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MAN page from openSUSE Leap 42 blas-man-3.5.0-9.1.noarch.rpm
ctbsv.fSection: LAPACK (3) Updated: Fri Nov 4 2016 Index NAMEctbsv.f - SYNOPSIS Functions/Subroutines
subroutine CTBSV (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
CTBSV
Function/Subroutine Documentation subroutine CTBSV (character UPLO, character TRANS, character DIAG, integer N, integer K, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX)CTBSV Purpose: CTBSV solves one of the systems of equations A*x = b, or A**T*x = b, or A**H*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine.
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 equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**H*x = b.
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 right-hand side vector b. On exit, X is overwritten with the solution 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. -- 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 191 of file ctbsv.f. 191 *192 * -- Reference BLAS level2 routine (version 3.4.0) --193 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--195 * November 2011196 *197 * .. Scalar Arguments ..198 INTEGER incx,k,lda,n199 CHARACTER diag,trans,uplo200 * ..201 * .. Array Arguments ..202 COMPLEX a(lda,*),x(*)203 * ..204 *205 * =====================================================================206 *207 * .. Parameters ..208 COMPLEX zero209 parameter(zero= (0.0e+0,0.0e+0))210 * ..211 * .. Local Scalars ..212 COMPLEX temp213 INTEGER i,info,ix,j,jx,kplus1,kx,l214 LOGICAL noconj,nounit215 * ..216 * .. External Functions ..217 LOGICAL lsame218 EXTERNAL lsame219 * ..220 * .. External Subroutines ..221 EXTERNAL xerbla222 * ..223 * .. Intrinsic Functions ..224 INTRINSIC conjg,max,min225 * ..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 (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.233 + .NOT.lsame(trans,'C')) THEN234 info = 2235 ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN236 info = 3237 ELSE IF (n.LT.0) THEN238 info = 4239 ELSE IF (k.LT.0) THEN240 info = 5241 ELSE IF (lda.LT. (k+1)) THEN242 info = 7243 ELSE IF (incx.EQ.0) THEN244 info = 9245 END IF246 IF (info.NE.0) THEN247 CALL xerbla('CTBSV ',info)248 RETURN249 END IF250 *251 * Quick return if possible.252 *253 IF (n.EQ.0) RETURN254 *255 noconj = lsame(trans,'T')256 nounit = lsame(diag,'N')257 *258 * Set up the start point in X if the increment is not unity. This259 * will be ( N - 1 )*INCX too small for descending loops.260 *261 IF (incx.LE.0) THEN262 kx = 1 - (n-1)*incx263 ELSE IF (incx.NE.1) THEN264 kx = 1265 END IF266 *267 * Start the operations. In this version the elements of A are268 * accessed by sequentially with one pass through A.269 *270 IF (lsame(trans,'N')) THEN271 *272 * Form x := inv( A )*x.273 *274 IF (lsame(uplo,'U')) THEN275 kplus1 = k + 1276 IF (incx.EQ.1) THEN277 DO 20 j = n,1,-1278 IF (x(j).NE.zero) THEN279 l = kplus1 - j280 IF (nounit) x(j) = x(j)/a(kplus1,j)281 temp = x(j)282 DO 10 i = j - 1,max(1,j-k),-1283 x(i) = x(i) - temp*a(l+i,j)284 10 CONTINUE285 END IF286 20 CONTINUE287 ELSE288 kx = kx + (n-1)*incx289 jx = kx290 DO 40 j = n,1,-1291 kx = kx - incx292 IF (x(jx).NE.zero) THEN293 ix = kx294 l = kplus1 - j295 IF (nounit) x(jx) = x(jx)/a(kplus1,j)296 temp = x(jx)297 DO 30 i = j - 1,max(1,j-k),-1298 x(ix) = x(ix) - temp*a(l+i,j)299 ix = ix - incx300 30 CONTINUE301 END IF302 jx = jx - incx303 40 CONTINUE304 END IF305 ELSE306 IF (incx.EQ.1) THEN307 DO 60 j = 1,n308 IF (x(j).NE.zero) THEN309 l = 1 - j310 IF (nounit) x(j) = x(j)/a(1,j)311 temp = x(j)312 DO 50 i = j + 1,min(n,j+k)313 x(i) = x(i) - temp*a(l+i,j)314 50 CONTINUE315 END IF316 60 CONTINUE317 ELSE318 jx = kx319 DO 80 j = 1,n320 kx = kx + incx321 IF (x(jx).NE.zero) THEN322 ix = kx323 l = 1 - j324 IF (nounit) x(jx) = x(jx)/a(1,j)325 temp = x(jx)326 DO 70 i = j + 1,min(n,j+k)327 x(ix) = x(ix) - temp*a(l+i,j)328 ix = ix + incx329 70 CONTINUE330 END IF331 jx = jx + incx332 80 CONTINUE333 END IF334 END IF335 ELSE336 *337 * Form x := inv( A**T )*x or x := inv( A**H )*x.338 *339 IF (lsame(uplo,'U')) THEN340 kplus1 = k + 1341 IF (incx.EQ.1) THEN342 DO 110 j = 1,n343 temp = x(j)344 l = kplus1 - j345 IF (noconj) THEN346 DO 90 i = max(1,j-k),j - 1347 temp = temp - a(l+i,j)*x(i)348 90 CONTINUE349 IF (nounit) temp = temp/a(kplus1,j)350 ELSE351 DO 100 i = max(1,j-k),j - 1352 temp = temp - conjg(a(l+i,j))*x(i)353 100 CONTINUE354 IF (nounit) temp = temp/conjg(a(kplus1,j))355 END IF356 x(j) = temp357 110 CONTINUE358 ELSE359 jx = kx360 DO 140 j = 1,n361 temp = x(jx)362 ix = kx363 l = kplus1 - j364 IF (noconj) THEN365 DO 120 i = max(1,j-k),j - 1366 temp = temp - a(l+i,j)*x(ix)367 ix = ix + incx368 120 CONTINUE369 IF (nounit) temp = temp/a(kplus1,j)370 ELSE371 DO 130 i = max(1,j-k),j - 1372 temp = temp - conjg(a(l+i,j))*x(ix)373 ix = ix + incx374 130 CONTINUE375 IF (nounit) temp = temp/conjg(a(kplus1,j))376 END IF377 x(jx) = temp378 jx = jx + incx379 IF (j.GT.k) kx = kx + incx380 140 CONTINUE381 END IF382 ELSE383 IF (incx.EQ.1) THEN384 DO 170 j = n,1,-1385 temp = x(j)386 l = 1 - j387 IF (noconj) THEN388 DO 150 i = min(n,j+k),j + 1,-1389 temp = temp - a(l+i,j)*x(i)390 150 CONTINUE391 IF (nounit) temp = temp/a(1,j)392 ELSE393 DO 160 i = min(n,j+k),j + 1,-1394 temp = temp - conjg(a(l+i,j))*x(i)395 160 CONTINUE396 IF (nounit) temp = temp/conjg(a(1,j))397 END IF398 x(j) = temp399 170 CONTINUE400 ELSE401 kx = kx + (n-1)*incx402 jx = kx403 DO 200 j = n,1,-1404 temp = x(jx)405 ix = kx406 l = 1 - j407 IF (noconj) THEN408 DO 180 i = min(n,j+k),j + 1,-1409 temp = temp - a(l+i,j)*x(ix)410 ix = ix - incx411 180 CONTINUE412 IF (nounit) temp = temp/a(1,j)413 ELSE414 DO 190 i = min(n,j+k),j + 1,-1415 temp = temp - conjg(a(l+i,j))*x(ix)416 ix = ix - incx417 190 CONTINUE418 IF (nounit) temp = temp/conjg(a(1,j))419 END IF420 x(jx) = temp421 jx = jx - incx422 IF ((n-j).GE.k) kx = kx - incx423 200 CONTINUE424 END IF425 END IF426 END IF427 *428 RETURN429 *430 * End of CTBSV .431 * AuthorGenerated automatically by Doxygen for LAPACK from the source code.
Index- NAME
- SYNOPSIS
- Functions/Subroutines
- Function/Subroutine Documentation
- subroutine CTBSV (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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