132
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 133
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 134
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 135
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 136
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 137
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 138
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 139
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 140
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 141
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 142
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 143
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 144
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 145
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 146
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 147
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 148
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 149
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 150
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 151
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 152
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 153
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 154
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 155
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 156
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 157
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 158
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 159
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 160
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 161
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 162
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 163
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 164
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 165
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 166
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 167
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 168
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 169
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 170
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 171
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 172
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 173
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 174
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 175
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 176
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 177
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 178
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 180
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 182
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 183
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 184
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 188
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 190
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 192
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
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SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 196
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 197
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 198
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 199
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 200
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 201
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 202
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 203
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 204
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 205
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 206
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 207
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 208
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 209
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 210
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 211
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 212
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 213
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 214
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 215
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 216
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 217
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 218
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 219
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 220
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 221
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 222
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 223
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 224
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 225
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 226
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 227
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 228
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 229
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 230
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 231
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 232
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 233
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 234
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 235
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 236
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 237
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 238
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 239
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 240
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 241
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 242
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 243
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 244
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 245
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 246
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 247
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 248
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 249
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 250
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 251
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 252
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 253
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 254
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 255
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 256
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 257
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 258
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 259
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 260
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 261
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 262
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 263
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 264
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 265
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 266
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 267
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 268
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 269
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 270
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 271
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 272
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 273
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 274
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 275
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 276
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 277
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 278
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 279
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 280
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 281
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 282
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 283
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 284
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 285
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 286
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 287
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 288
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 289
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 290
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 291
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 292
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 293
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 294
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 295
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 296
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 297
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 298
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 299
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 300
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 301
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 302
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 303
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 304
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 305
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 306
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 307
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 308
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 309
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 310
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 311
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 312
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 313
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 314
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 315
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 316
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 317
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 318
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 319
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 320
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 321
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 322
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 323
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 324
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 325
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 326
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 327
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 328
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 329
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 330
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 331
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 332
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 333
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 334
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 335
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 336
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 337
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 338
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 339
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 340
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 341
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 342
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 343
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 344
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 345
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 346
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 347
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 348
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 349
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 350
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 351
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 352
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 353
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 354
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 355
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 356
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 357
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 358
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 359
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 360
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 361
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 362
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 363
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 364
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 365
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 366
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 367
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 368
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 369
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 370
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 371
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 372
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 373
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 374
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 375
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 376
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 377
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 378
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 379
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 380
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 381
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 382
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 383
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 384
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 385
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 386
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 387
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 388
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 389
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 390
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 391
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 392
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 393
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 394
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 395
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 396
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 397
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 398
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 399
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 400
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 401
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 402
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 403
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 404
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 405
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 406
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 407
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 408
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 409
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 410
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 411
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 412
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 413
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 414
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 415
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 416
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 417
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 418
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 419
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 420
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 421
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 422
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 423
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 424
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 425
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 426
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 427
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 428
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 429
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 430
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 431
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 432
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 433
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 434
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 435
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 436
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 437
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 438
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 439
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 440
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 441
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 442
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 443
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 444
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 445
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 446
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 447
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 448
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 449
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 450
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 451
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 452
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 453
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 454
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 455
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 456
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 457
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 458
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 459
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 460
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 461
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 462
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 463
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 464
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 465
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 466
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 467
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 468
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 469
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 470
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 471
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 472
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 473
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 474
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 475
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 476
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 477
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 478
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 479
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 480
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 481
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 482
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 483
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 484
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 485
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 486
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 487
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 488
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 489
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 490
SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Name SDOTI/DDOTI/CDOTCI/CDOTUI/ZDOTCI/ZDOTUI Sparse dot product Purpose Given a real or complex sparse vector x stored in compact form via an index vector and a dense vector y stored in full storage form, these subprograms compute the sparse dot products n s = n ∑ xi yi and s = i=1 ∑ xi yi i=1 where x is the complex conjugate of x.
PAGE 491
Block sparse column matrix-matrix multiply SBSCMM/DBSCMM/CBSCMM/ZBSCMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix mb n kb alpha Number of block rows in matrix A. Number of columns in matrix C. Number of block columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
PAGE 492
SBSCMM/DBSCMM/CBSCMM/ZBSCMM Block sparse column matrix-matrix multiply bpntrb( ) Integer array of length kb such that bpntrb(j) points to location in bindx of the first block entry of the j-th block column of A. bpntre( ) lb b( ) ldb beta c( ) ldc work( ) lwork 464 HP MLIB User’s Guide Integer array of length kb such that bpntre(j)-1 points to location in bindx of the last block entry of the j-th block column of A. Dimension of dense blocks composing A. Rectangular array with leading dimension ldb.
PAGE 493
Block sparse column format triangular solve SBSCSM/DBSCSM/CBSCSM/ZBSCSM Name SBSCSM/DBSCSM/CBSCSM/ZBSCSM Block sparse column format triangular solve Purpose Block sparse column format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B with m=mb x lb, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
PAGE 494
SBSCSM/DBSCSM/CBSCSM/ZBSCSM Block sparse column format triangular solve SUBROUTINE ZBSCSM INTEGER*4 transa, mb, n, unitd, blda, lb, ldb, ldc, lwork INTEGER*4 descra(*), bindx(*), bpntrb(*), bpntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZBSCSM (transa, mb, n, unitd, dv, alpha, descra, val, bindx, bpntrb, bpntre, lb, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SBSCSM INTEGER*8 transa, mb, n, unitd, blda, lb, ldb, ldc, lwork INTEGER*8 descra(*), bindx(*), bp
PAGE 495
Block sparse column format triangular solve SBSCSM/DBSCSM/CBSCSM/ZBSCSM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix mb n unitd Number of block rows in matrix A. Number of columns in matrix C. Type of scaling. 1. Identity matrix (argument dv( ) is ignored) 2. Scale on left (row scaling) 3. Scale on right (column scaling) dv( ) alpha Diagonal scaling array of length lb*lb*mb. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array.
PAGE 496
SBSCSM/DBSCSM/CBSCSM/ZBSCSM val( ) bindx( ) Block sparse column format triangular solve Scalar array of length nnz containing matrix entries stored column-major within each dense block. Integer array of length bnnz consisting of the block row indices of the block entries of A. bpntrb( ) Integer array of length kb such that bpntrb(j) points to location in bindx of the first block entry of the j-th block column of A.
