numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/BLAS/SRC/strmv.f | 10009B | -rw-r--r-- |
001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341
*> \brief \b STRMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE STRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,LDA,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * REAL A(LDA,*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STRMV performs one of the matrix-vector operations *> *> x := A*x, or x := A**T*x, *> *> where x is an n element vector and A is an n by n unit, or non-unit, *> upper or lower triangular matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' x := A*x. *> *> TRANS = 'T' or 't' x := A**T*x. *> *> TRANS = 'C' or 'c' x := A**T*x. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit *> triangular as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is REAL array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is REAL array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. On exit, X is overwritten with the *> transformed vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup trmv * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE STRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * -- Reference BLAS level2 routine -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INCX,LDA,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. REAL A(LDA,*),X(*) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER (ZERO=0.0E+0) * .. * .. Local Scalars .. REAL TEMP INTEGER I,INFO,IX,J,JX,KX LOGICAL NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. + .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. + .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 6 ELSE IF (INCX.EQ.0) THEN INFO = 8 END IF IF (INFO.NE.0) THEN CALL XERBLA('STRMV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (LSAME(TRANS,'N')) THEN * * Form x := A*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = X(J) DO 10 I = 1,J - 1 X(I) = X(I) + TEMP*A(I,J) 10 CONTINUE IF (NOUNIT) X(J) = X(J)*A(J,J) END IF 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 30 I = 1,J - 1 X(IX) = X(IX) + TEMP*A(I,J) IX = IX + INCX 30 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(J,J) END IF JX = JX + INCX 40 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 60 J = N,1,-1 IF (X(J).NE.ZERO) THEN TEMP = X(J) DO 50 I = N,J + 1,-1 X(I) = X(I) + TEMP*A(I,J) 50 CONTINUE IF (NOUNIT) X(J) = X(J)*A(J,J) END IF 60 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 80 J = N,1,-1 IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 70 I = N,J + 1,-1 X(IX) = X(IX) + TEMP*A(I,J) IX = IX - INCX 70 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(J,J) END IF JX = JX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A**T*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 100 J = N,1,-1 TEMP = X(J) IF (NOUNIT) TEMP = TEMP*A(J,J) DO 90 I = J - 1,1,-1 TEMP = TEMP + A(I,J)*X(I) 90 CONTINUE X(J) = TEMP 100 CONTINUE ELSE JX = KX + (N-1)*INCX DO 120 J = N,1,-1 TEMP = X(JX) IX = JX IF (NOUNIT) TEMP = TEMP*A(J,J) DO 110 I = J - 1,1,-1 IX = IX - INCX TEMP = TEMP + A(I,J)*X(IX) 110 CONTINUE X(JX) = TEMP JX = JX - INCX 120 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 140 J = 1,N TEMP = X(J) IF (NOUNIT) TEMP = TEMP*A(J,J) DO 130 I = J + 1,N TEMP = TEMP + A(I,J)*X(I) 130 CONTINUE X(J) = TEMP 140 CONTINUE ELSE JX = KX DO 160 J = 1,N TEMP = X(JX) IX = JX IF (NOUNIT) TEMP = TEMP*A(J,J) DO 150 I = J + 1,N IX = IX + INCX TEMP = TEMP + A(I,J)*X(IX) 150 CONTINUE X(JX) = TEMP JX = JX + INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of STRMV * END