| 1 | SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) |
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| 2 | * .. Scalar Arguments .. |
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| 3 | INTEGER INCX,K,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 | COMPLEX 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 | * CTBSV solves one of the systems of equations |
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| 14 | * |
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| 15 | * A*x = b, or A'*x = b, or conjg( 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 band matrix, with ( k + 1 ) |
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| 19 | * diagonals. |
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| 20 | * |
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| 21 | * No test for singularity or near-singularity is included in this |
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| 22 | * routine. Such tests must be performed before calling this routine. |
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| 23 | * |
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| 24 | * Arguments |
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| 25 | * ========== |
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| 26 | * |
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| 27 | * UPLO - CHARACTER*1. |
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| 28 | * On entry, UPLO specifies whether the matrix is an upper or |
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| 29 | * lower triangular matrix as follows: |
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| 30 | * |
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| 31 | * UPLO = 'U' or 'u' A is an upper triangular matrix. |
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| 32 | * |
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| 33 | * UPLO = 'L' or 'l' A is a lower triangular matrix. |
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| 34 | * |
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| 35 | * Unchanged on exit. |
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| 36 | * |
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| 37 | * TRANS - CHARACTER*1. |
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| 38 | * On entry, TRANS specifies the equations to be solved as |
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| 39 | * follows: |
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| 40 | * |
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| 41 | * TRANS = 'N' or 'n' A*x = b. |
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| 42 | * |
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| 43 | * TRANS = 'T' or 't' A'*x = b. |
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| 44 | * |
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| 45 | * TRANS = 'C' or 'c' conjg( A' )*x = b. |
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| 46 | * |
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| 47 | * Unchanged on exit. |
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| 48 | * |
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| 49 | * DIAG - CHARACTER*1. |
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| 50 | * On entry, DIAG specifies whether or not A is unit |
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| 51 | * triangular as follows: |
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| 52 | * |
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| 53 | * DIAG = 'U' or 'u' A is assumed to be unit triangular. |
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| 54 | * |
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| 55 | * DIAG = 'N' or 'n' A is not assumed to be unit |
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| 56 | * triangular. |
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| 57 | * |
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| 58 | * Unchanged on exit. |
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| 59 | * |
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| 60 | * N - INTEGER. |
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| 61 | * On entry, N specifies the order of the matrix A. |
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| 62 | * N must be at least zero. |
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| 63 | * Unchanged on exit. |
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| 64 | * |
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| 65 | * K - INTEGER. |
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| 66 | * On entry with UPLO = 'U' or 'u', K specifies the number of |
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| 67 | * super-diagonals of the matrix A. |
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| 68 | * On entry with UPLO = 'L' or 'l', K specifies the number of |
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| 69 | * sub-diagonals of the matrix A. |
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| 70 | * K must satisfy 0 .le. K. |
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| 71 | * Unchanged on exit. |
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| 72 | * |
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| 73 | * A - COMPLEX array of DIMENSION ( LDA, n ). |
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| 74 | * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) |
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| 75 | * by n part of the array A must contain the upper triangular |
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| 76 | * band part of the matrix of coefficients, supplied column by |
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| 77 | * column, with the leading diagonal of the matrix in row |
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| 78 | * ( k + 1 ) of the array, the first super-diagonal starting at |
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| 79 | * position 2 in row k, and so on. The top left k by k triangle |
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| 80 | * of the array A is not referenced. |
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| 81 | * The following program segment will transfer an upper |
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| 82 | * triangular band matrix from conventional full matrix storage |
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| 83 | * to band storage: |
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| 84 | * |
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| 85 | * DO 20, J = 1, N |
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| 86 | * M = K + 1 - J |
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| 87 | * DO 10, I = MAX( 1, J - K ), J |
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| 88 | * A( M + I, J ) = matrix( I, J ) |
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| 89 | * 10 CONTINUE |
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| 90 | * 20 CONTINUE |
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| 91 | * |
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| 92 | * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) |
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| 93 | * by n part of the array A must contain the lower triangular |
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| 94 | * band part of the matrix of coefficients, supplied column by |
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| 95 | * column, with the leading diagonal of the matrix in row 1 of |