PAGE 497
Block sparse row matrix-matrix multiply SBSRMM/DBSRMM/CBSRMM/ZBSRMM Name SBSRMM/DBSRMM/CBSRMM/ZBSRMM Block sparse row matrix-matrix multiply Purpose Block sparse row matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix with m=mb x lb and k=kb x lb. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix. Here AT is the transpose and A* is the conjugate-transpose of A.
PAGE 498
SBSRMM/DBSRMM/CBSRMM/ZBSRMM Block sparse row matrix-matrix multiply SUBROUTINE ZBSRMM INTEGER*4 transa, mb, n, kb, lb, ldb, ldc, lwork INTEGER*4 descra(*), bindx(*), bpntrb(*), bpntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZBSRMM (transa, mb, n, kb, alpha, descra, val, bindx, bpntrb, bpntre, lb, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SBSRMM INTEGER*8 transa, mb, n, kb, lb, ldb, ldc, lwork INTEGER*8 descra(*), bindx(*), bpntrb(*), bpntre(*) REAL*4 alp
PAGE 499
Block sparse row matrix-matrix multiply SBSRMM/DBSRMM/CBSRMM/ZBSRMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix mb n kb alpha Number of block rows in matrix A. Number of columns in matrix C. Number of block columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
PAGE 500
SBSRMM/DBSRMM/CBSRMM/ZBSRMM Block sparse row matrix-matrix multiply bpntrb( ) Integer array of length mb such that bpntrb(j) points to location in bindx of the first block entry of the j-th block row of A. bpntre( ) lb b( ) ldb beta c( ) ldc work( ) lwork 472 HP MLIB User’s Guide Integer array of length mb such that bpntre(j)-1 points to location in bindx of the last block entry of the j-th block column of A. Dimension of dense blocks composing A. Rectangular array with leading dimension ldb.
PAGE 501
Block sparse row format triangular solve SBSRSM/DBSRSM/CBSRSM/ZBSRSM Name SBSRSM/DBSRSM/CBSRSM/ZBSRSM Block sparse row format triangular solve Purpose Block sparse row format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B with m=mb x lb, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
PAGE 502
SBSRSM/DBSRSM/CBSRSM/ZBSRSM Block sparse row format triangular solve SUBROUTINE ZBSRSM INTEGER*4 transa, mb, n, unitd, blda, lb, ldb, ldc, lwork INTEGER*4 descra(*), bindx(*), bpntrb(*), bpntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZBSRSM (transa, mb, n, unitd, dv, alpha, descra, val, bindx, bpntrb, bpntre, lb, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SBSRSM INTEGER*8 transa, mb, n, unitd, blda, lb, ldb, ldc, lwork INTEGER*8 descra(*), bindx(*), bpntr
PAGE 503
Block sparse row format triangular solve SBSRSM/DBSRSM/CBSRSM/ZBSRSM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix mb n unitd Number of block rows in matrix A. Number of columns in matrix C. Type of scaling. 1. Identity matrix (argument dv( ) is ignored) 2. Scale on left (row scaling) 3. Scale on right (column scaling) dv( ) alpha Diagonal scaling array of length lb*lb*mb. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array.
PAGE 504
SBSRSM/DBSRSM/CBSRSM/ZBSRSM val( ) bindx( ) Block sparse row format triangular solve Scalar array of length nnz containing matrix entries stored column-major within each dense block. Integer array of length bnnz consisting of the block row indices of the block entries of A. bpntrb( ) Integer array of length mb such that bpntrb(j) points to location in bindx of the first block entry of the j-th block row of A.
PAGE 505
Coordinate matrix-matrix multiply SCOOMM/DCOOMM/CCOOMM/ZCOOMM Name SCOOMM/DCOOMM/CCOOMM/ZCOOMM Coordinate matrix-matrix multiply Purpose Coordinate matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix. Here AT is the transpose and A* is the conjugate-transpose of A.
PAGE 506
SCOOMM/DCOOMM/CCOOMM/ZCOOMM Coordinate matrix-matrix multiply SUBROUTINE ZCOOMM INTEGER*4 transa, m, n, k, nnz, ldb, ldc, lwork INTEGER*4 descra(*), indx(*), jndx(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZCOOMM (transa, m, n, k, alpha, descra, val, indx, jndx, nnz, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SCOOMM INTEGER*8 transa, m, n, k, nnz, ldb, ldc, lwork INTEGER*8 descra(*), indx(*), jndx(*) REAL*4 alpha, beta REAL*4 val(*), b(ldb,*), c(ldc,*), work
PAGE 507
Coordinate matrix-matrix multiply SCOOMM/DCOOMM/CCOOMM/ZCOOMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n k alpha Number of rows in matrix A. Number of columns in matrix C. Number of columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
PAGE 508
SCOOMM/DCOOMM/CCOOMM/ZCOOMM b( ) ldb beta c( ) ldc work( ) lwork 480 HP MLIB User’s Guide Coordinate matrix-matrix multiply Rectangular array with leading dimension ldb. Leading dimension of b. Scalar parameter. Rectangular arrary with leading dimension ldc. Leading dimension of c. Scratch array of length lwork. Not used. Length of work array.
PAGE 509
Compressed sparse column matrix-matrix multiply SCSCMM/DCSCMM/CCSCMM/ZCSCMM Name SCSCMM/DCSCMM/CCSCMM/ZCSCMM Compressed sparse column matrix-matrix multiply Purpose Compressed sparse column matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix. Here AT is the transpose and A* is the conjugate-transpose of A.
