![]() |
LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
|
00001 *> \brief \b DTRSV 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 DTRSV(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 * DOUBLE PRECISION A(LDA,*),X(*) 00019 * .. 00020 * 00021 * 00022 *> \par Purpose: 00023 * ============= 00024 *> 00025 *> \verbatim 00026 *> 00027 *> DTRSV solves one of the systems of equations 00028 *> 00029 *> A*x = b, or A**T*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**T*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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 *> 00122 *> Level 2 Blas routine. 00123 *> 00124 *> -- Written on 22-October-1986. 00125 *> Jack Dongarra, Argonne National Lab. 00126 *> Jeremy Du Croz, Nag Central Office. 00127 *> Sven Hammarling, Nag Central Office. 00128 *> Richard Hanson, Sandia National Labs. 00129 *> \endverbatim 00130 * 00131 * Authors: 00132 * ======== 00133 * 00134 *> \author Univ. of Tennessee 00135 *> \author Univ. of California Berkeley 00136 *> \author Univ. of Colorado Denver 00137 *> \author NAG Ltd. 00138 * 00139 *> \date November 2011 00140 * 00141 *> \ingroup double_blas_level1 00142 * 00143 * ===================================================================== 00144 SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) 00145 * 00146 * -- Reference BLAS level1 routine (version 3.4.0) -- 00147 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00149 * November 2011 00150 * 00151 * .. Scalar Arguments .. 00152 INTEGER INCX,LDA,N 00153 CHARACTER DIAG,TRANS,UPLO 00154 * .. 00155 * .. Array Arguments .. 00156 DOUBLE PRECISION A(LDA,*),X(*) 00157 * .. 00158 * 00159 * ===================================================================== 00160 * 00161 * .. Parameters .. 00162 DOUBLE PRECISION ZERO 00163 PARAMETER (ZERO=0.0D+0) 00164 * .. 00165 * .. Local Scalars .. 00166 DOUBLE PRECISION TEMP 00167 INTEGER I,INFO,IX,J,JX,KX 00168 LOGICAL NOUNIT 00169 * .. 00170 * .. External Functions .. 00171 LOGICAL LSAME 00172 EXTERNAL LSAME 00173 * .. 00174 * .. External Subroutines .. 00175 EXTERNAL XERBLA 00176 * .. 00177 * .. Intrinsic Functions .. 00178 INTRINSIC MAX 00179 * .. 00180 * 00181 * Test the input parameters. 00182 * 00183 INFO = 0 00184 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00185 INFO = 1 00186 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00187 + .NOT.LSAME(TRANS,'C')) THEN 00188 INFO = 2 00189 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 00190 INFO = 3 00191 ELSE IF (N.LT.0) THEN 00192 INFO = 4 00193 ELSE IF (LDA.LT.MAX(1,N)) THEN 00194 INFO = 6 00195 ELSE IF (INCX.EQ.0) THEN 00196 INFO = 8 00197 END IF 00198 IF (INFO.NE.0) THEN 00199 CALL XERBLA('DTRSV ',INFO) 00200 RETURN 00201 END IF 00202 * 00203 * Quick return if possible. 