lahef(3)

NAME
lahef - la{he,sy}f: step in hetrf

SYNOPSIS

  Functions

subroutine clahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
subroutine clasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
subroutine dlasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
DLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
subroutine slasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.
subroutine zlahef (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
subroutine zlasyf (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Detailed Description

Function Documentation

  subroutine clahef (character uplo, integer n, integer nb, integer kb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)

CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

Purpose:

    !>
    !> CLAHEF computes a partial factorization of a complex Hermitian
    !> matrix A using the Bunch-Kaufman diagonal pivoting method. The
    !> partial factorization has the form:
    !>
    !> A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
    !>       ( 0  U22 ) (  0   D  ) ( U12**H U22**H )
    !>
    !> A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
    !>       ( L21  I ) (  0  A22 ) (  0      I     )
    !>
    !> where the order of D is at most NB. The actual order is returned in
    !> the argument KB, and is either NB or NB-1, or N if N <= NB.
    !> Note that U**H denotes the conjugate transpose of U.
    !>
    !> CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code
    !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
    !> A22 (if UPLO = 'L').
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          Hermitian matrix A is stored:
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The maximum number of columns of the matrix A that should be
    !>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
    !>          blocks.
    !>

    KB

    !>          KB is INTEGER
    !>          The number of columns of A that were actually factored.
    !>          KB is either NB-1 or NB, or N if N <= NB.
    !>

    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, A contains details of the partial factorization.
    !>

    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) = 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':
    !>             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) = 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.
    !>

    W

    !>          W is COMPLEX array, dimension (LDW,NB)
    !>

    LDW

    !>          LDW is INTEGER
    !>          The leading dimension of the array W.  LDW >= max(1,N).
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  November 2013,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>

  subroutine clasyf (character uplo, integer n, integer nb, integer kb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)

CLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Purpose:

    !>
    !> CLASYF computes a partial factorization of a complex symmetric matrix
    !> A using the Bunch-Kaufman diagonal pivoting method. The partial
    !> factorization has the form:
    !>
    !> A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
    !>       ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
    !>
    !> A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  if UPLO = 'L'
    !>       ( L21  I ) ( 0   A22 ) (  0       I    )
    !>
    !> where the order of D is at most NB. The actual order is returned in
    !> the argument KB, and is either NB or NB-1, or N if N <= NB.
    !> Note that U**T denotes the transpose of U.
    !>
    !> CLASYF is an auxiliary routine called by CSYTRF. It uses blocked code
    !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
    !> A22 (if UPLO = 'L').
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is stored:
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The maximum number of columns of the matrix A that should be
    !>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
    !>          blocks.
    !>

    KB

    !>          KB is INTEGER
    !>          The number of columns of A that were actually factored.
    !>          KB is either NB-1 or NB, or N if N <= NB.
    !>

    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, A contains details of the partial factorization.
    !>

    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) = 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':
    !>             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) = 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.
    !>

    W

    !>          W is COMPLEX array, dimension (LDW,NB)
    !>

    LDW

    !>          LDW is INTEGER
    !>          The leading dimension of the array W.  LDW >= max(1,N).
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  November 2013,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>

  subroutine dlasyf (character uplo, integer n, integer nb, integer kb, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldw, * ) w, integer ldw, integer info)

DLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Purpose:

    !>
    !> DLASYF computes a partial factorization of a real symmetric matrix A
    !> using the Bunch-Kaufman diagonal pivoting method. The partial
    !> factorization has the form:
    !>
    !> A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
    !>       ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
    !>
    !> A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
    !>       ( L21  I ) (  0  A22 ) (  0       I    )
    !>
    !> where the order of D is at most NB. The actual order is returned in
    !> the argument KB, and is either NB or NB-1, or N if N <= NB.
    !>
    !> DLASYF is an auxiliary routine called by DSYTRF. It uses blocked code
    !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
    !> A22 (if UPLO = 'L').
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is stored:
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The maximum number of columns of the matrix A that should be
    !>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
    !>          blocks.
    !>

    KB

    !>          KB is INTEGER
    !>          The number of columns of A that were actually factored.
    !>          KB is either NB-1 or NB, or N if N <= NB.
    !>

    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, A contains details of the partial factorization.
    !>

    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) = 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':
    !>             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) = 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.
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (LDW,NB)
    !>

    LDW

    !>          LDW is INTEGER
    !>          The leading dimension of the array W.  LDW >= max(1,N).
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  November 2013,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>

  subroutine slasyf (character uplo, integer n, integer nb, integer kb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldw, * ) w, integer ldw, integer info)

