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MAN page from openSUSE Leap 42 blas-man-3.5.0-9.1.noarch.rpm
chbmv.fSection: LAPACK (3) Updated: Fri Nov 4 2016 Index NAMEchbmv.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 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 Univ. of Colorado Denver 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 189 of file chbmv.f. 189 *190 * -- Reference BLAS level2 routine (version 3.4.0) --191 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--193 * November 2011194 *195 * .. Scalar Arguments ..196 COMPLEX alpha,beta197 INTEGER incx,incy,k,lda,n198 CHARACTER uplo199 * ..200 * .. Array Arguments ..201 COMPLEX a(lda,*),x(*),y(*)202 * ..203 *204 * =====================================================================205 *206 * .. Parameters ..207 COMPLEX one208 parameter(one= (1.0e+0,0.0e+0))209 COMPLEX zero210 parameter(zero= (0.0e+0,0.0e+0))211 * ..212 * .. Local Scalars ..213 COMPLEX temp1,temp2214 INTEGER i,info,ix,iy,j,jx,jy,kplus1,kx,ky,l215 * ..216 * .. External Functions ..217 LOGICAL lsame218 EXTERNAL lsame219 * ..220 * .. External Subroutines ..221 EXTERNAL xerbla222 * ..223 * .. Intrinsic Functions ..224 INTRINSIC conjg,max,min,real225 * ..226 *227 * Test the input parameters.228 *229 info = 0230 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN231 info = 1232 ELSE IF (n.LT.0) THEN233 info = 2234 ELSE IF (k.LT.0) THEN235 info = 3236 ELSE IF (lda.LT. (k+1)) THEN237 info = 6238 ELSE IF (incx.EQ.0) THEN239 info = 8240 ELSE IF (incy.EQ.0) THEN241 info = 11242 END IF243 IF (info.NE.0) THEN244 CALL xerbla('CHBMV ',info)245 RETURN246 END IF247 *248 * Quick return if possible.249 *250 IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN251 *252 * Set up the start points in X and Y.253 *254 IF (incx.GT.0) THEN255 kx = 1256 ELSE257 kx = 1 - (n-1)*incx258 END IF259 IF (incy.GT.0) THEN260 ky = 1261 ELSE262 ky = 1 - (n-1)*incy263 END IF264 *265 * Start the operations. In this version the elements of the array A266 * are accessed sequentially with one pass through A.267 *268 * First form y := beta*y.269 *270 IF (beta.NE.one) THEN271 IF (incy.EQ.1) THEN272 IF (beta.EQ.zero) THEN273 DO 10 i = 1,n274 y(i) = zero275 10 CONTINUE276 ELSE277 DO 20 i = 1,n278 y(i) = beta*y(i)279 20 CONTINUE280 END IF281 ELSE282 iy = ky283 IF (beta.EQ.zero) THEN284 DO 30 i = 1,n285 y(iy) = zero286 iy = iy + incy287 30 CONTINUE288 ELSE289 DO 40 i = 1,n290 y(iy) = beta*y(iy)291 iy = iy + incy292 40 CONTINUE293 END IF294 END IF295 END IF296 IF (alpha.EQ.zero) RETURN297 IF (lsame(uplo,'U')) THEN298 *299 * Form y when upper triangle of A is stored.300 *301 kplus1 = k + 1302 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN303 DO 60 j = 1,n304 temp1 = alpha*x(j)305 temp2 = zero306 l = kplus1 - j307 DO 50 i = max(1,j-k),j - 1308 y(i) = y(i) + temp1*a(l+i,j)309 temp2 = temp2 + conjg(a(l+i,j))*x(i)310 50 CONTINUE311 y(j) = y(j) + temp1*REAL(A(KPLUS1,J)) + alpha*temp2312 60 CONTINUE313 ELSE314 jx = kx315 jy = ky316 DO 80 j = 1,n317 temp1 = alpha*x(jx)318 temp2 = zero319 ix = kx320 iy = ky321 l = kplus1 - j322 DO 70 i = max(1,j-k),j - 1323 y(iy) = y(iy) + temp1*a(l+i,j)324 temp2 = temp2 + conjg(a(l+i,j))*x(ix)325 ix = ix + incx326 iy = iy + incy327 70 CONTINUE328 y(jy) = y(jy) + temp1*REAL(A(KPLUS1,J)) + alpha*temp2329 jx = jx + incx330 jy = jy + incy331 IF (j.GT.k) THEN332 kx = kx + incx333 ky = ky + incy334 END IF335 80 CONTINUE336 END IF337 ELSE338 *339 * Form y when lower triangle of A is stored.340 *341 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN342 DO 100 j = 1,n343 temp1 = alpha*x(j)344 temp2 = zero345 y(j) = y(j) + temp1*REAL(a(1,j))346 l = 1 - j347 DO 90 i = j + 1,min(n,j+k)348 y(i) = y(i) + temp1*a(l+i,j)349 temp2 = temp2 + conjg(a(l+i,j))*x(i)350 90 CONTINUE351 y(j) = y(j) + alpha*temp2352 100 CONTINUE353 ELSE354 jx = kx355 jy = ky356 DO 120 j = 1,n357 temp1 = alpha*x(jx)358 temp2 = zero359 y(jy) = y(jy) + temp1*REAL(a(1,j))360 l = 1 - j361 ix = jx362 iy = jy363 DO 110 i = j + 1,min(n,j+k)364 ix = ix + incx365 iy = iy + incy366 y(iy) = y(iy) + temp1*a(l+i,j)367 temp2 = temp2 + conjg(a(l+i,j))*x(ix)368 110 CONTINUE369 y(jy) = y(jy) + alpha*temp2370 jx = jx + incx371 jy = jy + incy372 120 CONTINUE373 END IF374 END IF375 *376 RETURN377 *378 * End of CHBMV .379 * AuthorGenerated automatically by Doxygen for LAPACK from the source code.
Index- NAME
- SYNOPSIS
- Functions/Subroutines
- 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)
- Author
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