Scroll to navigation

complex_blas_level2(3) LAPACK complex_blas_level2(3)

NAME

complex_blas_level2 - complex

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

Generated automatically by Doxygen for LAPACK from the source code.

Wed Sep 1 2021 Version 3.10.0