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annotate libcruft/lapack/sgbtrf.f @ 7789:82be108cc558

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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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1 SUBROUTINE SGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )
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2 *
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3 * -- LAPACK routine (version 3.1) --
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4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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5 * November 2006
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6 *
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7 * .. Scalar Arguments ..
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8 INTEGER INFO, KL, KU, LDAB, M, N
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9 * ..
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10 * .. Array Arguments ..
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11 INTEGER IPIV( * )
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12 REAL AB( LDAB, * )
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13 * ..
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14 *
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15 * Purpose
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16 * =======
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17 *
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18 * SGBTRF computes an LU factorization of a real m-by-n band matrix A
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19 * using partial pivoting with row interchanges.
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20 *
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21 * This is the blocked version of the algorithm, calling Level 3 BLAS.
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22 *
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23 * Arguments
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24 * =========
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25 *
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26 * M (input) INTEGER
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27 * The number of rows of the matrix A. M >= 0.
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28 *
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29 * N (input) INTEGER
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30 * The number of columns of the matrix A. N >= 0.
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31 *
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32 * KL (input) INTEGER
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33 * The number of subdiagonals within the band of A. KL >= 0.
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34 *
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35 * KU (input) INTEGER
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36 * The number of superdiagonals within the band of A. KU >= 0.
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37 *
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38 * AB (input/output) REAL array, dimension (LDAB,N)
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39 * On entry, the matrix A in band storage, in rows KL+1 to
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40 * 2*KL+KU+1; rows 1 to KL of the array need not be set.
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41 * The j-th column of A is stored in the j-th column of the
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42 * array AB as follows:
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43 * AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
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44 *
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45 * On exit, details of the factorization: U is stored as an
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46 * upper triangular band matrix with KL+KU superdiagonals in
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47 * rows 1 to KL+KU+1, and the multipliers used during the
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48 * factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
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49 * See below for further details.
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50 *
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51 * LDAB (input) INTEGER
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52 * The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
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53 *
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54 * IPIV (output) INTEGER array, dimension (min(M,N))
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55 * The pivot indices; for 1 <= i <= min(M,N), row i of the
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56 * matrix was interchanged with row IPIV(i).
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57 *
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58 * INFO (output) INTEGER
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59 * = 0: successful exit
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60 * < 0: if INFO = -i, the i-th argument had an illegal value
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61 * > 0: if INFO = +i, U(i,i) is exactly zero. The factorization
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62 * has been completed, but the factor U is exactly
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63 * singular, and division by zero will occur if it is used
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64 * to solve a system of equations.
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65 *
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66 * Further Details
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67 * ===============
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68 *
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69 * The band storage scheme is illustrated by the following example, when
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70 * M = N = 6, KL = 2, KU = 1:
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71 *
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72 * On entry: On exit:
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73 *
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74 * * * * + + + * * * u14 u25 u36
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75 * * * + + + + * * u13 u24 u35 u46
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76 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
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77 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
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78 * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
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79 * a31 a42 a53 a64 * * m31 m42 m53 m64 * *
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80 *
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81 * Array elements marked * are not used by the routine; elements marked
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82 * + need not be set on entry, but are required by the routine to store
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83 * elements of U because of fill-in resulting from the row interchanges.
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84 *
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85 * =====================================================================
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86 *
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87 * .. Parameters ..
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88 REAL ONE, ZERO
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89 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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90 INTEGER NBMAX, LDWORK
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91 PARAMETER ( NBMAX = 64, LDWORK = NBMAX+1 )
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92 * ..
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93 * .. Local Scalars ..
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94 INTEGER I, I2, I3, II, IP, J, J2, J3, JB, JJ, JM, JP,
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95 $ JU, K2, KM, KV, NB, NW
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96 REAL TEMP
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97 * ..
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98 * .. Local Arrays ..
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99 REAL WORK13( LDWORK, NBMAX ),
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100 $ WORK31( LDWORK, NBMAX )
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101 * ..
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102 * .. External Functions ..
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103 INTEGER ILAENV, ISAMAX
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104 EXTERNAL ILAENV, ISAMAX
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105 * ..
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106 * .. External Subroutines ..
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107 EXTERNAL SCOPY, SGBTF2, SGEMM, SGER, SLASWP, SSCAL,
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108 $ SSWAP, STRSM, XERBLA
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109 * ..
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110 * .. Intrinsic Functions ..
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111 INTRINSIC MAX, MIN
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112 * ..
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113 * .. Executable Statements ..
