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MAN page from openSUSE Leap 42 blas-man-3.5.0-9.1.noarch.rpm
ctbmv.fSection: LAPACK (3) Updated: Fri Nov 4 2016 Index NAMEctbmv.f - SYNOPSIS Functions/Subroutines
subroutine CTBMV (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBMV
Function/Subroutine Documentation 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 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 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 of 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 tranformed 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.
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 ctbmv.f. 188 *189 * -- Reference BLAS level2 routine (version 3.4.0) --190 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --191 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--192 * November 2011193 *194 * .. Scalar Arguments ..195 INTEGER incx,k,lda,n196 CHARACTER diag,trans,uplo197 * ..198 * .. Array Arguments ..199 COMPLEX a(lda,*),x(*)200 * ..201 *202 * =====================================================================203 *204 * .. Parameters ..205 COMPLEX zero206 parameter(zero= (0.0e+0,0.0e+0))207 * ..208 * .. Local Scalars ..209 COMPLEX temp210 INTEGER i,info,ix,j,jx,kplus1,kx,l211 LOGICAL noconj,nounit212 * ..213 * .. External Functions ..214 LOGICAL lsame215 EXTERNAL lsame216 * ..217 * .. External Subroutines ..218 EXTERNAL xerbla219 * ..220 * .. Intrinsic Functions ..221 INTRINSIC conjg,max,min222 * ..223 *224 * Test the input parameters.225 *226 info = 0227 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN228 info = 1229 ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.230 + .NOT.lsame(trans,'C')) THEN231 info = 2232 ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN233 info = 3234 ELSE IF (n.LT.0) THEN235 info = 4236 ELSE IF (k.LT.0) THEN237 info = 5238 ELSE IF (lda.LT. (k+1)) THEN239 info = 7240 ELSE IF (incx.EQ.0) THEN241 info = 9242 END IF243 IF (info.NE.0) THEN244 CALL xerbla('CTBMV ',info)245 RETURN246 END IF247 *248 * Quick return if possible.249 *250 IF (n.EQ.0) RETURN251 *252 noconj = lsame(trans,'T')253 nounit = lsame(diag,'N')254 *255 * Set up the start point in X if the increment is not unity. This256 * will be ( N - 1 )*INCX too small for descending loops.257 *258 IF (incx.LE.0) THEN259 kx = 1 - (n-1)*incx260 ELSE IF (incx.NE.1) THEN261 kx = 1262 END IF263 *264 * Start the operations. In this version the elements of A are265 * accessed sequentially with one pass through A.266 *267 IF (lsame(trans,'N')) THEN268 *269 * Form x := A*x.270 *271 IF (lsame(uplo,'U')) THEN272 kplus1 = k + 1273 IF (incx.EQ.1) THEN274 DO 20 j = 1,n275 IF (x(j).NE.zero) THEN276 temp = x(j)277 l = kplus1 - j278 DO 10 i = max(1,j-k),j - 1279 x(i) = x(i) + temp*a(l+i,j)280 10 CONTINUE281 IF (nounit) x(j) = x(j)*a(kplus1,j)282 END IF283 20 CONTINUE284 ELSE285 jx = kx286 DO 40 j = 1,n287 IF (x(jx).NE.zero) THEN288 temp = x(jx)289 ix = kx290 l = kplus1 - j291 DO 30 i = max(1,j-k),j - 1292 x(ix) = x(ix) + temp*a(l+i,j)293 ix = ix + incx294 30 CONTINUE295 IF (nounit) x(jx) = x(jx)*a(kplus1,j)296 END IF297 jx = jx + incx298 IF (j.GT.k) kx = kx + incx299 40 CONTINUE300 END IF301 ELSE302 IF (incx.EQ.1) THEN303 DO 60 j = n,1,-1304 IF (x(j).NE.zero) THEN305 temp = x(j)306 l = 1 - j307 DO 50 i = min(n,j+k),j + 1,-1308 x(i) = x(i) + temp*a(l+i,j)309 50 CONTINUE310 IF (nounit) x(j) = x(j)*a(1,j)311 END IF312 60 CONTINUE313 ELSE314 kx = kx + (n-1)*incx315 jx = kx316 DO 80 j = n,1,-1317 IF (x(jx).NE.zero) THEN318 temp = x(jx)319 ix = kx320 l = 1 - j321 DO 70 i = min(n,j+k),j + 1,-1322 x(ix) = x(ix) + temp*a(l+i,j)323 ix = ix - incx324 70 CONTINUE325 IF (nounit) x(jx) = x(jx)*a(1,j)326 END IF327 jx = jx - incx328 IF ((n-j).GE.k) kx = kx - incx329 80 CONTINUE330 END IF331 END IF332 ELSE333 *334 * Form x := A**T*x or x := A**H*x.335 *336 IF (lsame(uplo,'U')) THEN337 kplus1 = k + 1338 IF (incx.EQ.1) THEN339 DO 110 j = n,1,-1340 temp = x(j)341 l = kplus1 - j342 IF (noconj) THEN343 IF (nounit) temp = temp*a(kplus1,j)344 DO 90 i = j - 1,max(1,j-k),-1345 temp = temp + a(l+i,j)*x(i)346 90 CONTINUE347 ELSE348 IF (nounit) temp = temp*conjg(a(kplus1,j))349 DO 100 i = j - 1,max(1,j-k),-1350 temp = temp + conjg(a(l+i,j))*x(i)351 100 CONTINUE352 END IF353 x(j) = temp354 110 CONTINUE355 ELSE356 kx = kx + (n-1)*incx357 jx = kx358 DO 140 j = n,1,-1359 temp = x(jx)360 kx = kx - incx361 ix = kx362 l = kplus1 - j363 IF (noconj) THEN364 IF (nounit) temp = temp*a(kplus1,j)365 DO 120 i = j - 1,max(1,j-k),-1366 temp = temp + a(l+i,j)*x(ix)367 ix = ix - incx368 120 CONTINUE369 ELSE370 IF (nounit) temp = temp*conjg(a(kplus1,j))371 DO 130 i = j - 1,max(1,j-k),-1372 temp = temp + conjg(a(l+i,j))*x(ix)373 ix = ix - incx374 130 CONTINUE375 END IF376 x(jx) = temp377 jx = jx - incx378 140 CONTINUE379 END IF380 ELSE381 IF (incx.EQ.1) THEN382 DO 170 j = 1,n383 temp = x(j)384 l = 1 - j385 IF (noconj) THEN386 IF (nounit) temp = temp*a(1,j)387 DO 150 i = j + 1,min(n,j+k)388 temp = temp + a(l+i,j)*x(i)389 150 CONTINUE390 ELSE391 IF (nounit) temp = temp*conjg(a(1,j))392 DO 160 i = j + 1,min(n,j+k)393 temp = temp + conjg(a(l+i,j))*x(i)394 160 CONTINUE395 END IF396 x(j) = temp397 170 CONTINUE398 ELSE399 jx = kx400 DO 200 j = 1,n401 temp = x(jx)402 kx = kx + incx403 ix = kx404 l = 1 - j405 IF (noconj) THEN406 IF (nounit) temp = temp*a(1,j)407 DO 180 i = j + 1,min(n,j+k)408 temp = temp + a(l+i,j)*x(ix)409 ix = ix + incx410 180 CONTINUE411 ELSE412 IF (nounit) temp = temp*conjg(a(1,j))413 DO 190 i = j + 1,min(n,j+k)414 temp = temp + conjg(a(l+i,j))*x(ix)415 ix = ix + incx416 190 CONTINUE417 END IF418 x(jx) = temp419 jx = jx + incx420 200 CONTINUE421 END IF422 END IF423 END IF424 *425 RETURN426 *427 * End of CTBMV .428 * AuthorGenerated automatically by Doxygen for LAPACK from the source code.
Index- NAME
- SYNOPSIS
- Functions/Subroutines
- Function/Subroutine Documentation
- subroutine CTBMV (character UPLO, character TRANS, character DIAG, integer N, integer K, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX)
- Author
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