Annotation of rpl/lapack/blas/dtrsm.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
! 2: * .. Scalar Arguments ..
! 3: DOUBLE PRECISION ALPHA
! 4: INTEGER LDA,LDB,M,N
! 5: CHARACTER DIAG,SIDE,TRANSA,UPLO
! 6: * ..
! 7: * .. Array Arguments ..
! 8: DOUBLE PRECISION A(LDA,*),B(LDB,*)
! 9: * ..
! 10: *
! 11: * Purpose
! 12: * =======
! 13: *
! 14: * DTRSM solves one of the matrix equations
! 15: *
! 16: * op( A )*X = alpha*B, or X*op( A ) = alpha*B,
! 17: *
! 18: * where alpha is a scalar, X and B are m by n matrices, A is a unit, or
! 19: * non-unit, upper or lower triangular matrix and op( A ) is one of
! 20: *
! 21: * op( A ) = A or op( A ) = A'.
! 22: *
! 23: * The matrix X is overwritten on B.
! 24: *
! 25: * Arguments
! 26: * ==========
! 27: *
! 28: * SIDE - CHARACTER*1.
! 29: * On entry, SIDE specifies whether op( A ) appears on the left
! 30: * or right of X as follows:
! 31: *
! 32: * SIDE = 'L' or 'l' op( A )*X = alpha*B.
! 33: *
! 34: * SIDE = 'R' or 'r' X*op( A ) = alpha*B.
! 35: *
! 36: * Unchanged on exit.
! 37: *
! 38: * UPLO - CHARACTER*1.
! 39: * On entry, UPLO specifies whether the matrix A is an upper or
! 40: * lower triangular matrix as follows:
! 41: *
! 42: * UPLO = 'U' or 'u' A is an upper triangular matrix.
! 43: *
! 44: * UPLO = 'L' or 'l' A is a lower triangular matrix.
! 45: *
! 46: * Unchanged on exit.
! 47: *
! 48: * TRANSA - CHARACTER*1.
! 49: * On entry, TRANSA specifies the form of op( A ) to be used in
! 50: * the matrix multiplication as follows:
! 51: *
! 52: * TRANSA = 'N' or 'n' op( A ) = A.
! 53: *
! 54: * TRANSA = 'T' or 't' op( A ) = A'.
! 55: *
! 56: * TRANSA = 'C' or 'c' op( A ) = A'.
! 57: *
! 58: * Unchanged on exit.
! 59: *
! 60: * DIAG - CHARACTER*1.
! 61: * On entry, DIAG specifies whether or not A is unit triangular
! 62: * as follows:
! 63: *
! 64: * DIAG = 'U' or 'u' A is assumed to be unit triangular.
! 65: *
! 66: * DIAG = 'N' or 'n' A is not assumed to be unit
! 67: * triangular.
! 68: *
! 69: * Unchanged on exit.
! 70: *
! 71: * M - INTEGER.
! 72: * On entry, M specifies the number of rows of B. M must be at
! 73: * least zero.
! 74: * Unchanged on exit.
! 75: *
! 76: * N - INTEGER.
! 77: * On entry, N specifies the number of columns of B. N must be
! 78: * at least zero.
! 79: * Unchanged on exit.
! 80: *
! 81: * ALPHA - DOUBLE PRECISION.
! 82: * On entry, ALPHA specifies the scalar alpha. When alpha is
! 83: * zero then A is not referenced and B need not be set before
! 84: * entry.
! 85: * Unchanged on exit.
! 86: *
! 87: * A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
! 88: * when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
! 89: * Before entry with UPLO = 'U' or 'u', the leading k by k
! 90: * upper triangular part of the array A must contain the upper
! 91: * triangular matrix and the strictly lower triangular part of
! 92: * A is not referenced.
! 93: * Before entry with UPLO = 'L' or 'l', the leading k by k
! 94: * lower triangular part of the array A must contain the lower
! 95: * triangular matrix and the strictly upper triangular part of
! 96: * A is not referenced.
! 97: * Note that when DIAG = 'U' or 'u', the diagonal elements of
! 98: * A are not referenced either, but are assumed to be unity.
! 99: * Unchanged on exit.
! 100: *
! 101: * LDA - INTEGER.
! 102: * On entry, LDA specifies the first dimension of A as declared
! 103: * in the calling (sub) program. When SIDE = 'L' or 'l' then
! 104: * LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
! 105: * then LDA must be at least max( 1, n ).
! 106: * Unchanged on exit.
! 107: *
! 108: * B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
! 109: * Before entry, the leading m by n part of the array B must
! 110: * contain the right-hand side matrix B, and on exit is
! 111: * overwritten by the solution matrix X.
! 112: *
! 113: * LDB - INTEGER.
! 114: * On entry, LDB specifies the first dimension of B as declared
! 115: * in the calling (sub) program. LDB must be at least
! 116: * max( 1, m ).
! 117: * Unchanged on exit.
