# chbmv (3) - Linux Man Pages

chbmv.f -

## SYNOPSIS

### Functions/Subroutines

subroutine chbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CHBMV

## Function/Subroutine Documentation

### subroutine chbmv (characterUPLO, integerN, integerK, complexALPHA, complex, dimension(lda,*)A, integerLDA, complex, dimension(*)X, integerINCX, complexBETA, complex, dimension(*)Y, integerINCY)

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 of 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 of 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 of 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.

Date:

November 2011

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 188 of file chbmv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8035656,"math_prob":0.94706726,"size":3842,"snap":"2020-45-2020-50","text_gpt3_token_len":1059,"char_repetition_ratio":0.12219906,"word_repetition_ratio":0.27348065,"special_character_ratio":0.26548672,"punctuation_ratio":0.14819427,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98513323,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-29T22:53:21Z\",\"WARC-Record-ID\":\"<urn:uuid:d5df1bbd-2ecc-45ed-832b-8c86cabd177d>\",\"Content-Length\":\"13780\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fd7a9e3d-b0b2-4c9f-984f-9a7d82b49c8f>\",\"WARC-Concurrent-To\":\"<urn:uuid:10ac58e1-bb48-42ab-95d4-2fc9c1f81da1>\",\"WARC-IP-Address\":\"172.67.167.219\",\"WARC-Target-URI\":\"https://www.systutorials.com/docs/linux/man/3-chbmv/\",\"WARC-Payload-Digest\":\"sha1:JJZHE6YMCQKSUNBDPDDICRWBOOYNEDAW\",\"WARC-Block-Digest\":\"sha1:LPKXPKS2SNMTMGDFN5QE4KADCZBTVA2Z\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141203418.47_warc_CC-MAIN-20201129214615-20201130004615-00202.warc.gz\"}"}