00204 * 00205 IF (N.EQ.0) RETURN 00206 * 00207 NOUNIT = LSAME(DIAG,'N') 00208 * 00209 * Set up the start point in X if the increment is not unity. This 00210 * will be ( N - 1 )*INCX too small for descending loops. 00211 * 00212 IF (INCX.LE.0) THEN 00213 KX = 1 - (N-1)*INCX 00214 ELSE IF (INCX.NE.1) THEN 00215 KX = 1 00216 END IF 00217 * 00218 * Start the operations. In this version the elements of A are 00219 * accessed sequentially with one pass through A. 00220 * 00221 IF (LSAME(TRANS,'N')) THEN 00222 * 00223 * Form x := inv( A )*x. 00224 * 00225 IF (LSAME(UPLO,'U')) THEN 00226 IF (INCX.EQ.1) THEN 00227 DO 20 J = N,1,-1 00228 IF (X(J).NE.ZERO) THEN 00229 IF (NOUNIT) X(J) = X(J)/A(J,J) 00230 TEMP = X(J) 00231 DO 10 I = J - 1,1,-1 00232 X(I) = X(I) - TEMP*A(I,J) 00233 10 CONTINUE 00234 END IF 00235 20 CONTINUE 00236 ELSE 00237 JX = KX + (N-1)*INCX 00238 DO 40 J = N,1,-1 00239 IF (X(JX).NE.ZERO) THEN 00240 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 00241 TEMP = X(JX) 00242 IX = JX 00243 DO 30 I = J - 1,1,-1 00244 IX = IX - INCX 00245 X(IX) = X(IX) - TEMP*A(I,J) 00246 30 CONTINUE 00247 END IF 00248 JX = JX - INCX 00249 40 CONTINUE 00250 END IF 00251 ELSE 00252 IF (INCX.EQ.1) THEN 00253 DO 60 J = 1,N 00254 IF (X(J).NE.ZERO) THEN 00255 IF (NOUNIT) X(J) = X(J)/A(J,J) 00256 TEMP = X(J) 00257 DO 50 I = J + 1,N 00258 X(I) = X(I) - TEMP*A(I,J) 00259 50 CONTINUE 00260 END IF 00261 60 CONTINUE 00262 ELSE 00263 JX = KX 00264 DO 80 J = 1,N 00265 IF (X(JX).NE.ZERO) THEN 00266 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 00267 TEMP = X(JX) 00268 IX = JX 00269 DO 70 I = J + 1,N 00270 IX = IX + INCX 00271 X(IX) = X(IX) - TEMP*A(I,J) 00272 70 CONTINUE 00273 END IF 00274 JX = JX + INCX 00275 80 CONTINUE 00276 END IF 00277 END IF 00278 ELSE 00279 * 00280 * Form x := inv( A**T )*x. 00281 * 00282 IF (LSAME(UPLO,'U')) THEN 00283 IF (INCX.EQ.1) THEN 00284 DO 100 J = 1,N 00285 TEMP = X(J) 00286 DO 90 I = 1,J - 1 00287 TEMP = TEMP - A(I,J)*X(I) 00288 90 CONTINUE 00289 IF (NOUNIT) TEMP = TEMP/A(J,J) 00290 X(J) = TEMP 00291 100 CONTINUE 00292 ELSE 00293 JX = KX 00294 DO 120 J = 1,N 00295 TEMP = X(JX) 00296 IX = KX 00297 DO 110 I = 1,J - 1 00298 TEMP = TEMP - A(I,J)*X(IX) 00299 IX = IX + INCX 00300 110 CONTINUE 00301 IF (NOUNIT) TEMP = TEMP/A(J,J) 00302 X(JX) = TEMP 00303 JX = JX + INCX 00304 120 CONTINUE 00305 END IF 00306 ELSE 00307 IF (INCX.EQ.1) THEN 00308 DO 140 J = N,1,-1 00309 TEMP = X(J) 00310 DO 130 I = N,J + 1,-1 00311 TEMP = TEMP - A(I,J)*X(I) 00312 130 CONTINUE 00313 IF (NOUNIT) TEMP = TEMP/A(J,J) 00314 X(J) = TEMP 00315 140 CONTINUE 00316 ELSE 00317 KX = KX + (N-1)*INCX 00318 JX = KX 00319 DO 160 J = N,1,-1 00320 TEMP = X(JX) 00321 IX = KX 00322 DO 150 I = N,J + 1,-1 00323 TEMP = TEMP - A(I,J)*X(IX) 00324 IX = IX - INCX 00325 150 CONTINUE 00326 IF (NOUNIT) TEMP = TEMP/A(J,J) 00327 X(JX) = TEMP 00328 JX = JX - INCX 00329 160 CONTINUE 00330 END IF 00331 END IF 00332 END IF 00333 * 00334 RETURN 00335 * 00336 * End of DTRSV . 00337 * 00338 END