! 118: *
! 119: * Further Details
! 120: * ===============
! 121: *
! 122: * Level 3 Blas routine.
! 123: *
! 124: *
! 125: * -- Written on 8-February-1989.
! 126: * Jack Dongarra, Argonne National Laboratory.
! 127: * Iain Duff, AERE Harwell.
! 128: * Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 129: * Sven Hammarling, Numerical Algorithms Group Ltd.
! 130: *
! 131: * =====================================================================
! 132: *
! 133: * .. External Functions ..
! 134: LOGICAL LSAME
! 135: EXTERNAL LSAME
! 136: * ..
! 137: * .. External Subroutines ..
! 138: EXTERNAL XERBLA
! 139: * ..
! 140: * .. Intrinsic Functions ..
! 141: INTRINSIC MAX
! 142: * ..
! 143: * .. Local Scalars ..
! 144: DOUBLE PRECISION TEMP
! 145: INTEGER I,INFO,J,K,NROWA
! 146: LOGICAL LSIDE,NOUNIT,UPPER
! 147: * ..
! 148: * .. Parameters ..
! 149: DOUBLE PRECISION ONE,ZERO
! 150: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
! 151: * ..
! 152: *
! 153: * Test the input parameters.
! 154: *
! 155: LSIDE = LSAME(SIDE,'L')
! 156: IF (LSIDE) THEN
! 157: NROWA = M
! 158: ELSE
! 159: NROWA = N
! 160: END IF
! 161: NOUNIT = LSAME(DIAG,'N')
! 162: UPPER = LSAME(UPLO,'U')
! 163: *
! 164: INFO = 0
! 165: IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
! 166: INFO = 1
! 167: ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
! 168: INFO = 2
! 169: ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
! 170: + (.NOT.LSAME(TRANSA,'T')) .AND.
! 171: + (.NOT.LSAME(TRANSA,'C'))) THEN
! 172: INFO = 3
! 173: ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
! 174: INFO = 4
! 175: ELSE IF (M.LT.0) THEN
! 176: INFO = 5
! 177: ELSE IF (N.LT.0) THEN
! 178: INFO = 6
! 179: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
! 180: INFO = 9
! 181: ELSE IF (LDB.LT.MAX(1,M)) THEN
! 182: INFO = 11
! 183: END IF
! 184: IF (INFO.NE.0) THEN
! 185: CALL XERBLA('DTRSM ',INFO)
! 186: RETURN
! 187: END IF
! 188: *
! 189: * Quick return if possible.
! 190: *
! 191: IF (M.EQ.0 .OR. N.EQ.0) RETURN
! 192: *
! 193: * And when alpha.eq.zero.
! 194: *
! 195: IF (ALPHA.EQ.ZERO) THEN
! 196: DO 20 J = 1,N
! 197: DO 10 I = 1,M
! 198: B(I,J) = ZERO
! 199: 10 CONTINUE
! 200: 20 CONTINUE
! 201: RETURN
! 202: END IF
! 203: *
! 204: * Start the operations.
! 205: *
! 206: IF (LSIDE) THEN
! 207: IF (LSAME(TRANSA,'N')) THEN
! 208: *
! 209: * Form B := alpha*inv( A )*B.
! 210: *
! 211: IF (UPPER) THEN
! 212: DO 60 J = 1,N
! 213: IF (ALPHA.NE.ONE) THEN
! 214: DO 30 I = 1,M
! 215: B(I,J) = ALPHA*B(I,J)
! 216: 30 CONTINUE
! 217: END IF
! 218: DO 50 K = M,1,-1
! 219: IF (B(K,J).NE.ZERO) THEN
! 220: IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
! 221: DO 40 I = 1,K - 1
! 222: B(I,J) = B(I,J) - B(K,J)*A(I,K)
! 223: 40 CONTINUE
! 224: END IF
! 225: 50 CONTINUE
! 226: 60 CONTINUE
! 227: ELSE
! 228: DO 100 J = 1,N
! 229: IF (ALPHA.NE.ONE) THEN
! 230: DO 70 I = 1,M
! 231: B(I,J) = ALPHA*B(I,J)
! 232: 70 CONTINUE
! 233: END IF
! 234: DO 90 K = 1,M
! 235: IF (B(K,J).NE.ZERO) THEN
! 236: IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
! 237: DO 80 I = K + 1,M
! 238: B(I,J) = B(I,J) - B(K,J)*A(I,K)
! 239: 80 CONTINUE
! 240: END IF
! 241: 90 CONTINUE
! 242: 100 CONTINUE
! 243: END IF
! 244: ELSE
! 245: *
! 246: * Form B := alpha*inv( A' )*B.
