github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/internal/testdata/netlib/dtrmv.f (about) 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