SLASYF computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Purpose:

    !>
    !> SLASYF computes a partial factorization of a real symmetric matrix A
    !> using the Bunch-Kaufman diagonal pivoting method. The partial
    !> factorization has the form:
    !>
    !> A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
    !>       ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
    !>
    !> A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
    !>       ( L21  I ) (  0  A22 ) (  0       I    )
    !>
    !> where the order of D is at most NB. The actual order is returned in
    !> the argument KB, and is either NB or NB-1, or N if N <= NB.
    !>
    !> SLASYF is an auxiliary routine called by SSYTRF. It uses blocked code
    !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
    !> A22 (if UPLO = 'L').
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is stored:
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The maximum number of columns of the matrix A that should be
    !>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
    !>          blocks.
    !>

    KB

    !>          KB is INTEGER
    !>          The number of columns of A that were actually factored.
    !>          KB is either NB-1 or NB, or N if N <= NB.
    !>

    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, A contains details of the partial factorization.
    !>

    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) = 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':
    !>             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) = 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.
    !>

    W

    !>          W is REAL array, dimension (LDW,NB)
    !>

    LDW

    !>          LDW is INTEGER
    !>          The leading dimension of the array W.  LDW >= max(1,N).
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  November 2013,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>

  subroutine zlahef (character uplo, integer n, integer nb, integer kb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).

Purpose:

    !>
    !> ZLAHEF computes a partial factorization of a complex Hermitian
    !> matrix A using the Bunch-Kaufman diagonal pivoting method. The
    !> partial factorization has the form:
    !>
    !> A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
    !>       ( 0  U22 ) (  0   D  ) ( U12**H U22**H )
    !>
    !> A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
    !>       ( L21  I ) (  0  A22 ) (  0      I     )
    !>
    !> where the order of D is at most NB. The actual order is returned in
    !> the argument KB, and is either NB or NB-1, or N if N <= NB.
    !> Note that U**H denotes the conjugate transpose of U.
    !>
    !> ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code
    !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
    !> A22 (if UPLO = 'L').
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          Hermitian matrix A is stored:
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The maximum number of columns of the matrix A that should be
    !>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
    !>          blocks.
    !>

    KB

    !>          KB is INTEGER
    !>          The number of columns of A that were actually factored.
    !>          KB is either NB-1 or NB, or N if N <= NB.
    !>

    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, A contains details of the partial factorization.
    !>

    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) = 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':
    !>             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) = 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.
    !>

    W

    !>          W is COMPLEX*16 array, dimension (LDW,NB)
    !>

    LDW

    !>          LDW is INTEGER
    !>          The leading dimension of the array W.  LDW >= max(1,N).
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular.
    !>

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
    !>

  subroutine zlasyf (character uplo, integer n, integer nb, integer kb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)

ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method.

Purpose:

    !>
    !> ZLASYF computes a partial factorization of a complex symmetric matrix
    !> A using the Bunch-Kaufman diagonal pivoting method. The partial
    !> factorization has the form:
    !>
    !> A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
    !>       ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
    !>
    !> A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  if UPLO = 'L'
    !>       ( L21  I ) ( 0   A22 ) (  0       I    )
    !>
    !> where the order of D is at most NB. The actual order is returned in
    !> the argument KB, and is either NB or NB-1, or N if N <= NB.
    !> Note that U**T denotes the transpose of U.
    !>
    !> ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code
    !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
    !> A22 (if UPLO = 'L').
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is stored:
    !>          = 'U':  Upper triangular
    !>          = 'L':  Lower triangular
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The maximum number of columns of the matrix A that should be
    !>          factored.  NB should be at least 2 to allow for 2-by-2 pivot
    !>          blocks.
    !>

    KB

    !>          KB is INTEGER
    !>          The number of columns of A that were actually factored.
    !>          KB is either NB-1 or NB, or N if N <= NB.
    !>

    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, A contains details of the partial factorization.
    !>

    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) = 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':
    !>             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) = 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.
    !>

    W

    !>          W is COMPLEX*16 array, dimension (LDW,NB)
    !>

    LDW

    !>          LDW is INTEGER
    !>          The leading dimension of the array W.  LDW >= max(1,N).
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
    !>               has been completed, but the block diagonal matrix D is
    !>               exactly singular.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  November 2013,  Igor Kozachenko,
    !>                  Computer Science Division,
    !>                  University of California, Berkeley
    !>

Author

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