complex16_blas_level2(3)

NAME
complex16_blas_level2 - complex16

SYNOPSIS

  Functions
subroutine zgbmv (trans, m, n, kl, ku, alpha, a, lda, x, incx, beta, y, incy)
ZGBMV
subroutine zgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
ZGEMV
subroutine zgerc (m, n, alpha, x, incx, y, incy, a, lda)
ZGERC
subroutine zgeru (m, n, alpha, x, incx, y, incy, a, lda)
ZGERU
subroutine zhbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
ZHBMV
subroutine zhemv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
ZHEMV
subroutine zher (uplo, n, alpha, x, incx, a, lda)
ZHER
subroutine zher2 (uplo, n, alpha, x, incx, y, incy, a, lda)
ZHER2
subroutine zhpmv (uplo, n, alpha, ap, x, incx, beta, y, incy)
ZHPMV
subroutine zhpr (uplo, n, alpha, x, incx, ap)
ZHPR
subroutine zhpr2 (uplo, n, alpha, x, incx, y, incy, ap)
ZHPR2
subroutine ztbmv (uplo, trans, diag, n, k, a, lda, x, incx)
ZTBMV
subroutine ztbsv (uplo, trans, diag, n, k, a, lda, x, incx)
ZTBSV
subroutine ztpmv (uplo, trans, diag, n, ap, x, incx)
ZTPMV
subroutine ztpsv (uplo, trans, diag, n, ap, x, incx)
ZTPSV
subroutine ztrmv (uplo, trans, diag, n, a, lda, x, incx)
ZTRMV
subroutine ztrsv (uplo, trans, diag, n, a, lda, x, incx)
ZTRSV

Detailed Description

This is the group of complex16 LEVEL 2 BLAS routines.

Function Documentation

  subroutine zgbmv (character trans, integer m, integer n, integer kl, integer ku, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZGBMV

Purpose:

     ZGBMV  performs one of the matrix-vector operations
        y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
        y := alpha*A**H*x + beta*y,
     where alpha and beta are scalars, x and y are vectors and A is an
     m by n band matrix, with kl sub-diagonals and ku super-diagonals.

Parameters
    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                  TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
                  TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.

    M

              M is INTEGER
               On entry, M specifies the number of rows of the matrix A.
               M must be at least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of the matrix A.
               N must be at least zero.

    KL

              KL is INTEGER
               On entry, KL specifies the number of sub-diagonals of the
               matrix A. KL must satisfy  0 .le. KL.

    KU

              KU is INTEGER
               On entry, KU specifies the number of super-diagonals of the
               matrix A. KU must satisfy  0 .le. KU.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry, the leading ( kl + ku + 1 ) by n part of the
               array A must contain the matrix of coefficients, supplied
               column by column, with the leading diagonal of the matrix in
               row ( ku + 1 ) of the array, the first super-diagonal
               starting at position 2 in row ku, the first sub-diagonal
               starting at position 1 in row ( ku + 2 ), and so on.
               Elements in the array A that do not correspond to elements
               in the band matrix (such as the top left ku by ku triangle)
               are not referenced.
               The following program segment will transfer a band matrix
               from conventional full matrix storage to band storage:
                     DO 20, J = 1, N
                        K = KU + 1 - J
                        DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
                           A( K + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               ( kl + ku + 1 ).

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
               and at least
               ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
               Before entry, the incremented array X must contain the
               vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is COMPLEX*16
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
               and at least
               ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
               Before entry, the incremented array Y must contain the
               vector y. On exit, Y is overwritten by the updated vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 186 of file zgbmv.f.

  subroutine zgemv (character trans, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZGEMV

Purpose:

     ZGEMV  performs one of the matrix-vector operations
        y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
        y := alpha*A**H*x + beta*y,
     where alpha and beta are scalars, x and y are vectors and A is an
     m by n matrix.

Parameters
    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
                  TRANS = 'T' or 't'   y := alpha*A**T*x + beta*y.
                  TRANS = 'C' or 'c'   y := alpha*A**H*x + beta*y.

    M

              M is INTEGER
               On entry, M specifies the number of rows of the matrix A.
               M must be at least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry, the leading m by n part of the array A must
               contain the matrix of coefficients.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, m ).

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
               and at least
               ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
               Before entry, the incremented array X must contain the
               vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is COMPLEX*16
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
               and at least
               ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
               Before entry with BETA non-zero, the incremented array Y
               must contain the vector y. On exit, Y is overwritten by the
               updated vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 157 of file zgemv.f.

  subroutine zgerc (integer m, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(lda,*) a, integer lda)

ZGERC

Purpose:

     ZGERC  performs the rank 1 operation
        A := alpha*x*y**H + A,
     where alpha is a scalar, x is an m element vector, y is an n element
     vector and A is an m by n matrix.

Parameters
    M

              M is INTEGER
               On entry, M specifies the number of rows of the matrix A.
               M must be at least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( m - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the m
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry, the leading m by n part of the array A must
               contain the matrix of coefficients. On exit, A is
               overwritten by the updated matrix.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, m ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 129 of file zgerc.f.

  subroutine zgeru (integer m, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(lda,*) a, integer lda)

ZGERU

Purpose:

     ZGERU  performs the rank 1 operation
        A := alpha*x*y**T + A,
     where alpha is a scalar, x is an m element vector, y is an n element
     vector and A is an m by n matrix.

Parameters
    M

              M is INTEGER
               On entry, M specifies the number of rows of the matrix A.
               M must be at least zero.

    N

              N is INTEGER
               On entry, N specifies the number of columns of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( m - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the m
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry, the leading m by n part of the array A must
               contain the matrix of coefficients. On exit, A is
               overwritten by the updated matrix.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, m ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 129 of file zgeru.f.

  subroutine zhbmv (character uplo, integer n, integer k, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZHBMV

Purpose:

     ZHBMV  performs the matrix-vector  operation
        y := alpha*A*x + beta*y,
     where alpha and beta are scalars, x and y are n element vectors and
     A is an n by n hermitian band matrix, with k super-diagonals.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the band matrix A is being supplied as
               follows:
                  UPLO = 'U' or 'u'   The upper triangular part of A is
                                      being supplied.
                  UPLO = 'L' or 'l'   The lower triangular part of A is
                                      being supplied.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    K

              K is INTEGER
               On entry, K specifies the number of super-diagonals of the
               matrix A. K must satisfy  0 .le. K.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
               by n part of the array A must contain the upper triangular
               band part of the hermitian matrix, supplied column by
               column, with the leading diagonal of the matrix in row
               ( k + 1 ) of the array, the first super-diagonal starting at
               position 2 in row k, and so on. The top left k by k triangle
               of the array A is not referenced.
               The following program segment will transfer the upper
               triangular part of a hermitian band matrix from conventional
               full matrix storage to band storage:
                     DO 20, J = 1, N
                        M = K + 1 - J
                        DO 10, I = MAX( 1, J - K ), J
                           A( M + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE
               Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
               by n part of the array A must contain the lower triangular
               band part of the hermitian matrix, supplied column by
               column, with the leading diagonal of the matrix in row 1 of
               the array, the first sub-diagonal starting at position 1 in
               row 2, and so on. The bottom right k by k triangle of the
               array A is not referenced.
               The following program segment will transfer the lower
               triangular part of a hermitian band matrix from conventional
               full matrix storage to band storage:
                     DO 20, J = 1, N
                        M = 1 - J
                        DO 10, I = J, MIN( N, J + K )
                           A( M + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE
               Note that the imaginary parts of the diagonal elements need
               not be set and are assumed to be zero.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               ( k + 1 ).

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the
               vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is COMPLEX*16
               On entry, BETA specifies the scalar beta.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the
               vector y. On exit, Y is overwritten by the updated vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 186 of file zhbmv.f.

  subroutine zhemv (character uplo, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZHEMV

Purpose:

     ZHEMV  performs the matrix-vector  operation
        y := alpha*A*x + beta*y,
     where alpha and beta are scalars, x and y are n element vectors and
     A is an n by n hermitian matrix.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the array A is to be referenced as
               follows:
                  UPLO = 'U' or 'u'   Only the upper triangular part of A
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the lower triangular part of A
                                      is to be referenced.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular part of the hermitian matrix and the strictly
               lower triangular part of A is not referenced.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular part of the hermitian matrix and the strictly
               upper triangular part of A is not referenced.
               Note that the imaginary parts of the diagonal elements need
               not be set and are assumed to be zero.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is COMPLEX*16
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y. On exit, Y is overwritten by the updated
               vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 153 of file zhemv.f.

