|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 |
SUBROUTINE STRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
* .. Scalar Arguments .. REAL ALPHA INTEGER LDA,LDB,M,N CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. REAL A(LDA,*),B(LDB,*) * .. * * Purpose * ======= * * STRMM performs one of the matrix-matrix operations * * B := alpha*op( A )*B, or B := alpha*B*op( A ), * * where alpha is a scalar, B is an m by n matrix, A is a unit, or * non-unit, upper or lower triangular matrix and op( A ) is one of * * op( A ) = A or op( A ) = A**T. * * Arguments * ========== * * SIDE - CHARACTER*1. * On entry, SIDE specifies whether op( A ) multiplies B from * the left or right as follows: * * SIDE = 'L' or 'l' B := alpha*op( A )*B. * * SIDE = 'R' or 'r' B := alpha*B*op( A ). * * Unchanged on exit. * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix A 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. * * Unchanged on exit. * * TRANSA - CHARACTER*1. * On entry, TRANSA specifies the form of op( A ) to be used in * the matrix multiplication as follows: * * TRANSA = 'N' or 'n' op( A ) = A. * * TRANSA = 'T' or 't' op( A ) = A**T. * * TRANSA = 'C' or 'c' op( A ) = A**T. * * Unchanged on exit. * * DIAG - 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. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of B. M must be at * least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of B. N must be * at least zero. * Unchanged on exit. * * ALPHA - REAL . * On entry, ALPHA specifies the scalar alpha. When alpha is * zero then A is not referenced and B need not be set before * entry. * Unchanged on exit. * * A - REAL array of DIMENSION ( LDA, k ), where k is m * when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. * Before entry with UPLO = 'U' or 'u', the leading k by k * 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 k by k * 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. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. When SIDE = 'L' or 'l' then * LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' * then LDA must be at least max( 1, n ). * Unchanged on exit. * * B - REAL array of DIMENSION ( LDB, n ). * Before entry, the leading m by n part of the array B must * contain the matrix B, and on exit is overwritten by the * transformed matrix. * * LDB - INTEGER. * On entry, LDB specifies the first dimension of B as declared * in the calling (sub) program. LDB must be at least * max( 1, m ). * Unchanged on exit. * * Further Details * =============== * * Level 3 Blas routine. * * -- Written on 8-February-1989. * Jack Dongarra, Argonne National Laboratory. * Iain Duff, AERE Harwell. * Jeremy Du Croz, Numerical Algorithms Group Ltd. * Sven Hammarling, Numerical Algorithms Group Ltd. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Local Scalars .. REAL TEMP INTEGER I,INFO,J,K,NROWA LOGICAL LSIDE,NOUNIT,UPPER * .. * .. Parameters .. REAL ONE,ZERO PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) * .. * * Test the input parameters. * LSIDE = LSAME(SIDE,'L') IF (LSIDE) THEN NROWA = M ELSE NROWA = N END IF NOUNIT = LSAME(DIAG,'N') UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN INFO = 1 ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 2 ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. + (.NOT.LSAME(TRANSA,'T')) .AND. + (.NOT.LSAME(TRANSA,'C'))) THEN INFO = 3 ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN INFO = 4 ELSE IF (M.LT.0) THEN INFO = 5 ELSE IF (N.LT.0) THEN INFO = 6 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 9 ELSE IF (LDB.LT.MAX(1,M)) THEN INFO = 11 END IF IF (INFO.NE.0) THEN CALL XERBLA('STRMM ',INFO) RETURN END IF * * Quick return if possible. * IF (M.EQ.0 .OR. N.EQ.0) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M B(I,J) = ZERO 10 CONTINUE 20 CONTINUE RETURN END IF * * Start the operations. * IF (LSIDE) THEN IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*A*B. * IF (UPPER) THEN DO 50 J = 1,N DO 40 K = 1,M IF (B(K,J).NE.ZERO) THEN TEMP = ALPHA*B(K,J) DO 30 I = 1,K - 1 B(I,J) = B(I,J) + TEMP*A(I,K) 30 CONTINUE IF (NOUNIT) TEMP = TEMP*A(K,K) B(K,J) = TEMP END IF 40 CONTINUE 50 CONTINUE ELSE DO 80 J = 1,N DO 70 K = M,1,-1 IF (B(K,J).NE.ZERO) THEN TEMP = ALPHA*B(K,J) B(K,J) = TEMP IF (NOUNIT) B(K,J) = B(K,J)*A(K,K) DO 60 I = K + 1,M B(I,J) = B(I,J) + TEMP*A(I,K) 60 CONTINUE END IF 70 CONTINUE 80 CONTINUE END IF ELSE * * Form B := alpha*A**T*B. * IF (UPPER) THEN DO 110 J = 1,N DO 100 I = M,1,-1 TEMP = B(I,J) IF (NOUNIT) TEMP = TEMP*A(I,I) DO 90 K = 1,I - 1 TEMP = TEMP + A(K,I)*B(K,J) 90 CONTINUE B(I,J) = ALPHA*TEMP 100 CONTINUE 110 CONTINUE ELSE DO 140 J = 1,N DO 130 I = 1,M TEMP = B(I,J) IF (NOUNIT) TEMP = TEMP*A(I,I) DO 120 K = I + 1,M TEMP = TEMP + A(K,I)*B(K,J) 120 CONTINUE B(I,J) = ALPHA*TEMP 130 CONTINUE 140 CONTINUE END IF END IF ELSE IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*B*A. * IF (UPPER) THEN DO 180 J = N,1,-1 TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(J,J) DO 150 I = 1,M B(I,J) = TEMP*B(I,J) 150 CONTINUE DO 170 K = 1,J - 1 IF (A(K,J).NE.ZERO) THEN TEMP = ALPHA*A(K,J) DO 160 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE ELSE DO 220 J = 1,N TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(J,J) DO 190 I = 1,M B(I,J) = TEMP*B(I,J) 190 CONTINUE DO 210 K = J + 1,N IF (A(K,J).NE.ZERO) THEN TEMP = ALPHA*A(K,J) DO 200 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 200 CONTINUE END IF 210 CONTINUE 220 CONTINUE END IF ELSE * * Form B := alpha*B*A**T. * IF (UPPER) THEN DO 260 K = 1,N DO 240 J = 1,K - 1 IF (A(J,K).NE.ZERO) THEN TEMP = ALPHA*A(J,K) DO 230 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 230 CONTINUE END IF 240 CONTINUE TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(K,K) IF (TEMP.NE.ONE) THEN DO 250 I = 1,M B(I,K) = TEMP*B(I,K) 250 CONTINUE END IF 260 CONTINUE ELSE DO 300 K = N,1,-1 DO 280 J = K + 1,N IF (A(J,K).NE.ZERO) THEN TEMP = ALPHA*A(J,K) DO 270 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 270 CONTINUE END IF 280 CONTINUE TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(K,K) IF (TEMP.NE.ONE) THEN DO 290 I = 1,M B(I,K) = TEMP*B(I,K) 290 CONTINUE END IF 300 CONTINUE END IF END IF END IF * RETURN * * End of STRMM . * END |