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