  subroutine zher (character uplo, integer n, double precision alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(lda,*) a, integer lda)

ZHER

Purpose:

     ZHER   performs the hermitian rank 1 operation
        A := alpha*x*x**H + A,
     where alpha is a real scalar, x is an n element vector and A is an
     n by n hermitian matrix.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the array A is to be referenced as
               follows:
                  UPLO = 'U' or 'u'   Only the upper triangular part of A
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the lower triangular part of A
                                      is to be referenced.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry, ALPHA specifies the scalar alpha.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular part of the hermitian matrix and the strictly
               lower triangular part of A is not referenced. On exit, the
               upper triangular part of the array A is overwritten by the
               upper triangular part of the updated matrix.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular part of the hermitian matrix and the strictly
               upper triangular part of A is not referenced. On exit, the
               lower triangular part of the array A is overwritten by the
               lower triangular part of the updated matrix.
               Note that the imaginary parts of the diagonal elements need
               not be set, they are assumed to be zero, and on exit they
               are set to zero.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 134 of file zher.f.

  subroutine zher2 (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(lda,*) a, integer lda)

ZHER2

Purpose:

     ZHER2  performs the hermitian rank 2 operation
        A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
     where alpha is a scalar, x and y are n element vectors and A is an n
     by n hermitian matrix.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the array A is to be referenced as
               follows:
                  UPLO = 'U' or 'u'   Only the upper triangular part of A
                                      is to be referenced.
                  UPLO = 'L' or 'l'   Only the lower triangular part of A
                                      is to be referenced.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular part of the hermitian matrix and the strictly
               lower triangular part of A is not referenced. On exit, the
               upper triangular part of the array A is overwritten by the
               upper triangular part of the updated matrix.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular part of the hermitian matrix and the strictly
               upper triangular part of A is not referenced. On exit, the
               lower triangular part of the array A is overwritten by the
               lower triangular part of the updated matrix.
               Note that the imaginary parts of the diagonal elements need
               not be set, they are assumed to be zero, and on exit they
               are set to zero.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 149 of file zher2.f.

  subroutine zhpmv (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZHPMV

Purpose:

     ZHPMV  performs the matrix-vector operation
        y := alpha*A*x + beta*y,
     where alpha and beta are scalars, x and y are n element vectors and
     A is an n by n hermitian matrix, supplied in packed form.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the matrix A is supplied in the packed
               array AP as follows:
                  UPLO = 'U' or 'u'   The upper triangular part of A is
                                      supplied in AP.
                  UPLO = 'L' or 'l'   The lower triangular part of A is
                                      supplied in AP.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    AP

              AP is COMPLEX*16 array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with UPLO = 'U' or 'u', the array AP must
               contain the upper triangular part of the hermitian matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
               and a( 2, 2 ) respectively, and so on.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular part of the hermitian matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
               and a( 3, 1 ) respectively, and so on.
               Note that the imaginary parts of the diagonal elements need
               not be set and are assumed to be zero.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    BETA

              BETA is COMPLEX*16
               On entry, BETA specifies the scalar beta. When BETA is
               supplied as zero then Y need not be set on input.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y. On exit, Y is overwritten by the updated
               vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 148 of file zhpmv.f.

  subroutine zhpr (character uplo, integer n, double precision alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) ap)

ZHPR

Purpose:

     ZHPR    performs the hermitian rank 1 operation
        A := alpha*x*x**H + A,
     where alpha is a real scalar, x is an n element vector and A is an
     n by n hermitian matrix, supplied in packed form.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the matrix A is supplied in the packed
               array AP as follows:
                  UPLO = 'U' or 'u'   The upper triangular part of A is
                                      supplied in AP.
                  UPLO = 'L' or 'l'   The lower triangular part of A is
                                      supplied in AP.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry, ALPHA specifies the scalar alpha.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    AP

              AP is COMPLEX*16 array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with  UPLO = 'U' or 'u', the array AP must
               contain the upper triangular part of the hermitian matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
               and a( 2, 2 ) respectively, and so on. On exit, the array
               AP is overwritten by the upper triangular part of the
               updated matrix.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular part of the hermitian matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
               and a( 3, 1 ) respectively, and so on. On exit, the array
               AP is overwritten by the lower triangular part of the
               updated matrix.
               Note that the imaginary parts of the diagonal elements need
               not be set, they are assumed to be zero, and on exit they
               are set to zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 129 of file zhpr.f.

