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1 SUBROUTINE SPOTRF( UPLO, N, A, LDA, INFO ) |
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2 * |
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7034
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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 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 * SPOTRF computes the Cholesky factorization of a real symmetric |
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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**T * U, if UPLO = 'U', or |
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23 * A = L * L**T, 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 block version of the algorithm, calling Level 3 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 * = 'U': Upper triangle of A is stored; |
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33 * = 'L': Lower triangle of A is stored. |
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34 * |
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35 * N (input) INTEGER |
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36 * The order of the matrix A. N >= 0. |
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37 * |
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38 * A (input/output) REAL array, dimension (LDA,N) |
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39 * On entry, the symmetric matrix A. If UPLO = 'U', the leading |
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40 * N-by-N upper triangular part of A contains the upper |
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41 * triangular part of the matrix A, and the strictly lower |
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42 * triangular part of A is not referenced. If UPLO = 'L', the |
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43 * leading N-by-N lower triangular part of A contains the lower |
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44 * triangular part of the matrix A, and the strictly upper |
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45 * triangular part of A is not referenced. |
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46 * |
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47 * On exit, if INFO = 0, the factor U or L from the Cholesky |
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48 * factorization A = U**T*U or A = L*L**T. |
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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, the leading minor of order i is not |
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57 * positive definite, and the factorization could not be |
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58 * completed. |
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59 * |
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60 * ===================================================================== |
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61 * |
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62 * .. Parameters .. |
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63 REAL ONE |
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64 PARAMETER ( ONE = 1.0E+0 ) |
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65 * .. |
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66 * .. Local Scalars .. |
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67 LOGICAL UPPER |
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68 INTEGER J, JB, NB |
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69 * .. |
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70 * .. External Functions .. |
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71 LOGICAL LSAME |
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72 INTEGER ILAENV |
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73 EXTERNAL LSAME, ILAENV |
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74 * .. |
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75 * .. External Subroutines .. |
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76 EXTERNAL SGEMM, SPOTF2, SSYRK, STRSM, XERBLA |
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77 * .. |
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78 * .. Intrinsic Functions .. |
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79 INTRINSIC MAX, MIN |
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80 * .. |
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81 * .. Executable Statements .. |
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82 * |
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83 * Test the input parameters. |
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84 * |
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85 INFO = 0 |
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86 UPPER = LSAME( UPLO, 'U' ) |
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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( N.LT.0 ) THEN |
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90 INFO = -2 |
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91 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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92 INFO = -4 |
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93 END IF |
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94 IF( INFO.NE.0 ) THEN |
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95 CALL XERBLA( 'SPOTRF', -INFO ) |
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96 RETURN |
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97 END IF |
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98 * |
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99 * Quick return if possible |
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100 * |
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101 IF( N.EQ.0 ) |
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102 $ RETURN |
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103 * |
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104 * Determine the block size for this environment. |
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105 * |
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106 NB = ILAENV( 1, 'SPOTRF', UPLO, N, -1, -1, -1 ) |
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107 IF( NB.LE.1 .OR. NB.GE.N ) THEN |
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108 * |
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109 * Use unblocked code. |
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110 * |
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111 CALL SPOTF2( UPLO, N, A, LDA, INFO ) |
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112 ELSE |
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113 * |
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114 * Use blocked code. |
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115 * |
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116 IF( UPPER ) THEN |
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117 * |
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118 * Compute the Cholesky factorization A = U'*U. |
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119 * |
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120 DO 10 J = 1, N, NB |
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121 * |
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122 * Update and factorize the current diagonal block and test |
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123 * for non-positive-definiteness. |
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124 * |
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125 JB = MIN( NB, N-J+1 ) |
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126 CALL SSYRK( 'Upper', 'Transpose', JB, J-1, -ONE, |
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127 $ A( 1, J ), LDA, ONE, A( J, J ), LDA ) |
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128 CALL SPOTF2( 'Upper', JB, A( J, J ), LDA, INFO ) |
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129 IF( INFO.NE.0 ) |
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130 $ GO TO 30 |
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131 IF( J+JB.LE.N ) THEN |
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132 * |
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133 * Compute the current block row. |
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134 * |
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135 CALL SGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1, |
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136 $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ), |
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137 $ LDA, ONE, A( J, J+JB ), LDA ) |
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138 CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', |
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139 $ JB, N-J-JB+1, ONE, A( J, J ), LDA, |
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140 $ A( J, J+JB ), LDA ) |
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141 END IF |
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142 10 CONTINUE |
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143 * |
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144 ELSE |
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145 * |
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146 * Compute the Cholesky factorization A = L*L'. |
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147 * |
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148 DO 20 J = 1, N, NB |
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149 * |
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150 * Update and factorize the current diagonal block and test |
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151 * for non-positive-definiteness. |
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152 * |
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153 JB = MIN( NB, N-J+1 ) |
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154 CALL SSYRK( 'Lower', 'No transpose', JB, J-1, -ONE, |
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155 $ A( J, 1 ), LDA, ONE, A( J, J ), LDA ) |
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156 CALL SPOTF2( 'Lower', JB, A( J, J ), LDA, INFO ) |
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157 IF( INFO.NE.0 ) |
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158 $ GO TO 30 |
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159 IF( J+JB.LE.N ) THEN |
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160 * |
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161 * Compute the current block column. |
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162 * |
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163 CALL SGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, |
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164 $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), |
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165 $ LDA, ONE, A( J+JB, J ), LDA ) |
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166 CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', |
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167 $ N-J-JB+1, JB, ONE, A( J, J ), LDA, |
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168 $ A( J+JB, J ), LDA ) |
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169 END IF |
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170 20 CONTINUE |
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171 END IF |
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172 END IF |
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173 GO TO 40 |
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174 * |
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175 30 CONTINUE |
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176 INFO = INFO + J - 1 |
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177 * |
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178 40 CONTINUE |
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179 RETURN |
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180 * |
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181 * End of SPOTRF |
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182 * |
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183 END |
