Annotation of rpl/lapack/blas/dtrsv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
! 2: * .. Scalar Arguments ..
! 3: INTEGER INCX,LDA,N
! 4: CHARACTER DIAG,TRANS,UPLO
! 5: * ..
! 6: * .. Array Arguments ..
! 7: DOUBLE PRECISION A(LDA,*),X(*)
! 8: * ..
! 9: *
! 10: * Purpose
! 11: * =======
! 12: *
! 13: * DTRSV solves one of the systems of equations
! 14: *
! 15: * A*x = b, or A'*x = b,
! 16: *
! 17: * where b and x are n element vectors and A is an n by n unit, or
! 18: * non-unit, upper or lower triangular matrix.
! 19: *
! 20: * No test for singularity or near-singularity is included in this
! 21: * routine. Such tests must be performed before calling this routine.
! 22: *
! 23: * Arguments
! 24: * ==========
! 25: *
! 26: * UPLO - CHARACTER*1.
! 27: * On entry, UPLO specifies whether the matrix is an upper or
! 28: * lower triangular matrix as follows:
! 29: *
! 30: * UPLO = 'U' or 'u' A is an upper triangular matrix.
! 31: *
! 32: * UPLO = 'L' or 'l' A is a lower triangular matrix.
! 33: *
! 34: * Unchanged on exit.
! 35: *
! 36: * TRANS - CHARACTER*1.
! 37: * On entry, TRANS specifies the equations to be solved as
! 38: * follows:
! 39: *
! 40: * TRANS = 'N' or 'n' A*x = b.
! 41: *
! 42: * TRANS = 'T' or 't' A'*x = b.
! 43: *
! 44: * TRANS = 'C' or 'c' A'*x = b.
! 45: *
! 46: * Unchanged on exit.
! 47: *
! 48: * DIAG - CHARACTER*1.
! 49: * On entry, DIAG specifies whether or not A is unit
! 50: * triangular as follows:
! 51: *
! 52: * DIAG = 'U' or 'u' A is assumed to be unit triangular.
! 53: *
! 54: * DIAG = 'N' or 'n' A is not assumed to be unit
! 55: * triangular.
! 56: *
! 57: * Unchanged on exit.
! 58: *
! 59: * N - INTEGER.
! 60: * On entry, N specifies the order of the matrix A.
! 61: * N must be at least zero.
! 62: * Unchanged on exit.
! 63: *
! 64: * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
! 65: * Before entry with UPLO = 'U' or 'u', the leading n by n
! 66: * upper triangular part of the array A must contain the upper
! 67: * triangular matrix and the strictly lower triangular part of
! 68: * A is not referenced.
! 69: * Before entry with UPLO = 'L' or 'l', the leading n by n
! 70: * lower triangular part of the array A must contain the lower
! 71: * triangular matrix and the strictly upper triangular part of
! 72: * A is not referenced.
! 73: * Note that when DIAG = 'U' or 'u', the diagonal elements of
! 74: * A are not referenced either, but are assumed to be unity.
! 75: * Unchanged on exit.
! 76: *
! 77: * LDA - INTEGER.
! 78: * On entry, LDA specifies the first dimension of A as declared
! 79: * in the calling (sub) program. LDA must be at least
! 80: * max( 1, n ).
! 81: * Unchanged on exit.
! 82: *
! 83: * X - DOUBLE PRECISION array of dimension at least
! 84: * ( 1 + ( n - 1 )*abs( INCX ) ).
! 85: * Before entry, the incremented array X must contain the n
! 86: * element right-hand side vector b. On exit, X is overwritten
! 87: * with the solution vector x.
! 88: *
! 89: * INCX - INTEGER.
! 90: * On entry, INCX specifies the increment for the elements of
! 91: * X. INCX must not be zero.
! 92: * Unchanged on exit.
! 93: *
! 94: *
! 95: * Level 2 Blas routine.
! 96: *
! 97: * -- Written on 22-October-1986.
! 98: * Jack Dongarra, Argonne National Lab.
! 99: * Jeremy Du Croz, Nag Central Office.
! 100: * Sven Hammarling, Nag Central Office.
! 101: * Richard Hanson, Sandia National Labs.
! 102: *
! 103: * =====================================================================
! 104: *
! 105: * .. Parameters ..
! 106: DOUBLE PRECISION ZERO
! 107: PARAMETER (ZERO=0.0D+0)
! 108: * ..
! 109: * .. Local Scalars ..
! 110: DOUBLE PRECISION TEMP
! 111: INTEGER I,INFO,IX,J,JX,KX
! 112: LOGICAL NOUNIT
! 113: * ..
! 114: * .. External Functions ..
! 115: LOGICAL LSAME
! 116: EXTERNAL LSAME
! 117: * ..
! 118: * .. External Subroutines ..
! 119: EXTERNAL XERBLA
! 120: * ..
! 121: * .. Intrinsic Functions ..
! 122: INTRINSIC MAX
! 123: * ..
! 124: *
! 125: * Test the input parameters.
! 126: *
! 127: INFO = 0
! 128: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
! 129: INFO = 1
! 130: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
! 131: + .NOT.LSAME(TRANS,'C')) THEN
! 132: INFO = 2
! 133: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
! 134: INFO = 3
! 135: ELSE IF (N.LT.0) THEN
! 136: INFO = 4
! 137: ELSE IF (LDA.LT.MAX(1,N)) THEN
! 138: INFO = 6
! 139: ELSE IF (INCX.EQ.0) THEN
! 140: INFO = 8
! 141: END IF
! 142: IF (INFO.NE.0) THEN
! 143: CALL XERBLA('DTRSV ',INFO)
! 144: RETURN
! 145: END IF
! 146: *
! 147: * Quick return if possible.
! 148: *
! 149: IF (N.EQ.0) RETURN
! 150: *
! 151: NOUNIT = LSAME(DIAG,'N')
! 152: *
! 153: * Set up the start point in X if the increment is not unity. This
! 154: * will be ( N - 1 )*INCX too small for descending loops.
! 155: *
! 156: IF (INCX.LE.0) THEN
! 157: KX = 1 - (N-1)*INCX
! 158: ELSE IF (INCX.NE.1) THEN
! 159: KX = 1
! 160: END IF
! 161: *
! 162: * Start the operations. In this version the elements of A are
! 163: * accessed sequentially with one pass through A.
! 164: *
! 165: IF (LSAME(TRANS,'N')) THEN
! 166: *
! 167: * Form x := inv( A )*x.
! 168: *
! 169: IF (LSAME(UPLO,'U')) THEN
! 170: IF (INCX.EQ.1) THEN
! 171: DO 20 J = N,1,-1
! 172: IF (X(J).NE.ZERO) THEN
! 173: IF (NOUNIT) X(J) = X(J)/A(J,J)
! 174: TEMP = X(J)
! 175: DO 10 I = J - 1,1,-1
! 176: X(I) = X(I) - TEMP*A(I,J)
! 177: 10 CONTINUE
! 178: END IF
! 179: 20 CONTINUE
! 180: ELSE
! 181: JX = KX + (N-1)*INCX
! 182: DO 40 J = N,1,-1
! 183: IF (X(JX).NE.ZERO) THEN
! 184: IF (NOUNIT) X(JX) = X(JX)/A(J,J)
! 185: TEMP = X(JX)
! 186: IX = JX
! 187: DO 30 I = J - 1,1,-1
! 188: IX = IX - INCX
! 189: X(IX) = X(IX) - TEMP*A(I,J)
! 190: 30 CONTINUE
! 191: END IF
! 192: JX = JX - INCX
! 193: 40 CONTINUE
! 194: END IF
! 195: ELSE
! 196: IF (INCX.EQ.1) THEN
! 197: DO 60 J = 1,N
! 198: IF (X(J).NE.ZERO) THEN
! 199: IF (NOUNIT) X(J) = X(J)/A(J,J)
! 200: TEMP = X(J)
! 201: DO 50 I = J + 1,N
! 202: X(I) = X(I) - TEMP*A(I,J)
! 203: 50 CONTINUE
! 204: END IF
! 205: 60 CONTINUE
! 206: ELSE
! 207: JX = KX
! 208: DO 80 J = 1,N
! 209: IF (X(JX).NE.ZERO) THEN
! 210: IF (NOUNIT) X(JX) = X(JX)/A(J,J)
! 211: TEMP = X(JX)
! 212: IX = JX
! 213: DO 70 I = J + 1,N
! 214: IX = IX + INCX
! 215: X(IX) = X(IX) - TEMP*A(I,J)
! 216: 70 CONTINUE
! 217: END IF
! 218: JX = JX + INCX
! 219: 80 CONTINUE
! 220: END IF
! 221: END IF
! 222: ELSE
! 223: *
! 224: * Form x := inv( A' )*x.
! 225: *
! 226: IF (LSAME(UPLO,'U')) THEN
! 227: IF (INCX.EQ.1) THEN
! 228: DO 100 J = 1,N
! 229: TEMP = X(J)
! 230: DO 90 I = 1,J - 1
! 231: TEMP = TEMP - A(I,J)*X(I)
! 232: 90 CONTINUE
! 233: IF (NOUNIT) TEMP = TEMP/A(J,J)
! 234: X(J) = TEMP
! 235: 100 CONTINUE
! 236: ELSE
! 237: JX = KX
! 238: DO 120 J = 1,N
! 239: TEMP = X(JX)
! 240: IX = KX
! 241: DO 110 I = 1,J - 1
! 242: TEMP = TEMP - A(I,J)*X(IX)
! 243: IX = IX + INCX
! 244: 110 CONTINUE
! 245: IF (NOUNIT) TEMP = TEMP/A(J,J)
! 246: X(JX) = TEMP
! 247: JX = JX + INCX
! 248: 120 CONTINUE
! 249: END IF
! 250: ELSE
! 251: IF (INCX.EQ.1) THEN
! 252: DO 140 J = N,1,-1
! 253: TEMP = X(J)
! 254: DO 130 I = N,J + 1,-1
! 255: TEMP = TEMP - A(I,J)*X(I)
! 256: 130 CONTINUE
! 257: IF (NOUNIT) TEMP = TEMP/A(J,J)
! 258: X(J) = TEMP
! 259: 140 CONTINUE
! 260: ELSE
! 261: KX = KX + (N-1)*INCX
! 262: JX = KX
! 263: DO 160 J = N,1,-1
! 264: TEMP = X(JX)
! 265: IX = KX
! 266: DO 150 I = N,J + 1,-1
! 267: TEMP = TEMP - A(I,J)*X(IX)
! 268: IX = IX - INCX
! 269: 150 CONTINUE
! 270: IF (NOUNIT) TEMP = TEMP/A(J,J)
! 271: X(JX) = TEMP
! 272: JX = JX - INCX
! 273: 160 CONTINUE
! 274: END IF
! 275: END IF
! 276: END IF
! 277: *
! 278: RETURN
! 279: *
! 280: * End of DTRSV .
! 281: *
! 282: END
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