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| 96 | * the array, the first sub-diagonal starting at position 1 in |
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| 97 | * row 2, and so on. The bottom right k by k triangle of the |
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| 98 | * array A is not referenced. |
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| 99 | * The following program segment will transfer a lower |
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| 100 | * triangular band matrix from conventional full matrix storage |
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| 101 | * to band storage: |
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| 102 | * |
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| 103 | * DO 20, J = 1, N |
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| 104 | * M = 1 - J |
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| 105 | * DO 10, I = J, MIN( N, J + K ) |
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| 106 | * A( M + I, J ) = matrix( I, J ) |
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| 107 | * 10 CONTINUE |
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| 108 | * 20 CONTINUE |
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| 109 | * |
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| 110 | * Note that when DIAG = 'U' or 'u' the elements of the array A |
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| 111 | * corresponding to the diagonal elements of the matrix are not |
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| 112 | * referenced, but are assumed to be unity. |
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| 113 | * Unchanged on exit. |
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| 114 | * |
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| 115 | * LDA - INTEGER. |
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| 116 | * On entry, LDA specifies the first dimension of A as declared |
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| 117 | * in the calling (sub) program. LDA must be at least |
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| 118 | * ( k + 1 ). |
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| 119 | * Unchanged on exit. |
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| 120 | * |
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| 121 | * X - COMPLEX array of dimension at least |
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| 122 | * ( 1 + ( n - 1 )*abs( INCX ) ). |
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| 123 | * Before entry, the incremented array X must contain the n |
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| 124 | * element right-hand side vector b. On exit, X is overwritten |
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| 125 | * with the solution vector x. |
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| 126 | * |
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| 127 | * INCX - INTEGER. |
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| 128 | * On entry, INCX specifies the increment for the elements of |
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| 129 | * X. INCX must not be zero. |
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| 130 | * Unchanged on exit. |
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| 131 | * |
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| 132 | * |
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| 133 | * Level 2 Blas routine. |
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| 134 | * |
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| 135 | * -- Written on 22-October-1986. |
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| 136 | * Jack Dongarra, Argonne National Lab. |
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| 137 | * Jeremy Du Croz, Nag Central Office. |
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| 138 | * Sven Hammarling, Nag Central Office. |
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| 139 | * Richard Hanson, Sandia National Labs. |
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| 140 | * |
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| 141 | * |
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| 142 | * .. Parameters .. |
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| 143 | COMPLEX ZERO |
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| 144 | PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
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| 145 | * .. |
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| 146 | * .. Local Scalars .. |
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| 147 | COMPLEX TEMP |
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| 148 | INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L |
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| 149 | LOGICAL NOCONJ,NOUNIT |
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| 150 | * .. |
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| 151 | * .. External Functions .. |
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| 152 | LOGICAL LSAME |
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| 153 | EXTERNAL LSAME |
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| 154 | * .. |
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| 155 | * .. External Subroutines .. |
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| 156 | EXTERNAL XERBLA |
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| 157 | * .. |
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| 158 | * .. Intrinsic Functions .. |
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| 159 | INTRINSIC CONJG,MAX,MIN |
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| 160 | * .. |
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| 161 | * |
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| 162 | * Test the input parameters. |
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| 163 | * |
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| 164 | INFO = 0 |
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| 165 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
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| 166 | INFO = 1 |
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| 167 | ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. |
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| 168 | + .NOT.LSAME(TRANS,'C')) THEN |
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| 169 | INFO = 2 |
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| 170 | ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN |
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| 171 | INFO = 3 |
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| 172 | ELSE IF (N.LT.0) THEN |
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| 173 | INFO = 4 |
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| 174 | ELSE IF (K.LT.0) THEN |
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| 175 | INFO = 5 |
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| 176 | ELSE IF (LDA.LT. (K+1)) THEN |
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| 177 | INFO = 7 |
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| 178 | ELSE IF (INCX.EQ.0) THEN |
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| 179 | INFO = 9 |
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| 180 | END IF |
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| 181 | IF (INFO.NE.0) THEN |