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114 *
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115 * KV is the number of superdiagonals in the factor U, allowing for
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116 * fill-in
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117 *
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118 KV = KU + KL
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119 *
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120 * Test the input parameters.
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121 *
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122 INFO = 0
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123 IF( M.LT.0 ) THEN
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124 INFO = -1
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125 ELSE IF( N.LT.0 ) THEN
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126 INFO = -2
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127 ELSE IF( KL.LT.0 ) THEN
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128 INFO = -3
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129 ELSE IF( KU.LT.0 ) THEN
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130 INFO = -4
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131 ELSE IF( LDAB.LT.KL+KV+1 ) THEN
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132 INFO = -6
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133 END IF
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134 IF( INFO.NE.0 ) THEN
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135 CALL XERBLA( 'SGBTRF', -INFO )
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136 RETURN
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137 END IF
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138 *
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139 * Quick return if possible
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140 *
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141 IF( M.EQ.0 .OR. N.EQ.0 )
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142 $ RETURN
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143 *
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144 * Determine the block size for this environment
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145 *
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146 NB = ILAENV( 1, 'SGBTRF', ' ', M, N, KL, KU )
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147 *
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148 * The block size must not exceed the limit set by the size of the
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149 * local arrays WORK13 and WORK31.
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150 *
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151 NB = MIN( NB, NBMAX )
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152 *
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153 IF( NB.LE.1 .OR. NB.GT.KL ) THEN
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154 *
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155 * Use unblocked code
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156 *
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157 CALL SGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )
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158 ELSE
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159 *
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160 * Use blocked code
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161 *
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162 * Zero the superdiagonal elements of the work array WORK13
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163 *
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164 DO 20 J = 1, NB
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parents:
diff changeset
165 DO 10 I = 1, J - 1
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parents:
diff changeset
166 WORK13( I, J ) = ZERO
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parents:
diff changeset
167 10 CONTINUE
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parents:
diff changeset
168 20 CONTINUE
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parents:
diff changeset
169 *
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parents:
diff changeset
170 * Zero the subdiagonal elements of the work array WORK31
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parents:
diff changeset
171 *
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parents:
diff changeset
172 DO 40 J = 1, NB
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parents:
diff changeset
173 DO 30 I = J + 1, NB
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parents:
diff changeset
174 WORK31( I, J ) = ZERO
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175 30 CONTINUE
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parents:
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176 40 CONTINUE
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parents:
diff changeset
177 *
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parents:
diff changeset
178 * Gaussian elimination with partial pivoting
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parents:
diff changeset
179 *
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diff changeset
180 * Set fill-in elements in columns KU+2 to KV to zero
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parents:
diff changeset
181 *
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parents:
diff changeset
182 DO 60 J = KU + 2, MIN( KV, N )
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parents:
diff changeset
183 DO 50 I = KV - J + 2, KL
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diff changeset
184 AB( I, J ) = ZERO
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parents:
diff changeset
185 50 CONTINUE
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186 60 CONTINUE
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parents:
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187 *
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parents:
diff changeset
188 * JU is the index of the last column affected by the current
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parents:
diff changeset
189 * stage of the factorization
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parents:
diff changeset
190 *
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191 JU = 1
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parents:
diff changeset
192 *
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193 DO 180 J = 1, MIN( M, N ), NB
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194 JB = MIN( NB, MIN( M, N )-J+1 )
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195 *
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diff changeset
196 * The active part of the matrix is partitioned
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197 *
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198 * A11 A12 A13
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199 * A21 A22 A23
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diff changeset
200 * A31 A32 A33
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parents:
diff changeset
201 *
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202 * Here A11, A21 and A31 denote the current block of JB columns
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203 * which is about to be factorized. The number of rows in the
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parents:
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204 * partitioning are JB, I2, I3 respectively, and the numbers
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205 * of columns are JB, J2, J3. The superdiagonal elements of A13
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diff changeset
206 * and the subdiagonal elements of A31 lie outside the band.
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207 *
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208 I2 = MIN( KL-JB, M-J-JB+1 )
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209 I3 = MIN( JB, M-J-KL+1 )
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parents:
diff changeset
210 *
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diff changeset
211 * J2 and J3 are computed after JU has been updated.
