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complex_blas_level2(3) LAPACK complex_blas_level2(3)

NAME

complex_blas_level2

SYNOPSIS

Functions


subroutine cgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGBMV subroutine cgemv (TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV subroutine cgerc (M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CGERC subroutine cgeru (M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CGERU subroutine chbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CHBMV subroutine chemv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CHEMV subroutine cher (UPLO, N, ALPHA, X, INCX, A, LDA)
CHER subroutine cher2 (UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CHER2 subroutine chpmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CHPMV subroutine chpr (UPLO, N, ALPHA, X, INCX, AP)
CHPR subroutine chpr2 (UPLO, N, ALPHA, X, INCX, Y, INCY, AP)
CHPR2 subroutine ctbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBMV subroutine ctbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBSV subroutine ctpmv (UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV subroutine ctpsv (UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPSV subroutine ctrmv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRMV subroutine ctrsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRSV

Detailed Description

This is the group of complex LEVEL 2 BLAS routines.

Function Documentation

subroutine cgbmv (character TRANS, integer M, integer N, integer KL, integer KU, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY)

CGBMV

Purpose:

 CGBMV  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
           On entry, ALPHA specifies the scalar alpha.

A

          A is COMPLEX 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 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
           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 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.

Date:

December 2016

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.

subroutine cgemv (character TRANS, integer M, integer N, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY)

CGEMV

Purpose:

 CGEMV 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
           On entry, ALPHA specifies the scalar alpha.

A

          A is COMPLEX 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 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
           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 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.

Date:

December 2016

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.

subroutine cgerc (integer M, integer N, complex ALPHA, complex, dimension(*) X, integer INCX, complex, dimension(*) Y, integer INCY, complex, dimension(lda,*) A, integer LDA)

CGERC

Purpose:

 CGERC  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
           On entry, ALPHA specifies the scalar alpha.

X

          X is COMPLEX 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 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 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.

Date:

December 2016

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.

subroutine cgeru (integer M, integer N, complex ALPHA, complex, dimension(*) X, integer INCX, complex, dimension(*) Y, integer INCY, complex, dimension(lda,*) A, integer LDA)

CGERU

Purpose:

 CGERU  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
           On entry, ALPHA specifies the scalar alpha.

X

          X is COMPLEX 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 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 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.

Date:

December 2016

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.

subroutine chbmv (character UPLO, integer N, integer K, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY)

CHBMV

Purpose:

 CHBMV  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
           On entry, ALPHA specifies the scalar alpha.

A

          A is COMPLEX 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 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
           On entry, BETA specifies the scalar beta.

Y

          Y is COMPLEX 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.

Date:

December 2016

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.

subroutine chemv (character UPLO, integer N, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY)

CHEMV

Purpose:

 CHEMV  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
           On entry, ALPHA specifies the scalar alpha.

A

          A is COMPLEX 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 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
           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 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.

Date:

December 2016

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.

subroutine cher (character UPLO, integer N, real ALPHA, complex, dimension(*) X, integer INCX, complex, dimension(lda,*) A, integer LDA)

CHER

Purpose:

 CHER   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 REAL
           On entry, ALPHA specifies the scalar alpha.

X

          X is COMPLEX 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 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.

Date:

December 2016

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.

subroutine cher2 (character UPLO, integer N, complex ALPHA, complex, dimension(*) X, integer INCX, complex, dimension(*) Y, integer INCY, complex, dimension(lda,*) A, integer LDA)

CHER2

Purpose:

 CHER2  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
           On entry, ALPHA specifies the scalar alpha.

X

          X is COMPLEX 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 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 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.

Date:

December 2016

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.

subroutine chpmv (character UPLO, integer N, complex ALPHA, complex, dimension(*) AP, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY)

CHPMV

Purpose:

 CHPMV  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
           On entry, ALPHA specifies the scalar alpha.

AP

          AP is COMPLEX 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 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
           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 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.

Date:

December 2016

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.

subroutine chpr (character UPLO, integer N, real ALPHA, complex, dimension(*) X, integer INCX, complex, dimension(*) AP)

CHPR

Purpose:

 CHPR    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 REAL
           On entry, ALPHA specifies the scalar alpha.

X

          X is COMPLEX 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 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.

Date:

December 2016

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.

subroutine chpr2 (character UPLO, integer N, complex ALPHA, complex, dimension(*) X, integer INCX, complex, dimension(*) Y, integer INCY, complex, dimension(*) AP)

CHPR2

Purpose:

 CHPR2  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
           On entry, ALPHA specifies the scalar alpha.

X

          X is COMPLEX 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 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 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.

Date:

December 2016

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.

subroutine ctbmv (character UPLO, character TRANS, character DIAG, integer N, integer K, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX)

CTBMV

Purpose:

 CTBMV  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 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 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.

Date:

December 2016

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.

subroutine ctbsv (character UPLO, character TRANS, character DIAG, integer N, integer K, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX)

CTBSV

Purpose:

 CTBSV  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 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 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.

Date:

December 2016

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.

subroutine ctpmv (character UPLO, character TRANS, character DIAG, integer N, complex, dimension(*) AP, complex, dimension(*) X, integer INCX)

CTPMV

Purpose:

 CTPMV  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 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 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.

Date:

December 2016

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.

subroutine ctpsv (character UPLO, character TRANS, character DIAG, integer N, complex, dimension(*) AP, complex, dimension(*) X, integer INCX)

CTPSV

Purpose:

 CTPSV  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 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 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.

Date:

December 2016

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.

subroutine ctrmv (character UPLO, character TRANS, character DIAG, integer N, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX)

CTRMV

Purpose:

 CTRMV  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 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 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.

Date:

December 2016

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.

subroutine ctrsv (character UPLO, character TRANS, character DIAG, integer N, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX)

CTRSV

Purpose:

 CTRSV  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 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 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.

Date:

December 2016

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.

Author

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