[29] | 1 | |
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| 2 | SUBROUTINE SGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) |
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| 3 | * |
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| 4 | * -- LAPACK driver routine (version 2.0) -- |
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| 5 | * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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| 6 | * Courant Institute, Argonne National Lab, and Rice University |
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| 7 | * March 31, 1993 |
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| 8 | * |
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| 9 | * .. Scalar Arguments .. |
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| 10 | INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS |
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| 11 | * .. |
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| 12 | * .. Array Arguments .. |
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| 13 | INTEGER IPIV( * ) |
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| 14 | REAL AB( LDAB, * ), B( LDB, * ) |
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| 15 | * .. |
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| 16 | * |
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| 17 | * Purpose |
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| 18 | * ======= |
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| 19 | * |
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| 20 | * SGBSV computes the solution to a real system of linear equations |
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| 21 | * A * X = B, where A is a band matrix of order N with KL subdiagonals |
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| 22 | * and KU superdiagonals, and X and B are N-by-NRHS matrices. |
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| 23 | * |
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| 24 | * The LU decomposition with partial pivoting and row interchanges is |
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| 25 | * used to factor A as A = L * U, where L is a product of permutation |
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| 26 | * and unit lower triangular matrices with KL subdiagonals, and U is |
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| 27 | * upper triangular with KL+KU superdiagonals. The factored form of A |
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| 28 | * is then used to solve the system of equations A * X = B. |
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| 29 | * |
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| 30 | * Arguments |
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| 31 | * ========= |
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| 32 | * |
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| 33 | * N (input) INTEGER |
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| 34 | * The number of linear equations, i.e., the order of the |
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| 35 | * matrix A. N >= 0. |
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| 36 | * |
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| 37 | * KL (input) INTEGER |
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| 38 | * The number of subdiagonals within the band of A. KL >= 0. |
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| 39 | * |
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| 40 | * KU (input) INTEGER |
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| 41 | * The number of superdiagonals within the band of A. KU >= 0. |
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| 42 | * |
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| 43 | * NRHS (input) INTEGER |
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| 44 | * The number of right hand sides, i.e., the number of columns |
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| 45 | * of the matrix B. NRHS >= 0. |
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| 46 | * |
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| 47 | * AB (input/output) REAL array, dimension (LDAB,N) |
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| 48 | * On entry, the matrix A in band storage, in rows KL+1 to |
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| 49 | * 2*KL+KU+1; rows 1 to KL of the array need not be set. |
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| 50 | * The j-th column of A is stored in the j-th column of the |
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| 51 | * array AB as follows: |
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| 52 | * AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL) |
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| 53 | * On exit, details of the factorization: U is stored as an |
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| 54 | * upper triangular band matrix with KL+KU superdiagonals in |
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| 55 | * rows 1 to KL+KU+1, and the multipliers used during the |
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| 56 | * factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
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| 57 | * See below for further details. |
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| 58 | * |
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| 59 | * LDAB (input) INTEGER |
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| 60 | * The leading dimension of the array AB. LDAB >= 2*KL+KU+1. |
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| 61 | * |
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| 62 | * IPIV (output) INTEGER array, dimension (N) |
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| 63 | * The pivot indices that define the permutation matrix P; |
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| 64 | * row i of the matrix was interchanged with row IPIV(i). |
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| 65 | * |
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| 66 | * B (input/output) REAL array, dimension (LDB,NRHS) |
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| 67 | * On entry, the N-by-NRHS right hand side matrix B. |
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| 68 | * On exit, if INFO = 0, the N-by-NRHS solution matrix X. |
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| 69 | * |
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| 70 | * LDB (input) INTEGER |
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| 71 | * The leading dimension of the array B. LDB >= max(1,N). |
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| 72 | * |
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| 73 | * INFO (output) INTEGER |
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| 74 | * = 0: successful exit |
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| 75 | * < 0: if INFO = -i, the i-th argument had an illegal value |
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| 76 | * > 0: if INFO = i, U(i,i) is exactly zero. The factorization |
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| 77 | * has been completed, but the factor U is exactly |
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| 78 | * singular, and the solution has not been computed. |
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| 79 | * |
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| 80 | * Further Details |
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| 81 | * =============== |
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| 82 | * |
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| 83 | * The band storage scheme is illustrated by the following example, when |
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| 84 | * M = N = 6, KL = 2, KU = 1: |
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| 85 | * |
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| 86 | * On entry: On exit: |
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| 87 | * |
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| 88 | * * * * + + + * * * u14 u25 u36 |
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| 89 | * * * + + + + * * u13 u24 u35 u46 |
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| 90 | * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 |
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| 91 | * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 |
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| 92 | * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * |
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| 93 | * a31 a42 a53 a64 * * m31 m42 m53 m64 * * |
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| 94 | * |
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| 95 | * Array elements marked * are not used by the routine; elements marked |
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| 96 | * + need not be set on entry, but are required by the routine to store |
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| 97 | * elements of U because of fill-in resulting from the row interchanges. |
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| 98 | * |
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| 99 | * ===================================================================== |
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| 100 | * |
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| 101 | * .. External Subroutines .. |
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| 102 | EXTERNAL SGBTRF, SGBTRS, XERBLA |
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| 103 | * .. |
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| 104 | * .. Intrinsic Functions .. |
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| 105 | INTRINSIC MAX |
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| 106 | * .. |
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| 107 | * .. Executable Statements .. |
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| 108 | * |
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| 109 | * Test the input parameters. |
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| 110 | * |