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parents:
diff changeset
212 *
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diff changeset
213 * Factorize the current block of JB columns
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parents:
diff changeset
214 *
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215 DO 80 JJ = J, J + JB - 1
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parents:
diff changeset
216 *
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parents:
diff changeset
217 * Set fill-in elements in column JJ+KV to zero
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parents:
diff changeset
218 *
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parents:
diff changeset
219 IF( JJ+KV.LE.N ) THEN
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parents:
diff changeset
220 DO 70 I = 1, KL
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parents:
diff changeset
221 AB( I, JJ+KV ) = ZERO
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222 70 CONTINUE
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parents:
diff changeset
223 END IF
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parents:
diff changeset
224 *
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diff changeset
225 * Find pivot and test for singularity. KM is the number of
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parents:
diff changeset
226 * subdiagonal elements in the current column.
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parents:
diff changeset
227 *
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228 KM = MIN( KL, M-JJ )
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229 JP = ISAMAX( KM+1, AB( KV+1, JJ ), 1 )
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diff changeset
230 IPIV( JJ ) = JP + JJ - J
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diff changeset
231 IF( AB( KV+JP, JJ ).NE.ZERO ) THEN
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232 JU = MAX( JU, MIN( JJ+KU+JP-1, N ) )
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diff changeset
233 IF( JP.NE.1 ) THEN
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parents:
diff changeset
234 *
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parents:
diff changeset
235 * Apply interchange to columns J to J+JB-1
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parents:
diff changeset
236 *
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parents:
diff changeset
237 IF( JP+JJ-1.LT.J+KL ) THEN
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diff changeset
238 *
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diff changeset
239 CALL SSWAP( JB, AB( KV+1+JJ-J, J ), LDAB-1,
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diff changeset
240 $ AB( KV+JP+JJ-J, J ), LDAB-1 )
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parents:
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241 ELSE
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parents:
diff changeset
242 *
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diff changeset
243 * The interchange affects columns J to JJ-1 of A31
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parents:
diff changeset
244 * which are stored in the work array WORK31
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parents:
diff changeset
245 *
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diff changeset
246 CALL SSWAP( JJ-J, AB( KV+1+JJ-J, J ), LDAB-1,
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parents:
diff changeset
247 $ WORK31( JP+JJ-J-KL, 1 ), LDWORK )
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248 CALL SSWAP( J+JB-JJ, AB( KV+1, JJ ), LDAB-1,
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parents:
diff changeset
249 $ AB( KV+JP, JJ ), LDAB-1 )
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parents:
diff changeset
250 END IF
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parents:
diff changeset
251 END IF
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parents:
diff changeset
252 *
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parents:
diff changeset
253 * Compute multipliers
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parents:
diff changeset
254 *
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diff changeset
255 CALL SSCAL( KM, ONE / AB( KV+1, JJ ), AB( KV+2, JJ ),
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parents:
diff changeset
256 $ 1 )
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parents:
diff changeset
257 *
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parents:
diff changeset
258 * Update trailing submatrix within the band and within
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
259 * the current block. JM is the index of the last column
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parents:
diff changeset
260 * which needs to be updated.
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parents:
diff changeset
261 *
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parents:
diff changeset
262 JM = MIN( JU, J+JB-1 )
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parents:
diff changeset
263 IF( JM.GT.JJ )
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parents:
diff changeset
264 $ CALL SGER( KM, JM-JJ, -ONE, AB( KV+2, JJ ), 1,
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parents:
diff changeset
265 $ AB( KV, JJ+1 ), LDAB-1,
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parents:
diff changeset
266 $ AB( KV+1, JJ+1 ), LDAB-1 )
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parents:
diff changeset
267 ELSE
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parents:
diff changeset
268 *
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parents:
diff changeset
269 * If pivot is zero, set INFO to the index of the pivot
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parents:
diff changeset
270 * unless a zero pivot has already been found.
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parents:
diff changeset
271 *
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parents:
diff changeset
272 IF( INFO.EQ.0 )
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parents:
diff changeset
273 $ INFO = JJ
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parents:
diff changeset
274 END IF
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parents:
diff changeset
275 *
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parents:
diff changeset
276 * Copy current column of A31 into the work array WORK31
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parents:
diff changeset
277 *
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parents:
diff changeset
278 NW = MIN( JJ-J+1, I3 )
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parents:
diff changeset
279 IF( NW.GT.0 )
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parents:
diff changeset
280 $ CALL SCOPY( NW, AB( KV+KL+1-JJ+J, JJ ), 1,
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parents:
diff changeset
281 $ WORK31( 1, JJ-J+1 ), 1 )
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parents:
diff changeset
282 80 CONTINUE
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parents:
diff changeset
283 IF( J+JB.LE.N ) THEN
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
284 *
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
285 * Apply the row interchanges to the other blocks.
