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hetrs_aa_2stage(3) LAPACK 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.

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.

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.

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.

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.

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.

Author

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