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| 111 | c write(6,*) 'dans sgbsv' |
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| 112 | c write(6,*) 'n',n,' kl',kl,' ku',ku,' nrhs',nrhs |
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| 113 | c write(6,*) 'ldab',ldab,' ldb',ldb |
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| 114 | INFO = 0 |
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| 115 | IF( N.LT.0 ) THEN |
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| 116 | INFO = -1 |
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| 117 | ELSE IF( KL.LT.0 ) THEN |
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| 118 | INFO = -2 |
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| 119 | ELSE IF( KU.LT.0 ) THEN |
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| 120 | INFO = -3 |
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| 121 | ELSE IF( NRHS.LT.0 ) THEN |
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| 122 | INFO = -4 |
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| 123 | ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN |
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| 124 | INFO = -6 |
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| 125 | ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN |
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| 126 | INFO = -9 |
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| 127 | END IF |
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| 128 | IF( INFO.NE.0 ) THEN |
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| 129 | CALL XERBLA( 'SGBSV ', -INFO ) |
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| 130 | RETURN |
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| 131 | END IF |
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| 132 | * |
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| 133 | * |
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| 134 | * Compute the LU factorization of the band matrix A. |
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| 135 | * |
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| 136 | CALL SGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO ) |
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| 137 | IF( INFO.EQ.0 ) THEN |
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| 138 | * |
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| 139 | * Solve the system A*X = B, overwriting B with X. |
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| 140 | * |
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| 141 | CALL SGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV, |
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| 142 | $ B, LDB, INFO ) |
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| 143 | END IF |
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| 144 | RETURN |
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| 145 | * |
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| 146 | * End of SGBSV |
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| 147 | * |
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| 148 | END |
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| 149 | C ================================================================= |
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| 150 | SUBROUTINE SGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO ) |
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| 151 | * |
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| 152 | * -- LAPACK routine (version 2.0) -- |
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| 153 | * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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| 154 | * Courant Institute, Argonne National Lab, and Rice University |
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| 155 | * February 29, 1992 |
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| 156 | * |
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| 157 | * .. Scalar Arguments .. |
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| 158 | INTEGER INFO, KL, KU, LDAB, M, N |
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| 159 | * .. |
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| 160 | * .. Array Arguments .. |
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| 161 | INTEGER IPIV( * ) |
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| 162 | REAL AB( LDAB, * ) |
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| 163 | * .. |
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| 164 | * |
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| 165 | * Purpose |
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| 166 | * ======= |
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| 167 | * |
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| 168 | * SGBTF2 computes an LU factorization of a real m-by-n band matrix A |
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| 169 | * using partial pivoting with row interchanges. |
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| 170 | * |
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| 171 | * This is the unblocked version of the algorithm, calling Level 2 BLAS. |
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| 172 | * |
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| 173 | * Arguments |
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| 174 | * ========= |
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| 175 | * |
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| 176 | * M (input) INTEGER |
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| 177 | * The number of rows of the matrix A. M >= 0. |
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| 178 | * |
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| 179 | * N (input) INTEGER |
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| 180 | * The number of columns of the matrix A. N >= 0. |
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| 181 | * |
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| 182 | * KL (input) INTEGER |
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| 183 | * The number of subdiagonals within the band of A. KL >= 0. |
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| 184 | * |
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| 185 | * KU (input) INTEGER |
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| 186 | * The number of superdiagonals within the band of A. KU >= 0. |
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| 187 | * |
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| 188 | * AB (input/output) REAL array, dimension (LDAB,N) |
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| 189 | * On entry, the matrix A in band storage, in rows KL+1 to |
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| 190 | * 2*KL+KU+1; rows 1 to KL of the array need not be set. |
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| 191 | * The j-th column of A is stored in the j-th column of the |
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| 192 | * array AB as follows: |
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| 193 | * AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) |
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| 194 | * |
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| 195 | * On exit, details of the factorization: U is stored as an |
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| 196 | * upper triangular band matrix with KL+KU superdiagonals in |
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| 197 | * rows 1 to KL+KU+1, and the multipliers used during the |
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| 198 | * factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
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| 199 | * See below for further details. |
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| 200 | * |
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| 201 | * LDAB (input) INTEGER |
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| 202 | * The leading dimension of the array AB. LDAB >= 2*KL+KU+1. |
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| 203 | * |
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| 204 | * IPIV (output) INTEGER array, dimension (min(M,N)) |
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| 205 | * The pivot indices; for 1 <= i <= min(M,N), row i of the |
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| 206 | * matrix was interchanged with row IPIV(i). |
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| 207 | * |
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| 208 | * INFO (output) INTEGER |
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| 209 | * = 0: successful exit |
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| 210 | * < 0: if INFO = -i, the i-th argument had an illegal value |
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| 211 | * > 0: if INFO = +i, U(i,i) is exactly zero. The factorization |
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| 212 | * has been completed, but the factor U is exactly |
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| 213 | * singular, and division by zero will occur if it is used |
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| 214 | * to solve a system of equations. |
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| 215 | * |
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| 216 | * Further Details |
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| 217 | * =============== |
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| 218 | * |
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| 219 | * The band storage scheme is illustrated by the following example, when |
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| 220 | * M = N = 6, KL = 2, KU = 1: |
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| 221 | * |
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| 222 | * On entry: On exit: |
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| 223 | * |
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| 224 | * * * * + + + * * * u14 u25 u36 |
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| 225 | * * * + + + + * * u13 u24 u35 u46 |
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| 226 | * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 |