PAGE 510
SCSCMM/DCSCMM/CCSCMM/ZCSCMM Compressed sparse column matrix-matrix multiply SUBROUTINE ZCSCMM INTEGER*4 transa, m, n, k, ldb, ldc, lwork INTEGER*4 descra(*), indx(*), pntrb(*), pntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZCSCMM (transa, m, n, k, alpha, descra, val, indx, pntrb, pntre, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SCSCMM INTEGER*8 transa, m, n, k, ldb, ldc, lwork INTEGER*8 descra(*), indx(*), pntrb(*), pntre(*) REAL*4 alpha, beta REAL*4 val
PAGE 511
Compressed sparse column matrix-matrix multiply SCSCMM/DCSCMM/CCSCMM/ZCSCMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n k alpha Number of rows in matrix A. Number of columns in matrix C. Number of columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
PAGE 512
SCSCMM/DCSCMM/CCSCMM/ZCSCMM pntre( ) b( ) ldb beta c( ) ldc work( ) lwork 484 HP MLIB User’s Guide Compressed sparse column matrix-matrix multiply Integer array of length k such that pntre(j)-1 points to location in val of the last nonzero element in column j. Rectangular array with leading dimension ldb. Leading dimension of b. Scalar parameter. Rectangular arrary with leading dimension ldc. Leading dimension of c. Scratch array of length lwork. Not used. Length of work array.
PAGE 513
Compressed sparse column format triangular solve SCSCSM/DCSCSM/CCSCSM/ZCSCSM Name SCSCSM/DCSCSM/CCSCSM/ZCSCSM Compressed sparse column format triangular solve Purpose Compressed sparse column format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
PAGE 514
SCSCSM/DCSCSM/CCSCSM/ZCSCSM Compressed sparse column format triangular solve SUBROUTINE ZCSCSM INTEGER*4 transa, m, n, unitd, ldb, ldc, lwork INTEGER*4 descra(*), indx(*), pntrb(*), pntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZCSCSM (transa, m, n, unitd, dv, alpha, descra, val, indx, pntrb, pntre, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SCSCSM INTEGER*8 transa, m, n, unitd, ldb, ldc, lwork INTEGER*8 descra(*), indx(*), pntrb(*), pntre(*) REAL*4 alpha
PAGE 515
Compressed sparse column format triangular solve SCSCSM/DCSCSM/CCSCSM/ZCSCSM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n unitd Number of rows in matrix A. Number of columns in matrix C. Type of scaling. 1. Identity matrix (argument dv( ) is ignored) 2. Scale on left (row scaling) 3. Scale on right (column scaling) dv( ) alpha Diagonal scaling array of length M. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure.
PAGE 516
SCSCSM/DCSCSM/CCSCSM/ZCSCSM val( ) indx( ) pntrb( ) pntre( ) b( ) ldb beta c( ) ldc work( ) lwork 488 HP MLIB User’s Guide Compressed sparse column format triangular solve Scalar array of length nnz containing matrix entries. Integer array of length nnz containing row indices. Integer array of length k such that pntrb(j) points to location in val of the first nonzero element in column j. Integer array of length k such that pntre(j)-1 points to location in val of the first nonzero element in column j.
PAGE 517
Compressed sparse row matrix-matrix multiply SCSRMM/DCSRMM/CCSRMM/ZCSRMM Name SCSRMM/DCSRMM/CCSRMM/ZCSRMM Compressed sparse row matrix-matrix multiply Purpose Compressed sparse row matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix. Here AT is the transpose and A* is the conjugate-transpose of A.
PAGE 518
SCSRMM/DCSRMM/CCSRMM/ZCSRMM Compressed sparse row matrix-matrix multiply SUBROUTINE ZCSRMM INTEGER*4 transa, m, n, k, ldb, ldc, lwork INTEGER*4 descra(*), indx(*), pntrb(*), pntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZCSRMM (transa, m, n, k, alpha, descra, val, indx, pntrb, pntre, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SCSRMM INTEGER*8 transa, m, n, k, ldb, ldc, lwork INTEGER*8 descra(*), indx(*), pntrb(*), pntre(*) REAL*4 alpha, beta REAL*4 val(*)
PAGE 519
Compressed sparse row matrix-matrix multiply SCSRMM/DCSRMM/CCSRMM/ZCSRMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n k alpha Number of rows in matrix A. Number of columns in matrix C. Number of columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
PAGE 520
SCSRMM/DCSRMM/CCSRMM/ZCSRMM pntre( ) b( ) ldb beta c( ) ldc work( ) lwork 492 HP MLIB User’s Guide Compressed sparse row matrix-matrix multiply Integer array of length m such that pntre(j)-1 points to location in val of the last nonzero element in row j. Rectangular array with leading dimension ldb. Leading dimension of b. Scalar parameter. Rectangular arrary with leading dimension ldc. Leading dimension of c. Scratch array of length lwork. Not used. Length of work array.
PAGE 521
Compressed sparse row format triangular solve SCSRSM/DCSRSM/CCSRSM/ZCSRSM Name SCSRSM/DCSRSM/CCSRSM/ZCSRSM Compressed sparse row format triangular solve Purpose Compressed sparse row format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
PAGE 522
SCSRSM/DCSRSM/CCSRSM/ZCSRSM Compressed sparse row format triangular solve SUBROUTINE ZCSRSM INTEGER*4 transa, m, n, unitd, ldb, ldc, lwork INTEGER*4 descra(*), indx(*), pntrb(*), pntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZCSRSM (transa, m, n, unitd, dv, alpha, descra, val, indx, pntrb, pntre, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SCSRSM INTEGER*8 transa, m, n, unitd, ldb, ldc, lwork INTEGER*8 descra(*), indx(*), pntrb(*), pntre(*) REAL*4 alpha, b
PAGE 523
Compressed sparse row format triangular solve SCSRSM/DCSRSM/CCSRSM/ZCSRSM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n unitd Number of rows in matrix A. Number of columns in matrix C. Type of scaling. 1. Identity matrix (argument dv( ) is ignored) 2. Scale on left (row scaling) 3. Scale on right (column scaling) dv( ) alpha Diagonal scaling array of length M. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure.
PAGE 524
SCSRSM/DCSRSM/CCSRSM/ZCSRSM val( ) indx( ) pntrb( ) pntre( ) b( ) ldb beta c( ) ldc work( ) lwork 496 HP MLIB User’s Guide Compressed sparse row format triangular solve Scalar array of length nnz containing matrix entries. Integer array of length nnz containing column indices. Integer array of length m such that pntrb(j) points to location in val of the first nonzero element in row j. Integer array of length m such that pntre(j)-1 points to location in val of the first nonzero element in row j.
