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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZTRSV 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) 00012 * 00013 * .. Scalar Arguments .. 00014 * INTEGER INCX,LDA,N 00015 * CHARACTER DIAG,TRANS,UPLO 00016 * .. 00017 * .. Array Arguments .. 00018 * COMPLEX*16 A(LDA,*),X(*) 00019 * .. 00020 * 00021 * 00022 *> \par Purpose: 00023 * ============= 00024 *> 00025 *> \verbatim 00026 *> 00027 *> ZTRSV solves one of the systems of equations 00028 *> 00029 *> A*x = b, or A**T*x = b, or A**H*x = b, 00030 *> 00031 *> where b and x are n element vectors and A is an n by n unit, or 00032 *> non-unit, upper or lower triangular matrix. 00033 *> 00034 *> No test for singularity or near-singularity is included in this 00035 *> routine. Such tests must be performed before calling this routine. 00036 *> \endverbatim 00037 * 00038 * Arguments: 00039 * ========== 00040 * 00041 *> \param[in] UPLO 00042 *> \verbatim 00043 *> UPLO is CHARACTER*1 00044 *> On entry, UPLO specifies whether the matrix is an upper or 00045 *> lower triangular matrix as follows: 00046 *> 00047 *> UPLO = 'U' or 'u' A is an upper triangular matrix. 00048 *> 00049 *> UPLO = 'L' or 'l' A is a lower triangular matrix. 00050 *> \endverbatim 00051 *> 00052 *> \param[in] TRANS 00053 *> \verbatim 00054 *> TRANS is CHARACTER*1 00055 *> On entry, TRANS specifies the equations to be solved as 00056 *> follows: 00057 *> 00058 *> TRANS = 'N' or 'n' A*x = b. 00059 *> 00060 *> TRANS = 'T' or 't' A**T*x = b. 00061 *> 00062 *> TRANS = 'C' or 'c' A**H*x = b. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] DIAG 00066 *> \verbatim 00067 *> DIAG is CHARACTER*1 00068 *> On entry, DIAG specifies whether or not A is unit 00069 *> triangular as follows: 00070 *> 00071 *> DIAG = 'U' or 'u' A is assumed to be unit triangular. 00072 *> 00073 *> DIAG = 'N' or 'n' A is not assumed to be unit 00074 *> triangular. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] N 00078 *> \verbatim 00079 *> N is INTEGER 00080 *> On entry, N specifies the order of the matrix A. 00081 *> N must be at least zero. 00082 *> \endverbatim 00083 *> 00084 *> \param[in] A 00085 *> \verbatim 00086 *> A is COMPLEX*16 array of DIMENSION ( LDA, n ). 00087 *> Before entry with UPLO = 'U' or 'u', the leading n by n 00088 *> upper triangular part of the array A must contain the upper 00089 *> triangular matrix and the strictly lower triangular part of 00090 *> A is not referenced. 00091 *> Before entry with UPLO = 'L' or 'l', the leading n by n 00092 *> lower triangular part of the array A must contain the lower 00093 *> triangular matrix and the strictly upper triangular part of 00094 *> A is not referenced. 00095 *> Note that when DIAG = 'U' or 'u', the diagonal elements of 00096 *> A are not referenced either, but are assumed to be unity. 00097 *> \endverbatim 00098 *> 00099 *> \param[in] LDA 00100 *> \verbatim 00101 *> LDA is INTEGER 00102 *> On entry, LDA specifies the first dimension of A as declared 00103 *> in the calling (sub) program. LDA must be at least 00104 *> max( 1, n ). 00105 *> \endverbatim 00106 *> 00107 *> \param[in,out] X 00108 *> \verbatim 00109 *> X is COMPLEX*16 array of dimension at least 00110 *> ( 1 + ( n - 1 )*abs( INCX ) ). 