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| 227 | * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 |
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| 228 | * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * |
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| 229 | * a31 a42 a53 a64 * * m31 m42 m53 m64 * * |
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| 230 | * |
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| 231 | * Array elements marked * are not used by the routine; elements marked |
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| 232 | * + need not be set on entry, but are required by the routine to store |
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| 233 | * elements of U, because of fill-in resulting from the row |
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| 234 | * interchanges. |
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| 235 | * |
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| 236 | * ===================================================================== |
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| 237 | * |
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| 238 | * .. Parameters .. |
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| 239 | REAL ONE, ZERO |
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| 240 | PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) |
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| 241 | * .. |
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| 242 | * .. Local Scalars .. |
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| 243 | INTEGER I, J, JP, JU, KM, KV |
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| 244 | * .. |
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| 245 | * .. External Functions .. |
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| 246 | INTEGER ISAMAX |
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| 247 | EXTERNAL ISAMAX |
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| 248 | * .. |
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| 249 | * .. External Subroutines .. |
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| 250 | EXTERNAL SGER, SSCAL, SSWAP, XERBLA |
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| 251 | * .. |
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| 252 | * .. Intrinsic Functions .. |
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| 253 | INTRINSIC MAX, MIN |
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| 254 | * .. |
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| 255 | * .. Executable Statements .. |
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| 256 | * |
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| 257 | * KV is the number of superdiagonals in the factor U, allowing for |
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| 258 | * fill-in. |
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| 259 | * |
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| 260 | KV = KU + KL |
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| 261 | * |
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| 262 | * Test the input parameters. |
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| 263 | * |
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| 264 | INFO = 0 |
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| 265 | IF( M.LT.0 ) THEN |
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| 266 | INFO = -1 |
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| 267 | ELSE IF( N.LT.0 ) THEN |
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| 268 | INFO = -2 |
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| 269 | ELSE IF( KL.LT.0 ) THEN |
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| 270 | INFO = -3 |
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| 271 | ELSE IF( KU.LT.0 ) THEN |
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| 272 | INFO = -4 |
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| 273 | ELSE IF( LDAB.LT.KL+KV+1 ) THEN |
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| 274 | INFO = -6 |
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| 275 | END IF |
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| 276 | IF( INFO.NE.0 ) THEN |
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| 277 | CALL XERBLA( 'SGBTF2', -INFO ) |
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| 278 | RETURN |
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| 279 | END IF |
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| 280 | * |
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| 281 | * Quick return if possible |
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| 282 | * |
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| 283 | IF( M.EQ.0 .OR. N.EQ.0 ) |
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| 284 | $ RETURN |
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| 285 | * |
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| 286 | * Gaussian elimination with partial pivoting |
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| 287 | * |
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| 288 | * Set fill-in elements in columns KU+2 to KV to zero. |
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| 289 | * |
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| 290 | DO 20 J = KU + 2, MIN( KV, N ) |
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| 291 | DO 10 I = KV - J + 2, KL |
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| 292 | AB( I, J ) = ZERO |
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| 293 | 10 CONTINUE |
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| 294 | 20 CONTINUE |
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| 295 | * |
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| 296 | * JU is the index of the last column affected by the current stage |
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| 297 | * of the factorization. |
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| 298 | * |
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| 299 | JU = 1 |
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| 300 | * |
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| 301 | DO 40 J = 1, MIN( M, N ) |
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| 302 | * |
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| 303 | * Set fill-in elements in column J+KV to zero. |
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| 304 | * |
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| 305 | IF( J+KV.LE.N ) THEN |
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| 306 | DO 30 I = 1, KL |
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| 307 | AB( I, J+KV ) = ZERO |
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| 308 | 30 CONTINUE |
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| 309 | END IF |
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| 310 | * |
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| 311 | * Find pivot and test for singularity. KM is the number of |
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| 312 | * subdiagonal elements in the current column. |
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| 313 | * |
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| 314 | KM = MIN( KL, M-J ) |
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| 315 | JP = ISAMAX( KM+1, AB( KV+1, J ), 1 ) |
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| 316 | IPIV( J ) = JP + J - 1 |
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| 317 | IF( AB( KV+JP, J ).NE.ZERO ) THEN |
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| 318 | JU = MAX( JU, MIN( J+KU+JP-1, N ) ) |
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| 319 | * |
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| 320 | * Apply interchange to columns J to JU. |
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| 321 | * |
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| 322 | IF( JP.NE.1 ) |
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| 323 | $ CALL SSWAP( JU-J+1, AB( KV+JP, J ), LDAB-1, |
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| 324 | $ AB( KV+1, J ), LDAB-1 ) |
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| 325 | * |
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| 326 | IF( KM.GT.0 ) THEN |
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| 327 | * |
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| 328 | * Compute multipliers. |
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| 329 | * |
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| 330 | CALL SSCAL( KM, ONE / AB( KV+1, J ), AB( KV+2, J ), 1 ) |
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| 331 | * |
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| 332 | * Update trailing submatrix within the band. |
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| 333 | * |
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| 334 | IF( JU.GT.J ) |
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| 335 | $ CALL SGER( KM, JU-J, -ONE, AB( KV+2, J ), 1, |
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| 336 | $ AB( KV, J+1 ), LDAB-1, AB( KV+1, J+1 ), |
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| 337 | $ LDAB-1 ) |
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| 338 | END IF |
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| 339 | ELSE |
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| 340 | * |
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| 341 | * If pivot is zero, set INFO to the index of the pivot |
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| 342 | * unless a zero pivot has already been found. |
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| 343 | * |
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| 344 | IF( INFO.EQ.0 ) |
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| 345 | $ INFO = J |
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| 346 | END IF |
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| 347 | 40 CONTINUE |
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| 348 | RETURN |
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| 349 | * |
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| 350 | * End of SGBTF2 |
