annotate libcruft/lapack/spotf2.f @ 5301:9302581b820d ss-2-9-2

[project @ 2005-04-22 17:08:07 by jwe]
author jwe
date Fri, 22 Apr 2005 17:09:11 +0000
parents d53c33d93440
children 68db500cb558
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1 SUBROUTINE SPOTF2( UPLO, N, A, LDA, INFO )
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2 *
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3 * -- LAPACK routine (version 3.0) --
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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 * February 29, 1992
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7 *
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8 * .. Scalar Arguments ..
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9 CHARACTER UPLO
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10 INTEGER INFO, LDA, N
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11 * ..
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12 * .. Array Arguments ..
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13 REAL 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 * SPOTF2 computes the Cholesky factorization of a real symmetric
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20 * positive definite matrix A.
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21 *
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22 * The factorization has the form
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23 * A = U' * U , if UPLO = 'U', or
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24 * A = L * L', if UPLO = 'L',
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25 * where U is an upper triangular matrix and L is lower triangular.
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26 *
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27 * This is the unblocked version of the algorithm, calling Level 2 BLAS.
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28 *
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29 * Arguments
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30 * =========
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31 *
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32 * UPLO (input) CHARACTER*1
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33 * Specifies whether the upper or lower triangular part of the
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34 * symmetric matrix A is stored.
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35 * = 'U': Upper triangular
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36 * = 'L': Lower triangular
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37 *
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38 * N (input) INTEGER
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39 * The order of the matrix A. N >= 0.
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40 *
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41 * A (input/output) REAL array, dimension (LDA,N)
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42 * On entry, the symmetric matrix A. If UPLO = 'U', the leading
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43 * n by n upper triangular part of A contains the upper
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44 * triangular part of the matrix A, and the strictly lower
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45 * triangular part of A is not referenced. If UPLO = 'L', the
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46 * leading n by n lower triangular part of A contains the lower
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47 * triangular part of the matrix A, and the strictly upper
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48 * triangular part of A is not referenced.
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49 *
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50 * On exit, if INFO = 0, the factor U or L from the Cholesky
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51 * factorization A = U'*U or A = L*L'.
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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 * > 0: if INFO = k, the leading minor of order k is not
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60 * positive definite, and the factorization could not be
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61 * completed.
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62 *
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63 * =====================================================================
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64 *
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65 * .. Parameters ..
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66 REAL ONE, ZERO
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67 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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68 * ..
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69 * .. Local Scalars ..
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70 LOGICAL UPPER
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71 INTEGER J
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72 REAL AJJ
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73 * ..
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74 * .. External Functions ..
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75 LOGICAL LSAME
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76 REAL SDOT
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77 EXTERNAL LSAME, SDOT
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78 * ..
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79 * .. External Subroutines ..
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80 EXTERNAL SGEMV, SSCAL, XERBLA
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81 * ..
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82 * .. Intrinsic Functions ..
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83 INTRINSIC MAX, SQRT
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84 * ..
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85 * .. Executable Statements ..
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86 *
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87 * Test the input parameters.
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88 *
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89 INFO = 0
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90 UPPER = LSAME( UPLO, 'U' )
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91 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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92 INFO = -1
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93 ELSE IF( N.LT.0 ) THEN
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94 INFO = -2
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95 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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96 INFO = -4
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97 END IF
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98 IF( INFO.NE.0 ) THEN
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99 CALL XERBLA( 'SPOTF2', -INFO )
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100 RETURN
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101 END IF
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102 *
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103 * Quick return if possible
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104 *
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105 IF( N.EQ.0 )
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106 $ RETURN
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107 *
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108 IF( UPPER ) THEN
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109 *
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110 * Compute the Cholesky factorization A = U'*U.
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111 *
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112 DO 10 J = 1, N
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113 *
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114 * Compute U(J,J) and test for non-positive-definiteness.
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115 *
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116 AJJ = A( J, J ) - SDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
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117 IF( AJJ.LE.ZERO ) THEN
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118 A( J, J ) = AJJ
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119 GO TO 30
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120 END IF
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121 AJJ = SQRT( AJJ )
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122 A( J, J ) = AJJ
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123 *
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124 * Compute elements J+1:N of row J.
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125 *
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126 IF( J.LT.N ) THEN
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127 CALL SGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
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128 $ LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
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129 CALL SSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
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130 END IF
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131 10 CONTINUE
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132 ELSE
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133 *
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134 * Compute the Cholesky factorization A = L*L'.
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135 *
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136 DO 20 J = 1, N
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137 *
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138 * Compute L(J,J) and test for non-positive-definiteness.
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139 *
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140 AJJ = A( J, J ) - SDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
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141 $ LDA )
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142 IF( AJJ.LE.ZERO ) THEN
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143 A( J, J ) = AJJ
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144 GO TO 30
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145 END IF
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146 AJJ = SQRT( AJJ )
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147 A( J, J ) = AJJ
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148 *
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149 * Compute elements J+1:N of column J.
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150 *
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151 IF( J.LT.N ) THEN
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152 CALL SGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
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153 $ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
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154 CALL SSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
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155 END IF
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156 20 CONTINUE
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157 END IF
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158 GO TO 40
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159 *
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160 30 CONTINUE
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161 INFO = J
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162 *
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163 40 CONTINUE
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164 RETURN
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165 *
d53c33d93440 [project @ 2003-02-18 20:00:48 by jwe]
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166 * End of SPOTF2
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167 *
d53c33d93440 [project @ 2003-02-18 20:00:48 by jwe]
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168 END