  subroutine zhpr2 (character uplo, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(*) ap)

ZHPR2

Purpose:

     ZHPR2  performs the hermitian rank 2 operation
        A := alpha*x*y**H + conjg( alpha )*y*x**H + A,
     where alpha is a scalar, x and y are n element vectors and A is an
     n by n hermitian matrix, supplied in packed form.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the upper or lower
               triangular part of the matrix A is supplied in the packed
               array AP as follows:
                  UPLO = 'U' or 'u'   The upper triangular part of A is
                                      supplied in AP.
                  UPLO = 'L' or 'l'   The lower triangular part of A is
                                      supplied in AP.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    ALPHA

              ALPHA is COMPLEX*16
               On entry, ALPHA specifies the scalar alpha.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

    Y

              Y is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCY ) ).
               Before entry, the incremented array Y must contain the n
               element vector y.

    INCY

              INCY is INTEGER
               On entry, INCY specifies the increment for the elements of
               Y. INCY must not be zero.

    AP

              AP is COMPLEX*16 array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with  UPLO = 'U' or 'u', the array AP must
               contain the upper triangular part of the hermitian matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
               and a( 2, 2 ) respectively, and so on. On exit, the array
               AP is overwritten by the upper triangular part of the
               updated matrix.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular part of the hermitian matrix
               packed sequentially, column by column, so that AP( 1 )
               contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
               and a( 3, 1 ) respectively, and so on. On exit, the array
               AP is overwritten by the lower triangular part of the
               updated matrix.
               Note that the imaginary parts of the diagonal elements need
               not be set, they are assumed to be zero, and on exit they
               are set to zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 144 of file zhpr2.f.

  subroutine ztbmv (character uplo, character trans, character diag, integer n, integer k, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTBMV

Purpose:

     ZTBMV  performs one of the matrix-vector operations
        x := A*x,   or   x := A**T*x,   or   x := A**H*x,
     where x is an n element vector and  A is an n by n unit, or non-unit,
     upper or lower triangular band matrix, with ( k + 1 ) diagonals.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   x := A*x.
                  TRANS = 'T' or 't'   x := A**T*x.
                  TRANS = 'C' or 'c'   x := A**H*x.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit
               triangular as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    K

              K is INTEGER
               On entry with UPLO = 'U' or 'u', K specifies the number of
               super-diagonals of the matrix A.
               On entry with UPLO = 'L' or 'l', K specifies the number of
               sub-diagonals of the matrix A.
               K must satisfy  0 .le. K.

    A

              A is COMPLEX*16 array, dimension ( LDA, N ).
               Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
               by n part of the array A must contain the upper triangular
               band part of the matrix of coefficients, supplied column by
               column, with the leading diagonal of the matrix in row
               ( k + 1 ) of the array, the first super-diagonal starting at
               position 2 in row k, and so on. The top left k by k triangle
               of the array A is not referenced.
               The following program segment will transfer an upper
               triangular band matrix from conventional full matrix storage
               to band storage:
                     DO 20, J = 1, N
                        M = K + 1 - J
                        DO 10, I = MAX( 1, J - K ), J
                           A( M + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE
               Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
               by n part of the array A must contain the lower triangular
               band part of the matrix of coefficients, supplied column by
               column, with the leading diagonal of the matrix in row 1 of
               the array, the first sub-diagonal starting at position 1 in
               row 2, and so on. The bottom right k by k triangle of the
               array A is not referenced.
               The following program segment will transfer a lower
               triangular band matrix from conventional full matrix storage
               to band storage:
                     DO 20, J = 1, N
                        M = 1 - J
                        DO 10, I = J, MIN( N, J + K )
                           A( M + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE
               Note that when DIAG = 'U' or 'u' the elements of the array A
               corresponding to the diagonal elements of the matrix are not
               referenced, but are assumed to be unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               ( k + 1 ).

