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1 SUBROUTINE ZTRTI2( UPLO, DIAG, N, A, LDA, 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 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 COMPLEX*16 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 * ZTRTI2 computes the inverse of a complex upper or lower triangular |
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19 * matrix. |
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20 * |
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21 * This is the Level 2 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 * Specifies whether the matrix A is upper or lower triangular. |
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28 * = 'U': Upper triangular |
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29 * = 'L': Lower triangular |
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30 * |
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31 * DIAG (input) CHARACTER*1 |
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32 * Specifies whether or not the matrix A is unit triangular. |
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33 * = 'N': Non-unit triangular |
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34 * = 'U': Unit triangular |
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35 * |
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36 * N (input) INTEGER |
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37 * The order 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 triangular matrix A. If UPLO = 'U', the |
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41 * leading n by n upper triangular part of the array A contains |
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42 * the upper triangular matrix, and the strictly lower |
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43 * triangular part of A is not referenced. If UPLO = 'L', the |
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44 * leading n by n lower triangular part of the array A contains |
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45 * the lower triangular matrix, and the strictly upper |
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46 * triangular part of A is not referenced. If DIAG = 'U', the |
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47 * diagonal elements of A are also not referenced and are |
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48 * assumed to be 1. |
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49 * |
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50 * On exit, the (triangular) inverse of the original matrix, in |
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51 * the same storage format. |
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52 * |
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53 * LDA (input) INTEGER |
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54 * The leading dimension of the array A. LDA >= max(1,N). |
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55 * |
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56 * INFO (output) INTEGER |
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57 * = 0: successful exit |
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58 * < 0: if INFO = -k, the k-th argument had an illegal value |
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59 * |
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60 * ===================================================================== |
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61 * |
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62 * .. Parameters .. |
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63 COMPLEX*16 ONE |
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64 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) |
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65 * .. |
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66 * .. Local Scalars .. |
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67 LOGICAL NOUNIT, UPPER |
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68 INTEGER J |
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69 COMPLEX*16 AJJ |
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70 * .. |
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71 * .. External Functions .. |
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72 LOGICAL LSAME |
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73 EXTERNAL LSAME |
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74 * .. |
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75 * .. External Subroutines .. |
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76 EXTERNAL XERBLA, ZSCAL, ZTRMV |
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77 * .. |
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78 * .. Intrinsic Functions .. |
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79 INTRINSIC MAX |
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80 * .. |
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81 * .. Executable Statements .. |
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82 * |
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83 * Test the input parameters. |
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84 * |
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85 INFO = 0 |
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86 UPPER = LSAME( UPLO, 'U' ) |
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87 NOUNIT = LSAME( DIAG, 'N' ) |
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88 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN |
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89 INFO = -1 |
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90 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN |
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91 INFO = -2 |
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92 ELSE IF( N.LT.0 ) THEN |
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93 INFO = -3 |
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94 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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95 INFO = -5 |
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96 END IF |
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97 IF( INFO.NE.0 ) THEN |
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98 CALL XERBLA( 'ZTRTI2', -INFO ) |
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99 RETURN |
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100 END IF |
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101 * |
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102 IF( UPPER ) THEN |
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103 * |
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104 * Compute inverse of upper triangular matrix. |
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105 * |
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106 DO 10 J = 1, N |
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107 IF( NOUNIT ) THEN |
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108 A( J, J ) = ONE / A( J, J ) |
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109 AJJ = -A( J, J ) |
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110 ELSE |
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111 AJJ = -ONE |
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112 END IF |
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113 * |
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114 * Compute elements 1:j-1 of j-th column. |
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115 * |
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116 CALL ZTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA, |
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117 $ A( 1, J ), 1 ) |
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118 CALL ZSCAL( J-1, AJJ, A( 1, J ), 1 ) |
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119 10 CONTINUE |
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120 ELSE |
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121 * |
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122 * Compute inverse of lower triangular matrix. |
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123 * |
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124 DO 20 J = N, 1, -1 |
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125 IF( NOUNIT ) THEN |
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126 A( J, J ) = ONE / A( J, J ) |
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127 AJJ = -A( J, J ) |
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128 ELSE |
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129 AJJ = -ONE |
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130 END IF |
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131 IF( J.LT.N ) THEN |
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132 * |
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133 * Compute elements j+1:n of j-th column. |
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134 * |
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135 CALL ZTRMV( 'Lower', 'No transpose', DIAG, N-J, |
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136 $ A( J+1, J+1 ), LDA, A( J+1, J ), 1 ) |
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137 CALL ZSCAL( N-J, AJJ, A( J+1, J ), 1 ) |
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138 END IF |
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139 20 CONTINUE |
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140 END IF |
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141 * |
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142 RETURN |
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143 * |
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144 * End of ZTRTI2 |
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145 * |
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146 END |