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| 182 | CALL XERBLA('CTBSV ',INFO) |
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| 183 | RETURN |
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| 184 | END IF |
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| 185 | * |
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| 186 | * Quick return if possible. |
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| 187 | * |
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| 188 | IF (N.EQ.0) RETURN |
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| 189 | * |
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| 190 | NOCONJ = LSAME(TRANS,'T') |
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| 191 | NOUNIT = LSAME(DIAG,'N') |
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| 192 | * |
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| 193 | * Set up the start point in X if the increment is not unity. This |
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| 194 | * will be ( N - 1 )*INCX too small for descending loops. |
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| 195 | * |
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| 196 | IF (INCX.LE.0) THEN |
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| 197 | KX = 1 - (N-1)*INCX |
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| 198 | ELSE IF (INCX.NE.1) THEN |
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| 199 | KX = 1 |
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| 200 | END IF |
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| 201 | * |
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| 202 | * Start the operations. In this version the elements of A are |
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| 203 | * accessed by sequentially with one pass through A. |
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| 204 | * |
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| 205 | IF (LSAME(TRANS,'N')) THEN |
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| 206 | * |
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| 207 | * Form x := inv( A )*x. |
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| 208 | * |
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| 209 | IF (LSAME(UPLO,'U')) THEN |
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| 210 | KPLUS1 = K + 1 |
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| 211 | IF (INCX.EQ.1) THEN |
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| 212 | DO 20 J = N,1,-1 |
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| 213 | IF (X(J).NE.ZERO) THEN |
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| 214 | L = KPLUS1 - J |
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| 215 | IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J) |
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| 216 | TEMP = X(J) |
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| 217 | DO 10 I = J - 1,MAX(1,J-K),-1 |
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| 218 | X(I) = X(I) - TEMP*A(L+I,J) |
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| 219 | 10 CONTINUE |
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| 220 | END IF |
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| 221 | 20 CONTINUE |
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| 222 | ELSE |
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| 223 | KX = KX + (N-1)*INCX |
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| 224 | JX = KX |
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| 225 | DO 40 J = N,1,-1 |
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| 226 | KX = KX - INCX |
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| 227 | IF (X(JX).NE.ZERO) THEN |
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| 228 | IX = KX |
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| 229 | L = KPLUS1 - J |
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| 230 | IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J) |
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| 231 | TEMP = X(JX) |
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| 232 | DO 30 I = J - 1,MAX(1,J-K),-1 |
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| 233 | X(IX) = X(IX) - TEMP*A(L+I,J) |
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| 234 | IX = IX - INCX |
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| 235 | 30 CONTINUE |
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| 236 | END IF |
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| 237 | JX = JX - INCX |
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| 238 | 40 CONTINUE |
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| 239 | END IF |
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| 240 | ELSE |
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| 241 | IF (INCX.EQ.1) THEN |
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| 242 | DO 60 J = 1,N |
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| 243 | IF (X(J).NE.ZERO) THEN |
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| 244 | L = 1 - J |
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| 245 | IF (NOUNIT) X(J) = X(J)/A(1,J) |
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| 246 | TEMP = X(J) |
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| 247 | DO 50 I = J + 1,MIN(N,J+K) |
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| 248 | X(I) = X(I) - TEMP*A(L+I,J) |
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| 249 | 50 CONTINUE |
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| 250 | END IF |
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| 251 | 60 CONTINUE |
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| 252 | ELSE |
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| 253 | JX = KX |
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| 254 | DO 80 J = 1,N |
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| 255 | KX = KX + INCX |
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| 256 | IF (X(JX).NE.ZERO) THEN |
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| 257 | IX = KX |
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| 258 | L = 1 - J |
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| 259 | IF (NOUNIT) X(JX) = X(JX)/A(1,J) |
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| 260 | TEMP = X(JX) |
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| 261 | DO 70 I = J + 1,MIN(N,J+K) |
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| 262 | X(IX) = X(IX) - TEMP*A(L+I,J) |
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| 263 | IX = IX + INCX |
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| 264 | 70 CONTINUE |
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| 265 | END IF |
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| 266 | JX = JX + INCX |
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| 267 | 80 CONTINUE |
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| 268 | END IF |
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| 269 | END IF |
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| 270 | ELSE |
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| 271 | * |
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| 272 | * Form x := inv( A' )*x or x := inv( conjg( A') )*x. |
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| 273 | * |
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| 274 | IF (LSAME(UPLO,'U')) THEN |
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| 275 | KPLUS1 = K + 1 |
