HP Fortran for OpenVMS

ManualsBrandsHP ManualsSoftwareOpenVMS 8.4

• Solve the linear equality constrained least squares

(LSE) problem

• Solve the Gauss-Markov linear model problem

• Perform LQ factorization without pivoting

• Unblocked LQ factorization

• Solve underdetermined linear system (based on LQ

factorization)

• Generate a real orthogonal or complex unitary matrix

as a product of Householder matrices

• Unblocked generation of real orthogonal or unitary

matrix

• Multiply a matrix by a real orthogonal or complex uni-

tary matrix by applying a product of Householder ma-

trices

• Unblocked version of multiplication of a matrix by a

real orthogonal or complex unitary matrix by applying

a product of Householder matrices

• Reduce a square matrix to upper Hessenberg form

• Unblocked version of square matrix reduction

• Reduce a symmetric matrix to real symmetric tridiag-

onal form

• Reduce a band matrix to bidiagonal form

• Unblocked version of symmetric matrix reduction

• Reduce a rectangular matrix to bidiagonal form

• Reduce a band symmetric/Hermitian matrix to tridi-

agonal form

• Reduce a symmetric/Hermitian-deﬁnite banded gen-

eralized eigenproblem to standard form

• Compute various norms of a complex Hermitian tridi-

agonal matrix

• Compute eigenvalues and optional Schur factoriza-

tion or eigenvectors using QR algorithm

• Compute selected eigenvectors by inverse iteration

• Compute eigenvectors from Schur factorization

• Compute eigenvectors using the Pal-Walker-Kahan

variant of the QL or QR algorithm

• For a pair of N-by-N real nonsymmetric matrices,

compute the generalized eigenvalues, the real Schur

form, and the left and/or right Schur vectors

• For a pair of N-by-N real nonsymmetric matrices,

compute the generalized eigenvalues, and the left

and/or right generalized eigenvectors

• Solve the generalized nonsymmetric eigenproblem

Ax = lambda Bx

• Solve the generalized deﬁnite banded eigenproblem

Ax = lambda Bx

• Solve the generalized symmetric/Hermitian-deﬁnite

banded eigenproblem

• Solve the symmetric eigenproblem using divide-and-

conquer algorithm

• Compute singular values and, optionally, singular

vectors using the QR algorithm

• Compute the generalized (quotient) singular value

decomposition

• Compute the generalized singular value decompo-

sition (GSVD) on the M-by-N matrix A and P-by-N

matrix B

• Solve a generalized linear regression model problem

Sparse System Solver Subprograms

The CXML Sparse System Solver library contains a set

of subprograms that can be used to solve sparse linear

systems of equations. Two packages providing direct

and iterative methods are supported.

Direct Method Sparse Solver Package:

The direct solver package includes skyline (proﬁle)

solvers for symmetric and nonsymmetric matrices. Sep-

arate factorization and solver routines are provided to

allow repeated use of the solver for multiple right hand

sides, without repeating the factorization. To make

the subprograms easier to use, both simple and ex-

pert driver routines are provided. Functions provided

include:

• LDU factorization

• Solve

• Norm evaluation

• Condition number estimation

• Iterative reﬁnement

• Simple and expert drivers

These storage schemes are supported for symmetric

and nonsymmetric matrices:

• Proﬁle-in storage

• Structurally symmetric, proﬁle-in storage (for non-

symmetric only)

• Diagonal-out storage

Iterative Method Sparse Solver Package:

For the iterative method, the library provides a modular

set of storage schemes, preconditioners, and solvers.

These solvers and preconditioners are easily accessed

through an integrated driver routine.