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| 351 | * |
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| 352 | END |
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| 353 | |
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| 354 | C ================================================================== |
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| 355 | |
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| 356 | SUBROUTINE SGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO ) |
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| 357 | * |
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| 358 | * -- LAPACK routine (version 2.0) -- |
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| 359 | * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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| 360 | * Courant Institute, Argonne National Lab, and Rice University |
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| 361 | * February 29, 1992 |
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| 362 | * |
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| 363 | * .. Scalar Arguments .. |
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| 364 | INTEGER INFO, KL, KU, LDAB, M, N |
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| 365 | * .. |
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| 366 | * .. Array Arguments .. |
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| 367 | INTEGER IPIV( * ) |
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| 368 | REAL AB( LDAB, * ) |
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| 369 | * .. |
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| 370 | * |
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| 371 | * Purpose |
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| 372 | * ======= |
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| 373 | * |
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| 374 | * SGBTRF computes an LU factorization of a real m-by-n band matrix A |
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| 375 | * using partial pivoting with row interchanges. |
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| 376 | * |
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| 377 | * This is the blocked version of the algorithm, calling Level 3 BLAS. |
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| 378 | * |
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| 379 | * Arguments |
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| 380 | * ========= |
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| 381 | * |
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| 382 | * M (input) INTEGER |
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| 383 | * The number of rows of the matrix A. M >= 0. |
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| 384 | * |
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| 385 | * N (input) INTEGER |
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| 386 | * The number of columns of the matrix A. N >= 0. |
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| 387 | * |
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| 388 | * KL (input) INTEGER |
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| 389 | * The number of subdiagonals within the band of A. KL >= 0. |
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| 390 | * |
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| 391 | * KU (input) INTEGER |
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| 392 | * The number of superdiagonals within the band of A. KU >= 0. |
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| 393 | * |
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| 394 | * AB (input/output) REAL array, dimension (LDAB,N) |
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| 395 | * On entry, the matrix A in band storage, in rows KL+1 to |
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| 396 | * 2*KL+KU+1; rows 1 to KL of the array need not be set. |
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| 397 | * The j-th column of A is stored in the j-th column of the |
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| 398 | * array AB as follows: |
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| 399 | * AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) |
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| 400 | * |
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| 401 | * On exit, details of the factorization: U is stored as an |
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| 402 | * upper triangular band matrix with KL+KU superdiagonals in |
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| 403 | * rows 1 to KL+KU+1, and the multipliers used during the |
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| 404 | * factorization are stored in rows KL+KU+2 to 2*KL+KU+1. |
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| 405 | * See below for further details. |
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| 406 | * |
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| 407 | * LDAB (input) INTEGER |
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| 408 | * The leading dimension of the array AB. LDAB >= 2*KL+KU+1. |
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| 409 | * |
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| 410 | * IPIV (output) INTEGER array, dimension (min(M,N)) |
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| 411 | * The pivot indices; for 1 <= i <= min(M,N), row i of the |
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| 412 | * matrix was interchanged with row IPIV(i). |
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| 413 | * |
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| 414 | * INFO (output) INTEGER |
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| 415 | * = 0: successful exit |
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| 416 | * < 0: if INFO = -i, the i-th argument had an illegal value |
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| 417 | * > 0: if INFO = +i, U(i,i) is exactly zero. The factorization |
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| 418 | * has been completed, but the factor U is exactly |
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| 419 | * singular, and division by zero will occur if it is used |
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| 420 | * to solve a system of equations. |
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| 421 | * |
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| 422 | * Further Details |
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| 423 | * =============== |
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| 424 | * |
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| 425 | * The band storage scheme is illustrated by the following example, when |
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| 426 | * M = N = 6, KL = 2, KU = 1: |
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| 427 | * |
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| 428 | * On entry: On exit: |
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| 429 | * |
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| 430 | * * * * + + + * * * u14 u25 u36 |
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| 431 | * * * + + + + * * u13 u24 u35 u46 |
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| 432 | * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 |
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| 433 | * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 |
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| 434 | * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * |
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| 435 | * a31 a42 a53 a64 * * m31 m42 m53 m64 * * |
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| 436 | * |
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| 437 | * Array elements marked * are not used by the routine; elements marked |
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| 438 | * + need not be set on entry, but are required by the routine to store |
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| 439 | * elements of U because of fill-in resulting from the row interchanges. |
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| 440 | * |
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| 441 | * ===================================================================== |
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| 442 | * |
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| 443 | * .. Parameters .. |
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| 444 | REAL ONE, ZERO |
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| 445 | PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) |
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| 446 | INTEGER NBMAX, LDWORK |
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| 447 | PARAMETER ( NBMAX = 64, LDWORK = NBMAX+1 ) |
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| 448 | * .. |
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| 449 | * .. Local Scalars .. |
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| 450 | INTEGER I, I2, I3, II, IP, J, J2, J3, JB, JJ, JM, JP, |
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| 451 | $ JU, K2, KM, KV, NB, NW |
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| 452 | REAL TEMP |
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| 453 | * .. |
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| 454 | * .. Local Arrays .. |
---|
| 455 | REAL WORK13( LDWORK, NBMAX ), |
---|
| 456 | $ WORK31( LDWORK, NBMAX ) |
---|
| 457 | * .. |
---|
| 458 | * .. External Functions .. |
---|
| 459 | INTEGER ILAENV, ISAMAX |
---|
| 460 | EXTERNAL ILAENV, ISAMAX |
---|
| 461 | * .. |
---|
| 462 | * .. External Subroutines .. |
---|
| 463 | EXTERNAL SCOPY, SGBTF2, SGEMM, SGER, SLASWP, SSCAL, |
---|
| 464 | $ SSWAP, STRSM, XERBLA |
---|
| 465 | * .. |
---|
| 466 | * .. Intrinsic Functions .. |
---|
| 467 | INTRINSIC MAX, MIN |
---|
| 468 | * .. |
---|
| 469 | * .. Executable Statements .. |
---|
| 470 | * |
---|
| 471 | * KV is the number of superdiagonals in the factor U, allowing for |
---|
| 472 | * fill-in |
---|
| 473 | * |
---|
| 474 | KV = KU + KL |
---|
| 475 | * |
---|