PAGE 525
Diagonal matrix-matrix multiply SDIAMM/DDIAMM/CDIAMM/ZDIAMM Name SDIAMM/DDIAMM/CDIAMM/ZDIAMM Diagonal matrix-matrix multiply Purpose Diagonal matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix. Here AT is the transpose and A* is the conjugate-transpose of A.
PAGE 526
SDIAMM/DDIAMM/CDIAMM/ZDIAMM Diagonal matrix-matrix multiply SUBROUTINE ZDIAMM INTEGER*4 transa, m, n, k, lda, ndiag, ldb, ldc, lwork INTEGER*4 descra(*), idiag(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZDIAMM (transa, m, n, k, alpha, descra, val, lda, idiag, ndiag, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SDIAMM INTEGER*8 transa, m, n, k, lda, ndiag, ldb, ldc, lwork INTEGER*8 descra(*), idiag(*) REAL*4 alpha, beta REAL*4 val(*), b(ldb,*), c(ldc,*), work(*
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Diagonal matrix-matrix multiply SDIAMM/DDIAMM/CDIAMM/ZDIAMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n k alpha Number of rows in matrix A. Number of columns in matrix C. Number of columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
PAGE 528
SDIAMM/DDIAMM/CDIAMM/ZDIAMM lda idiag( ) ndiag b( ) ldb beta c( ) ldc work( ) lwork 500 HP MLIB User’s Guide Diagonal matrix-matrix multiply Leading dimension of val, must be greater or equal to min (m,k). Integer array of length ndiag consisting of the corresponding diagonal offsets of the nonzero diagonals of A in val. Lower triangular diagonals have negative offsets, the main diagonal has offset 0, and upper triangular diagonals have positive offset. Number of nonzero diagonals in A.
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Diagonal format triangular solve SDIASM/DDIASM/CDIASM/ZDIASM Name SDIASM/DDIASM/CDIASM/ZDIASM Diagonal format triangular solve Purpose Diagonal format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
PAGE 530
SDIASM/DDIASM/CDIASM/ZDIASM Diagonal format triangular solve SUBROUTINE ZDIASM INTEGER*4 transa, m, n, unitd, lda, ndiag, ldb, ldc, lwork INTEGER*4 descra(*), idiag(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZDIASM (transa, m, n, unitd, dv, alpha, descra, val, lda, idiag, ndiag, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SDIASM INTEGER*8 transa, m, n, unitd, lda, ndiag, ldb, ldc, lwork INTEGER*8 descra(*), idiag(*) REAL*4 alpha, beta REAL*4 val(*), b(ldb,*),
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Diagonal format triangular solve SDIASM/DDIASM/CDIASM/ZDIASM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n unitd Number of rows in matrix A. Number of columns in matrix C. Type of scaling. 1. Identity matrix (argument dv( ) is ignored) 2. Scale on left (row scaling) 3. Scale on right (column scaling) dv( ) alpha Diagonal scaling array of length M. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure.
PAGE 532
SDIASM/DDIASM/CDIASM/ZDIASM val( ) lda idiag( ) ndiag b( ) ldb beta c( ) ldc work( ) lwork 504 HP MLIB User’s Guide Diagonal format triangular solve Two dimensional lda-by-ndiag array such that val(:, i) consists of nonzero elements on diagonal idiag(i) of A. Diagonals in the lower triangular part of A are padded from the top, and those in the upper triangular part are padded from the bottom. Leading dimension of val, must be greater or equal to min(m,k).
PAGE 533
Ellpack matrix-matrix multiply SELLMM/DELLMM/CELLMM/ZELLMM Name SELLMM/DELLMM/CELLMM/ZELLMM Ellpack matrix-matrix multiply Purpose Ellpack matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix. Here AT is the transpose and A* is the conjugate-transpose of A.
PAGE 534
SELLMM/DELLMM/CELLMM/ZELLMM Ellpack matrix-matrix multiply SUBROUTINE ZELLMM INTEGER*4 transa, m, n, k, lda, maxnz, ldb, ldc, lwork INTEGER*4 descra(*), indx(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZELLMM (transa, m, n, k, alpha, descra, val, lda, indx, maxnz, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SELLMM INTEGER*8 transa, m, n, k, lda, maxnz, ldb, ldc, lwork INTEGER*8 descra(*), indx(*) REAL*4 alpha, beta REAL*4 val(*), b(ldb,*), c(ldc,*), work(*) CA
PAGE 535
Ellpack matrix-matrix multiply SELLMM/DELLMM/CELLMM/ZELLMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n k alpha Number of rows in matrix A. Number of columns in matrix C. Number of columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
PAGE 536
SELLMM/DELLMM/CELLMM/ZELLMM indx( ) maxnz b( ) ldb beta c( ) ldc work( ) lwork 508 HP MLIB User’s Guide Ellpack matrix-matrix multiply Two dimensional integer blda-by-maxbnz array such that indx (i, :) consists of the column indices of the nonzero elements in row i, padded by the integer value i if the number of nonzeros is less than maxnz. Max number of nonzero elements per row. Rectangular array with leading dimension ldb. Leading dimension of b. Scalar parameter.
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Ellpack format triangular solve SELLSM/DELLSM/CELLSM/ZELLSM Name SELLSM/DELLSM/CELLSM/ZELLSM Ellpack format triangular solve Purpose Ellpack format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
PAGE 538
SELLSM/DELLSM/CELLSM/ZELLSM Ellpack format triangular solve SUBROUTINE ZELLSM INTEGER*4 transa, m, n, unitd, lda, maxnz, ldb, ldc, lwork INTEGER*4 descra(*), indx(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZELLSM (transa, m, n, unitd, dv, alpha, descra, val, lda, indx, maxnz, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SELLSM INTEGER*8 transa, m, n, unitd, lda, maxnz, ldb, ldc, lwork INTEGER*8 descra(*), indx(*) REAL*4 alpha, beta REAL*4 val(*), b(ldb,*), c(l
PAGE 539
Ellpack format triangular solve SELLSM/DELLSM/CELLSM/ZELLSM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n unitd Number of rows in matrix A. Number of columns in matrix C. Type of scaling. 1. Identity matrix (argument dv( ) is ignored) 2. Scale on left (row scaling) 3. Scale on right (column scaling) dv( ) alpha Diagonal scaling array of length M. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure.
