1*> \brief \b DTRSV 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) 12* 13* .. Scalar Arguments .. 14* INTEGER INCX,LDA,N 15* CHARACTER DIAG,TRANS,UPLO 16* .. 17* .. Array Arguments .. 18* DOUBLE PRECISION A(LDA,*),X(*) 19* .. 20* 21* 22*> \par Purpose: 23* ============= 24*> 25*> \verbatim 26*> 27*> DTRSV solves one of the systems of equations 28*> 29*> A*x = b, or A**T*x = b, 30*> 31*> where b and x are n element vectors and A is an n by n unit, or 32*> non-unit, upper or lower triangular matrix. 33*> 34*> No test for singularity or near-singularity is included in this 35*> routine. Such tests must be performed before calling this routine. 36*> \endverbatim 37* 38* Arguments: 39* ========== 40* 41*> \param[in] UPLO 42*> \verbatim 43*> UPLO is CHARACTER*1 44*> On entry, UPLO specifies whether the matrix is an upper or 45*> lower triangular matrix as follows: 46*> 47*> UPLO = 'U' or 'u' A is an upper triangular matrix. 48*> 49*> UPLO = 'L' or 'l' A is a lower triangular matrix. 50*> \endverbatim 51*> 52*> \param[in] TRANS 53*> \verbatim 54*> TRANS is CHARACTER*1 55*> On entry, TRANS specifies the equations to be solved as 56*> follows: 57*> 58*> TRANS = 'N' or 'n' A*x = b. 59*> 60*> TRANS = 'T' or 't' A**T*x = b. 61*> 62*> TRANS = 'C' or 'c' A**T*x = b. 63*> \endverbatim 64*> 65*> \param[in] DIAG 66*> \verbatim 67*> DIAG is CHARACTER*1 68*> On entry, DIAG specifies whether or not A is unit 69*> triangular as follows: 70*> 71*> DIAG = 'U' or 'u' A is assumed to be unit triangular. 72*> 73*> DIAG = 'N' or 'n' A is not assumed to be unit 74*> triangular. 75*> \endverbatim 76*> 77*> \param[in] N 78*> \verbatim 79*> N is INTEGER 80*> On entry, N specifies the order of the matrix A. 81*> N must be at least zero. 82*> \endverbatim 83*> 84*> \param[in] A 85*> \verbatim 86*> A is DOUBLE PRECISION array, dimension ( LDA, N ) 87*> Before entry with UPLO = 'U' or 'u', the leading n by n 88*> upper triangular part of the array A must contain the upper 89*> triangular matrix and the strictly lower triangular part of 90*> A is not referenced. 91*> Before entry with UPLO = 'L' or 'l', the leading n by n 92*> lower triangular part of the array A must contain the lower 93*> triangular matrix and the strictly upper triangular part of 94*> A is not referenced. 95*> Note that when DIAG = 'U' or 'u', the diagonal elements of 96*> A are not referenced either, but are assumed to be unity. 97*> \endverbatim 98*> 99*> \param[in] LDA 100*> \verbatim 101*> LDA is INTEGER 102*> On entry, LDA specifies the first dimension of A as declared 103*> in the calling (sub) program. LDA must be at least 104*> max( 1, n ). 105*> \endverbatim 106*> 107*> \param[in,out] X 108*> \verbatim 109*> X is DOUBLE PRECISION array, dimension at least 110*> ( 1 + ( n - 1 )*abs( INCX ) ). 111*> Before entry, the incremented array X must contain the n 112*> element right-hand side vector b. On exit, X is overwritten 113*> with the solution vector x. 114*> \endverbatim 115*> 116*> \param[in] INCX 117*> \verbatim 118*> INCX is INTEGER 119*> On entry, INCX specifies the increment for the elements of 120*> X. INCX must not be zero. 121*> 122*> Level 2 Blas routine. 123*> 124*> -- Written on 22-October-1986. 125*> Jack Dongarra, Argonne National Lab. 126*> Jeremy Du Croz, Nag Central Office. 127*> Sven Hammarling, Nag Central Office. 128*> Richard Hanson, Sandia National Labs. 129*> \endverbatim 130* 131* Authors: 132* ======== 133* 134*> \author Univ. of Tennessee 135*> \author Univ. of California Berkeley 136*> \author Univ. of Colorado Denver 137*> \author NAG Ltd. 138* 139*> \ingroup double_blas_level1 140* 141* ===================================================================== 142 SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) 143* 144* -- Reference BLAS level1 routine -- 145* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 146* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 147* 148* .. Scalar Arguments .. 