00111 *> Before entry, the incremented array X must contain the n 00112 *> element right-hand side vector b. On exit, X is overwritten 00113 *> with the solution vector x. 00114 *> \endverbatim 00115 *> 00116 *> \param[in] INCX 00117 *> \verbatim 00118 *> INCX is INTEGER 00119 *> On entry, INCX specifies the increment for the elements of 00120 *> X. INCX must not be zero. 00121 *> \endverbatim 00122 * 00123 * Authors: 00124 * ======== 00125 * 00126 *> \author Univ. of Tennessee 00127 *> \author Univ. of California Berkeley 00128 *> \author Univ. of Colorado Denver 00129 *> \author NAG Ltd. 00130 * 00131 *> \date November 2011 00132 * 00133 *> \ingroup complex16_blas_level2 00134 * 00135 *> \par Further Details: 00136 * ===================== 00137 *> 00138 *> \verbatim 00139 *> 00140 *> Level 2 Blas routine. 00141 *> 00142 *> -- Written on 22-October-1986. 00143 *> Jack Dongarra, Argonne National Lab. 00144 *> Jeremy Du Croz, Nag Central Office. 00145 *> Sven Hammarling, Nag Central Office. 00146 *> Richard Hanson, Sandia National Labs. 00147 *> \endverbatim 00148 *> 00149 * ===================================================================== 00150 SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) 00151 * 00152 * -- Reference BLAS level2 routine (version 3.4.0) -- 00153 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00155 * November 2011 00156 * 00157 * .. Scalar Arguments .. 00158 INTEGER INCX,LDA,N 00159 CHARACTER DIAG,TRANS,UPLO 00160 * .. 00161 * .. Array Arguments .. 00162 COMPLEX*16 A(LDA,*),X(*) 00163 * .. 00164 * 00165 * ===================================================================== 00166 * 00167 * .. Parameters .. 00168 COMPLEX*16 ZERO 00169 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 00170 * .. 00171 * .. Local Scalars .. 00172 COMPLEX*16 TEMP 00173 INTEGER I,INFO,IX,J,JX,KX 00174 LOGICAL NOCONJ,NOUNIT 00175 * .. 00176 * .. External Functions .. 00177 LOGICAL LSAME 00178 EXTERNAL LSAME 00179 * .. 00180 * .. External Subroutines .. 00181 EXTERNAL XERBLA 00182 * .. 00183 * .. Intrinsic Functions .. 00184 INTRINSIC DCONJG,MAX 00185 * .. 00186 * 00187 * Test the input parameters. 00188 * 00189 INFO = 0 00190 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00191 INFO = 1 00192 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00193 + .NOT.LSAME(TRANS,'C')) THEN 00194 INFO = 2 00195 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00196 INFO = 3 00197 ELSE IF (N.LT.0) THEN 00198 INFO = 4 00199 ELSE IF (LDA.LT.MAX(1,N)) THEN 00200 INFO = 6 00201 ELSE IF (INCX.EQ.0) THEN 00202 INFO = 8 00203 END IF 00204 IF (INFO.NE.0) THEN 00205 CALL XERBLA('ZTRSV ',INFO) 00206 RETURN 00207 END IF 00208 * 00209 * Quick return if possible. 00210 * 00211 IF (N.EQ.0) RETURN 00212 * 00213 NOCONJ = LSAME(TRANS,'T') 00214 NOUNIT = LSAME(DIAG,'N') 00215 * 00216 * Set up the start point in X if the increment is not unity. This 00217 * will be ( N - 1 )*INCX too small for descending loops. 