| 476 | * Test the input parameters. |
---|
| 477 | * |
---|
| 478 | INFO = 0 |
---|
| 479 | IF( M.LT.0 ) THEN |
---|
| 480 | INFO = -1 |
---|
| 481 | ELSE IF( N.LT.0 ) THEN |
---|
| 482 | INFO = -2 |
---|
| 483 | ELSE IF( KL.LT.0 ) THEN |
---|
| 484 | INFO = -3 |
---|
| 485 | ELSE IF( KU.LT.0 ) THEN |
---|
| 486 | INFO = -4 |
---|
| 487 | ELSE IF( LDAB.LT.KL+KV+1 ) THEN |
---|
| 488 | INFO = -6 |
---|
| 489 | END IF |
---|
| 490 | IF( INFO.NE.0 ) THEN |
---|
| 491 | CALL XERBLA( 'SGBTRF', -INFO ) |
---|
| 492 | RETURN |
---|
| 493 | END IF |
---|
| 494 | * |
---|
| 495 | * Quick return if possible |
---|
| 496 | * |
---|
| 497 | IF( M.EQ.0 .OR. N.EQ.0 ) |
---|
| 498 | $ RETURN |
---|
| 499 | * |
---|
| 500 | * Determine the block size for this environment |
---|
| 501 | * |
---|
| 502 | NB = ILAENV( 1, 'SGBTRF', ' ', M, N, KL, KU ) |
---|
| 503 | * |
---|
| 504 | * The block size must not exceed the limit set by the size of the |
---|
| 505 | * local arrays WORK13 and WORK31. |
---|
| 506 | * |
---|
| 507 | NB = MIN( NB, NBMAX ) |
---|
| 508 | * |
---|
| 509 | IF( NB.LE.1 .OR. NB.GT.KL ) THEN |
---|
| 510 | * |
---|
| 511 | * Use unblocked code |
---|
| 512 | * |
---|
| 513 | CALL SGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO ) |
---|
| 514 | ELSE |
---|
| 515 | * |
---|
| 516 | * Use blocked code |
---|
| 517 | * |
---|
| 518 | * Zero the superdiagonal elements of the work array WORK13 |
---|
| 519 | * |
---|
| 520 | DO 20 J = 1, NB |
---|
| 521 | DO 10 I = 1, J - 1 |
---|
| 522 | WORK13( I, J ) = ZERO |
---|
| 523 | 10 CONTINUE |
---|
| 524 | 20 CONTINUE |
---|
| 525 | * |
---|
| 526 | * Zero the subdiagonal elements of the work array WORK31 |
---|
| 527 | * |
---|
| 528 | DO 40 J = 1, NB |
---|
| 529 | DO 30 I = J + 1, NB |
---|
| 530 | WORK31( I, J ) = ZERO |
---|
| 531 | 30 CONTINUE |
---|
| 532 | 40 CONTINUE |
---|
| 533 | * |
---|
| 534 | * Gaussian elimination with partial pivoting |
---|
| 535 | * |
---|
| 536 | * Set fill-in elements in columns KU+2 to KV to zero |
---|
| 537 | * |
---|
| 538 | DO 60 J = KU + 2, MIN( KV, N ) |
---|
| 539 | DO 50 I = KV - J + 2, KL |
---|
| 540 | AB( I, J ) = ZERO |
---|
| 541 | 50 CONTINUE |
---|
| 542 | 60 CONTINUE |
---|
| 543 | * |
---|
| 544 | * JU is the index of the last column affected by the current |
---|
| 545 | * stage of the factorization |
---|
| 546 | * |
---|
| 547 | JU = 1 |
---|
| 548 | * |
---|
| 549 | DO 180 J = 1, MIN( M, N ), NB |
---|
| 550 | JB = MIN( NB, MIN( M, N )-J+1 ) |
---|
| 551 | * |
---|
| 552 | * The active part of the matrix is partitioned |
---|
| 553 | * |
---|
| 554 | * A11 A12 A13 |
---|
| 555 | * A21 A22 A23 |
---|
| 556 | * A31 A32 A33 |
---|
| 557 | * |
---|
| 558 | * Here A11, A21 and A31 denote the current block of JB columns |
---|
| 559 | * which is about to be factorized. The number of rows in the |
---|
| 560 | * partitioning are JB, I2, I3 respectively, and the numbers |
---|
| 561 | * of columns are JB, J2, J3. The superdiagonal elements of A13 |
---|
| 562 | * and the subdiagonal elements of A31 lie outside the band. |
---|
| 563 | * |
---|
| 564 | I2 = MIN( KL-JB, M-J-JB+1 ) |
---|
| 565 | I3 = MIN( JB, M-J-KL+1 ) |
---|
| 566 | * |
---|
| 567 | * J2 and J3 are computed after JU has been updated. |
---|
| 568 | * |
---|
| 569 | * Factorize the current block of JB columns |
---|
| 570 | * |
---|
| 571 | DO 80 JJ = J, J + JB - 1 |
---|
| 572 | * |
---|
| 573 | * Set fill-in elements in column JJ+KV to zero |
---|
| 574 | * |
---|
| 575 | IF( JJ+KV.LE.N ) THEN |
---|
| 576 | DO 70 I = 1, KL |
---|
| 577 | AB( I, JJ+KV ) = ZERO |
---|
| 578 | 70 CONTINUE |
---|
| 579 | END IF |
---|
| 580 | * |
---|
| 581 | * Find pivot and test for singularity. KM is the number of |
---|
| 582 | * subdiagonal elements in the current column. |
---|
| 583 | * |
---|
| 584 | KM = MIN( KL, M-JJ ) |
---|
| 585 | JP = ISAMAX( KM+1, AB( KV+1, JJ ), 1 ) |
---|
| 586 | IPIV( JJ ) = JP + JJ - J |
---|
| 587 | IF( AB( KV+JP, JJ ).NE.ZERO ) THEN |
---|
| 588 | JU = MAX( JU, MIN( JJ+KU+JP-1, N ) ) |
---|
| 589 | IF( JP.NE.1 ) THEN |
---|
| 590 | * |
---|
| 591 | * Apply interchange to columns J to J+JB-1 |
---|
| 592 | * |
---|
| 593 | IF( JP+JJ-1.LT.J+KL ) THEN |
---|
| 594 | * |
---|
| 595 | CALL SSWAP( JB, AB( KV+1+JJ-J, J ), LDAB-1, |
---|
| 596 | $ AB( KV+JP+JJ-J, J ), LDAB-1 ) |
---|
| 597 | ELSE |
---|
| 598 | * |
---|
| 599 | * The interchange affects columns J to JJ-1 of A31 |
---|
| 600 | * which are stored in the work array WORK31 |
---|
| 601 | * |
---|
| 602 | CALL SSWAP( JJ-J, AB( KV+1+JJ-J, J ), LDAB-1, |
---|
| 603 | $ WORK31( JP+JJ-J-KL, 1 ), LDWORK ) |
---|
| 604 | CALL SSWAP( J+JB-JJ, AB( KV+1, JJ ), LDAB-1, |
---|
| 605 | $ AB( KV+JP, JJ ), LDAB-1 ) |
---|
| 606 | END IF |
---|
| 607 | END IF |
---|
| 608 | * |
---|
| 609 | * Compute multipliers |
---|
| 610 | * |
---|
| 611 | CALL SSCAL( KM, ONE / AB( KV+1, JJ ), AB( KV+2, JJ ), |
---|
| 612 | $ 1 ) |
---|
| 613 | * |
---|
| 614 | * Update trailing submatrix within the band and within |
---|
| 615 | * the current block. JM is the index of the last column |
---|
| 616 | * which needs to be updated. |
---|
| 617 | * |
---|
| 618 | JM = MIN( JU, J+JB-1 ) |
---|
| 619 | IF( JM.GT.JJ ) |
---|
| 620 | $ CALL SGER( KM, JM-JJ, -ONE, AB( KV+2, JJ ), 1, |
---|
| 621 | $ AB( KV, JJ+1 ), LDAB-1, |
---|
| 622 | $ AB( KV+1, JJ+1 ), LDAB-1 ) |
---|
| 623 | ELSE |
---|
| 624 | * |
---|
| 625 | * If pivot is zero, set INFO to the index of the pivot |
---|
| 626 | * unless a zero pivot has already been found. |
---|
| 627 | * |
---|
| 628 | IF( INFO.EQ.0 ) |
---|
| 629 | $ INFO = JJ |
---|
| 630 | END IF |
---|
| 631 | * |
---|
| 632 | * Copy current column of A31 into the work array WORK31 |
---|
| 633 | * |
---|
| 634 | NW = MIN( JJ-J+1, I3 ) |
---|
| 635 | IF( NW.GT.0 ) |
---|
| 636 | $ CALL SCOPY( NW, AB( KV+KL+1-JJ+J, JJ ), 1, |
---|
| 637 | $ WORK31( 1, JJ-J+1 ), 1 ) |
---|
| 638 | 80 CONTINUE |
---|
| 639 | IF( J+JB.LE.N ) THEN |
---|
| 640 | * |
---|
| 641 | * Apply the row interchanges to the other blocks. |
---|
| 642 | * |
---|
| 643 | J2 = MIN( JU-J+1, KV ) - JB |
---|
| 644 | J3 = MAX( 0, JU-J-KV+1 ) |
---|
| 645 | * |
---|
| 646 | * Use SLASWP to apply the row interchanges to A12, A22, and |
---|
| 647 | * A32. |
---|
| 648 | * |
---|
| 649 | CALL SLASWP( J2, AB( KV+1-JB, J+JB ), LDAB-1, 1, JB, |
---|
| 650 | $ IPIV( J ), 1 ) |
---|
| 651 | * |
---|
| 652 | * Adjust the pivot indices. |
---|
| 653 | * |
---|
| 654 | DO 90 I = J, J + JB - 1 |
---|
| 655 | IPIV( I ) = IPIV( I ) + J - 1 |
---|
| 656 | 90 CONTINUE |
---|
| 657 | * |
---|
| 658 | * Apply the row interchanges to A13, A23, and A33 |
---|
| 659 | * columnwise. |
---|
| 660 | * |
---|
| 661 | K2 = J - 1 + JB + J2 |
---|
| 662 | DO 110 I = 1, J3 |
---|
| 663 | JJ = K2 + I |
---|
| 664 | DO 100 II = J + I - 1, J + JB - 1 |
---|
| 665 | IP = IPIV( II ) |
---|
| 666 | IF( IP.NE.II ) THEN |
---|
| 667 | TEMP = AB( KV+1+II-JJ, JJ ) |
---|
| 668 | AB( KV+1+II-JJ, JJ ) = AB( KV+1+IP-JJ, JJ ) |
---|
| 669 | AB( KV+1+IP-JJ, JJ ) = TEMP |
---|
| 670 | END IF |
---|
| 671 | 100 CONTINUE |
---|
| 672 | 110 CONTINUE |
---|
| 673 | * |
---|
| 674 | * Update the relevant part of the trailing submatrix |
---|
| 675 | * |
---|
| 676 | IF( J2.GT.0 ) THEN |
---|
| 677 | * |
---|
| 678 | * Update A12 |
---|
| 679 | * |
---|
| 680 | CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit', |
---|
| 681 | $ JB, J2, ONE, AB( KV+1, J ), LDAB-1, |
---|
| 682 | $ AB( KV+1-JB, J+JB ), LDAB-1 ) |
---|
| 683 | * |
---|
| 684 | IF( I2.GT.0 ) THEN |
---|
| 685 | * |
---|
| 686 | * Update A22 |
---|
| 687 | * |
---|
| 688 | CALL SGEMM( 'No transpose', 'No transpose', I2, J2, |
---|
| 689 | $ JB, -ONE, AB( KV+1+JB, J ), LDAB-1, |
---|
| 690 | $ AB( KV+1-JB, J+JB ), LDAB-1, ONE, |
---|
| 691 | $ AB( KV+1, J+JB ), LDAB-1 ) |
---|
| 692 | END IF |
---|
| 693 | * |
---|
| 694 | IF( I3.GT.0 ) THEN |
---|
| 695 | * |
---|
| 696 | * Update A32 |
---|
| 697 | * |
---|
| 698 | CALL SGEMM( 'No transpose', 'No transpose', I3, J2, |
---|
| 699 | $ JB, -ONE, WORK31, LDWORK, |
---|
| 700 | $ AB( KV+1-JB, J+JB ), LDAB-1, ONE, |
---|
| 701 | $ AB( KV+KL+1-JB, J+JB ), LDAB-1 ) |
---|
| 702 | END IF |
---|
| 703 | END IF |
---|
| 704 | * |
---|
| 705 | IF( J3.GT.0 ) THEN |
---|
| 706 | * |
---|
| 707 | * Copy the lower triangle of A13 into the work array |
---|
| 708 | * WORK13 |
---|
| 709 | * |
---|
| 710 | DO 130 JJ = 1, J3 |
---|
| 711 | DO 120 II = JJ, JB |
---|
| 712 | WORK13( II, JJ ) = AB( II-JJ+1, JJ+J+KV-1 ) |
---|
| 713 | 120 CONTINUE |
---|
| 714 | 130 CONTINUE |
---|
| 715 | * |
---|
| 716 | * Update A13 in the work array |
---|
| 717 | * |
---|
| 718 | CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit', |
---|
| 719 | $ JB, J3, ONE, AB( KV+1, J ), LDAB-1, |
---|
| 720 | $ WORK13, LDWORK ) |
---|
| 721 | * |
---|
| 722 | IF( I2.GT.0 ) THEN |
---|
| 723 | * |
---|
| 724 | * Update A23 |
---|
| 725 | * |
---|
| 726 | CALL SGEMM( 'No transpose', 'No transpose', I2, J3, |
---|
| 727 | $ JB, -ONE, AB( KV+1+JB, J ), LDAB-1, |
---|
| 728 | $ WORK13, LDWORK, ONE, AB( 1+JB, J+KV ), |
---|
| 729 | $ LDAB-1 ) |
---|
| 730 | END IF |
---|
| 731 | * |
---|
| 732 | IF( I3.GT.0 ) THEN |
---|
| 733 | * |
---|
| 734 | * Update A33 |
---|
| 735 | * |
---|
| 736 | CALL SGEMM( 'No transpose', 'No transpose', I3, J3, |
---|
| 737 | $ JB, -ONE, WORK31, LDWORK, WORK13, |
---|
| 738 | $ LDWORK, ONE, AB( 1+KL, J+KV ), LDAB-1 ) |
---|
| 739 | END IF |
---|
| 740 | * |
---|
| 741 | * Copy the lower triangle of A13 back into place |
---|
| 742 | * |
---|
| 743 | DO 150 JJ = 1, J3 |
---|
| 744 | DO 140 II = JJ, JB |
---|
| 745 | AB( II-JJ+1, JJ+J+KV-1 ) = WORK13( II, JJ ) |
---|
| 746 | 140 CONTINUE |
---|
| 747 | 150 CONTINUE |
---|
| 748 | END IF |
---|
| 749 | ELSE |
---|
| 750 | * |
---|
| 751 | * Adjust the pivot indices. |
---|
| 752 | * |
---|
| 753 | DO 160 I = J, J + JB - 1 |
---|
| 754 | IPIV( I ) = IPIV( I ) + J - 1 |
---|
| 755 | 160 CONTINUE |
---|
| 756 | END IF |
---|
| 757 | * |
---|
| 758 | * Partially undo the interchanges in the current block to |
---|
| 759 | * restore the upper triangular form of A31 and copy the upper |
---|
| 760 | * triangle of A31 back into place |
---|
| 761 | * |
---|
| 762 | DO 170 JJ = J + JB - 1, J, -1 |
---|
| 763 | JP = IPIV( JJ ) - JJ + 1 |
---|
| 764 | IF( JP.NE.1 ) THEN |
---|
| 765 | * |
---|
| 766 | * Apply interchange to columns J to JJ-1 |
---|