PAGE 540
SELLSM/DELLSM/CELLSM/ZELLSM val( ) lda indx( ) maxnz b( ) ldb beta c( ) ldc work( ) lwork 512 HP MLIB User’s Guide Ellpack format triangular solve Two dimensional lda-by-maxnz array such that val(i, :) consists of nonzero elements in row i of A, padded by zero values if the row contains less than maxnz. Leading dimension of val and indx.
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Jagged diagonal matrix-matrix multiply SJADMM/DJADMM/CJADMM/ZJADMM Name SJADMM/DJADMM/CJADMM/ZJADMM Jagged diagonal matrix-matrix multiply Purpose Jagged diagonal matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix. Here AT is the transpose and A* is the conjugate-transpose of A.
PAGE 542
SJADMM/DJADMM/CJADMM/ZJADMM Jagged diagonal matrix-matrix multiply SUBROUTINE ZJADMM INTEGER*4 transa, m, n, k, maxnz, ldb, ldc, lwork INTEGER*4 descra(*), indx(*), pntr(*), iperm(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZJADMM (transa, m, n, k, alpha, descra, val, pntr, iperm, indx, maxnz, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SJADMM INTEGER*8 transa, m, n, k, maxnz, ldb, ldc, lwork INTEGER*8 descra(*), indx(*), pntr(*), iperm(*) REAL*4 alpha, beta R
PAGE 543
Jagged diagonal matrix-matrix multiply SJADMM/DJADMM/CJADMM/ZJADMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n k alpha Number of rows in matrix A. Number of columns in matrix C. Number of columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
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SJADMM/DJADMM/CJADMM/ZJADMM indx( ) pntr( ) iperm( ) maxnz b( ) ldb beta c( ) ldc work( ) lwork 516 HP MLIB User’s Guide Jagged diagonal matrix-matrix multiply jagged diagonal consists of the first nonzero entry of each row, and it is stored first in val(*); the second jagged diagonal consists of the second nonzero entry of each row, and it is stored second in val(*); and so on. Array of length nnz consisting of the column indices of the corresponding entries in val.
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Jagged diagonal format triangular solve SJADSM/DJADSM/CJADSM/ZJADSM Name SJADSM/DJADSM/CJADSM/ZJADSM Jagged diagonal format triangular solve Purpose Jagged diagonal format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
PAGE 546
SJADSM/DJADSM/CJADSM/ZJADSM Jagged diagonal format triangular solve SUBROUTINE ZJADSM INTEGER*4 transa, m, n, unitd, maxnz, ldb, ldc, lwork INTEGER*4 descra(*), indx(*), pntr(*), iperm(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZJADSM (transa, m, n, unitd, dv, alpha, descra, val, pntr, iperm, indx, maxnz, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SJADSM INTEGER*8 transa, m, n, unitd, maxnz, ldb, ldc, lwork INTEGER*8 descra(*), indx(*), pntr(*), iperm(*) REA
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Jagged diagonal format triangular solve SJADSM/DJADSM/CJADSM/ZJADSM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n unitd Number of rows in matrix A. Number of columns in matrix C. Type of scaling. 1. Identity matrix (argument dv( ) is ignored) 2. Scale on left (row scaling) 3. Scale on right (column scaling) dv( ) alpha Diagonal scaling array of length M. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure.
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SJADSM/DJADSM/CJADSM/ZJADSM val( ) indx( ) pntr( ) iperm( ) maxnz b( ) ldb beta c( ) ldc work( ) lwork 520 HP MLIB User’s Guide Jagged diagonal format triangular solve Array of length nnz (the total number of nonzero entries in A) containing the jagged diagonals of the row-permuted representation of A. (The row-permutations are performed such that the number of nonzero entries in each row is decreasing.
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Skyline matrix-matrix multiply SSKYMM/DSKYMM/CSKYMM/ZSKYMM Name SSKYMM/DSKYMM/CSKYMM/ZSKYMM Skyline matrix-matrix multiply Purpose Skyline matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix. Here AT is the transpose and A* is the conjugate-transpose of A.
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SSKYMM/DSKYMM/CSKYMM/ZSKYMM Skyline matrix-matrix multiply SUBROUTINE ZSKYMM INTEGER*4 transa, m, n, k, ldb, ldc, lwork INTEGER*4 descra(*), pntr(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZSKYMM (transa, m, n, k, alpha, descra, val, pntr, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SSKYMM INTEGER*8 transa, m, n, k, ldb, ldc, lwork INTEGER*8 descra(*), pntr(*) REAL*4 alpha, beta REAL*4 val(*), b(ldb,*), c(ldc,*), work(*) CALL SSKYMM (transa, m, n, k, alpha, d
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Skyline matrix-matrix multiply SSKYMM/DSKYMM/CSKYMM/ZSKYMM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n k alpha Number of rows in matrix A. Number of columns in matrix C. Number of columns in matrix A. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure. 0: General 1: Symmetric 2: Hermitian 3: Triangular 4: Skew (Anti)-Symmetric 5: Diagonal descra(2) Upper/Lower triangular indicator.
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SSKYMM/DSKYMM/CSKYMM/ZSKYMM pntr( ) b( ) ldb beta c( ) ldc work( ) lwork 524 HP MLIB User’s Guide Skyline matrix-matrix multiply upper triangular matrix (descra(2)=2). All entries from the first nonzero entry through the diagonal entry of a row (column) are stored. Array of length m+1 (A lower triangular) or k+1 (A upper triangular) such that pntr(i) and pntr(i)+1-1, respectively, point to the location in val of the first entry and last entry of the Skyline profile in row (column) i.
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Skyline format triangular solve SSKYSM/DSKYSM/CSKYSM/ZSKYSM Name SSKYSM/DSKYSM/CSKYSM/ZSKYSM Skyline format triangular solve Purpose Skyline format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
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SSKYSM/DSKYSM/CSKYSM/ZSKYSM Skyline format triangular solve SUBROUTINE ZSKYSM INTEGER*4 transa, m, n, unitd, ldb, ldc, lwork INTEGER*4 descra(*), pntr(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZSKYSM (transa, m, n, unitd, dv, alpha, descra, val, pntr, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE SSKYSM INTEGER*8 transa, m, n, unitd, ldb, ldc, lwork INTEGER*8 descra(*), pntr(*) REAL*4 alpha, beta REAL*4 val(*), b(ldb,*), c(ldc,*), work(*) CALL SSKYSM (transa,
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Skyline format triangular solve SSKYSM/DSKYSM/CSKYSM/ZSKYSM 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix m n unitd Number of rows in matrix A. Number of columns in matrix C. Type of scaling. 1. Identity matrix (argument dv( ) is ignored) 2. Scale on left (row scaling) 3. Scale on right (column scaling) dv( ) alpha Diagonal scaling array of length M. Scalar parameter. descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure.