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parents:
diff changeset
286 *
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parents:
diff changeset
287 J2 = MIN( JU-J+1, KV ) - JB
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parents:
diff changeset
288 J3 = MAX( 0, JU-J-KV+1 )
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parents:
diff changeset
289 *
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parents:
diff changeset
290 * Use SLASWP to apply the row interchanges to A12, A22, and
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
291 * A32.
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
292 *
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parents:
diff changeset
293 CALL SLASWP( J2, AB( KV+1-JB, J+JB ), LDAB-1, 1, JB,
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parents:
diff changeset
294 $ IPIV( J ), 1 )
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
295 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
296 * Adjust the pivot indices.
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
297 *
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parents:
diff changeset
298 DO 90 I = J, J + JB - 1
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parents:
diff changeset
299 IPIV( I ) = IPIV( I ) + J - 1
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parents:
diff changeset
300 90 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
301 *
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
302 * Apply the row interchanges to A13, A23, and A33
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parents:
diff changeset
303 * columnwise.
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
304 *
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parents:
diff changeset
305 K2 = J - 1 + JB + J2
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parents:
diff changeset
306 DO 110 I = 1, J3
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David Bateman <dbateman@free.fr>
parents:
diff changeset
307 JJ = K2 + I
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parents:
diff changeset
308 DO 100 II = J + I - 1, J + JB - 1
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parents:
diff changeset
309 IP = IPIV( II )
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parents:
diff changeset
310 IF( IP.NE.II ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
311 TEMP = AB( KV+1+II-JJ, JJ )
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parents:
diff changeset
312 AB( KV+1+II-JJ, JJ ) = AB( KV+1+IP-JJ, JJ )
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parents:
diff changeset
313 AB( KV+1+IP-JJ, JJ ) = TEMP
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parents:
diff changeset
314 END IF
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parents:
diff changeset
315 100 CONTINUE
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David Bateman <dbateman@free.fr>
parents:
diff changeset
316 110 CONTINUE
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
317 *
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parents:
diff changeset
318 * Update the relevant part of the trailing submatrix
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parents:
diff changeset
319 *
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
320 IF( J2.GT.0 ) THEN
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
321 *
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
322 * Update A12
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parents:
diff changeset
323 *
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
324 CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit',
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
325 $ JB, J2, ONE, AB( KV+1, J ), LDAB-1,
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parents:
diff changeset
326 $ AB( KV+1-JB, J+JB ), LDAB-1 )
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parents:
diff changeset
327 *
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parents:
diff changeset
328 IF( I2.GT.0 ) THEN
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
329 *
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
330 * Update A22
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
331 *
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
332 CALL SGEMM( 'No transpose', 'No transpose', I2, J2,
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parents:
diff changeset
333 $ JB, -ONE, AB( KV+1+JB, J ), LDAB-1,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
334 $ AB( KV+1-JB, J+JB ), LDAB-1, ONE,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
335 $ AB( KV+1, J+JB ), LDAB-1 )
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parents:
diff changeset
336 END IF
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parents:
diff changeset
337 *
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parents:
diff changeset
338 IF( I3.GT.0 ) THEN
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parents:
diff changeset
339 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
340 * Update A32
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David Bateman <dbateman@free.fr>
parents:
diff changeset
341 *
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parents:
diff changeset
342 CALL SGEMM( 'No transpose', 'No transpose', I3, J2,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
343 $ JB, -ONE, WORK31, LDWORK,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
344 $ AB( KV+1-JB, J+JB ), LDAB-1, ONE,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
345 $ AB( KV+KL+1-JB, J+JB ), LDAB-1 )
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parents:
diff changeset
346 END IF
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David Bateman <dbateman@free.fr>
parents:
diff changeset
347 END IF
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parents:
diff changeset
348 *
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parents:
diff changeset
349 IF( J3.GT.0 ) THEN
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parents:
diff changeset
350 *
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parents:
diff changeset
351 * Copy the lower triangle of A13 into the work array
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parents:
diff changeset
352 * WORK13
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David Bateman <dbateman@free.fr>
parents:
diff changeset
353 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
354 DO 130 JJ = 1, J3
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David Bateman <dbateman@free.fr>
parents:
diff changeset
355 DO 120 II = JJ, JB
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David Bateman <dbateman@free.fr>
parents:
diff changeset
356 WORK13( II, JJ ) = AB( II-JJ+1, JJ+J+KV-1 )
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parents:
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357 120 CONTINUE
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parents:
diff changeset
358 130 CONTINUE
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David Bateman <dbateman@free.fr>
parents:
diff changeset
359 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
360 * Update A13 in the work array
