complex_blas_level2(3) LAPACK complex_blas_level2(3)

complex_blas_level2 - complex


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

This is the group of complex LEVEL 2 BLAS routines.

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.

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 cgbmv.f.

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.

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 cgemv.f.

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.

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 cgerc.f.

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.

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 cgeru.f.

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.

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 chbmv.f.

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.

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 chemv.f.

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.

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 cher.f.

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.

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 cher2.f.

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.

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 chpmv.f.

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.

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 chpr.f.

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.

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 chpr2.f.

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.

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 ctbmv.f.

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.

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 ctbsv.f.

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.

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 ctpmv.f.

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.

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 ctpsv.f.

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.

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 ctrmv.f.

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.

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 ctrsv.f.

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