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1 SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO ) |
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2 * |
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3 * -- LAPACK routine (version 1.0) -- |
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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 * DPOTRF 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 block version of the algorithm, calling Level 3 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 |
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67 PARAMETER ( ONE = 1.0D+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, JB, NB |
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72 * .. |
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73 * .. External Functions .. |
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74 LOGICAL LSAME |
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75 INTEGER ILAENV |
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76 EXTERNAL LSAME, ILAENV |
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77 * .. |
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78 * .. External Subroutines .. |
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79 EXTERNAL DGEMM, DPOTF2, DSYRK, DTRSM, XERBLA |
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80 * .. |
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81 * .. Intrinsic Functions .. |
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82 INTRINSIC MAX, MIN |
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83 * .. |
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84 * .. Executable Statements .. |
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85 * |
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86 * Test the input parameters. |
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87 * |
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88 INFO = 0 |
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89 UPPER = LSAME( UPLO, 'U' ) |
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90 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN |
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91 INFO = -1 |
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92 ELSE IF( N.LT.0 ) THEN |
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93 INFO = -2 |
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94 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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95 INFO = -4 |
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96 END IF |
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97 IF( INFO.NE.0 ) THEN |
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98 CALL XERBLA( 'DPOTRF', -INFO ) |
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99 RETURN |
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100 END IF |
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101 * |
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102 * Quick return if possible |
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103 * |
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104 IF( N.EQ.0 ) |
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105 $ RETURN |
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106 * |
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107 * Determine the block size for this environment. |
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108 * |
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109 NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 ) |
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110 IF( NB.LE.1 .OR. NB.GE.N ) THEN |
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111 * |
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112 * Use unblocked code. |
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113 * |
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114 CALL DPOTF2( UPLO, N, A, LDA, INFO ) |
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115 ELSE |
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116 * |
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117 * Use blocked code. |
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118 * |
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119 IF( UPPER ) THEN |
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120 * |
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121 * Compute the Cholesky factorization A = U'*U. |
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122 * |
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123 DO 10 J = 1, N, NB |
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124 * |
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125 * Update and factorize the current diagonal block and test |
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126 * for non-positive-definiteness. |
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127 * |
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128 JB = MIN( NB, N-J+1 ) |
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129 CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE, |
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130 $ A( 1, J ), LDA, ONE, A( J, J ), LDA ) |
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131 CALL DPOTF2( 'Upper', JB, A( J, J ), LDA, INFO ) |
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132 IF( INFO.NE.0 ) |
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133 $ GO TO 30 |
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134 IF( J+JB.LE.N ) THEN |
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135 * |
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136 * Compute the current block row. |
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137 * |
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138 CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1, |
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139 $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ), |
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140 $ LDA, ONE, A( J, J+JB ), LDA ) |
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141 CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', |
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142 $ JB, N-J-JB+1, ONE, A( J, J ), LDA, |
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143 $ A( J, J+JB ), LDA ) |
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144 END IF |
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145 10 CONTINUE |
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146 * |
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147 ELSE |
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148 * |
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149 * Compute the Cholesky factorization A = L*L'. |
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150 * |
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151 DO 20 J = 1, N, NB |
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152 * |
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153 * Update and factorize the current diagonal block and test |
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154 * for non-positive-definiteness. |
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155 * |
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156 JB = MIN( NB, N-J+1 ) |
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157 CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE, |
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158 $ A( J, 1 ), LDA, ONE, A( J, J ), LDA ) |
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159 CALL DPOTF2( 'Lower', JB, A( J, J ), LDA, INFO ) |
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160 IF( INFO.NE.0 ) |
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161 $ GO TO 30 |
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162 IF( J+JB.LE.N ) THEN |
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163 * |
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164 * Compute the current block column. |
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165 * |
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166 CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, |
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167 $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), |
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168 $ LDA, ONE, A( J+JB, J ), LDA ) |
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169 CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', |
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170 $ N-J-JB+1, JB, ONE, A( J, J ), LDA, |
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171 $ A( J+JB, J ), LDA ) |
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172 END IF |
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173 20 CONTINUE |
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174 END IF |
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175 END IF |
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176 GO TO 40 |
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177 * |
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178 30 CONTINUE |
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179 INFO = INFO + J - 1 |
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180 * |
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181 40 CONTINUE |
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182 RETURN |
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183 * |
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184 * End of DPOTRF |
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185 * |
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186 END |
