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

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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7789
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1 SUBROUTINE STRTRI( 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 REAL 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 * STRTRI 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) REAL 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 REAL ONE, ZERO
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63 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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 STRMM, STRSM, STRTI2, 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( 'STRTRI', -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, 'STRTRI', 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 STRTI2( 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 STRMM( '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 STRSM( '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 STRTI2( '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 STRMM( '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 STRSM( '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 STRTI2( '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 STRTRI
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175 *
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176 END