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hetrs_aa_2stage(3) Library Functions Manual hetrs_aa_2stage(3)

NAME

hetrs_aa_2stage - {he,sy}trs_aa_2stage: triangular solve using factor

SYNOPSIS

Functions


subroutine CHETRS_AA_2STAGE (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
CHETRS_AA_2STAGE subroutine CSYTRS_AA_2STAGE (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
CSYTRS_AA_2STAGE subroutine DSYTRS_AA_2STAGE (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
DSYTRS_AA_2STAGE subroutine SSYTRS_AA_2STAGE (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
SSYTRS_AA_2STAGE subroutine ZHETRS_AA_2STAGE (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
ZHETRS_AA_2STAGE subroutine ZSYTRS_AA_2STAGE (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info)
ZSYTRS_AA_2STAGE

Detailed Description

Function Documentation

subroutine CHETRS_AA_2STAGE (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, integer info)

CHETRS_AA_2STAGE

Purpose:

!>
!> CHETRS_AA_2STAGE solves a system of linear equations A*X = B with a real
!> hermitian matrix A using the factorization A = U**T*T*U or
!> A = L*T*L**T computed by CHETRF_AA_2STAGE.
!>

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

!>          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

!>          A is COMPLEX array, dimension (LDA,N)
!>          Details of factors computed by CHETRF_AA_2STAGE.
!>

LDA

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

TB

!>          TB is COMPLEX array, dimension (LTB)
!>          Details of factors computed by CHETRF_AA_2STAGE.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          CHETRF_AA_2STAGE.
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          CHETRF_AA_2STAGE.
!>

B

!>          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).
!>

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 139 of file chetrs_aa_2stage.f.

subroutine CSYTRS_AA_2STAGE (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, integer info)

CSYTRS_AA_2STAGE

Purpose:

!>
!> CSYTRS_AA_2STAGE 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_2STAGE.
!>

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

!>          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

!>          A is COMPLEX array, dimension (LDA,N)
!>          Details of factors computed by CSYTRF_AA_2STAGE.
!>

LDA

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

TB

!>          TB is COMPLEX array, dimension (LTB)
!>          Details of factors computed by CSYTRF_AA_2STAGE.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          CSYTRF_AA_2STAGE.
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          CSYTRF_AA_2STAGE.
!>

B

!>          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).
!>

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 137 of file csytrs_aa_2stage.f.

subroutine DSYTRS_AA_2STAGE (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DSYTRS_AA_2STAGE

Purpose:

!>
!> DSYTRS_AA_2STAGE 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_2STAGE.
!>

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

!>          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

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          Details of factors computed by DSYTRF_AA_2STAGE.
!>

LDA

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

TB

!>          TB is DOUBLE PRECISION array, dimension (LTB)
!>          Details of factors computed by DSYTRF_AA_2STAGE.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          DSYTRF_AA_2STAGE.
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          DSYTRF_AA_2STAGE.
!>

B

!>          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).
!>

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 137 of file dsytrs_aa_2stage.f.

subroutine SSYTRS_AA_2STAGE (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( ldb, * ) b, integer ldb, integer info)

SSYTRS_AA_2STAGE

Purpose:

!>
!> SSYTRS_AA_2STAGE 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_2STAGE.
!>

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

!>          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

!>          A is REAL array, dimension (LDA,N)
!>          Details of factors computed by SSYTRF_AA_2STAGE.
!>

LDA

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

TB

!>          TB is REAL array, dimension (LTB)
!>          Details of factors computed by SSYTRF_AA_2STAGE.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          SSYTRF_AA_2STAGE.
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          SSYTRF_AA_2STAGE.
!>

B

!>          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).
!>

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 137 of file ssytrs_aa_2stage.f.

subroutine ZHETRS_AA_2STAGE (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZHETRS_AA_2STAGE

Purpose:

!>
!> ZHETRS_AA_2STAGE solves a system of linear equations A*X = B with a 
!> hermitian matrix A using the factorization A = U**H*T*U or
!> A = L*T*L**H computed by ZHETRF_AA_2STAGE.
!>

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

!>          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

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          Details of factors computed by ZHETRF_AA_2STAGE.
!>

LDA

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

TB

!>          TB is COMPLEX*16 array, dimension (LTB)
!>          Details of factors computed by ZHETRF_AA_2STAGE.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          ZHETRF_AA_2STAGE.
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          ZHETRF_AA_2STAGE.
!>

B

!>          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).
!>

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 139 of file zhetrs_aa_2stage.f.

subroutine ZSYTRS_AA_2STAGE (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZSYTRS_AA_2STAGE

Purpose:

!>
!> ZSYTRS_AA_2STAGE 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_2STAGE.
!>

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

!>          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

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          Details of factors computed by ZSYTRF_AA_2STAGE.
!>

LDA

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

TB

!>          TB is COMPLEX*16 array, dimension (LTB)
!>          Details of factors computed by ZSYTRF_AA_2STAGE.
!>

LTB

!>          LTB is INTEGER
!>          The size of the array TB. LTB >= 4*N.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          ZSYTRF_AA_2STAGE.
!>

IPIV2

!>          IPIV2 is INTEGER array, dimension (N)
!>          Details of the interchanges as computed by
!>          ZSYTRF_AA_2STAGE.
!>

B

!>          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).
!>

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 137 of file zsytrs_aa_2stage.f.

Author

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