149 INTEGER INCX,LDA,N 150 CHARACTER DIAG,TRANS,UPLO 151* .. 152* .. Array Arguments .. 153 DOUBLE PRECISION A(LDA,*),X(*) 154* .. 155* 156* ===================================================================== 157* 158* .. Parameters .. 159 DOUBLE PRECISION ZERO 160 PARAMETER (ZERO=0.0D+0) 161* .. 162* .. Local Scalars .. 163 DOUBLE PRECISION TEMP 164 INTEGER I,INFO,IX,J,JX,KX 165 LOGICAL NOUNIT 166* .. 167* .. External Functions .. 168 LOGICAL LSAME 169 EXTERNAL LSAME 170* .. 171* .. External Subroutines .. 172 EXTERNAL XERBLA 173* .. 174* .. Intrinsic Functions .. 175 INTRINSIC MAX 176* .. 177* 178* Test the input parameters. 179* 180 INFO = 0 181 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 182 INFO = 1 183 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 184 + .NOT.LSAME(TRANS,'C')) THEN 185 INFO = 2 186 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 187 INFO = 3 188 ELSE IF (N.LT.0) THEN 189 INFO = 4 190 ELSE IF (LDA.LT.MAX(1,N)) THEN 191 INFO = 6 192 ELSE IF (INCX.EQ.0) THEN 193 INFO = 8 194 END IF 195 IF (INFO.NE.0) THEN 196 CALL XERBLA('DTRSV ',INFO) 197 RETURN 198 END IF 199* 200* Quick return if possible. 201* 202 IF (N.EQ.0) RETURN 203* 204 NOUNIT = LSAME(DIAG,'N') 205* 206* Set up the start point in X if the increment is not unity. This 207* will be ( N - 1 )*INCX too small for descending loops. 208* 209 IF (INCX.LE.0) THEN 210 KX = 1 - (N-1)*INCX 211 ELSE IF (INCX.NE.1) THEN 212 KX = 1 213 END IF 214* 215* Start the operations. In this version the elements of A are 216* accessed sequentially with one pass through A. 217* 218 IF (LSAME(TRANS,'N')) THEN 219* 220* Form x := inv( A )*x. 221* 222 IF (LSAME(UPLO,'U')) THEN 223 IF (INCX.EQ.1) THEN 224 DO 20 J = N,1,-1 225 IF (X(J).NE.ZERO) THEN 226 IF (NOUNIT) X(J) = X(J)/A(J,J) 227 TEMP = X(J) 228 DO 10 I = J - 1,1,-1 229 X(I) = X(I) - TEMP*A(I,J) 230 10 CONTINUE 231 END IF 232 20 CONTINUE 233 ELSE 234 JX = KX + (N-1)*INCX 235 DO 40 J = N,1,-1 236 IF (X(JX).NE.ZERO) THEN 237 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 238 TEMP = X(JX) 239 IX = JX 240 DO 30 I = J - 1,1,-1 241 IX = IX - INCX 242 X(IX) = X(IX) - TEMP*A(I,J) 243 30 CONTINUE 244 END IF 245 JX = JX - INCX 246 40 CONTINUE 247 END IF 248 ELSE 249 IF (INCX.EQ.1) THEN 250 DO 60 J = 1,N 251 IF (X(J).NE.ZERO) THEN 252 IF (NOUNIT) X(J) = X(J)/A(J,J) 253 TEMP = X(J) 254 DO 50 I = J + 1,N 255 X(I) = X(I) - TEMP*A(I,J) 256 50 CONTINUE 257 END IF 258 60 CONTINUE 259 ELSE 260 JX = KX 261 DO 80 J = 1,N 262 IF (X(JX).NE.ZERO) THEN 263 IF (NOUNIT) X(JX) = X(JX)/A(J,J) 264 TEMP = X(JX) 265 IX = JX 266 DO 70 I = J + 1,N 267 IX = IX + INCX 268 X(IX) = X(IX) - TEMP*A(I,J) 269 70 CONTINUE 270 END IF 271 JX = JX + INCX 272 80 CONTINUE 273 END IF 274 END IF 275 ELSE 276* 277* Form x := inv( A**T )*x. 278* 279 IF (LSAME(UPLO,'U')) THEN 280 IF (INCX.EQ.1) THEN 281 DO 100 J = 1,N 282 TEMP = X(J) 283 DO 90 I = 1,J - 1 284 TEMP = TEMP - A(I,J)*X(I) 285 90 CONTINUE 286 IF (NOUNIT) TEMP = TEMP/A(J,J) 287 X(J) = TEMP 288 100 CONTINUE 289 ELSE 290 JX = KX 291 DO 120 J = 1,N 292 TEMP = X(JX) 293 IX = KX 294 DO 110 I = 1,J - 1 295 TEMP = TEMP - A(I,J)*X(IX) 296 IX = IX + INCX 297 110 CONTINUE 298 IF (NOUNIT) TEMP = TEMP/A(J,J) 299 X(JX) = TEMP 300 JX = JX + INCX 301 120 CONTINUE 302 END IF 303 ELSE 304 IF (INCX.EQ.1) THEN 305 DO 140 J = N,1,-1 306 TEMP = X(J) 307 DO 130 I = N,J + 1,-1 308 TEMP = TEMP - A(I,J)*X(I) 309 130 CONTINUE 310 IF (NOUNIT) TEMP = TEMP/A(J,J) 311 X(J) = TEMP 312 140 CONTINUE 313 ELSE 314 KX = KX + (N-1)*INCX 315 JX = KX 316 DO 160 J = N,1,-1 317 TEMP = X(JX) 318 IX = KX 319 DO 150 I = N,J + 1,-1 320 TEMP = TEMP - A(I,J)*X(IX) 321 IX = IX - INCX 322 150 CONTINUE 323 IF (NOUNIT) TEMP = TEMP/A(J,J) 324 X(JX) = TEMP 325 JX = JX - INCX 326 160 CONTINUE 327 END IF 328 END IF 329 END IF 330* 331 RETURN 332* 333* End of DTRSV 334* 335 END 336