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| 276 | IF (INCX.EQ.1) THEN |
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| 277 | DO 110 J = 1,N |
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| 278 | TEMP = X(J) |
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| 279 | L = KPLUS1 - J |
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| 280 | IF (NOCONJ) THEN |
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| 281 | DO 90 I = MAX(1,J-K),J - 1 |
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| 282 | TEMP = TEMP - A(L+I,J)*X(I) |
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| 283 | 90 CONTINUE |
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| 284 | IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) |
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| 285 | ELSE |
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| 286 | DO 100 I = MAX(1,J-K),J - 1 |
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| 287 | TEMP = TEMP - CONJG(A(L+I,J))*X(I) |
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| 288 | 100 CONTINUE |
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| 289 | IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J)) |
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| 290 | END IF |
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| 291 | X(J) = TEMP |
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| 292 | 110 CONTINUE |
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| 293 | ELSE |
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| 294 | JX = KX |
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| 295 | DO 140 J = 1,N |
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| 296 | TEMP = X(JX) |
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| 297 | IX = KX |
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| 298 | L = KPLUS1 - J |
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| 299 | IF (NOCONJ) THEN |
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| 300 | DO 120 I = MAX(1,J-K),J - 1 |
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| 301 | TEMP = TEMP - A(L+I,J)*X(IX) |
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| 302 | IX = IX + INCX |
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| 303 | 120 CONTINUE |
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| 304 | IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) |
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| 305 | ELSE |
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| 306 | DO 130 I = MAX(1,J-K),J - 1 |
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| 307 | TEMP = TEMP - CONJG(A(L+I,J))*X(IX) |
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| 308 | IX = IX + INCX |
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| 309 | 130 CONTINUE |
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| 310 | IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J)) |
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| 311 | END IF |
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| 312 | X(JX) = TEMP |
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| 313 | JX = JX + INCX |
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| 314 | IF (J.GT.K) KX = KX + INCX |
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| 315 | 140 CONTINUE |
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| 316 | END IF |
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| 317 | ELSE |
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| 318 | IF (INCX.EQ.1) THEN |
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| 319 | DO 170 J = N,1,-1 |
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| 320 | TEMP = X(J) |
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| 321 | L = 1 - J |
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| 322 | IF (NOCONJ) THEN |
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| 323 | DO 150 I = MIN(N,J+K),J + 1,-1 |
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| 324 | TEMP = TEMP - A(L+I,J)*X(I) |
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| 325 | 150 CONTINUE |
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| 326 | IF (NOUNIT) TEMP = TEMP/A(1,J) |
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| 327 | ELSE |
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| 328 | DO 160 I = MIN(N,J+K),J + 1,-1 |
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| 329 | TEMP = TEMP - CONJG(A(L+I,J))*X(I) |
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| 330 | 160 CONTINUE |
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| 331 | IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J)) |
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| 332 | END IF |
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| 333 | X(J) = TEMP |
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| 334 | 170 CONTINUE |
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| 335 | ELSE |
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| 336 | KX = KX + (N-1)*INCX |
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| 337 | JX = KX |
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| 338 | DO 200 J = N,1,-1 |
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| 339 | TEMP = X(JX) |
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| 340 | IX = KX |
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| 341 | L = 1 - J |
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| 342 | IF (NOCONJ) THEN |
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| 343 | DO 180 I = MIN(N,J+K),J + 1,-1 |
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| 344 | TEMP = TEMP - A(L+I,J)*X(IX) |
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| 345 | IX = IX - INCX |
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| 346 | 180 CONTINUE |
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| 347 | IF (NOUNIT) TEMP = TEMP/A(1,J) |
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| 348 | ELSE |
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| 349 | DO 190 I = MIN(N,J+K),J + 1,-1 |
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| 350 | TEMP = TEMP - CONJG(A(L+I,J))*X(IX) |
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| 351 | IX = IX - INCX |
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| 352 | 190 CONTINUE |
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| 353 | IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J)) |
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| 354 | END IF |
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| 355 | X(JX) = TEMP |
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| 356 | JX = JX - INCX |
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| 357 | IF ((N-J).GE.K) KX = KX - INCX |
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| 358 | 200 CONTINUE |
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| 359 | END IF |
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| 360 | END IF |
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| 361 | END IF |
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| 362 | * |
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| 363 | RETURN |
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| 364 | * |
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| 365 | * End of CTBSV . |
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| 366 | * |
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| 367 | END |
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