HP Fortran for OpenVMS

HP Fortran for OpenVMS
Three types of matrices are supported by these BLAS
Level 3 routines:
• General
• Symmetric/Hermitian
• Triangular
A set of additional matrix-matrix routines is provided:
• Add two matrices
• Subtract one matrix from another
• Transpose a matrix, in-place or out-of-place
Array Math Functions
The Array Math Functions provide a set of basic math
functions that operate on arrays of numbers rather than
on scalars. On vector and superscalar architectures,
such functions have a performance advantage over a
loop of scalar operations. The library includes the fol-
lowing array functions for double precision numbers:
• Sine of array
• Cosine of array
• Cosine and sine of array
• Exponent of array
• Logarithm of array
• Square root of array
• Reciprocal of array
LAPACK Library Contents
LAPACK is a library of linear algebra subprograms in-
tended to solve a wide range of problems in linear alge-
bra. LAPACK can be used to solve dense systems of
linear equations, linear least squares problems, eigen-
value problems, and singular value problems. It is also
useful in doing other computations such as matrix fac-
torizations and estimations of condition numbers.
The CXML LAPACK library provides the complete LA-
PACK v2 package. CXML´s version of LAPACK is pro-
vided as a packaged library, compiled, tested, and ready
to use. Combined with the optimized BLAS Level 3 rou-
tines, the CXML LAPACK will provide optimal perfor-
mance on all supported platforms. LAPACK should be
used in place of LINPACK and EISPACK, because it is
more efficient, accurate, and robust.
LAPACK supports both real and complex, single and
double precision data. It operates on the following types
of matrices:
• Bidiagonal
• General band
• General unsymmetric
• General tridiagonal
• Hermitian
• Hermitian, packed storage
• Upper Hessenberg, generalized problem
• Upper Hessenberg
• Orthogonal
• Orthogonal, packed storage
• Symmetric/Hermitian positive definite band
• Symmetric/Hermitian positive definite
• Symmetric/Hermitian positive definite, packed stor-
age
• Symmetric/Hermitian positive definite tridiagonal
• Symmetric band
• Symmetric, packed storage
• Symmetric tridiagonal
• Symmetric
• Triangular band
• Triangular, generalized problem
• Triangular, packed storage
• Triangular
• Trapezoidal
• Unitary
• Unitary, packed storage
LAPACK provides the following operations:
• Triangular factorization
• Unblocked triangular factorization
• Solve a system of linear equations (based on trian-
gular factorization)
• Compute the inverse (based on triangular factoriza-
tion)
• Compute a split Cholesky factorization of a symmet-
ric/Hermitian positive definite band matrix
• Unblocked computation of inverse
• Estimate condition number
• Refine initial solution returned by solver
• Perform QR factorization without pivoting
• Unblocked QR factorization
• Solve linear least squares problem (based on QR
factorization)
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