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SSKYSM/DSKYSM/CSKYSM/ZSKYSM val( ) pntr( ) b( ) ldb beta c( ) ldc work( ) lwork 528 HP MLIB User’s Guide Skyline format triangular solve Array of length pntr(m+1)-1 (see below for pntr) containing all the nonzero entries, and maybe some zero entries of A. A must be a square triangular matrix (m=k). val( ) is row-oriented if A is a lower triangular matrix (descra(2)=1) and column oriented if A is an upper triangular matrix (descra(2)=2).
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Variable block row matrix-matrix multiply SVBRMM/DVBRMM/CVBRMM/ZVBRMM Name SVBRMM/DVBRMM/CVBRMM/ZVBRMM Variable block row matrix-matrix multiply Purpose Variable block row matrix-matrix multiply. These subprograms compute the matrix-matrix product AB, where A is a m-by-k sparse matrix, and B is a k-by-n matrix with m=mb x lb and k=kb x lb. Optionally, A may be replaced by AT or A*, where AT or A* is a k-by-m matrix, and B is a m-by-n matrix.
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SVBRMM/DVBRMM/CVBRMM/ZVBRMM Variable block row matrix-matrix multiply SUBROUTINE INTEGER*4 INTEGER*4 ZVBRMM transa, mb, n, kb, ldb, ldc, lwork descra(*), indx(*), bindx(*), rpntr(*), cpntr(*), bpntrb(*), bpntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZVBRMM (transa, mb, n, kb, alpha, descra, val, indx, bindx, rpntr, cpntr, bpntrb, bpntre, b, ldb, beta, c, ldc, work, lwork) VECLIB8: SUBROUTINE INTEGER*8 INTEGER*8 SVBRMM transa, mb, n, kb, ldb, ldc, lwork descra(*),
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Variable block row matrix-matrix multiply Input SVBRMM/DVBRMM/CVBRMM/ZVBRMM transa Indicates how to operate with the sparse matrix. 0: Operate with matrix 1: Operate with transpose matrix 2: Operate with conjugate-transpose matrix mb Number of block rows in matrix A. Number of columns in matrix C. Number of block columns in matrix A. Scalar parameter. n kb alpha descra( ) descra(1) Descriptor argument. Five element integer array. Matrix structure.
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SVBRMM/DVBRMM/CVBRMM/ZVBRMM indx(*) bindx( ) rpntr( ) cpntr( ) Variable block row matrix-matrix multiply Integer array of length bnnz+1 such that the i-th element of indx( ) points to the location in val of the (1,1) element of the i-th block entry. Integer array of length bnnz consisting of the block row indices of the block entries of A. Integer array of length mb+1 such that rpntr(i)-rpntr(1) is the row index of the first point row in the i-th block row. rpntr(m;+1) is set to m+rpntr(1).
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Variable block row format triangular solve SVBRSM/DVBRSM/CVBRSM/ZVBRSM Name SVBRSM/DVBRSM/CVBRSM/ZVBRSM Variable block row format triangular solve Purpose Variable block row format triangular solve. Given a scalar α, an upper- or lower-triangular sparse matrix A, and a m-by-n matrix B with m=mb x lb, these subprograms compute either of the matrix solutions αA–1B, or αDA–1B, or αA–1DB, where D is a diagonal matrix. The size of A is m-by-m. Optionally, A–1 may be replaced by A–T, or by A–*.
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SVBRSM/DVBRSM/CVBRSM/ZVBRSM Variable block row format triangular solve SUBROUTINE INTEGER*4 INTEGER*4 CVBRSM transa, mb, n, unitd, blda, ldb, ldc, lwork descra(*), indx(*), bindx(*), rpntr(*), cpntr(*), bpntrb(*), bpntre(*) COMPLEX*8 alpha, beta COMPLEX*8 val(*), b(ldb,*), c(ldc,*), work(*) CALL CVBRSM (transa, mb, n, unitd, dv, alpha, descra, val, indx, bindx, rpntr, cpntr, bpntrb, bpntre, b, ldb, beta, c, ldc, work, lwork) SUBROUTINE INTEGER*4 INTEGER*4 ZVBRSM transa, mb, n, unitd, blda, ldb, ldc, lwo
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Variable block row format triangular solve SVBRSM/DVBRSM/CVBRSM/ZVBRSM SUBROUTINE INTEGER*8 INTEGER*8 ZVBRSM transa, mb, n, unitd, blda, ldb, ldc, lwork descra(*), indx(*), bindx(*), rpntr(*), cpntr(*), bpntrb(*), bpntre(*) COMPLEX*16 alpha, beta COMPLEX*16 val(*), b(ldb,*), c(ldc,*), work(*) CALL ZVBRSM (transa, mb, n, unitd, dv, alpha, descra, val, indx, bindx, rpntr, cpntr, bpntrb, bpntre, b, ldb, beta, c, ldc, work, lwork) Input transa Indicates how to operate with the sparse matrix.
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SVBRSM/DVBRSM/CVBRSM/ZVBRSM Variable block row format triangular solve descra(3) Main diagonal type. 0: Non-unit 1: Unit descra(4) Array base. 0: C/C++ compatible Not Supported 1: Fortran compatible descra(5) Repeated indices. 0: Unknown 1: No repeated indices val( ) Scalar array of length nnz containing matrix entries. Integer array of length bnnz+1 such that the i-th element of indx( ) points to the location in val of the (1, 1) element of the i-th block entry.
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Variable block row format triangular solve beta c( ) ldc work( ) lwork SVBRSM/DVBRSM/CVBRSM/ZVBRSM Scalar parameter. Rectangular array with leading dimension ldc. Leading dimension of c. Scratch array of length lwork. lwork should be at least mb x lb x min(lb, n). Length of work array.
