1*> \brief \b DTRMV 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 DTRMV(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*> DTRMV performs one of the matrix-vector operations 28*> 29*> x := A*x, or x := A**T*x, 30*> 31*> where x is an n element vector and A is an n by n unit, or non-unit, 32*> upper or lower triangular matrix. 33*> \endverbatim 34* 35* Arguments: 36* ========== 37* 38*> \param[in] UPLO 39*> \verbatim 40*> UPLO is CHARACTER*1 41*> On entry, UPLO specifies whether the matrix is an upper or 42*> lower triangular matrix as follows: 43*> 44*> UPLO = 'U' or 'u' A is an upper triangular matrix. 45*> 46*> UPLO = 'L' or 'l' A is a lower triangular matrix. 47*> \endverbatim 48*> 49*> \param[in] TRANS 50*> \verbatim 51*> TRANS is CHARACTER*1 52*> On entry, TRANS specifies the operation to be performed as 53*> follows: 54*> 55*> TRANS = 'N' or 'n' x := A*x. 56*> 57*> TRANS = 'T' or 't' x := A**T*x. 58*> 59*> TRANS = 'C' or 'c' x := A**T*x. 60*> \endverbatim 61*> 62*> \param[in] DIAG 63*> \verbatim 64*> DIAG is CHARACTER*1 65*> On entry, DIAG specifies whether or not A is unit 66*> triangular as follows: 67*> 68*> DIAG = 'U' or 'u' A is assumed to be unit triangular. 69*> 70*> DIAG = 'N' or 'n' A is not assumed to be unit 71*> triangular. 72*> \endverbatim 73*> 74*> \param[in] N 75*> \verbatim 76*> N is INTEGER 77*> On entry, N specifies the order of the matrix A. 78*> N must be at least zero. 79*> \endverbatim 80*> 81*> \param[in] A 82*> \verbatim 83*> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). 84*> Before entry with UPLO = 'U' or 'u', the leading n by n 85*> upper triangular part of the array A must contain the upper 86*> triangular matrix and the strictly lower triangular part of 87*> A is not referenced. 88*> Before entry with UPLO = 'L' or 'l', the leading n by n 89*> lower triangular part of the array A must contain the lower 90*> triangular matrix and the strictly upper triangular part of 91*> A is not referenced. 92*> Note that when DIAG = 'U' or 'u', the diagonal elements of 93*> A are not referenced either, but are assumed to be unity. 94*> \endverbatim 95*> 96*> \param[in] LDA 97*> \verbatim 98*> LDA is INTEGER 99*> On entry, LDA specifies the first dimension of A as declared 100*> in the calling (sub) program. LDA must be at least 101*> max( 1, n ). 102*> \endverbatim 103*> 104*> \param[in,out] X 105*> \verbatim 106*> X is DOUBLE PRECISION array of dimension at least 107*> ( 1 + ( n - 1 )*abs( INCX ) ). 108*> Before entry, the incremented array X must contain the n 109*> element vector x. On exit, X is overwritten with the 110*> tranformed vector x. 111*> \endverbatim 112*> 113*> \param[in] INCX 114*> \verbatim 115*> INCX is INTEGER 116*> On entry, INCX specifies the increment for the elements of 117*> X. INCX must not be zero. 118*> \endverbatim 119* 120* Authors: 121* ======== 122* 123*> \author Univ. of Tennessee 124*> \author Univ. of California Berkeley 125*> \author Univ. of Colorado Denver 126*> \author NAG Ltd. 127* 128*> \date November 2011 129* 130*> \ingroup double_blas_level2 131* 132*> \par Further Details: 133* ===================== 134*> 135*> \verbatim 136*> 137*> Level 2 Blas routine. 138*> The vector and matrix arguments are not referenced when N = 0, or M = 0 139*> 140*> -- Written on 22-October-1986. 141*> Jack Dongarra, Argonne National Lab. 142*> Jeremy Du Croz, Nag Central Office. 143*> Sven Hammarling, Nag Central Office. 144*> Richard Hanson, Sandia National Labs. 145*> \endverbatim 146*> 147* ===================================================================== 148 SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) 149* 150* -- Reference BLAS level2 routine (version 3.4.0) -- 151* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 152* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 153* November 2011 154* 155* .. Scalar Arguments .. 