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1 SUBROUTINE DPOTF2( 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 DOUBLE PRECISION 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 * DPOTF2 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) DOUBLE PRECISION 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 DOUBLE PRECISION ONE, ZERO |
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67 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+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 DOUBLE PRECISION 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 DOUBLE PRECISION DDOT |
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77 EXTERNAL LSAME, DDOT |
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78 * .. |
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79 * .. External Subroutines .. |
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80 EXTERNAL DGEMV, DSCAL, 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( 'DPOTF2', -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 ) - DDOT( 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 DGEMV( '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 DSCAL( 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 ) - DDOT( 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 DGEMV( '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 DSCAL( 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 * |
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166 * End of DPOTF2 |
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167 * |
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168 END |
