hesv_rook(3)

NAME
hesv_rook - {he,sy}sv_rook: rook (v2)

SYNOPSIS

  Functions

subroutine chesv_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman (rook")diagonalpivotingmethod
subroutine csysv_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
subroutine dsysv_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
subroutine ssysv_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices
subroutine zhesv_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman (rook")diagonalpivotingmethod
subroutine zsysv_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices

Detailed Description

Function Documentation

  subroutine chesv_rook (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_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method

Purpose:

    !>
    !> CHESV_ROOK 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 bounded Bunch-Kaufman () 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 Hermitian and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.
    !>
    !> CHETRF_ROOK is called to compute the factorization of a complex
    !> Hermition matrix A using the bounded Bunch-Kaufman () diagonal
    !> pivoting method.
    !>
    !> The factored form of A is then used to solve the system
    !> of equations A * X = B by calling CHETRS_ROOK (uses BLAS 2).
    !>

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_ROOK.
    !>

    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.
    !>
    !>          If UPLO = 'U':
    !>             Only the last KB elements of IPIV are set.
    !>
    !>             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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>             columns k and -IPIV(k) were interchanged and rows and
    !>             columns k-1 and -IPIV(k-1) were inerchaged,
    !>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>             Only the first KB elements of IPIV are set.
    !>
    !>             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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>             columns k and -IPIV(k) were interchanged and rows and
    !>             columns k+1 and -IPIV(k+1) were inerchaged,
    !>             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_ROOK.
    !>          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.

!>
!>  November 2013,  Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>
!>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
!>                  School of Mathematics,
!>                  University of Manchester
!>
!> .fi

  subroutine csysv_rook (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_ROOK computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> CSYSV_ROOK 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.
    !>
    !> CSYTRF_ROOK is called to compute the factorization of a complex
    !> symmetric matrix A using the bounded Bunch-Kaufman () diagonal
    !> pivoting method.
    !>
    !> The factored form of A is then used to solve the system
    !> of equations A * X = B by calling CSYTRS_ROOK.
    !>

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_ROOK.
    !>

    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_ROOK.
    !>
    !>          If UPLO = 'U':
    !>               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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k-1 and -IPIV(k-1) were inerchaged,
    !>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>               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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k+1 and -IPIV(k+1) were inerchaged,
    !>               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_ROOK.
    !>
    !>          TRS will be done with Level 2 BLAS
    !>
    !>          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.

Contributors:

    !>
    !>   April 2012, Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

  subroutine dsysv_rook (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_ROOK computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> DSYSV_ROOK 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.
    !>
    !> DSYTRF_ROOK is called to compute the factorization of a real
    !> symmetric matrix A using the bounded Bunch-Kaufman () diagonal
    !> pivoting method.
    !>
    !> The factored form of A is then used to solve the system
    !> of equations A * X = B by calling DSYTRS_ROOK.
    !>

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_ROOK.
    !>

    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_ROOK.
    !>
    !>          If UPLO = 'U':
    !>               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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k-1 and -IPIV(k-1) were inerchaged,
    !>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>               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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k+1 and -IPIV(k+1) were inerchaged,
    !>               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_ROOK.
    !>
    !>          TRS will be done with Level 2 BLAS
    !>
    !>          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.

Contributors:

    !>
    !>   April 2012, Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

  subroutine ssysv_rook (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_ROOK computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> SSYSV_ROOK 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.
    !>
    !> SSYTRF_ROOK is called to compute the factorization of a real
    !> symmetric matrix A using the bounded Bunch-Kaufman () diagonal
    !> pivoting method.
    !>
    !> The factored form of A is then used to solve the system
    !> of equations A * X = B by calling SSYTRS_ROOK.
    !>

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_ROOK.
    !>

    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_ROOK.
    !>
    !>          If UPLO = 'U':
    !>               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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k-1 and -IPIV(k-1) were inerchaged,
    !>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>               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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k+1 and -IPIV(k+1) were inerchaged,
    !>               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_ROOK.
    !>
    !>          TRS will be done with Level 2 BLAS
    !>
    !>          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.

Contributors:

    !>
    !>   April 2012, Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

  subroutine zhesv_rook (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_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method

Purpose:

    !>
    !> ZHESV_ROOK 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 bounded Bunch-Kaufman () 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 Hermitian and block diagonal with
    !> 1-by-1 and 2-by-2 diagonal blocks.
    !>
    !> ZHETRF_ROOK is called to compute the factorization of a complex
    !> Hermition matrix A using the bounded Bunch-Kaufman () diagonal
    !> pivoting method.
    !>
    !> The factored form of A is then used to solve the system
    !> of equations A * X = B by calling ZHETRS_ROOK (uses BLAS 2).
    !>

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_ROOK.
    !>

    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.
    !>
    !>          If UPLO = 'U':
    !>             Only the last KB elements of IPIV are set.
    !>
    !>             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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>             columns k and -IPIV(k) were interchanged and rows and
    !>             columns k-1 and -IPIV(k-1) were inerchaged,
    !>             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>             Only the first KB elements of IPIV are set.
    !>
    !>             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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>             columns k and -IPIV(k) were interchanged and rows and
    !>             columns k+1 and -IPIV(k+1) were inerchaged,
    !>             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_ROOK.
    !>          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.

!>
!>  November 2013,  Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>
!>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
!>                  School of Mathematics,
!>                  University of Manchester
!>
!> .fi

  subroutine zsysv_rook (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_ROOK computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

    !>
    !> ZSYSV_ROOK 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.
    !>
    !> ZSYTRF_ROOK is called to compute the factorization of a complex
    !> symmetric matrix A using the bounded Bunch-Kaufman () diagonal
    !> pivoting method.
    !>
    !> The factored form of A is then used to solve the system
    !> of equations A * X = B by calling ZSYTRS_ROOK.
    !>

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_ROOK.
    !>

    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_ROOK.
    !>
    !>          If UPLO = 'U':
    !>               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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k-1 and -IPIV(k-1) were inerchaged,
    !>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
    !>
    !>          If UPLO = 'L':
    !>               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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
    !>               columns k and -IPIV(k) were interchanged and rows and
    !>               columns k+1 and -IPIV(k+1) were inerchaged,
    !>               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_ROOK.
    !>
    !>          TRS will be done with Level 2 BLAS
    !>
    !>          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.

Contributors:

    !>
    !>   December 2016, Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>
    !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
    !>                  School of Mathematics,
    !>                  University of Manchester
    !>
    !>

Author

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