156 INTEGER INCX,LDA,N 157 CHARACTER DIAG,TRANS,UPLO 158* .. 159* .. Array Arguments .. 160 DOUBLE PRECISION A(LDA,*),X(*) 161* .. 162* 163* ===================================================================== 164* 165* .. Parameters .. 166 DOUBLE PRECISION ZERO 167 PARAMETER (ZERO=0.0D+0) 168* .. 169* .. Local Scalars .. 170 DOUBLE PRECISION TEMP 171 INTEGER I,INFO,IX,J,JX,KX 172 LOGICAL NOUNIT 173* .. 174* .. External Functions .. 175 LOGICAL LSAME 176 EXTERNAL LSAME 177* .. 178* .. External Subroutines .. 179 EXTERNAL XERBLA 180* .. 181* .. Intrinsic Functions .. 182 INTRINSIC MAX 183* .. 184* 185* Test the input parameters. 186* 187 INFO = 0 188 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 189 INFO = 1 190 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 191 + .NOT.LSAME(TRANS,'C')) THEN 192 INFO = 2 193 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 194 INFO = 3 195 ELSE IF (N.LT.0) THEN 196 INFO = 4 197 ELSE IF (LDA.LT.MAX(1,N)) THEN 198 INFO = 6 199 ELSE IF (INCX.EQ.0) THEN 200 INFO = 8 201 END IF 202 IF (INFO.NE.0) THEN 203 CALL XERBLA('DTRMV ',INFO) 204 RETURN 205 END IF 206* 207* Quick return if possible. 208* 209 IF (N.EQ.0) RETURN 210* 211 NOUNIT = LSAME(DIAG,'N') 212* 213* Set up the start point in X if the increment is not unity. This 214* will be ( N - 1 )*INCX too small for descending loops. 215* 216 IF (INCX.LE.0) THEN 217 KX = 1 - (N-1)*INCX 218 ELSE IF (INCX.NE.1) THEN 219 KX = 1 220 END IF 221* 222* Start the operations. In this version the elements of A are 223* accessed sequentially with one pass through A. 224* 225 IF (LSAME(TRANS,'N')) THEN 226* 227* Form x := A*x. 228* 229 IF (LSAME(UPLO,'U')) THEN 230 IF (INCX.EQ.1) THEN 231 DO 20 J = 1,N 232 IF (X(J).NE.ZERO) THEN 233 TEMP = X(J) 234 DO 10 I = 1,J - 1 235 X(I) = X(I) + TEMP*A(I,J) 236 10 CONTINUE 237 IF (NOUNIT) X(J) = X(J)*A(J,J) 238 END IF 239 20 CONTINUE 240 ELSE 241 JX = KX 242 DO 40 J = 1,N 243 IF (X(JX).NE.ZERO) THEN 244 TEMP = X(JX) 245 IX = KX 246 DO 30 I = 1,J - 1 247 X(IX) = X(IX) + TEMP*A(I,J) 248 IX = IX + INCX 249 30 CONTINUE 250 IF (NOUNIT) X(JX) = X(JX)*A(J,J) 251 END IF 252 JX = JX + INCX 253 40 CONTINUE 254 END IF 255 ELSE 256 IF (INCX.EQ.1) THEN 257 DO 60 J = N,1,-1 258 IF (X(J).NE.ZERO) THEN 259 TEMP = X(J) 260 DO 50 I = N,J + 1,-1 261 X(I) = X(I) + TEMP*A(I,J) 262 50 CONTINUE 263 IF (NOUNIT) X(J) = X(J)*A(J,J) 264 END IF 265 60 CONTINUE 266 ELSE 267 KX = KX + (N-1)*INCX 268 JX = KX 269 DO 80 J = N,1,-1 270 IF (X(JX).NE.ZERO) THEN 271 TEMP = X(JX) 272 IX = KX 273 DO 70 I = N,J + 1,-1 274 X(IX) = X(IX) + TEMP*A(I,J) 275 IX = IX - INCX 276 70 CONTINUE 277 IF (NOUNIT) X(JX) = X(JX)*A(J,J) 278 END IF 279 JX = JX - INCX 280 80 CONTINUE 281 END IF 282 END IF 283 ELSE 284* 285* Form x := A**T*x. 286* 287 IF (LSAME(UPLO,'U')) THEN 288 IF (INCX.EQ.1) THEN 289 DO 100 J = N,1,-1 290 TEMP = X(J) 291 IF (NOUNIT) TEMP = TEMP*A(J,J) 292 DO 90 I = J - 1,1,-1 293 TEMP = TEMP + A(I,J)*X(I) 294 90 CONTINUE 295 X(J) = TEMP 296 100 CONTINUE 297 ELSE 298 JX = KX + (N-1)*INCX 299 DO 120 J = N,1,-1 300 TEMP = X(JX) 301 IX = JX 302 IF (NOUNIT) TEMP = TEMP*A(J,J) 303 DO 110 I = J - 1,1,-1 304 IX = IX - INCX 305 TEMP = TEMP + A(I,J)*X(IX) 306 110 CONTINUE 307 X(JX) = TEMP 308 JX = JX - INCX 309 120 CONTINUE 310 END IF 311 ELSE 312 IF (INCX.EQ.1) THEN 313 DO 140 J = 1,N 314 TEMP = X(J) 315 IF (NOUNIT) TEMP = TEMP*A(J,J) 316 DO 130 I = J + 1,N 317 TEMP = TEMP + A(I,J)*X(I) 318 130 CONTINUE 319 X(J) = TEMP 320 140 CONTINUE 321 ELSE 322 JX = KX 323 DO 160 J = 1,N 324 TEMP = X(JX) 325 IX = JX 326 IF (NOUNIT) TEMP = TEMP*A(J,J) 327 DO 150 I = J + 1,N 328 IX = IX + INCX 329 TEMP = TEMP + A(I,J)*X(IX) 330 150 CONTINUE 331 X(JX) = TEMP 332 JX = JX + INCX 333 160 CONTINUE 334 END IF 335 END IF 336 END IF 337* 338 RETURN 339* 340* End of DTRMV . 341* 342 END 343