| 767 | * |
---|
| 768 | IF( JP+JJ-1.LT.J+KL ) THEN |
---|
| 769 | * |
---|
| 770 | * The interchange does not affect A31 |
---|
| 771 | * |
---|
| 772 | CALL SSWAP( JJ-J, AB( KV+1+JJ-J, J ), LDAB-1, |
---|
| 773 | $ AB( KV+JP+JJ-J, J ), LDAB-1 ) |
---|
| 774 | ELSE |
---|
| 775 | * |
---|
| 776 | * The interchange does affect A31 |
---|
| 777 | * |
---|
| 778 | CALL SSWAP( JJ-J, AB( KV+1+JJ-J, J ), LDAB-1, |
---|
| 779 | $ WORK31( JP+JJ-J-KL, 1 ), LDWORK ) |
---|
| 780 | END IF |
---|
| 781 | END IF |
---|
| 782 | * |
---|
| 783 | * Copy the current column of A31 back into place |
---|
| 784 | * |
---|
| 785 | NW = MIN( I3, JJ-J+1 ) |
---|
| 786 | IF( NW.GT.0 ) |
---|
| 787 | $ CALL SCOPY( NW, WORK31( 1, JJ-J+1 ), 1, |
---|
| 788 | $ AB( KV+KL+1-JJ+J, JJ ), 1 ) |
---|
| 789 | 170 CONTINUE |
---|
| 790 | 180 CONTINUE |
---|
| 791 | END IF |
---|
| 792 | * |
---|
| 793 | RETURN |
---|
| 794 | * |
---|
| 795 | * End of SGBTRF |
---|
| 796 | * |
---|
| 797 | END |
---|
| 798 | |
---|
| 799 | C ======================================================================= |
---|
| 800 | |
---|
| 801 | SUBROUTINE SGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, |
---|
| 802 | $ INFO ) |
---|
| 803 | * |
---|
| 804 | * -- LAPACK routine (version 2.0) -- |
---|
| 805 | * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
---|
| 806 | * Courant Institute, Argonne National Lab, and Rice University |
---|
| 807 | * March 31, 1993 |
---|
| 808 | * |
---|
| 809 | * .. Scalar Arguments .. |
---|
| 810 | CHARACTER TRANS |
---|
| 811 | INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS |
---|
| 812 | * .. |
---|
| 813 | * .. Array Arguments .. |
---|
| 814 | INTEGER IPIV( * ) |
---|
| 815 | REAL AB( LDAB, * ), B( LDB, * ) |
---|
| 816 | * .. |
---|
| 817 | * |
---|
| 818 | * Purpose |
---|
| 819 | * ======= |
---|
| 820 | * |
---|
| 821 | * SGBTRS solves a system of linear equations |
---|
| 822 | * A * X = B or A' * X = B |
---|
| 823 | * with a general band matrix A using the LU factorization computed |
---|
| 824 | * by SGBTRF. |
---|
| 825 | * |
---|
| 826 | * Arguments |
---|
| 827 | * ========= |
---|
| 828 | * |
---|
| 829 | * TRANS (input) CHARACTER*1 |
---|
| 830 | * Specifies the form of the system of equations. |
---|
| 831 | * = 'N': A * X = B (No transpose) |
---|
| 832 | * = 'T': A'* X = B (Transpose) |
---|
| 833 | * = 'C': A'* X = B (Conjugate transpose = Transpose) |
---|
| 834 | * |
---|
| 835 | * N (input) INTEGER |
---|
| 836 | * The order of the matrix A. N >= 0. |
---|
| 837 | * |
---|
| 838 | * KL (input) INTEGER |
---|
| 839 | * The number of subdiagonals within the band of A. KL >= 0. |
---|
| 840 | * |
---|
| 841 | * KU (input) INTEGER |
---|
| 842 | * The number of superdiagonals within the band of A. KU >= 0. |
---|
| 843 | * |
---|
| 844 | * NRHS (input) INTEGER |
---|
| 845 | * The number of right hand sides, i.e., the number of columns |
---|
| 846 | * of the matrix B. NRHS >= 0. |
---|
| 847 | * |
---|
| 848 | * AB (input) REAL array, dimension (LDAB,N) |
---|
| 849 | * Details of the LU factorization of the band matrix A, as |
---|
| 850 | * computed by SGBTRF. U is stored as an upper triangular band |
---|
| 851 | * matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and |
---|
| 852 | * the multipliers used during the factorization are stored in |
---|
| 853 | * rows KL+KU+2 to 2*KL+KU+1. |
---|
| 854 | * |
---|
| 855 | * LDAB (input) INTEGER |
---|
| 856 | * The leading dimension of the array AB. LDAB >= 2*KL+KU+1. |
---|
| 857 | * |
---|
| 858 | * IPIV (input) INTEGER array, dimension (N) |
---|
| 859 | * The pivot indices; for 1 <= i <= N, row i of the matrix was |
---|
| 860 | * interchanged with row IPIV(i). |
---|
| 861 | * |
---|
| 862 | * B (input/output) REAL array, dimension (LDB,NRHS) |
---|
| 863 | * On entry, the right hand side matrix B. |
---|
| 864 | * On exit, the solution matrix X. |
---|
| 865 | * |
---|
| 866 | * LDB (input) INTEGER |
---|
| 867 | * The leading dimension of the array B. LDB >= max(1,N). |
---|
| 868 | * |
---|
| 869 | * INFO (output) INTEGER |
---|
| 870 | * = 0: successful exit |
---|
| 871 | * < 0: if INFO = -i, the i-th argument had an illegal value |
---|
| 872 | * |
---|
| 873 | * ===================================================================== |
---|
| 874 | * |
---|
| 875 | * .. Parameters .. |
---|
| 876 | REAL ONE |
---|
| 877 | PARAMETER ( ONE = 1.0E+0 ) |
---|
| 878 | * .. |
---|
| 879 | * .. Local Scalars .. |
---|
| 880 | LOGICAL LNOTI, NOTRAN |
---|
| 881 | INTEGER I, J, KD, L, LM |
---|
| 882 | * .. |
---|
| 883 | * .. External Functions .. |
---|
| 884 | LOGICAL LSAME |
---|
| 885 | EXTERNAL LSAME |
---|
| 886 | * .. |
---|
| 887 | * .. External Subroutines .. |
---|
| 888 | EXTERNAL SGEMV, SGER, SSWAP, STBSV, XERBLA |
---|
| 889 | * .. |
---|
| 890 | * .. Intrinsic Functions .. |
---|
| 891 | INTRINSIC MAX, MIN |
---|
| 892 | * .. |
---|
| 893 | * .. Executable Statements .. |
---|
| 894 | * |
---|
| 895 | * Test the input parameters. |
---|
| 896 | * |
---|
| 897 | INFO = 0 |
---|
| 898 | NOTRAN = LSAME( TRANS, 'N' ) |
---|
| 899 | IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. |
---|
| 900 | $ LSAME( TRANS, 'C' ) ) THEN |
---|
| 901 | INFO = -1 |
---|
| 902 | ELSE IF( N.LT.0 ) THEN |
---|
| 903 | INFO = -2 |
---|
| 904 | ELSE IF( KL.LT.0 ) THEN |
---|
| 905 | INFO = -3 |
---|
| 906 | ELSE IF( KU.LT.0 ) THEN |
---|
| 907 | INFO = -4 |
---|
| 908 | ELSE IF( NRHS.LT.0 ) THEN |
---|
| 909 | INFO = -5 |
---|
| 910 | ELSE IF( LDAB.LT.( 2*KL+KU+1 ) ) THEN |
---|
| 911 | INFO = -7 |
---|
| 912 | ELSE IF( LDB.LT.MAX( 1, N ) ) THEN |
---|
| 913 | INFO = -10 |
---|
| 914 | END IF |
---|
| 915 | IF( INFO.NE.0 ) THEN |
---|
| 916 | CALL XERBLA( 'SGBTRS', -INFO ) |
---|
| 917 | RETURN |
---|
| 918 | END IF |
---|
| 919 | * |
---|
| 920 | * Quick return if possible |
---|
| 921 | * |
---|
| 922 | IF( N.EQ.0 .OR. NRHS.EQ.0 ) |
---|
| 923 | $ RETURN |
---|
| 924 | * |
---|
| 925 | KD = KU + KL + 1 |
---|
| 926 | LNOTI = KL.GT.0 |
---|
| 927 | * |
---|
| 928 | IF( NOTRAN ) THEN |
---|
| 929 | * |
---|
| 930 | * Solve A*X = B. |
---|
| 931 | * |
---|
| 932 | * Solve L*X = B, overwriting B with X. |
---|
| 933 | * |
---|
| 934 | * L is represented as a product of permutations and unit lower |
---|
| 935 | * triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1), |
---|
| 936 | * where each transformation L(i) is a rank-one modification of |
---|
| 937 | * the identity matrix. |
---|
| 938 | * |
---|
| 939 | IF( LNOTI ) THEN |
---|
| 940 | DO 10 J = 1, N - 1 |
---|
| 941 | LM = MIN( KL, N-J ) |
---|
| 942 | L = IPIV( J ) |
---|
| 943 | IF( L.NE.J ) |
---|
| 944 | $ CALL SSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB ) |
---|
| 945 | CALL SGER( LM, NRHS, -ONE, AB( KD+1, J ), 1, B( J, 1 ), |
---|
| 946 | $ LDB, B( J+1, 1 ), LDB ) |
---|
| 947 | 10 CONTINUE |
---|
| 948 | END IF |
---|
| 949 | * |
---|
| 950 | DO 20 I = 1, NRHS |
---|
| 951 | * |
---|
| 952 | * Solve U*X = B, overwriting B with X. |
---|
| 953 | * |
---|
| 954 | CALL STBSV( 'Upper', 'No transpose', 'Non-unit', N, KL+KU, |
---|
| 955 | $ AB, LDAB, B( 1, I ), 1 ) |
---|
| 956 | 20 CONTINUE |
---|
| 957 | * |
---|
| 958 | ELSE |
---|
| 959 | * |
---|
| 960 | * Solve A'*X = B. |
---|
| 961 | * |
---|
| 962 | DO 30 I = 1, NRHS |
---|
| 963 | * |
---|
| 964 | * Solve U'*X = B, overwriting B with X. |
---|
| 965 | * |
---|
| 966 | CALL STBSV( 'Upper', 'Transpose', 'Non-unit', N, KL+KU, AB, |
---|
| 967 | $ LDAB, B( 1, I ), 1 ) |
---|
| 968 | 30 CONTINUE |
---|
| 969 | * |
---|
| 970 | * Solve L'*X = B, overwriting B with X. |
---|
| 971 | * |
---|
| 972 | IF( LNOTI ) THEN |
---|
| 973 | DO 40 J = N - 1, 1, -1 |
---|
| 974 | LM = MIN( KL, N-J ) |
---|
| 975 | CALL SGEMV( 'Transpose', LM, NRHS, -ONE, B( J+1, 1 ), |
---|
| 976 | $ LDB, AB( KD+1, J ), 1, ONE, B( J, 1 ), LDB ) |
---|
| 977 | L = IPIV( J ) |
---|
| 978 | IF( L.NE.J ) |
---|
| 979 | $ CALL SSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB ) |
---|
| 980 | 40 CONTINUE |
---|
| 981 | END IF |
---|
| 982 | END IF |
---|
| 983 | RETURN |
---|
| 984 | * |
---|
| 985 | * End of SGBTRS |
---|
| 986 | * |
---|
| 987 | END |
---|
| 988 | C ======================================================================= |
---|
| 989 | SUBROUTINE SLASWP( N, A, LDA, K1, K2, IPIV, INCX ) |
---|
| 990 | * |
---|
| 991 | * -- LAPACK auxiliary routine (version 2.0) -- |
---|
| 992 | * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
---|
| 993 | * Courant Institute, Argonne National Lab, and Rice University |
---|
| 994 | * October 31, 1992 |
---|
| 995 | * |
---|
| 996 | * .. Scalar Arguments .. |
---|
| 997 | INTEGER INCX, K1, K2, LDA, N |
---|
| 998 | * .. |
---|
| 999 | * .. Array Arguments .. |
---|
| 1000 | INTEGER IPIV( * ) |
---|
| 1001 | REAL A( LDA, * ) |
---|
| 1002 | * .. |
---|
| 1003 | * |
---|
| 1004 | * Purpose |
---|
| 1005 | * ======= |
---|
| 1006 | * |
---|
| 1007 | * SLASWP performs a series of row interchanges on the matrix A. |
---|
| 1008 | * One row interchange is initiated for each of rows K1 through K2 of A. |
---|
| 1009 | * |
---|
| 1010 | * Arguments |
---|
| 1011 | * ========= |
---|
| 1012 | * |
---|
| 1013 | * N (input) INTEGER |
---|
| 1014 | * The number of columns of the matrix A. |
---|
| 1015 | * |
---|
| 1016 | * A (input/output) REAL array, dimension (LDA,N) |
---|
| 1017 | * On entry, the matrix of column dimension N to which the row |
---|
| 1018 | * interchanges will be applied. |
---|
| 1019 | * On exit, the permuted matrix. |
---|
| 1020 | * |
---|
| 1021 | * LDA (input) INTEGER |
---|
| 1022 | * The leading dimension of the array A. |
---|
| 1023 | * |
---|
| 1024 | * K1 (input) INTEGER |
---|
| 1025 | * The first element of IPIV for which a row interchange will |
---|
| 1026 | * be done. |
---|
| 1027 | * |
---|
| 1028 | * K2 (input) INTEGER |
---|
| 1029 | * The last element of IPIV for which a row interchange will |
---|
| 1030 | * be done. |
---|
| 1031 | * |
---|
| 1032 | * IPIV (input) INTEGER array, dimension (M*abs(INCX)) |
---|
| 1033 | * The vector of pivot indices. Only the elements in positions |
---|
| 1034 | * K1 through K2 of IPIV are accessed. |
---|
| 1035 | * IPIV(K) = L implies rows K and L are to be interchanged. |
---|
| 1036 | * |
---|
| 1037 | * INCX (input) INTEGER |
---|
| 1038 | * The increment between successive values of IPIV. If IPIV |
---|