00218 * 00219 IF (INCX.LE.0) THEN 00220 KX = 1 - (N-1)*INCX 00221 ELSE IF (INCX.NE.1) THEN 00222 KX = 1 00223 END IF 00224 * 00225 * Start the operations. In this version the elements of A are 00226 * accessed sequentially with one pass through A. 00227 * 00228 IF (LSAME(TRANS,'N')) THEN 00229 * 00230 * Form x := inv( A )*x. 00231 * 00232 IF (LSAME(UPLO,'U')) THEN 00233 IF (INCX.EQ.1) THEN 00234 DO 20 J = N,1,-1 00235 IF (X(J).NE.ZERO) THEN 00236 IF (NOUNIT) X(J) = X(J)/A(J,J) 00237 TEMP = X(J) 00238 DO 10 I = J - 1,1,-1 00239 X(I) = X(I) - TEMP*A(I,J) 00240 10 CONTINUE 00241 END IF 00242 20 CONTINUE 00243 ELSE 00244 JX = KX + (N-1)*INCX 00245 DO 40 J = N,1,-1 00246 IF (X(JX).NE.ZERO) THEN 00247 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 00248 TEMP = X(JX) 00249 IX = JX 00250 DO 30 I = J - 1,1,-1 00251 IX = IX - INCX 00252 X(IX) = X(IX) - TEMP*A(I,J) 00253 30 CONTINUE 00254 END IF 00255 JX = JX - INCX 00256 40 CONTINUE 00257 END IF 00258 ELSE 00259 IF (INCX.EQ.1) THEN 00260 DO 60 J = 1,N 00261 IF (X(J).NE.ZERO) THEN 00262 IF (NOUNIT) X(J) = X(J)/A(J,J) 00263 TEMP = X(J) 00264 DO 50 I = J + 1,N 00265 X(I) = X(I) - TEMP*A(I,J) 00266 50 CONTINUE 00267 END IF 00268 60 CONTINUE 00269 ELSE 00270 JX = KX 00271 DO 80 J = 1,N 00272 IF (X(JX).NE.ZERO) THEN 00273 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 00274 TEMP = X(JX) 00275 IX = JX 00276 DO 70 I = J + 1,N 00277 IX = IX + INCX 00278 X(IX) = X(IX) - TEMP*A(I,J) 00279 70 CONTINUE 00280 END IF 00281 JX = JX + INCX 00282 80 CONTINUE 00283 END IF 00284 END IF 00285 ELSE 00286 * 00287 * Form x := inv( A**T )*x or x := inv( A**H )*x. 00288 * 00289 IF (LSAME(UPLO,'U')) THEN 00290 IF (INCX.EQ.1) THEN 00291 DO 110 J = 1,N 00292 TEMP = X(J) 00293 IF (NOCONJ) THEN 00294 DO 90 I = 1,J - 1 00295 TEMP = TEMP - A(I,J)*X(I) 00296 90 CONTINUE 00297 IF (NOUNIT) TEMP = TEMP/A(J,J) 00298 ELSE 00299 DO 100 I = 1,J - 1 00300 TEMP = TEMP - DCONJG(A(I,J))*X(I) 00301 100 CONTINUE 00302 IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) 00303 END IF 00304 X(J) = TEMP 00305 110 CONTINUE 00306 ELSE 00307 JX = KX 00308 DO 140 J = 1,N 00309 IX = KX 00310 TEMP = X(JX) 00311 IF (NOCONJ) THEN 00312 DO 120 I = 1,J - 1 00313 TEMP = TEMP - A(I,J)*X(IX) 00314 IX = IX + INCX 00315 120 CONTINUE 00316 IF (NOUNIT) TEMP = TEMP/A(J,J) 00317 ELSE 00318 DO 130 I = 1,J - 1 00319 TEMP = TEMP - DCONJG(A(I,J))*X(IX) 00320 IX = IX + INCX 00321 130 CONTINUE 00322 IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) 00323 END IF 00324 X(JX) = TEMP 00325 JX = JX + INCX 00326 140 CONTINUE 00327 END IF 00328 ELSE 00329 IF (INCX.EQ.1) THEN 00330 DO 170 J = N,1,-1 00331 TEMP = X(J) 00332 IF (NOCONJ) THEN 00333 DO 150 I = N,J + 1,-1 00334 TEMP = TEMP - A(I,J)*X(I) 00335 150 CONTINUE 00336 IF (NOUNIT) TEMP = TEMP/A(J,J) 00337 ELSE 00338 DO 160 I = N,J + 1,-1 00339 TEMP = TEMP - DCONJG(A(I,J))*X(I) 00340 160 CONTINUE 00341 IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) 00342 END IF 00343 X(J) = TEMP 00344 170 CONTINUE 00345 ELSE 00346 KX = KX + (N-1)*INCX 00347 JX = KX 00348 DO 200 J = N,1,-1 00349 IX = KX 00350 TEMP = X(JX) 00351 IF (NOCONJ) THEN 00352 DO 180 I = N,J + 1,-1 00353 TEMP = TEMP - A(I,J)*X(IX) 00354 IX = IX - INCX 00355 180 CONTINUE 00356 IF (NOUNIT) TEMP = TEMP/A(J,J) 00357 ELSE 00358 DO 190 I = N,J + 1,-1 00359 TEMP = TEMP - DCONJG(A(I,J))*X(IX) 00360 IX = IX - INCX 00361 190 CONTINUE 00362 IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) 00363 END IF 00364 X(JX) = TEMP 00365 JX = JX - INCX 00366 200 CONTINUE 00367 END IF 00368 END IF 00369 END IF 00370 * 00371 RETURN 00372 * 00373 * End of ZTRSV . 00374 * 00375 END