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David Bateman <dbateman@free.fr>
parents:
diff changeset
361 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
362 CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit',
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David Bateman <dbateman@free.fr>
parents:
diff changeset
363 $ JB, J3, ONE, AB( KV+1, J ), LDAB-1,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
364 $ WORK13, LDWORK )
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David Bateman <dbateman@free.fr>
parents:
diff changeset
365 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
366 IF( I2.GT.0 ) THEN
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David Bateman <dbateman@free.fr>
parents:
diff changeset
367 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
368 * Update A23
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David Bateman <dbateman@free.fr>
parents:
diff changeset
369 *
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parents:
diff changeset
370 CALL SGEMM( 'No transpose', 'No transpose', I2, J3,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
371 $ JB, -ONE, AB( KV+1+JB, J ), LDAB-1,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
372 $ WORK13, LDWORK, ONE, AB( 1+JB, J+KV ),
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David Bateman <dbateman@free.fr>
parents:
diff changeset
373 $ LDAB-1 )
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David Bateman <dbateman@free.fr>
parents:
diff changeset
374 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
375 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
376 IF( I3.GT.0 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
377 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
378 * Update A33
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David Bateman <dbateman@free.fr>
parents:
diff changeset
379 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
380 CALL SGEMM( 'No transpose', 'No transpose', I3, J3,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
381 $ JB, -ONE, WORK31, LDWORK, WORK13,
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David Bateman <dbateman@free.fr>
parents:
diff changeset
382 $ LDWORK, ONE, AB( 1+KL, J+KV ), LDAB-1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
383 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
384 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
385 * Copy the lower triangle of A13 back into place
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David Bateman <dbateman@free.fr>
parents:
diff changeset
386 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
387 DO 150 JJ = 1, J3
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David Bateman <dbateman@free.fr>
parents:
diff changeset
388 DO 140 II = JJ, JB
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parents:
diff changeset
389 AB( II-JJ+1, JJ+J+KV-1 ) = WORK13( II, JJ )
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parents:
diff changeset
390 140 CONTINUE
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parents:
diff changeset
391 150 CONTINUE
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parents:
diff changeset
392 END IF
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
393 ELSE
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
394 *
82be108cc558 First attempt at single precision tyeps
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parents:
diff changeset
395 * Adjust the pivot indices.
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parents:
diff changeset
396 *
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parents:
diff changeset
397 DO 160 I = J, J + JB - 1
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parents:
diff changeset
398 IPIV( I ) = IPIV( I ) + J - 1
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parents:
diff changeset
399 160 CONTINUE
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parents:
diff changeset
400 END IF
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parents:
diff changeset
401 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
402 * Partially undo the interchanges in the current block to
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
403 * restore the upper triangular form of A31 and copy the upper
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
404 * triangle of A31 back into place
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
405 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
406 DO 170 JJ = J + JB - 1, J, -1
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parents:
diff changeset
407 JP = IPIV( JJ ) - JJ + 1
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parents:
diff changeset
408 IF( JP.NE.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
409 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
410 * Apply interchange to columns J to JJ-1
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David Bateman <dbateman@free.fr>
parents:
diff changeset
411 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
412 IF( JP+JJ-1.LT.J+KL ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
413 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
414 * The interchange does not affect A31
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
415 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
416 CALL SSWAP( JJ-J, AB( KV+1+JJ-J, J ), LDAB-1,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
417 $ AB( KV+JP+JJ-J, J ), LDAB-1 )
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parents:
diff changeset
418 ELSE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
419 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
420 * The interchange does affect A31
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
421 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
422 CALL SSWAP( JJ-J, AB( KV+1+JJ-J, J ), LDAB-1,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
423 $ WORK31( JP+JJ-J-KL, 1 ), LDWORK )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
424 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
425 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
426 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
427 * Copy the current column of A31 back into place
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
428 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
429 NW = MIN( I3, JJ-J+1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
430 IF( NW.GT.0 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
431 $ CALL SCOPY( NW, WORK31( 1, JJ-J+1 ), 1,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
432 $ AB( KV+KL+1-JJ+J, JJ ), 1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
433 170 CONTINUE
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David Bateman <dbateman@free.fr>
parents:
diff changeset
434 180 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
435 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
436 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
437 RETURN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
438 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
439 * End of SGBTRF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
440 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
441 END