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SVBRSM/DVBRSM/CVBRSM/ZVBRSM 538 HP MLIB User’s Guide Variable block row format triangular solve
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Index Symbols +noppu 14, 639, 701, 732 Itanium processor 15, 640, 703, 733 Itanium processors 15, 640, 703, 733 PA-RISC 14, 640, 702, 733 +ppu 14, 639, 701, 732 Itanium processor 15, 640, 703, 733 Itanium processors 15, 640, 703, 733 PA-RISC 14, 640, 702, 733 1-way Dissection reordering 934 A accessing VECLIB 3 accessing VECLIB 3 accuracy of computed eigenvaules and eigenvectors 1018 apply Givens rotation general 114 modified 123 sparse 120 arguments BLAS Standard 36 array Fortran argument association 34 F
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CGERU 237 CGETRA 241 CGTHR 94 CGTHRZ 96 CHBMV 244 check accuracy of eigenvalue and eigenvector results 1018 CHEMM 265 CHEMV 270 CHER 275 CHER2 279 CHER2K 284 CHERK 289 CHPMV 249 CHPR 254 CHPR2 259 CLANGB 657 CLANGE 661 CLANGT 663 CLANHB 666 CLANHE 680 CLANHP 671 CLANHT 676 CLANSB 666 CLANSP 671 CLANSY 680 clear vector 150 clip vector left-sided 74 right-sided 77 two-sided 71 CLSTEQ 99 CLSTNE 99 combine AXPY and DOT 164 compiling linking LAPACK 629 linking libisamstub.
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CZERO 150 D D1DFFT 544 D2DFFT 549 D3DFFT 553 DAMAX 56 DAMIN 59 DASUM 62 data types 23 DAXPY 65 DAXPYI 68 DBCOMM 441 DBDIMM 445 DBDISM 449 DBELMM 453 DBELSM 457 DBSCMM 461 DBSCSM 465 DBSRMM 469 DBSRSM 473 DCLIP 71 DCLIPL 74 DCLIPR 77 DCONV 594, 599 DCOOMM 477 DCOPY 80 DCSCMM 481 DCSCSM 485 DCSRMM 489, 497 DCSRSM 493 DDIASM 501 DDOT 84 DDOTI 88 deallocate working storage 894, 1020 DELLMM 505, 513 DELLSM 509, 517 determine extent of parallelism 607, 608 DFFTS 560 DFRAC 92 DFT 540 DGBMV 212 DGECPY 219 DGEFA 10
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DSEVVE 1073 DSEVVM 1076 DSKYMM 521 DSKYSM 525 DSLECO 891 DSLEDA 894 DSLEFA 896 DSLEFF 900 DSLEFS 903 DSLEI1 909 DSLEIC 911 DSLEIE 914 DSLEIF 916 DSLEIM 917 DSLEIN 921 DSLELU 923 DSLEMA 929 DSLEOC 931 DSLEOP 933 DSLEOR 937 DSLEPS 940 DSLERD 941 DSLESL 944 DSLEV1 947 DSLEVC 950 DSLEVE 954 DSLEVM 957 DSORT 620 DSPMV 249 DSPR 254 DSPR2 259 DSUM 139 DSWAP 141 DSYMM 265 DSYMV 270 DSYR 275 DSYR2 279 DSYR2K 284 DSYRK 289 DTBMV 294 DTBSV 301 DTPMV 308 DTPSV 313 DTRMM 318 DTRMV 323 DTRSM 327 DTRSV 332 DVBRMM 529 DVBR
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compute 107 squared 110 extended BLAS 205 extract fractional parts 92 F F_BLASERROR 605 F_CAMAX_VAL 153 F_CAMIN_VAL 155 F_CAPPLY_GROT 158 F_CAXPBY 161 F_CAXPY_DOT 164 F_CCOPY 167 F_CDOT 169 F_CGBMV 355 F_CGE_COPY 358 F_CGE_TRANS 360 F_CGEMM 362 F_CGEMV 365 F_CGEMVER 368 F_CGEMVT 372 F_CGEN_GROT 174 F_CGEN_HOUSE 175 F_CGEN_JROT 178 F_CGER 375 F_CHBMV 340 F_CHEMV 342 F_CHER 344 F_CHER2 346 F_CHPMV 348 F_CHPR 350 F_CHPR2 352 F_CPERMUTE 187 F_CRSCALE 190 F_CSBMV 378 F_CSPMV 381 F_CSPR 384 F_CSPR2 386 F_CSUM 19
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F_SGEN_GROT 174 F_SGEN_HOUSE 175 F_SGEN_JROT 178 F_SGER 375 F_SMAX_VAL 181 F_SMIN_VAL 183 F_SNORM 185 F_SPERMUTE 187 F_SRSCALE 190 F_SSBMV 378 F_SSORT 192 F_SSORTV 193 F_SSPMV 381 F_SSPR 384 F_SSPR2 386 F_SSUM 195 F_SSUMSQ 197 F_SSWAP 200 F_SSYMV 389 F_SSYR 392 F_SSYR2 394 F_STBMV 397 F_STBSV 400 F_STPMV 403 F_STPSV 406 F_STRMV 408 F_STRMVT 411 F_STRSM 414 F_STRSV 417 F_SWAXPBY 202 F_ZAMAX_VAL 153 F_ZAMIN_VAL 155 F_ZAPPLY_GROT 158 F_ZAXPBY 161 F_ZAXPY_DOT 164 F_ZCOPY 167 F_ZDOT 169 F_ZGBMV 355 F_ZGE_COPY 35
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one-dimensional 556, 560, 582, 587 real-to-complex 582, 587 separate real arrays 560 three-dimensional general 551 real-to-complex 576, 579 separate real arrays 553 two-dimensional general 547 real-to-complex 570, 573 separate real arrays 549 find first vector element 53 selected vector element 99 floating point machine specific characteristics 172, 354 parameters for F_FPINFO 173 Fortran array argument association 34 storage of arrays 34 forward storage 35 fractional parts, extract 92 full Hermitian matrix
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ill-conditioned problems See roundoff effects ILSTEQ 99 ILSTGE 99 ILSTGT 99 ILSTLE 99 ILSTLT 99 ILSTNE 99 IMAX 103 IMIN 105 index element of vector maximum 49 minimum 51 magnitudes maximum 40 minimum 43 maximum element of vector 49 magnitudes 40 minimum element of vector 51 magnitudes 43 Indexed Sequential Access Method See ISAM initialize sparse eigenvalues/eigenvectors 1054 sparse linear equations 921 vector to zero 150 initMLIB 1094 inner rotation 26 input matrix structure by column 911, 1045 by finite e
