Man page - hbmv(3)

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Manual

hbmv

NAME
SYNOPSIS
Functions
Detailed Description
Function 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)
subroutine dsbmv (character uplo, integer n, integer k, double precisionalpha, double precision, dimension(lda,*) a, integer lda, doubleprecision, dimension(*) x, integer incx, double precision beta, doubleprecision, dimension(*) y, integer incy)
subroutine ssbmv (character uplo, integer n, integer k, real alpha, real,dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx,real beta, real, dimension(*) y, integer incy)
subroutine zhbmv (character uplo, integer n, integer k, complex*16 alpha,complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*)x, integer incx, complex*16 beta, complex*16, dimension(*) y, integerincy)
Author

NAME

hbmv - {hb,sb}mv: Hermitian/symmetric matrix-vector multiply

SYNOPSIS

Functions

subroutine chbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
CHBMV
subroutine dsbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
DSBMV
subroutine ssbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
SSBMV
subroutine zhbmv (uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
ZHBMV

Detailed Description

Function 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 = ā€™Uā€™ or ā€™uā€™ The upper triangular part of A is
being supplied.

UPLO = ā€™Lā€™ or ā€™lā€™ 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 = ā€™Uā€™ or ā€™uā€™, 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 = ā€™Lā€™ or ā€™lā€™, 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 dsbmv (character uplo, integer n, integer k, double precisionalpha, double precision, dimension(lda,*) a, integer lda, doubleprecision, dimension(*) x, integer incx, double precision beta, doubleprecision, dimension(*) y, integer incy)

DSBMV

Purpose:

DSBMV 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 symmetric 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 = ā€™Uā€™ or ā€™uā€™ The upper triangular part of A is
being supplied.

UPLO = ā€™Lā€™ or ā€™lā€™ 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 DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.

A

A is DOUBLE PRECISION array, dimension ( LDA, N )
Before entry with UPLO = ā€™Uā€™ or ā€™uā€™, the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the symmetric 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 symmetric 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 = ā€™Lā€™ or ā€™lā€™, the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the symmetric 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 symmetric 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

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 DOUBLE PRECISION 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 DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.

Y

Y is DOUBLE PRECISION 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 ssbmv (character uplo, integer n, integer k, real alpha, real,dimension(lda,*) a, integer lda, real, dimension(*) x, integer incx,real beta, real, dimension(*) y, integer incy)

SSBMV

Purpose:

SSBMV 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 symmetric 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 = ā€™Uā€™ or ā€™uā€™ The upper triangular part of A is
being supplied.

UPLO = ā€™Lā€™ or ā€™lā€™ 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 REAL
On entry, ALPHA specifies the scalar alpha.

A

A is REAL array, dimension ( LDA, N )
Before entry with UPLO = ā€™Uā€™ or ā€™uā€™, the leading ( k + 1 )
by n part of the array A must contain the upper triangular
band part of the symmetric 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 symmetric 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 = ā€™Lā€™ or ā€™lā€™, the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the symmetric 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 symmetric 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

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 REAL 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 REAL
On entry, BETA specifies the scalar beta.

Y

Y is REAL 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 zhbmv (character uplo, integer n, integer k, complex*16 alpha,complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*)x, integer incx, complex*16 beta, complex*16, dimension(*) y, integerincy)

ZHBMV

Purpose:

ZHBMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and
A is an n by n hermitian band matrix, with k super-diagonals.

Parameters

UPLO

UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the band matrix A is being supplied as
follows:

UPLO = ā€™Uā€™ or ā€™uā€™ The upper triangular part of A is
being supplied.

UPLO = ā€™Lā€™ or ā€™lā€™ The lower triangular part of A is
being supplied.

N

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

K

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

ALPHA

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

A

A is COMPLEX*16 array, dimension ( LDA, N )
Before entry with UPLO = ā€™Uā€™ or ā€™uā€™, 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 = ā€™Lā€™ or ā€™lā€™, the leading ( k + 1 )
by n part of the array A must contain the lower triangular
band part of the hermitian matrix, supplied column by
column, with the leading diagonal of the matrix in row 1 of
the array, the first sub-diagonal starting at position 1 in
row 2, and so on. The bottom right k by k triangle of the
array A is not referenced.
The following program segment will transfer the lower
triangular part of a hermitian band matrix from conventional
full matrix storage to band storage:

DO 20, J = 1, N
M = 1 - J
DO 10, I = J, MIN( N, J + K )
A( M + I, J ) = matrix( I, J )
10 CONTINUE
20 CONTINUE

Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.

LDA

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

X

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

INCX

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

BETA

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

Y

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

INCY

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

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

Author

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