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annotate libcruft/lapack/cpotf2.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 CPOTF2( UPLO, 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 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 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 * CPOTF2 computes the Cholesky factorization of a complex Hermitian
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19 * positive definite matrix A.
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20 *
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21 * The factorization has the form
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22 * A = U' * U , if UPLO = 'U', or
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23 * A = L * L', if UPLO = 'L',
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24 * where U is an upper triangular matrix and L is lower triangular.
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25 *
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26 * This is the unblocked version of the algorithm, calling Level 2 BLAS.
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27 *
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28 * Arguments
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29 * =========
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30 *
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31 * UPLO (input) CHARACTER*1
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32 * Specifies whether the upper or lower triangular part of the
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33 * Hermitian matrix A is stored.
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34 * = 'U': Upper triangular
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35 * = 'L': Lower triangular
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36 *
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37 * N (input) INTEGER
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38 * The order of the matrix A. N >= 0.
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39 *
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40 * A (input/output) COMPLEX array, dimension (LDA,N)
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41 * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
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42 * n by n upper triangular part of A contains the upper
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43 * triangular part of the matrix A, and the strictly lower
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44 * triangular part of A is not referenced. If UPLO = 'L', the
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45 * leading n by n lower triangular part of A contains the lower
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46 * triangular part of the matrix A, and the strictly upper
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47 * triangular part of A is not referenced.
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48 *
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49 * On exit, if INFO = 0, the factor U or L from the Cholesky
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50 * factorization A = U'*U or A = L*L'.
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51 *
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52 * LDA (input) INTEGER
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53 * The leading dimension of the array A. LDA >= max(1,N).
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54 *
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55 * INFO (output) INTEGER
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56 * = 0: successful exit
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57 * < 0: if INFO = -k, the k-th argument had an illegal value
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58 * > 0: if INFO = k, the leading minor of order k is not
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59 * positive definite, and the factorization could not be
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60 * completed.
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61 *
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62 * =====================================================================
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63 *
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64 * .. Parameters ..
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65 REAL ONE, ZERO
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66 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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67 COMPLEX CONE
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68 PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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69 * ..
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70 * .. Local Scalars ..
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71 LOGICAL UPPER
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72 INTEGER J
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73 REAL AJJ
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74 * ..
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75 * .. External Functions ..
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76 LOGICAL LSAME
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77 COMPLEX CDOTC
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78 EXTERNAL LSAME, CDOTC
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79 * ..
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80 * .. External Subroutines ..
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81 EXTERNAL CGEMV, CLACGV, CSSCAL, XERBLA
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82 * ..
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83 * .. Intrinsic Functions ..
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84 INTRINSIC MAX, REAL, SQRT
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85 * ..
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86 * .. Executable Statements ..
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87 *
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88 * Test the input parameters.
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89 *
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90 INFO = 0
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91 UPPER = LSAME( UPLO, 'U' )
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92 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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93 INFO = -1
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94 ELSE IF( N.LT.0 ) THEN
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95 INFO = -2
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96 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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97 INFO = -4
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98 END IF
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99 IF( INFO.NE.0 ) THEN
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100 CALL XERBLA( 'CPOTF2', -INFO )
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101 RETURN
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102 END IF
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103 *
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104 * Quick return if possible
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105 *
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106 IF( N.EQ.0 )
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107 $ RETURN
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108 *
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109 IF( UPPER ) THEN
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110 *
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111 * Compute the Cholesky factorization A = U'*U.
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112 *
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113 DO 10 J = 1, N
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114 *
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115 * Compute U(J,J) and test for non-positive-definiteness.
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116 *
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117 AJJ = REAL( A( J, J ) ) - CDOTC( J-1, A( 1, J ), 1,
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118 $ A( 1, J ), 1 )
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119 IF( AJJ.LE.ZERO ) THEN
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120 A( J, J ) = AJJ
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121 GO TO 30
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122 END IF
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123 AJJ = SQRT( AJJ )
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124 A( J, J ) = AJJ
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125 *
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126 * Compute elements J+1:N of row J.
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127 *
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128 IF( J.LT.N ) THEN
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129 CALL CLACGV( J-1, A( 1, J ), 1 )
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130 CALL CGEMV( 'Transpose', J-1, N-J, -CONE, A( 1, J+1 ),
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131 $ LDA, A( 1, J ), 1, CONE, A( J, J+1 ), LDA )
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132 CALL CLACGV( J-1, A( 1, J ), 1 )
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133 CALL CSSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
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134 END IF
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135 10 CONTINUE
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136 ELSE
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137 *
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138 * Compute the Cholesky factorization A = L*L'.
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139 *
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140 DO 20 J = 1, N
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141 *
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142 * Compute L(J,J) and test for non-positive-definiteness.
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143 *
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144 AJJ = REAL( A( J, J ) ) - CDOTC( J-1, A( J, 1 ), LDA,
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145 $ A( J, 1 ), LDA )
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146 IF( AJJ.LE.ZERO ) THEN
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147 A( J, J ) = AJJ
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148 GO TO 30
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149 END IF
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150 AJJ = SQRT( AJJ )
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151 A( J, J ) = AJJ
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152 *
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153 * Compute elements J+1:N of column J.
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154 *
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155 IF( J.LT.N ) THEN
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156 CALL CLACGV( J-1, A( J, 1 ), LDA )
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157 CALL CGEMV( 'No transpose', N-J, J-1, -CONE, A( J+1, 1 ),
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158 $ LDA, A( J, 1 ), LDA, CONE, A( J+1, J ), 1 )
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159 CALL CLACGV( J-1, A( J, 1 ), LDA )
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160 CALL CSSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
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161 END IF
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162 20 CONTINUE
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163 END IF
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164 GO TO 40
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165 *
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David Bateman <dbateman@free.fr>
parents:
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166 30 CONTINUE
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parents:
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167 INFO = J
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168 *
82be108cc558 First attempt at single precision tyeps
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169 40 CONTINUE
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170 RETURN
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171 *
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172 * End of CPOTF2
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173 *
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174 END