hesv_aa(3)

NAME
hesv_aa - {he,sy}sv_aa: Aasen

SYNOPSIS

  Functions
subroutine chesv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CHESV_AA computes the solution to system of linear equations A * X = B for HE matrices
subroutine csysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine dsysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine ssysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine zhesv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices
subroutine zsysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Detailed Description

Function Documentation

  subroutine chesv_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)

CHESV_AA computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

     CHESV_AA computes the solution to a complex system of linear equations
        A * X = B,
     where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
     matrices.
     Aasen's algorithm is used to factor A as
        A = U**H * T * U,  if UPLO = 'U', or
        A = L * T * L**H,  if UPLO = 'L',
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, and T is Hermitian and tridiagonal. The factored form
     of A is then used to solve the system of equations A * X = B.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
              The number of linear equations, i.e., 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)
              On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
              N-by-N upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading N-by-N lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, if INFO = 0, the tridiagonal matrix T and the
              multipliers used to obtain the factor U or L from the
              factorization A = U**H*T*U or A = L*T*L**H as 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)
              On exit, it contains the details of the interchanges, i.e.,
              the row and column k of A were interchanged with the
              row and column IPIV(k).

    B

              B is COMPLEX array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS 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))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for best
              performance LWORK >= MAX(1,N*NB), where NB is the optimal
              blocksize for CHETRF.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal 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
              > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, so the solution could not be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 160 of file chesv_aa.f.

  subroutine csysv_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)

CSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

     CSYSV computes the solution to a complex system of linear equations
        A * X = B,
     where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
     matrices.
     Aasen's algorithm is used to factor A as
        A = U**T * T * U,  if UPLO = 'U', or
        A = L * T * L**T,  if UPLO = 'L',
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, and T is symmetric tridiagonal. The factored
     form of A is then used to solve the system of equations A * X = B.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
              The number of linear equations, i.e., 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)
              On entry, the symmetric matrix A.  If UPLO = 'U', the leading
              N-by-N upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading N-by-N lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, if INFO = 0, the tridiagonal matrix T and the
              multipliers used to obtain the factor U or L from the
              factorization A = U**T*T*U or A = L*T*L**T as computed by
              CSYTRF.

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              On exit, it contains the details of the interchanges, i.e.,
              the row and column k of A were interchanged with the
              row and column IPIV(k).

    B

              B is COMPLEX array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS 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))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The length of WORK.  LWORK >= MAX(2*N, 3*N-2), and for
              the best performance, LWORK >= max(1,N*NB), where NB is
              the optimal blocksize for CSYTRF_AA.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal 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
              > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, so the solution could not be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 160 of file csysv_aa.f.

  subroutine dsysv_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)

DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

     DSYSV computes the solution to a real system of linear equations
        A * X = B,
     where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
     matrices.
     Aasen's algorithm is used to factor A as
        A = U**T * T * U,  if UPLO = 'U', or
        A = L * T * L**T,  if UPLO = 'L',
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, and T is symmetric tridiagonal. The factored
     form of A is then used to solve the system of equations A * X = B.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
              The number of linear equations, i.e., 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)
              On entry, the symmetric matrix A.  If UPLO = 'U', the leading
              N-by-N upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading N-by-N lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, if INFO = 0, the tridiagonal matrix T and the
              multipliers used to obtain the factor U or L from the
              factorization A = U**T*T*U or A = L*T*L**T as computed by
              DSYTRF.

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              On exit, it contains the details of the interchanges, i.e.,
              the row and column k of A were interchanged with the
              row and column IPIV(k).