| 1039 | * is negative, the pivots are applied in reverse order. |
---|
| 1040 | * |
---|
| 1041 | * ===================================================================== |
---|
| 1042 | * |
---|
| 1043 | * .. Local Scalars .. |
---|
| 1044 | INTEGER I, IP, IX |
---|
| 1045 | * .. |
---|
| 1046 | * .. External Subroutines .. |
---|
| 1047 | EXTERNAL SSWAP |
---|
| 1048 | * .. |
---|
| 1049 | * .. Executable Statements .. |
---|
| 1050 | * |
---|
| 1051 | * Interchange row I with row IPIV(I) for each of rows K1 through K2. |
---|
| 1052 | * |
---|
| 1053 | IF( INCX.EQ.0 ) |
---|
| 1054 | $ RETURN |
---|
| 1055 | IF( INCX.GT.0 ) THEN |
---|
| 1056 | IX = K1 |
---|
| 1057 | ELSE |
---|
| 1058 | IX = 1 + ( 1-K2 )*INCX |
---|
| 1059 | END IF |
---|
| 1060 | IF( INCX.EQ.1 ) THEN |
---|
| 1061 | DO 10 I = K1, K2 |
---|
| 1062 | IP = IPIV( I ) |
---|
| 1063 | IF( IP.NE.I ) |
---|
| 1064 | $ CALL SSWAP( N, A( I, 1 ), LDA, A( IP, 1 ), LDA ) |
---|
| 1065 | 10 CONTINUE |
---|
| 1066 | ELSE IF( INCX.GT.1 ) THEN |
---|
| 1067 | DO 20 I = K1, K2 |
---|
| 1068 | IP = IPIV( IX ) |
---|
| 1069 | IF( IP.NE.I ) |
---|
| 1070 | $ CALL SSWAP( N, A( I, 1 ), LDA, A( IP, 1 ), LDA ) |
---|
| 1071 | IX = IX + INCX |
---|
| 1072 | 20 CONTINUE |
---|
| 1073 | ELSE IF( INCX.LT.0 ) THEN |
---|
| 1074 | DO 30 I = K2, K1, -1 |
---|
| 1075 | IP = IPIV( IX ) |
---|
| 1076 | IF( IP.NE.I ) |
---|
| 1077 | $ CALL SSWAP( N, A( I, 1 ), LDA, A( IP, 1 ), LDA ) |
---|
| 1078 | IX = IX + INCX |
---|
| 1079 | 30 CONTINUE |
---|
| 1080 | END IF |
---|
| 1081 | * |
---|
| 1082 | RETURN |
---|
| 1083 | * |
---|
| 1084 | * End of SLASWP |
---|
| 1085 | * |
---|
| 1086 | END |
---|
| 1087 | C ===================================================================== |
---|
| 1088 | INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, |
---|
| 1089 | $ N4 ) |
---|
| 1090 | * |
---|
| 1091 | * -- LAPACK auxiliary routine (version 2.0) -- |
---|
| 1092 | * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
---|
| 1093 | * Courant Institute, Argonne National Lab, and Rice University |
---|
| 1094 | * September 30, 1994 |
---|
| 1095 | * |
---|
| 1096 | * .. Scalar Arguments .. |
---|
| 1097 | CHARACTER*( * ) NAME, OPTS |
---|
| 1098 | INTEGER ISPEC, N1, N2, N3, N4 |
---|
| 1099 | * .. |
---|
| 1100 | * |
---|
| 1101 | * Purpose |
---|
| 1102 | * ======= |
---|
| 1103 | * |
---|
| 1104 | * ILAENV is called from the LAPACK routines to choose problem-dependent |
---|
| 1105 | * parameters for the local environment. See ISPEC for a description of |
---|
| 1106 | * the parameters. |
---|
| 1107 | * |
---|
| 1108 | * This version provides a set of parameters which should give good, |
---|
| 1109 | * but not optimal, performance on many of the currently available |
---|
| 1110 | * computers. Users are encouraged to modify this subroutine to set |
---|
| 1111 | * the tuning parameters for their particular machine using the option |
---|
| 1112 | * and problem size information in the arguments. |
---|
| 1113 | * |
---|
| 1114 | * This routine will not function correctly if it is converted to all |
---|
| 1115 | * lower case. Converting it to all upper case is allowed. |
---|
| 1116 | * |
---|
| 1117 | * Arguments |
---|
| 1118 | * ========= |
---|
| 1119 | * |
---|
| 1120 | * ISPEC (input) INTEGER |
---|
| 1121 | * Specifies the parameter to be returned as the value of |
---|
| 1122 | * ILAENV. |
---|
| 1123 | * = 1: the optimal blocksize; if this value is 1, an unblocked |
---|
| 1124 | * algorithm will give the best performance. |
---|
| 1125 | * = 2: the minimum block size for which the block routine |
---|
| 1126 | * should be used; if the usable block size is less than |
---|
| 1127 | * this value, an unblocked routine should be used. |
---|
| 1128 | * = 3: the crossover point (in a block routine, for N less |
---|
| 1129 | * than this value, an unblocked routine should be used) |
---|
| 1130 | * = 4: the number of shifts, used in the nonsymmetric |
---|
| 1131 | * eigenvalue routines |
---|
| 1132 | * = 5: the minimum column dimension for blocking to be used; |
---|
| 1133 | * rectangular blocks must have dimension at least k by m, |
---|
| 1134 | * where k is given by ILAENV(2,...) and m by ILAENV(5,...) |
---|
| 1135 | * = 6: the crossover point for the SVD (when reducing an m by n |
---|
| 1136 | * matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds |
---|
| 1137 | * this value, a QR factorization is used first to reduce |
---|
| 1138 | * the matrix to a triangular form.) |
---|
| 1139 | * = 7: the number of processors |
---|
| 1140 | * = 8: the crossover point for the multishift QR and QZ methods |
---|
| 1141 | * for nonsymmetric eigenvalue problems. |
---|
| 1142 | * |
---|
| 1143 | * NAME (input) CHARACTER*(*) |
---|
| 1144 | * The name of the calling subroutine, in either upper case or |
---|
| 1145 | * lower case. |
---|
| 1146 | * |
---|
| 1147 | * OPTS (input) CHARACTER*(*) |
---|
| 1148 | * The character options to the subroutine NAME, concatenated |
---|
| 1149 | * into a single character string. For example, UPLO = 'U', |
---|
| 1150 | * TRANS = 'T', and DIAG = 'N' for a triangular routine would |
---|
| 1151 | * be specified as OPTS = 'UTN'. |
---|
| 1152 | * |
---|
| 1153 | * N1 (input) INTEGER |
---|
| 1154 | * N2 (input) INTEGER |
---|
| 1155 | * N3 (input) INTEGER |
---|
| 1156 | * N4 (input) INTEGER |
---|
| 1157 | * Problem dimensions for the subroutine NAME; these may not all |
---|
| 1158 | * be required. |
---|
| 1159 | * |
---|
| 1160 | * (ILAENV) (output) INTEGER |
---|
| 1161 | * >= 0: the value of the parameter specified by ISPEC |
---|
| 1162 | * < 0: if ILAENV = -k, the k-th argument had an illegal value. |
---|
| 1163 | * |
---|
| 1164 | * Further Details |
---|
| 1165 | * =============== |
---|
| 1166 | * |
---|
| 1167 | * The following conventions have been used when calling ILAENV from the |
---|
| 1168 | * LAPACK routines: |
---|
| 1169 | * 1) OPTS is a concatenation of all of the character options to |
---|
| 1170 | * subroutine NAME, in the same order that they appear in the |
---|
| 1171 | * argument list for NAME, even if they are not used in determining |
---|
| 1172 | * the value of the parameter specified by ISPEC. |
---|
| 1173 | * 2) The problem dimensions N1, N2, N3, N4 are specified in the order |
---|
| 1174 | * that they appear in the argument list for NAME. N1 is used |
---|
| 1175 | * first, N2 second, and so on, and unused problem dimensions are |
---|
| 1176 | * passed a value of -1. |
---|
| 1177 | * 3) The parameter value returned by ILAENV is checked for validity in |
---|
| 1178 | * the calling subroutine. For example, ILAENV is used to retrieve |
---|
| 1179 | * the optimal blocksize for STRTRI as follows: |
---|
| 1180 | * |
---|
| 1181 | * NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) |
---|
| 1182 | * IF( NB.LE.1 ) NB = MAX( 1, N ) |
---|
| 1183 | * |
---|
| 1184 | * ===================================================================== |
---|
| 1185 | * |
---|
| 1186 | * .. Local Scalars .. |
---|
| 1187 | LOGICAL CNAME, SNAME |
---|
| 1188 | CHARACTER*1 C1 |
---|
| 1189 | CHARACTER*2 C2, C4 |
---|
| 1190 | CHARACTER*3 C3 |
---|
| 1191 | CHARACTER*6 SUBNAM |
---|
| 1192 | INTEGER I, IC, IZ, NB, NBMIN, NX |
---|
| 1193 | * .. |
---|
| 1194 | * .. Intrinsic Functions .. |
---|
| 1195 | INTRINSIC CHAR, ICHAR, INT, MIN, REAL |
---|
| 1196 | * .. |
---|
| 1197 | * .. Executable Statements .. |
---|
| 1198 | * |
---|
| 1199 | GO TO ( 100, 100, 100, 400, 500, 600, 700, 800 ) ISPEC |
---|
| 1200 | * |
---|
| 1201 | * Invalid value for ISPEC |
---|
| 1202 | * |
---|
| 1203 | ILAENV = -1 |
---|
| 1204 | RETURN |
---|
| 1205 | * |
---|
| 1206 | 100 CONTINUE |
---|
| 1207 | * |
---|
| 1208 | * Convert NAME to upper case if the first character is lower case. |
---|
| 1209 | * |
---|
| 1210 | ILAENV = 1 |
---|
| 1211 | SUBNAM = NAME |
---|
| 1212 | IC = ICHAR( SUBNAM( 1:1 ) ) |
---|
| 1213 | IZ = ICHAR( 'Z' ) |
---|
| 1214 | IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN |
---|
| 1215 | * |
---|
| 1216 | * ASCII character set |
---|
| 1217 | * |
---|
| 1218 | IF( IC.GE.97 .AND. IC.LE.122 ) THEN |
---|
| 1219 | SUBNAM( 1:1 ) = CHAR( IC-32 ) |
---|
| 1220 | DO 10 I = 2, 6 |
---|
| 1221 | IC = ICHAR( SUBNAM( I:I ) ) |
---|
| 1222 | IF( IC.GE.97 .AND. IC.LE.122 ) |
---|
| 1223 | $ SUBNAM( I:I ) = CHAR( IC-32 ) |
---|
| 1224 | 10 CONTINUE |
---|
| 1225 | END IF |
---|
| 1226 | * |
---|
| 1227 | ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN |
---|
| 1228 | * |
---|
| 1229 | * EBCDIC character set |
---|
| 1230 | * |
---|
| 1231 | IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. |
---|
| 1232 | $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. |
---|
| 1233 | $ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN |
---|
| 1234 | SUBNAM( 1:1 ) = CHAR( IC+64 ) |
---|
| 1235 | DO 20 I = 2, 6 |
---|
| 1236 | IC = ICHAR( SUBNAM( I:I ) ) |
---|
| 1237 | IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. |
---|
| 1238 | $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. |
---|
| 1239 | $ ( IC.GE.162 .AND. IC.LE.169 ) ) |
---|
| 1240 | $ SUBNAM( I:I ) = CHAR( IC+64 ) |
---|
| 1241 | 20 CONTINUE |
---|
| 1242 | END IF |
---|
| 1243 | * |
---|
| 1244 | ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN |
---|
| 1245 | * |
---|
| 1246 | * Prime machines: ASCII+128 |
---|
| 1247 | * |
---|
| 1248 | IF( IC.GE.225 .AND. IC.LE.250 ) THEN |
---|
| 1249 | SUBNAM( 1:1 ) = CHAR( IC-32 ) |
---|
| 1250 | DO 30 I = 2, 6 |
---|
| 1251 | IC = ICHAR( SUBNAM( I:I ) ) |
---|
| 1252 | IF( IC.GE.225 .AND. IC.LE.250 ) |
---|
| 1253 | $ SUBNAM( I:I ) = CHAR( IC-32 ) |
---|
| 1254 | 30 CONTINUE |
---|
| 1255 | END IF |
---|
| 1256 | END IF |
---|
| 1257 | * |
---|
| 1258 | C1 = SUBNAM( 1:1 ) |
---|
| 1259 | SNAME = C1.EQ.'S' .OR. C1.EQ.'D' |
---|
| 1260 | CNAME = C1.EQ.'C' .OR. C1.EQ.'Z' |
---|
| 1261 | IF( .NOT.( CNAME .OR. SNAME ) ) |
---|
| 1262 | $ RETURN |
---|
| 1263 | C2 = SUBNAM( 2:3 ) |
---|
| 1264 | C3 = SUBNAM( 4:6 ) |
---|
| 1265 | C4 = C3( 2:3 ) |
---|
| 1266 | * |
---|
| 1267 | GO TO ( 110, 200, 300 ) ISPEC |
---|
| 1268 | * |
---|
| 1269 | 110 CONTINUE |
---|
| 1270 | * |
---|
| 1271 | * ISPEC = 1: block size |
---|
| 1272 | * |
---|
| 1273 | * In these examples, separate code is provided for setting NB for |
---|
| 1274 | * real and complex. We assume that NB will take the same value in |
---|
| 1275 | * single or double precision. |
