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1 SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO ) |
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2 * |
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7034
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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 CHARACTER DIAG, UPLO |
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9 INTEGER INFO, LDA, N |
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10 * .. |
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11 * .. Array Arguments .. |
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12 DOUBLE PRECISION A( LDA, * ) |
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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 * DTRTRI computes the inverse of a real upper or lower triangular |
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19 * matrix A. |
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20 * |
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21 * This is the Level 3 BLAS version of the algorithm. |
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22 * |
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23 * Arguments |
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24 * ========= |
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25 * |
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26 * UPLO (input) CHARACTER*1 |
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27 * = 'U': A is upper triangular; |
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28 * = 'L': A is lower triangular. |
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29 * |
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30 * DIAG (input) CHARACTER*1 |
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31 * = 'N': A is non-unit triangular; |
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32 * = 'U': A is unit triangular. |
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33 * |
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34 * N (input) INTEGER |
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35 * The order of the matrix A. N >= 0. |
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36 * |
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37 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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38 * On entry, the triangular matrix A. If UPLO = 'U', the |
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39 * leading N-by-N upper triangular part of the array A contains |
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40 * the upper triangular matrix, and the strictly lower |
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41 * triangular part of A is not referenced. If UPLO = 'L', the |
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42 * leading N-by-N lower triangular part of the array A contains |
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43 * the lower triangular matrix, and the strictly upper |
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44 * triangular part of A is not referenced. If DIAG = 'U', the |
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45 * diagonal elements of A are also not referenced and are |
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46 * assumed to be 1. |
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47 * On exit, the (triangular) inverse of the original matrix, in |
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48 * the same storage format. |
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49 * |
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50 * LDA (input) INTEGER |
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51 * The leading dimension of the array A. LDA >= max(1,N). |
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52 * |
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53 * INFO (output) INTEGER |
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54 * = 0: successful exit |
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55 * < 0: if INFO = -i, the i-th argument had an illegal value |
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56 * > 0: if INFO = i, A(i,i) is exactly zero. The triangular |
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57 * matrix is singular and its inverse can not be computed. |
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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 DOUBLE PRECISION ONE, ZERO |
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63 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
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64 * .. |
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65 * .. Local Scalars .. |
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66 LOGICAL NOUNIT, UPPER |
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67 INTEGER J, JB, NB, NN |
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68 * .. |
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69 * .. External Functions .. |
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70 LOGICAL LSAME |
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71 INTEGER ILAENV |
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72 EXTERNAL LSAME, ILAENV |
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73 * .. |
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74 * .. External Subroutines .. |
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75 EXTERNAL DTRMM, DTRSM, DTRTI2, XERBLA |
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76 * .. |
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77 * .. Intrinsic Functions .. |
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78 INTRINSIC MAX, MIN |
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79 * .. |
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80 * .. Executable Statements .. |
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81 * |
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82 * Test the input parameters. |
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83 * |
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84 INFO = 0 |
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85 UPPER = LSAME( UPLO, 'U' ) |
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86 NOUNIT = LSAME( DIAG, 'N' ) |
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87 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN |
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88 INFO = -1 |
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89 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN |
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90 INFO = -2 |
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91 ELSE IF( N.LT.0 ) THEN |
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92 INFO = -3 |
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93 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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94 INFO = -5 |
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95 END IF |
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96 IF( INFO.NE.0 ) THEN |
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97 CALL XERBLA( 'DTRTRI', -INFO ) |
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98 RETURN |
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99 END IF |
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100 * |
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101 * Quick return if possible |
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102 * |
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103 IF( N.EQ.0 ) |
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104 $ RETURN |
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105 * |
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106 * Check for singularity if non-unit. |
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107 * |
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108 IF( NOUNIT ) THEN |
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109 DO 10 INFO = 1, N |
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110 IF( A( INFO, INFO ).EQ.ZERO ) |
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111 $ RETURN |
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112 10 CONTINUE |
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113 INFO = 0 |
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114 END IF |
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115 * |
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116 * Determine the block size for this environment. |
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117 * |
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118 NB = ILAENV( 1, 'DTRTRI', UPLO // DIAG, N, -1, -1, -1 ) |
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119 IF( NB.LE.1 .OR. NB.GE.N ) THEN |
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120 * |
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121 * Use unblocked code |
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122 * |
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123 CALL DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) |
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124 ELSE |
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125 * |
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126 * Use blocked code |
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127 * |
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128 IF( UPPER ) THEN |
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129 * |
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130 * Compute inverse of upper triangular matrix |
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131 * |
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132 DO 20 J = 1, N, NB |
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133 JB = MIN( NB, N-J+1 ) |
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134 * |
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135 * Compute rows 1:j-1 of current block column |
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136 * |
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137 CALL DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1, |
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138 $ JB, ONE, A, LDA, A( 1, J ), LDA ) |
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139 CALL DTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1, |
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140 $ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA ) |
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141 * |
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142 * Compute inverse of current diagonal block |
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143 * |
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144 CALL DTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO ) |
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145 20 CONTINUE |
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146 ELSE |
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147 * |
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148 * Compute inverse of lower triangular matrix |
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149 * |
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150 NN = ( ( N-1 ) / NB )*NB + 1 |
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151 DO 30 J = NN, 1, -NB |
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152 JB = MIN( NB, N-J+1 ) |
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153 IF( J+JB.LE.N ) THEN |
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154 * |
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155 * Compute rows j+jb:n of current block column |
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156 * |
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157 CALL DTRMM( 'Left', 'Lower', 'No transpose', DIAG, |
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158 $ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA, |
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159 $ A( J+JB, J ), LDA ) |
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160 CALL DTRSM( 'Right', 'Lower', 'No transpose', DIAG, |
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161 $ N-J-JB+1, JB, -ONE, A( J, J ), LDA, |
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162 $ A( J+JB, J ), LDA ) |
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163 END IF |
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164 * |
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165 * Compute inverse of current diagonal block |
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166 * |
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167 CALL DTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO ) |
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168 30 CONTINUE |
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169 END IF |
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170 END IF |
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171 * |
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172 RETURN |
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173 * |
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174 * End of DTRTRI |
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175 * |
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176 END |
