chbmv.f - Man Page

BLAS/SRC/chbmv.f

Synopsis

Functions/Subroutines

subroutine chbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
CHBMV

Function/Subroutine Documentation

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

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.

Author

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Referenced By

The man page chbmv(3) is an alias of chbmv.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK