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