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x. On exit, X is overwritten with the
               transformed vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 185 of file ztbmv.f.

  subroutine ztbsv (character uplo, character trans, character diag, integer n, integer k, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTBSV

Purpose:

     ZTBSV  solves one of the systems of equations
        A*x = b,   or   A**T*x = b,   or   A**H*x = b,
     where b and x are n element vectors and A is an n by n unit, or
     non-unit, upper or lower triangular band matrix, with ( k + 1 )
     diagonals.
     No test for singularity or near-singularity is included in this
     routine. Such tests must be performed before calling this routine.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the equations to be solved as
               follows:
                  TRANS = 'N' or 'n'   A*x = b.
                  TRANS = 'T' or 't'   A**T*x = b.
                  TRANS = 'C' or 'c'   A**H*x = b.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit
               triangular as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    K

              K is INTEGER
               On entry with UPLO = 'U' or 'u', K specifies the number of
               super-diagonals of the matrix A.
               On entry with UPLO = 'L' or 'l', K specifies the number of
               sub-diagonals of the matrix A.
               K must satisfy  0 .le. K.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
               by n part of the array A must contain the upper triangular
               band part of the matrix of coefficients, supplied column by
               column, with the leading diagonal of the matrix in row
               ( k + 1 ) of the array, the first super-diagonal starting at
               position 2 in row k, and so on. The top left k by k triangle
               of the array A is not referenced.
               The following program segment will transfer an upper
               triangular band matrix from conventional full matrix storage
               to band storage:
                     DO 20, J = 1, N
                        M = K + 1 - J
                        DO 10, I = MAX( 1, J - K ), J
                           A( M + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE
               Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
               by n part of the array A must contain the lower triangular
               band part of the matrix of coefficients, supplied column by
               column, with the leading diagonal of the matrix in row 1 of
               the array, the first sub-diagonal starting at position 1 in
               row 2, and so on. The bottom right k by k triangle of the
               array A is not referenced.
               The following program segment will transfer a lower
               triangular band matrix from conventional full matrix storage
               to band storage:
                     DO 20, J = 1, N
                        M = 1 - J
                        DO 10, I = J, MIN( N, J + K )
                           A( M + I, J ) = matrix( I, J )
                  10    CONTINUE
                  20 CONTINUE
               Note that when DIAG = 'U' or 'u' the elements of the array A
               corresponding to the diagonal elements of the matrix are not
               referenced, but are assumed to be unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               ( k + 1 ).

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element right-hand side vector b. On exit, X is overwritten
               with the solution vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 188 of file ztbsv.f.

  subroutine ztpmv (character uplo, character trans, character diag, integer n, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx)

ZTPMV

Purpose:

     ZTPMV  performs one of the matrix-vector operations
        x := A*x,   or   x := A**T*x,   or   x := A**H*x,
     where x is an n element vector and  A is an n by n unit, or non-unit,
     upper or lower triangular matrix, supplied in packed form.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   x := A*x.
                  TRANS = 'T' or 't'   x := A**T*x.
                  TRANS = 'C' or 'c'   x := A**H*x.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit
               triangular as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    AP

              AP is COMPLEX*16 array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with  UPLO = 'U' or 'u', the array AP must
               contain the upper triangular matrix packed sequentially,
               column by column, so that AP( 1 ) contains a( 1, 1 ),
               AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
               respectively, and so on.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular matrix packed sequentially,
               column by column, so that AP( 1 ) contains a( 1, 1 ),
               AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
               respectively, and so on.
               Note that when  DIAG = 'U' or 'u', the diagonal elements of
               A are not referenced, but are assumed to be unity.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x. On exit, X is overwritten with the
               transformed vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 141 of file ztpmv.f.

  subroutine ztpsv (character uplo, character trans, character diag, integer n, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx)

ZTPSV

Purpose:

     ZTPSV  solves one of the systems of equations
        A*x = b,   or   A**T*x = b,   or   A**H*x = b,
     where b and x are n element vectors and A is an n by n unit, or
     non-unit, upper or lower triangular matrix, supplied in packed form.
     No test for singularity or near-singularity is included in this
     routine. Such tests must be performed before calling this routine.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the equations to be solved as
               follows:
                  TRANS = 'N' or 'n'   A*x = b.
                  TRANS = 'T' or 't'   A**T*x = b.
                  TRANS = 'C' or 'c'   A**H*x = b.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit
               triangular as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    AP

              AP is COMPLEX*16 array, dimension at least
               ( ( n*( n + 1 ) )/2 ).
               Before entry with  UPLO = 'U' or 'u', the array AP must
               contain the upper triangular matrix packed sequentially,
               column by column, so that AP( 1 ) contains a( 1, 1 ),
               AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
               respectively, and so on.
               Before entry with UPLO = 'L' or 'l', the array AP must
               contain the lower triangular matrix packed sequentially,
               column by column, so that AP( 1 ) contains a( 1, 1 ),
               AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
               respectively, and so on.
               Note that when  DIAG = 'U' or 'u', the diagonal elements of
               A are not referenced, but are assumed to be unity.

