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1 SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO ) |
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2 * |
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3 * -- LAPACK routine (version 2.0) -- |
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4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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5 * Courant Institute, Argonne National Lab, and Rice University |
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6 * September 30, 1994 |
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7 * |
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8 * .. Scalar Arguments .. |
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9 INTEGER INFO, LDA, M, N |
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10 * .. |
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11 * .. Array Arguments .. |
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12 INTEGER IPIV( * ) |
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13 COMPLEX*16 A( LDA, * ) |
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14 * .. |
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15 * |
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16 * Purpose |
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17 * ======= |
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18 * |
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19 * ZGETRF computes an LU factorization of a general M-by-N matrix A |
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20 * using partial pivoting with row interchanges. |
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21 * |
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22 * The factorization has the form |
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23 * A = P * L * U |
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24 * where P is a permutation matrix, L is lower triangular with unit |
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25 * diagonal elements (lower trapezoidal if m > n), and U is upper |
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26 * triangular (upper trapezoidal if m < n). |
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27 * |
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28 * This is the right-looking Level 3 BLAS version of the algorithm. |
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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 * M (input) INTEGER |
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34 * The number of rows of the matrix A. M >= 0. |
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35 * |
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36 * N (input) INTEGER |
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37 * The number of columns of the matrix A. N >= 0. |
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38 * |
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39 * A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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40 * On entry, the M-by-N matrix to be factored. |
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41 * On exit, the factors L and U from the factorization |
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42 * A = P*L*U; the unit diagonal elements of L are not stored. |
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43 * |
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44 * LDA (input) INTEGER |
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45 * The leading dimension of the array A. LDA >= max(1,M). |
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46 * |
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47 * IPIV (output) INTEGER array, dimension (min(M,N)) |
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48 * The pivot indices; for 1 <= i <= min(M,N), row i of the |
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49 * matrix was interchanged with row IPIV(i). |
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50 * |
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51 * INFO (output) INTEGER |
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52 * = 0: successful exit |
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53 * < 0: if INFO = -i, the i-th argument had an illegal value |
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54 * > 0: if INFO = i, U(i,i) is exactly zero. The factorization |
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55 * has been completed, but the factor U is exactly |
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56 * singular, and division by zero will occur if it is used |
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57 * to solve a system of equations. |
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58 * |
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59 * ===================================================================== |
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60 * |
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61 * .. Parameters .. |
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62 COMPLEX*16 ONE |
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63 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) |
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64 * .. |
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65 * .. Local Scalars .. |
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66 INTEGER I, IINFO, J, JB, NB |
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67 * .. |
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68 * .. External Subroutines .. |
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69 EXTERNAL XERBLA, ZGEMM, ZGETF2, ZLASWP, ZTRSM |
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70 * .. |
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71 * .. External Functions .. |
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72 INTEGER ILAENV |
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73 EXTERNAL ILAENV |
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74 * .. |
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75 * .. Intrinsic Functions .. |
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76 INTRINSIC MAX, MIN |
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77 * .. |
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78 * .. Executable Statements .. |
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79 * |
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80 * Test the input parameters. |
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81 * |
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82 INFO = 0 |
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83 IF( M.LT.0 ) THEN |
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84 INFO = -1 |
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85 ELSE IF( N.LT.0 ) THEN |
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86 INFO = -2 |
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87 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN |
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88 INFO = -4 |
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89 END IF |
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90 IF( INFO.NE.0 ) THEN |
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91 CALL XERBLA( 'ZGETRF', -INFO ) |
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92 RETURN |
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93 END IF |
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94 * |
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95 * Quick return if possible |
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96 * |
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97 IF( M.EQ.0 .OR. N.EQ.0 ) |
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98 $ RETURN |
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99 * |
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100 * Determine the block size for this environment. |
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101 * |
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102 NB = ILAENV( 1, 'ZGETRF', ' ', M, N, -1, -1 ) |
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103 IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN |
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104 * |
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105 * Use unblocked code. |
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106 * |
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107 CALL ZGETF2( M, N, A, LDA, IPIV, INFO ) |
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108 ELSE |
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109 * |
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110 * Use blocked code. |
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111 * |
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112 DO 20 J = 1, MIN( M, N ), NB |
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113 JB = MIN( MIN( M, N )-J+1, NB ) |
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114 * |
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115 * Factor diagonal and subdiagonal blocks and test for exact |
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116 * singularity. |
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117 * |
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118 CALL ZGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO ) |
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119 * |
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120 * Adjust INFO and the pivot indices. |
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121 * |
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122 IF( INFO.EQ.0 .AND. IINFO.GT.0 ) |
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123 $ INFO = IINFO + J - 1 |
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124 DO 10 I = J, MIN( M, J+JB-1 ) |
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125 IPIV( I ) = J - 1 + IPIV( I ) |
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126 10 CONTINUE |
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127 * |
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128 * Apply interchanges to columns 1:J-1. |
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129 * |
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130 CALL ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) |
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131 * |
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132 IF( J+JB.LE.N ) THEN |
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133 * |
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134 * Apply interchanges to columns J+JB:N. |
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135 * |
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136 CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, |
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137 $ IPIV, 1 ) |
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138 * |
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139 * Compute block row of U. |
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140 * |
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141 CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, |
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142 $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ), |
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143 $ LDA ) |
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144 IF( J+JB.LE.M ) THEN |
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145 * |
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146 * Update trailing submatrix. |
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147 * |
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148 CALL ZGEMM( 'No transpose', 'No transpose', M-J-JB+1, |
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149 $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA, |
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150 $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ), |
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151 $ LDA ) |
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152 END IF |
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153 END IF |
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154 20 CONTINUE |
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155 END IF |
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156 RETURN |
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157 * |
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158 * End of ZGETRF |
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159 * |
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160 END |