    B

              B is DOUBLE PRECISION array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS 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))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for
              the best performance, LWORK >= MAX(1,N*NB), where NB is
              the optimal blocksize for DSYTRF_AA.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal 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
              > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, so the solution could not be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 160 of file dsysv_aa.f.

  subroutine ssysv_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)

SSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

     SSYSV computes the solution to a real system of linear equations
        A * X = B,
     where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
     matrices.
     Aasen's algorithm is used to factor A as
        A = U**T * T * U,  if UPLO = 'U', or
        A = L * T * L**T,  if UPLO = 'L',
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, and T is symmetric tridiagonal. The factored
     form of A is then used to solve the system of equations A * X = B.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
              The number of linear equations, i.e., 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)
              On entry, the symmetric matrix A.  If UPLO = 'U', the leading
              N-by-N upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading N-by-N lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, if INFO = 0, the tridiagonal matrix T and the
              multipliers used to obtain the factor U or L from the
              factorization A = U**T*T*U or A = L*T*L**T as computed by
              SSYTRF.

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              On exit, it contains the details of the interchanges, i.e.,
              the row and column k of A were interchanged with the
              row and column IPIV(k).

    B

              B is REAL array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS 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))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for
              the best performance, LWORK >= MAX(1,N*NB), where NB is
              the optimal blocksize for SSYTRF_AA.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal 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
              > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, so the solution could not be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 160 of file ssysv_aa.f.

  subroutine zhesv_aa (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)

ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

     ZHESV_AA computes the solution to a complex system of linear equations
        A * X = B,
     where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
     matrices.
     Aasen's algorithm is used to factor A as
        A = U**H * T * U,  if UPLO = 'U', or
        A = L * T * L**H,  if UPLO = 'L',
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, and T is Hermitian and tridiagonal. The factored form
     of A is then used to solve the system of equations A * X = B.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
              The number of linear equations, i.e., 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)
              On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
              N-by-N upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading N-by-N lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, if INFO = 0, the tridiagonal matrix T and the
              multipliers used to obtain the factor U or L from the
              factorization A = U**H*T*U or A = L*T*L**H as 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)
              On exit, it contains the details of the interchanges, i.e.,
              the row and column k of A were interchanged with the
              row and column IPIV(k).

    B

              B is COMPLEX*16 array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS 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))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for best
              performance LWORK >= max(1,N*NB), where NB is the optimal
              blocksize for ZHETRF.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal 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
              > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, so the solution could not be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 160 of file zhesv_aa.f.

  subroutine zsysv_aa (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)

ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

     ZSYSV computes the solution to a complex system of linear equations
        A * X = B,
     where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
     matrices.
     Aasen's algorithm is used to factor A as
        A = U**T * T * U,  if UPLO = 'U', or
        A = L * T * L**T,  if UPLO = 'L',
     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, and T is symmetric tridiagonal. The factored
     form of A is then used to solve the system of equations A * X = B.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
              The number of linear equations, i.e., 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)
              On entry, the symmetric matrix A.  If UPLO = 'U', the leading
              N-by-N upper triangular part of A contains the upper
              triangular part of the matrix A, and the strictly lower
              triangular part of A is not referenced.  If UPLO = 'L', the
              leading N-by-N lower triangular part of A contains the lower
              triangular part of the matrix A, and the strictly upper
              triangular part of A is not referenced.
              On exit, if INFO = 0, the tridiagonal matrix T and the
              multipliers used to obtain the factor U or L from the
              factorization A = U**T*T*U or A = L*T*L**T as computed by
              ZSYTRF.

    LDA

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

    IPIV

              IPIV is INTEGER array, dimension (N)
              On exit, it contains the details of the interchanges, i.e.,
              the row and column k of A were interchanged with the
              row and column IPIV(k).

    B

              B is COMPLEX*16 array, dimension (LDB,NRHS)
              On entry, the N-by-NRHS right hand side matrix B.
              On exit, if INFO = 0, the N-by-NRHS 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))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The length of WORK.  LWORK >= MAX(1,2*N,3*N-2), and for
              the best performance, LWORK >= MAX(1,N*NB), where NB is
              the optimal blocksize for ZSYTRF_AA.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal 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
              > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                   has been completed, but the block diagonal matrix D is
                   exactly singular, so the solution could not be computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 160 of file zsysv_aa.f.

Author

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