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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