hetrs_aa(3)

Library Functions Manual

hetrs_aa(3)

NAME

hetrs_aa - {he,sy}trs_aa: triangular solve using factor

SYNOPSIS

Functions

subroutine chetrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CHETRS_AA subroutine csytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CSYTRS_AA subroutine dsytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
DSYTRS_AA subroutine ssytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYTRS_AA subroutine zhetrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZHETRS_AA subroutine zsytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZSYTRS_AA

Detailed Description

Function Documentation

subroutine chetrs_aa (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CHETRS_AA

Purpose:

!>
!> CHETRS_AA solves a system of linear equations A*X = B with a complex
!> hermitian matrix A using the factorization A = U**H*T*U or
!> A = L*T*L**H computed by CHETRF_AA.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U**H*T*U;
!>          = 'L':  Lower triangular, form is A = L*T*L**H.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

!>          A is COMPLEX array, dimension (LDA,N)
!>          Details of factors computed by CHETRF_AA.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by CHETRF_AA.
!>

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

WORK

!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the minimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 135 of file chetrs_aa.f.

subroutine csytrs_aa (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CSYTRS_AA

Purpose:

!>
!> CSYTRS_AA solves a system of linear equations A*X = B with a complex
!> symmetric matrix A using the factorization A = U**T*T*U or
!> A = L*T*L**T computed by CSYTRF_AA.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U**T*T*U;
!>          = 'L':  Lower triangular, form is A = L*T*L**T.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

!>          A is COMPLEX array, dimension (LDA,N)
!>          Details of factors computed by CSYTRF_AA.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by CSYTRF_AA.
!>

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

WORK

!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK >= max(1,3*N-2).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 129 of file csytrs_aa.f.

subroutine dsytrs_aa (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRS_AA

Purpose:

!>
!> DSYTRS_AA solves a system of linear equations A*X = B with a real
!> symmetric matrix A using the factorization A = U**T*T*U or
!> A = L*T*L**T computed by DSYTRF_AA.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U**T*T*U;
!>          = 'L':  Lower triangular, form is A = L*T*L**T.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          Details of factors computed by DSYTRF_AA.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by DSYTRF_AA.
!>

!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the minimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 135 of file dsytrs_aa.f.

subroutine ssytrs_aa (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)

SSYTRS_AA

Purpose:

!>
!> SSYTRS_AA solves a system of linear equations A*X = B with a real
!> symmetric matrix A using the factorization A = U**T*T*U or
!> A = L*T*L**T computed by SSYTRF_AA.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U**T*T*U;
!>          = 'L':  Lower triangular, form is A = L*T*L**T.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

!>          A is REAL array, dimension (LDA,N)
!>          Details of factors computed by SSYTRF_AA.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by SSYTRF_AA.
!>

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the minimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 135 of file ssytrs_aa.f.

subroutine zhetrs_aa (character uplo, integer n, integer nrhs, complex16, dimension( lda, ) a, integer lda, integer, dimension( * ) ipiv, complex16, dimension( ldb, ) b, integer ldb, complex16, dimension( ) work, integer lwork, integer info)

ZHETRS_AA

Purpose:

!>
!> ZHETRS_AA solves a system of linear equations A*X = B with a complex
!> hermitian matrix A using the factorization A = U**H*T*U or
!> A = L*T*L**H computed by ZHETRF_AA.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U**H*T*U;
!>          = 'L':  Lower triangular, form is A = L*T*L**H.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          Details of factors computed by ZHETRF_AA.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by ZHETRF_AA.
!>

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

WORK

!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the minimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 136 of file zhetrs_aa.f.

subroutine zsytrs_aa (character uplo, integer n, integer nrhs, complex16, dimension( lda, ) a, integer lda, integer, dimension( * ) ipiv, complex16, dimension( ldb, ) b, integer ldb, complex16, dimension( ) work, integer lwork, integer info)

ZSYTRS_AA

Purpose:

!>
!> ZSYTRS_AA solves a system of linear equations A*X = B with a complex
!> symmetric matrix A using the factorization A = U**T*T*U or
!> A = L*T*L**T computed by ZSYTRF_AA.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U**T*T*U;
!>          = 'L':  Lower triangular, form is A = L*T*L**T.
!>

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          Details of factors computed by ZSYTRF_AA.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by ZSYTRF_AA.
!>

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix X.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

WORK

!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK >= max(1,3*N-2).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 129 of file zsytrs_aa.f.

Author

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