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element right-hand side vector b. On exit, X is overwritten
               with the solution vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 143 of file ztpsv.f.

  subroutine ztrmv (character uplo, character trans, character diag, integer n, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTRMV

Purpose:

     ZTRMV  performs one of the matrix-vector operations
        x := A*x,   or   x := A**T*x,   or   x := A**H*x,
     where x is an n element vector and  A is an n by n unit, or non-unit,
     upper or lower triangular matrix.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the operation to be performed as
               follows:
                  TRANS = 'N' or 'n'   x := A*x.
                  TRANS = 'T' or 't'   x := A**T*x.
                  TRANS = 'C' or 'c'   x := A**H*x.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit
               triangular as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    A

              A is COMPLEX*16 array, dimension ( LDA, N ).
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular matrix and the strictly lower triangular part of
               A is not referenced.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular matrix and the strictly upper triangular part of
               A is not referenced.
               Note that when  DIAG = 'U' or 'u', the diagonal elements of
               A are not referenced either, but are assumed to be unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element vector x. On exit, X is overwritten with the
               transformed vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      The vector and matrix arguments are not referenced when N = 0, or M = 0
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 146 of file ztrmv.f.

  subroutine ztrsv (character uplo, character trans, character diag, integer n, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)

ZTRSV

Purpose:

     ZTRSV  solves one of the systems of equations
        A*x = b,   or   A**T*x = b,   or   A**H*x = b,
     where b and x are n element vectors and A is an n by n unit, or
     non-unit, upper or lower triangular matrix.
     No test for singularity or near-singularity is included in this
     routine. Such tests must be performed before calling this routine.

Parameters
    UPLO

              UPLO is CHARACTER*1
               On entry, UPLO specifies whether the matrix is an upper or
               lower triangular matrix as follows:
                  UPLO = 'U' or 'u'   A is an upper triangular matrix.
                  UPLO = 'L' or 'l'   A is a lower triangular matrix.

    TRANS

              TRANS is CHARACTER*1
               On entry, TRANS specifies the equations to be solved as
               follows:
                  TRANS = 'N' or 'n'   A*x = b.
                  TRANS = 'T' or 't'   A**T*x = b.
                  TRANS = 'C' or 'c'   A**H*x = b.

    DIAG

              DIAG is CHARACTER*1
               On entry, DIAG specifies whether or not A is unit
               triangular as follows:
                  DIAG = 'U' or 'u'   A is assumed to be unit triangular.
                  DIAG = 'N' or 'n'   A is not assumed to be unit
                                      triangular.

    N

              N is INTEGER
               On entry, N specifies the order of the matrix A.
               N must be at least zero.

    A

              A is COMPLEX*16 array, dimension ( LDA, N )
               Before entry with  UPLO = 'U' or 'u', the leading n by n
               upper triangular part of the array A must contain the upper
               triangular matrix and the strictly lower triangular part of
               A is not referenced.
               Before entry with UPLO = 'L' or 'l', the leading n by n
               lower triangular part of the array A must contain the lower
               triangular matrix and the strictly upper triangular part of
               A is not referenced.
               Note that when  DIAG = 'U' or 'u', the diagonal elements of
               A are not referenced either, but are assumed to be unity.

    LDA

              LDA is INTEGER
               On entry, LDA specifies the first dimension of A as declared
               in the calling (sub) program. LDA must be at least
               max( 1, n ).

    X

              X is COMPLEX*16 array, dimension at least
               ( 1 + ( n - 1 )*abs( INCX ) ).
               Before entry, the incremented array X must contain the n
               element right-hand side vector b. On exit, X is overwritten
               with the solution vector x.

    INCX

              INCX is INTEGER
               On entry, INCX specifies the increment for the elements of
               X. INCX must not be zero.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Level 2 Blas routine.
      -- Written on 22-October-1986.
         Jack Dongarra, Argonne National Lab.
         Jeremy Du Croz, Nag Central Office.
         Sven Hammarling, Nag Central Office.
         Richard Hanson, Sandia National Labs.

Definition at line 148 of file ztrsv.f.

Author

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