hesv(3)

NAME
hesv - {he,sy}sv: rook (v1)

SYNOPSIS

  Functions

subroutine chesv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CHESV computes the solution to system of linear equations A * X = B for HE matrices
subroutine csysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CSYSV computes the solution to system of linear equations A * X = B for SY matrices
subroutine dsysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
DSYSV computes the solution to system of linear equations A * X = B for SY matrices
subroutine ssysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYSV computes the solution to system of linear equations A * X = B for SY matrices
subroutine zhesv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZHESV computes the solution to system of linear equations A * X = B for HE matrices
subroutine zsysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZSYSV computes the solution to system of linear equations A * X = B for SY matrices

Detailed Description

Function Documentation

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

Purpose:

    !>
    !> CHESV 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.
    !>
    !> The diagonal pivoting method is used to factor A as
    !>    A = U * D * U**H,  if UPLO = 'U', or
    !>    A = L * D * L**H,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is Hermitian and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U*D*U**H or A = L*D*L**H as computed by
    !>          CHETRF.
    !>

    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 and the block structure of D, as
    !>          determined by CHETRF.  If IPIV(k) > 0, then rows and columns
    !>          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
    !>          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
    !>          then rows and columns k-1 and -IPIV(k) were interchanged and
    !>          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
    !>          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
    !>          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
    !>          diagonal block.
    !>

    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 >= 1, and for best performance
    !>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
    !>          CHETRF.
    !>          for LWORK < N, TRS will be done with Level BLAS 2
    !>          for LWORK >= N, TRS will be done with Level BLAS 3
    !>
    !>          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.

  subroutine csysv (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 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.
    !>
    !> The diagonal pivoting method is used to factor A as
    !>    A = U * D * U**T,  if UPLO = 'U', or
    !>    A = L * D * L**T,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is symmetric and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U*D*U**T or A = L*D*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)
    !>          Details of the interchanges and the block structure of D, as
    !>          determined by CSYTRF.  If IPIV(k) > 0, then rows and columns
    !>          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
    !>          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
    !>          then rows and columns k-1 and -IPIV(k) were interchanged and
    !>          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
    !>          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
    !>          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
    !>          diagonal block.
    !>

    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 >= 1, and for best performance
    !>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
    !>          CSYTRF.
    !>          for LWORK < N, TRS will be done with Level BLAS 2
    !>          for LWORK >= N, TRS will be done with Level BLAS 3
    !>
    !>          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.

  subroutine dsysv (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 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.
    !>
    !> The diagonal pivoting method is used to factor A as
    !>    A = U * D * U**T,  if UPLO = 'U', or
    !>    A = L * D * L**T,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is symmetric and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U*D*U**T or A = L*D*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)
    !>          Details of the interchanges and the block structure of D, as
    !>          determined by DSYTRF.  If IPIV(k) > 0, then rows and columns
    !>          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
    !>          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
    !>          then rows and columns k-1 and -IPIV(k) were interchanged and
    !>          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
    !>          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
    !>          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
    !>          diagonal block.
    !>

    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 >= 1, and for best performance
    !>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
    !>          DSYTRF.
    !>          for LWORK < N, TRS will be done with Level BLAS 2
    !>          for LWORK >= N, TRS will be done with Level BLAS 3
    !>
    !>          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.

  subroutine ssysv (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 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.
    !>
    !> The diagonal pivoting method is used to factor A as
    !>    A = U * D * U**T,  if UPLO = 'U', or
    !>    A = L * D * L**T,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is symmetric and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U*D*U**T or A = L*D*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)
    !>          Details of the interchanges and the block structure of D, as
    !>          determined by SSYTRF.  If IPIV(k) > 0, then rows and columns
    !>          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
    !>          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
    !>          then rows and columns k-1 and -IPIV(k) were interchanged and
    !>          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
    !>          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
    !>          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
    !>          diagonal block.
    !>

    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 >= 1, and for best performance
    !>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
    !>          SSYTRF.
    !>          for LWORK < N, TRS will be done with Level BLAS 2
    !>          for LWORK >= N, TRS will be done with Level BLAS 3
    !>
    !>          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.

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

Purpose:

    !>
    !> ZHESV 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.
    !>
    !> The diagonal pivoting method is used to factor A as
    !>    A = U * D * U**H,  if UPLO = 'U', or
    !>    A = L * D * L**H,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is Hermitian and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U*D*U**H or A = L*D*L**H as computed by
    !>          ZHETRF.
    !>

    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 and the block structure of D, as
    !>          determined by ZHETRF.  If IPIV(k) > 0, then rows and columns
    !>          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
    !>          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
    !>          then rows and columns k-1 and -IPIV(k) were interchanged and
    !>          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
    !>          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
    !>          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
    !>          diagonal block.
    !>

    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 >= 1, and for best performance
    !>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
    !>          ZHETRF.
    !>          for LWORK < N, TRS will be done with Level BLAS 2
    !>          for LWORK >= N, TRS will be done with Level BLAS 3
    !>
    !>          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.

  subroutine zsysv (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 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.
    !>
    !> The diagonal pivoting method is used to factor A as
    !>    A = U * D * U**T,  if UPLO = 'U', or
    !>    A = L * D * L**T,  if UPLO = 'L',
    !> where U (or L) is a product of permutation and unit upper (lower)
    !> triangular matrices, and D is symmetric and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.  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 block diagonal matrix D and the
    !>          multipliers used to obtain the factor U or L from the
    !>          factorization A = U*D*U**T or A = L*D*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)
    !>          Details of the interchanges and the block structure of D, as
    !>          determined by ZSYTRF.  If IPIV(k) > 0, then rows and columns
    !>          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
    !>          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
    !>          then rows and columns k-1 and -IPIV(k) were interchanged and
    !>          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
    !>          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
    !>          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
    !>          diagonal block.
    !>

    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 >= 1, and for best performance
    !>          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
    !>          ZSYTRF.
    !>          for LWORK < N, TRS will be done with Level BLAS 2
    !>          for LWORK >= N, TRS will be done with Level BLAS 3
    !>
    !>          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.

Author

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