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DGESL 1097 subprograms in VECLIB 1098 list selected vector elements 99 long period random number generator scalar 615 vector 617 LSAME 606 LU factorization 1098 M machine independence 655 machine specific charactristics See F_SFPINFO machine-dependent parameters, return 655 magnitudes compute maximum 56 minimum 59 index magnitudes 40 maximum 40 minimum 43 maximum compute 56 index 40 minimum compute 59 index 43 sum 62 man pages 30, 650 matrix band compute norm 657 band symmetric compute norm 666 compute nor
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by matrix 917, 1050 by single entry 909, 1043 end 916, 1049 symmetric sample program 887 symmetric band compute orm 666 symmetric full compute norm 680 symmetric packed compute norm 671 symmetric tridiagonal, compute norm 676 transposition 360 tridiagonal compute norm 676 tridiagonal general compute norm 663 value input by column 950, 1068 by finite element 954, 1073 by matrix 957, 1076 by single entry 947, 1066 to main diagonal 1071 maximum absolute vector 153 compute magnitudes 56 element of vector, index
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symmetric matrix 389 symmetric packed matrix 381 triangular band matrix 397 triangular matrix 408 triangular matrix and n-vector 323 triangular packed matrix 403 N naming conventions Extended BLAS 207–209 Sparse BLAS 423–424 VECLIB subroutines 24–25 natural reordering 934 non parallel processing controlling at link time 643 nonsymmetric matrix sample program 888 norm 36, 185, 209 defined 25 general band matrix 657 general full matrix 661 general tridiagonal matrix 663 Hermitian band matrix 666 Hermitian fu
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rotation apply plane 158 Givens 174 Jacobi 178 roundoff effects 23, 648 runtime, controlling parallel processing 18, 643 S S1DFFT 544 S2DFFT 549 S3DFFT 553 SAMAX 56 SAMIN 59 SASUM 62 save problem state to savefile 1065 SAXPY 65 SAXPYI 68 SBCOMM 441 SBDIMM 445 SBDISM 449 SBELMM 453 SBELSM 457 SBSCMM 461 SBSCSM 465 SBSRMM 469 SBSRSM 473 ScaLAPACK xviii, 689–716 arguments 709 array 714 INFO 716 option 709 scalar 714 associated documentation 690 functionality 705 linear equations 706 linear least squares 707 n
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sort vector 192, 193 sorted rotation 26 sparse 120 BLAS 31, 421 dot product 88 eigenextraction 1030, 1036 eigenvalues initialize 1054 one-call usage 1021 subprograms 1003–1079 eigenvectors initialize 1054 subprograms 1003–1079 Givens rotation, apply 120 linear equations initialize 921 solve 944 specify 929 subprograms 875–962 vector elementary operation 68 gather 94 gather and zero 96 scatter 136 zero and gather 96 specify coefficient matrix sparse linear equations 929 specify singularity treatment 900 SRAM
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symmetric tridiagonal matrix compute norm 676 SZERO 150 T thread definition 643 time CPU time 604 wall-clock time 622 trans 36, 209 defined 25 transform Householder 175 transposition 360 triangular band system solve 301, 400 multiply matrix-matrix 318 matrix-vector 308 matrix-vector and n-vector 323 packed solve 406 system solve 313, 327, 332, 414, 417 triangular factorization 1098, 1100 triangular solve block diagonal format triangular solve 449, 457 block sparse column format triangular solve 465 block s
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vdSin 833 vdsin 812 vdSinCos 834 vdsincos 866 vdSinh 835 vdsinh 813, 867 vdSqrt 836 vdsqrt 868 vdTan 837 vdtan 869 vdTanh 838 vdtanh 870 vdUnpackI 839 vdunpacki 871 vdUnpackM 839 vdunpackm 871 vdUnpackV 839 vdunpackv 871 VECLIB 1 error handling 684 VECLIB, accessing 3 VECLIB8 1 libraries 3 vector clear 150 clip left-sided 74 right-sided 77 two-sided 71 copy 80, 167 elementary operation 65 elements, count selected 46 index of maximum element 49, 51 list selected elements 99 long period random-number generato
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vsln 859 vsLog10 828 vslog10 860 vsPackI 829 vspacki 861 vsPackM 829 vspackm, vdpacki 861 vsPackV 829 vspackv 861 vsPow 831 vspow 863 vsPowx 832 vspowx 864 vsqrt 865 vsSin 833 vsSinCos 834 vssincos 866 vsSinh 835 vssinh 867 vsSqrt 836 vssqrt 868 vsTan 837 vstan 869 vsTanh 838 vstanh 870 vsUnpackI 839 vsunpacki 871 vsUnpackM 839 vsunpackm 871 vsUnpackV 839 vsunpackv 871 W wall-clock time 622 WALLTIME 622 weighted dot product, compute 145 working storage 648 working storage, deallocate 894, 1020 X XERBLA 33
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ZLANHE 680 ZLANHP 671 ZLANHT 676 ZLANSB 666 ZLANSP 671 ZLANSY 680 ZLSTEQ 99 ZLSTNE 99 ZRC1FT 564 ZRC2FT 570 ZRC3FT 576 ZRCFTS 582 ZROT 114 ZROTG 118 ZRSCL 130 ZSCAL 133 ZSCALC 133 ZSCTR 136 ZSKYMM 521 ZSKYSM 525 ZSUM 139 ZSWAP 141 ZSYMM 265 ZSYR2K 284 ZSYRK 289 ZTBMV 294 ZTBSV 301 ZTPMV 308 ZTPSV 313 ZTRMM 318 ZTRMV 323 ZTRSM 327 ZTRSV 332 ZVBRMM 529 ZVBRSM 533 ZWDOTC 145 ZWDOTU 145 ZZERO 150 1123
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1124