! 247: *
! 248: IF (UPPER) THEN
! 249: DO 130 J = 1,N
! 250: DO 120 I = 1,M
! 251: TEMP = ALPHA*B(I,J)
! 252: DO 110 K = 1,I - 1
! 253: TEMP = TEMP - A(K,I)*B(K,J)
! 254: 110 CONTINUE
! 255: IF (NOUNIT) TEMP = TEMP/A(I,I)
! 256: B(I,J) = TEMP
! 257: 120 CONTINUE
! 258: 130 CONTINUE
! 259: ELSE
! 260: DO 160 J = 1,N
! 261: DO 150 I = M,1,-1
! 262: TEMP = ALPHA*B(I,J)
! 263: DO 140 K = I + 1,M
! 264: TEMP = TEMP - A(K,I)*B(K,J)
! 265: 140 CONTINUE
! 266: IF (NOUNIT) TEMP = TEMP/A(I,I)
! 267: B(I,J) = TEMP
! 268: 150 CONTINUE
! 269: 160 CONTINUE
! 270: END IF
! 271: END IF
! 272: ELSE
! 273: IF (LSAME(TRANSA,'N')) THEN
! 274: *
! 275: * Form B := alpha*B*inv( A ).
! 276: *
! 277: IF (UPPER) THEN
! 278: DO 210 J = 1,N
! 279: IF (ALPHA.NE.ONE) THEN
! 280: DO 170 I = 1,M
! 281: B(I,J) = ALPHA*B(I,J)
! 282: 170 CONTINUE
! 283: END IF
! 284: DO 190 K = 1,J - 1
! 285: IF (A(K,J).NE.ZERO) THEN
! 286: DO 180 I = 1,M
! 287: B(I,J) = B(I,J) - A(K,J)*B(I,K)
! 288: 180 CONTINUE
! 289: END IF
! 290: 190 CONTINUE
! 291: IF (NOUNIT) THEN
! 292: TEMP = ONE/A(J,J)
! 293: DO 200 I = 1,M
! 294: B(I,J) = TEMP*B(I,J)
! 295: 200 CONTINUE
! 296: END IF
! 297: 210 CONTINUE
! 298: ELSE
! 299: DO 260 J = N,1,-1
! 300: IF (ALPHA.NE.ONE) THEN
! 301: DO 220 I = 1,M
! 302: B(I,J) = ALPHA*B(I,J)
! 303: 220 CONTINUE
! 304: END IF
! 305: DO 240 K = J + 1,N
! 306: IF (A(K,J).NE.ZERO) THEN
! 307: DO 230 I = 1,M
! 308: B(I,J) = B(I,J) - A(K,J)*B(I,K)
! 309: 230 CONTINUE
! 310: END IF
! 311: 240 CONTINUE
! 312: IF (NOUNIT) THEN
! 313: TEMP = ONE/A(J,J)
! 314: DO 250 I = 1,M
! 315: B(I,J) = TEMP*B(I,J)
! 316: 250 CONTINUE
! 317: END IF
! 318: 260 CONTINUE
! 319: END IF
! 320: ELSE
! 321: *
! 322: * Form B := alpha*B*inv( A' ).
! 323: *
! 324: IF (UPPER) THEN
! 325: DO 310 K = N,1,-1
! 326: IF (NOUNIT) THEN
! 327: TEMP = ONE/A(K,K)
! 328: DO 270 I = 1,M
! 329: B(I,K) = TEMP*B(I,K)
! 330: 270 CONTINUE
! 331: END IF
! 332: DO 290 J = 1,K - 1
! 333: IF (A(J,K).NE.ZERO) THEN
! 334: TEMP = A(J,K)
! 335: DO 280 I = 1,M
! 336: B(I,J) = B(I,J) - TEMP*B(I,K)
! 337: 280 CONTINUE
! 338: END IF
! 339: 290 CONTINUE
! 340: IF (ALPHA.NE.ONE) THEN
! 341: DO 300 I = 1,M
! 342: B(I,K) = ALPHA*B(I,K)
! 343: 300 CONTINUE
! 344: END IF
! 345: 310 CONTINUE
! 346: ELSE
! 347: DO 360 K = 1,N
! 348: IF (NOUNIT) THEN
! 349: TEMP = ONE/A(K,K)
! 350: DO 320 I = 1,M
! 351: B(I,K) = TEMP*B(I,K)
! 352: 320 CONTINUE
! 353: END IF
! 354: DO 340 J = K + 1,N
! 355: IF (A(J,K).NE.ZERO) THEN
! 356: TEMP = A(J,K)
! 357: DO 330 I = 1,M
! 358: B(I,J) = B(I,J) - TEMP*B(I,K)
! 359: 330 CONTINUE
! 360: END IF
! 361: 340 CONTINUE
! 362: IF (ALPHA.NE.ONE) THEN
! 363: DO 350 I = 1,M
! 364: B(I,K) = ALPHA*B(I,K)
! 365: 350 CONTINUE
! 366: END IF
! 367: 360 CONTINUE
! 368: END IF
! 369: END IF
! 370: END IF
! 371: *
! 372: RETURN
! 373: *
! 374: * End of DTRSM .
! 375: *
! 376: END
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