---|
| 1276 | * |
---|
| 1277 | NB = 1 |
---|
| 1278 | * |
---|
| 1279 | IF( C2.EQ.'GE' ) THEN |
---|
| 1280 | IF( C3.EQ.'TRF' ) THEN |
---|
| 1281 | IF( SNAME ) THEN |
---|
| 1282 | NB = 64 |
---|
| 1283 | ELSE |
---|
| 1284 | NB = 64 |
---|
| 1285 | END IF |
---|
| 1286 | ELSE IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. |
---|
| 1287 | $ C3.EQ.'QLF' ) THEN |
---|
| 1288 | IF( SNAME ) THEN |
---|
| 1289 | NB = 32 |
---|
| 1290 | ELSE |
---|
| 1291 | NB = 32 |
---|
| 1292 | END IF |
---|
| 1293 | ELSE IF( C3.EQ.'HRD' ) THEN |
---|
| 1294 | IF( SNAME ) THEN |
---|
| 1295 | NB = 32 |
---|
| 1296 | ELSE |
---|
| 1297 | NB = 32 |
---|
| 1298 | END IF |
---|
| 1299 | ELSE IF( C3.EQ.'BRD' ) THEN |
---|
| 1300 | IF( SNAME ) THEN |
---|
| 1301 | NB = 32 |
---|
| 1302 | ELSE |
---|
| 1303 | NB = 32 |
---|
| 1304 | END IF |
---|
| 1305 | ELSE IF( C3.EQ.'TRI' ) THEN |
---|
| 1306 | IF( SNAME ) THEN |
---|
| 1307 | NB = 64 |
---|
| 1308 | ELSE |
---|
| 1309 | NB = 64 |
---|
| 1310 | END IF |
---|
| 1311 | END IF |
---|
| 1312 | ELSE IF( C2.EQ.'PO' ) THEN |
---|
| 1313 | IF( C3.EQ.'TRF' ) THEN |
---|
| 1314 | IF( SNAME ) THEN |
---|
| 1315 | NB = 64 |
---|
| 1316 | ELSE |
---|
| 1317 | NB = 64 |
---|
| 1318 | END IF |
---|
| 1319 | END IF |
---|
| 1320 | ELSE IF( C2.EQ.'SY' ) THEN |
---|
| 1321 | IF( C3.EQ.'TRF' ) THEN |
---|
| 1322 | IF( SNAME ) THEN |
---|
| 1323 | NB = 64 |
---|
| 1324 | ELSE |
---|
| 1325 | NB = 64 |
---|
| 1326 | END IF |
---|
| 1327 | ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN |
---|
| 1328 | NB = 1 |
---|
| 1329 | ELSE IF( SNAME .AND. C3.EQ.'GST' ) THEN |
---|
| 1330 | NB = 64 |
---|
| 1331 | END IF |
---|
| 1332 | ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN |
---|
| 1333 | IF( C3.EQ.'TRF' ) THEN |
---|
| 1334 | NB = 64 |
---|
| 1335 | ELSE IF( C3.EQ.'TRD' ) THEN |
---|
| 1336 | NB = 1 |
---|
| 1337 | ELSE IF( C3.EQ.'GST' ) THEN |
---|
| 1338 | NB = 64 |
---|
| 1339 | END IF |
---|
| 1340 | ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN |
---|
| 1341 | IF( C3( 1:1 ).EQ.'G' ) THEN |
---|
| 1342 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1343 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1344 | $ C4.EQ.'BR' ) THEN |
---|
| 1345 | NB = 32 |
---|
| 1346 | END IF |
---|
| 1347 | ELSE IF( C3( 1:1 ).EQ.'M' ) THEN |
---|
| 1348 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1349 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1350 | $ C4.EQ.'BR' ) THEN |
---|
| 1351 | NB = 32 |
---|
| 1352 | END IF |
---|
| 1353 | END IF |
---|
| 1354 | ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN |
---|
| 1355 | IF( C3( 1:1 ).EQ.'G' ) THEN |
---|
| 1356 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1357 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1358 | $ C4.EQ.'BR' ) THEN |
---|
| 1359 | NB = 32 |
---|
| 1360 | END IF |
---|
| 1361 | ELSE IF( C3( 1:1 ).EQ.'M' ) THEN |
---|
| 1362 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1363 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1364 | $ C4.EQ.'BR' ) THEN |
---|
| 1365 | NB = 32 |
---|
| 1366 | END IF |
---|
| 1367 | END IF |
---|
| 1368 | ELSE IF( C2.EQ.'GB' ) THEN |
---|
| 1369 | IF( C3.EQ.'TRF' ) THEN |
---|
| 1370 | IF( SNAME ) THEN |
---|
| 1371 | IF( N4.LE.64 ) THEN |
---|
| 1372 | NB = 1 |
---|
| 1373 | ELSE |
---|
| 1374 | NB = 32 |
---|
| 1375 | END IF |
---|
| 1376 | ELSE |
---|
| 1377 | IF( N4.LE.64 ) THEN |
---|
| 1378 | NB = 1 |
---|
| 1379 | ELSE |
---|
| 1380 | NB = 32 |
---|
| 1381 | END IF |
---|
| 1382 | END IF |
---|
| 1383 | END IF |
---|
| 1384 | ELSE IF( C2.EQ.'PB' ) THEN |
---|
| 1385 | IF( C3.EQ.'TRF' ) THEN |
---|
| 1386 | IF( SNAME ) THEN |
---|
| 1387 | IF( N2.LE.64 ) THEN |
---|
| 1388 | NB = 1 |
---|
| 1389 | ELSE |
---|
| 1390 | NB = 32 |
---|
| 1391 | END IF |
---|
| 1392 | ELSE |
---|
| 1393 | IF( N2.LE.64 ) THEN |
---|
| 1394 | NB = 1 |
---|
| 1395 | ELSE |
---|
| 1396 | NB = 32 |
---|
| 1397 | END IF |
---|
| 1398 | END IF |
---|
| 1399 | END IF |
---|
| 1400 | ELSE IF( C2.EQ.'TR' ) THEN |
---|
| 1401 | IF( C3.EQ.'TRI' ) THEN |
---|
| 1402 | IF( SNAME ) THEN |
---|
| 1403 | NB = 64 |
---|
| 1404 | ELSE |
---|
| 1405 | NB = 64 |
---|
| 1406 | END IF |
---|
| 1407 | END IF |
---|
| 1408 | ELSE IF( C2.EQ.'LA' ) THEN |
---|
| 1409 | IF( C3.EQ.'UUM' ) THEN |
---|
| 1410 | IF( SNAME ) THEN |
---|
| 1411 | NB = 64 |
---|
| 1412 | ELSE |
---|
| 1413 | NB = 64 |
---|
| 1414 | END IF |
---|
| 1415 | END IF |
---|
| 1416 | ELSE IF( SNAME .AND. C2.EQ.'ST' ) THEN |
---|
| 1417 | IF( C3.EQ.'EBZ' ) THEN |
---|
| 1418 | NB = 1 |
---|
| 1419 | END IF |
---|
| 1420 | END IF |
---|
| 1421 | ILAENV = NB |
---|
| 1422 | RETURN |
---|
| 1423 | * |
---|
| 1424 | 200 CONTINUE |
---|
| 1425 | * |
---|
| 1426 | * ISPEC = 2: minimum block size |
---|
| 1427 | * |
---|
| 1428 | NBMIN = 2 |
---|
| 1429 | IF( C2.EQ.'GE' ) THEN |
---|
| 1430 | IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. |
---|
| 1431 | $ C3.EQ.'QLF' ) THEN |
---|
| 1432 | IF( SNAME ) THEN |
---|
| 1433 | NBMIN = 2 |
---|
| 1434 | ELSE |
---|
| 1435 | NBMIN = 2 |
---|
| 1436 | END IF |
---|
| 1437 | ELSE IF( C3.EQ.'HRD' ) THEN |
---|
| 1438 | IF( SNAME ) THEN |
---|
| 1439 | NBMIN = 2 |
---|
| 1440 | ELSE |
---|
| 1441 | NBMIN = 2 |
---|
| 1442 | END IF |
---|
| 1443 | ELSE IF( C3.EQ.'BRD' ) THEN |
---|
| 1444 | IF( SNAME ) THEN |
---|
| 1445 | NBMIN = 2 |
---|
| 1446 | ELSE |
---|
| 1447 | NBMIN = 2 |
---|
| 1448 | END IF |
---|
| 1449 | ELSE IF( C3.EQ.'TRI' ) THEN |
---|
| 1450 | IF( SNAME ) THEN |
---|
| 1451 | NBMIN = 2 |
---|
| 1452 | ELSE |
---|
| 1453 | NBMIN = 2 |
---|
| 1454 | END IF |
---|
| 1455 | END IF |
---|
| 1456 | ELSE IF( C2.EQ.'SY' ) THEN |
---|
| 1457 | IF( C3.EQ.'TRF' ) THEN |
---|
| 1458 | IF( SNAME ) THEN |
---|
| 1459 | NBMIN = 8 |
---|
| 1460 | ELSE |
---|
| 1461 | NBMIN = 8 |
---|
| 1462 | END IF |
---|
| 1463 | ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN |
---|
| 1464 | NBMIN = 2 |
---|
| 1465 | END IF |
---|
| 1466 | ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN |
---|
| 1467 | IF( C3.EQ.'TRD' ) THEN |
---|
| 1468 | NBMIN = 2 |
---|
| 1469 | END IF |
---|
| 1470 | ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN |
---|
| 1471 | IF( C3( 1:1 ).EQ.'G' ) THEN |
---|
| 1472 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1473 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1474 | $ C4.EQ.'BR' ) THEN |
---|
| 1475 | NBMIN = 2 |
---|
| 1476 | END IF |
---|
| 1477 | ELSE IF( C3( 1:1 ).EQ.'M' ) THEN |
---|
| 1478 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1479 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1480 | $ C4.EQ.'BR' ) THEN |
---|
| 1481 | NBMIN = 2 |
---|
| 1482 | END IF |
---|
| 1483 | END IF |
---|
| 1484 | ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN |
---|
| 1485 | IF( C3( 1:1 ).EQ.'G' ) THEN |
---|
| 1486 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1487 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1488 | $ C4.EQ.'BR' ) THEN |
---|
| 1489 | NBMIN = 2 |
---|
| 1490 | END IF |
---|
| 1491 | ELSE IF( C3( 1:1 ).EQ.'M' ) THEN |
---|
| 1492 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1493 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1494 | $ C4.EQ.'BR' ) THEN |
---|
| 1495 | NBMIN = 2 |
---|
| 1496 | END IF |
---|
| 1497 | END IF |
---|
| 1498 | END IF |
---|
| 1499 | ILAENV = NBMIN |
---|
| 1500 | RETURN |
---|
| 1501 | * |
---|
| 1502 | 300 CONTINUE |
---|
| 1503 | * |
---|
| 1504 | * ISPEC = 3: crossover point |
---|
| 1505 | * |
---|
| 1506 | NX = 0 |
---|
| 1507 | IF( C2.EQ.'GE' ) THEN |
---|
| 1508 | IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. |
---|
| 1509 | $ C3.EQ.'QLF' ) THEN |
---|
| 1510 | IF( SNAME ) THEN |
---|
| 1511 | NX = 128 |
---|
| 1512 | ELSE |
---|
| 1513 | NX = 128 |
---|
| 1514 | END IF |
---|
| 1515 | ELSE IF( C3.EQ.'HRD' ) THEN |
---|
| 1516 | IF( SNAME ) THEN |
---|
| 1517 | NX = 128 |
---|
| 1518 | ELSE |
---|
| 1519 | NX = 128 |
---|
| 1520 | END IF |
---|
| 1521 | ELSE IF( C3.EQ.'BRD' ) THEN |
---|
| 1522 | IF( SNAME ) THEN |
---|
| 1523 | NX = 128 |
---|
| 1524 | ELSE |
---|
| 1525 | NX = 128 |
---|
| 1526 | END IF |
---|
| 1527 | END IF |
---|
| 1528 | ELSE IF( C2.EQ.'SY' ) THEN |
---|
| 1529 | IF( SNAME .AND. C3.EQ.'TRD' ) THEN |
---|
| 1530 | NX = 1 |
---|
| 1531 | END IF |
---|
| 1532 | ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN |
---|
| 1533 | IF( C3.EQ.'TRD' ) THEN |
---|
| 1534 | NX = 1 |
---|
| 1535 | END IF |
---|
| 1536 | ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN |
---|
| 1537 | IF( C3( 1:1 ).EQ.'G' ) THEN |
---|
| 1538 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1539 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1540 | $ C4.EQ.'BR' ) THEN |
---|
| 1541 | NX = 128 |
---|
| 1542 | END IF |
---|
| 1543 | END IF |
---|
| 1544 | ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN |
---|
| 1545 | IF( C3( 1:1 ).EQ.'G' ) THEN |
---|
| 1546 | IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. |
---|
| 1547 | $ C4.EQ.'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. |
---|
| 1548 | $ C4.EQ.'BR' ) THEN |
---|
| 1549 | NX = 128 |
---|
| 1550 | END IF |
---|
| 1551 | END IF |
---|
| 1552 | END IF |
---|
| 1553 | ILAENV = NX |
---|
| 1554 | RETURN |
---|
| 1555 | * |
---|
| 1556 | 400 CONTINUE |
---|
| 1557 | * |
---|
| 1558 | * ISPEC = 4: number of shifts (used by xHSEQR) |
---|
| 1559 | * |
---|
| 1560 | ILAENV = 6 |
---|
| 1561 | RETURN |
---|
| 1562 | * |
---|
| 1563 | 500 CONTINUE |
---|
| 1564 | * |
---|
| 1565 | * ISPEC = 5: minimum column dimension (not used) |
---|
| 1566 | * |
---|
| 1567 | ILAENV = 2 |
---|
| 1568 | RETURN |
---|
| 1569 | * |
---|
| 1570 | 600 CONTINUE |
---|
| 1571 | * |
---|
| 1572 | * ISPEC = 6: crossover point for SVD (used by xGELSS and xGESVD) |
---|
| 1573 | * |
---|
| 1574 | ILAENV = INT( REAL( MIN( N1, N2 ) )*1.6E0 ) |
---|
| 1575 | RETURN |
---|
| 1576 | * |
---|
| 1577 | 700 CONTINUE |
---|
| 1578 | * |
---|
| 1579 | * ISPEC = 7: number of processors (not used) |
---|
| 1580 | * |
---|
| 1581 | ILAENV = 1 |
---|
| 1582 | RETURN |
---|
| 1583 | * |
---|
| 1584 | 800 CONTINUE |
---|
| 1585 | * |
---|
| 1586 | * ISPEC = 8: crossover point for multishift (used by xHSEQR) |
---|
| 1587 | * |
---|
| 1588 | ILAENV = 50 |
---|
| 1589 | RETURN |
---|
| 1590 | * |
---|
| 1591 | * End of ILAENV |
---|
| 1592 | * |
---|
| 1593 | END |
---|
| 1594 | |
---|