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annotate libcruft/lapack/spbtf2.f @ 9122:8ca06fd9c6ef

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test lazy copying in structures
author Thorsten Meyer <thorsten.meyier@gmx.de>
date Wed, 15 Apr 2009 12:29:31 +0200
parents 82be108cc558
children
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1 SUBROUTINE SPBTF2( UPLO, N, KD, AB, LDAB, 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, KD, LDAB, N
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10 * ..
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11 * .. Array Arguments ..
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12 REAL AB( LDAB, * )
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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 * SPBTF2 computes the Cholesky factorization of a real symmetric
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19 * positive definite band 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, U' is the transpose of U, and
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25 * 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 * KD (input) INTEGER
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42 * The number of super-diagonals of the matrix A if UPLO = 'U',
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43 * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
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44 *
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45 * AB (input/output) REAL array, dimension (LDAB,N)
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46 * On entry, the upper or lower triangle of the symmetric band
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47 * matrix A, stored in the first KD+1 rows of the array. The
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48 * j-th column of A is stored in the j-th column of the array AB
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49 * as follows:
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50 * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
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51 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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52 *
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53 * On exit, if INFO = 0, the triangular factor U or L from the
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54 * Cholesky factorization A = U'*U or A = L*L' of the band
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55 * matrix A, in the same storage format as A.
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56 *
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57 * LDAB (input) INTEGER
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58 * The leading dimension of the array AB. LDAB >= KD+1.
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59 *
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60 * INFO (output) INTEGER
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61 * = 0: successful exit
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62 * < 0: if INFO = -k, the k-th argument had an illegal value
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63 * > 0: if INFO = k, the leading minor of order k is not
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64 * positive definite, and the factorization could not be
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65 * completed.
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66 *
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67 * Further Details
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68 * ===============
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69 *
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70 * The band storage scheme is illustrated by the following example, when
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71 * N = 6, KD = 2, and UPLO = 'U':
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72 *
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73 * On entry: On exit:
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74 *
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75 * * * a13 a24 a35 a46 * * u13 u24 u35 u46
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76 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
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77 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
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78 *
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79 * Similarly, if UPLO = 'L' the format of A is as follows:
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80 *
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81 * On entry: On exit:
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82 *
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83 * a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
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84 * a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
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85 * a31 a42 a53 a64 * * l31 l42 l53 l64 * *
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86 *
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87 * Array elements marked * are not used by the routine.
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88 *
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89 * =====================================================================
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90 *
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91 * .. Parameters ..
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92 REAL ONE, ZERO
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93 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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94 * ..
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95 * .. Local Scalars ..
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96 LOGICAL UPPER
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97 INTEGER J, KLD, KN
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98 REAL AJJ
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99 * ..
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100 * .. External Functions ..
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101 LOGICAL LSAME
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102 EXTERNAL LSAME
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103 * ..
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104 * .. External Subroutines ..
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105 EXTERNAL SSCAL, SSYR, XERBLA
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106 * ..
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107 * .. Intrinsic Functions ..
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108 INTRINSIC MAX, MIN, SQRT
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109 * ..
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110 * .. Executable Statements ..
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111 *
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112 * Test the input parameters.
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113 *
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114 INFO = 0
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115 UPPER = LSAME( UPLO, 'U' )
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116 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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117 INFO = -1
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118 ELSE IF( N.LT.0 ) THEN
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119 INFO = -2
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120 ELSE IF( KD.LT.0 ) THEN
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121 INFO = -3
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122 ELSE IF( LDAB.LT.KD+1 ) THEN
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123 INFO = -5
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124 END IF
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125 IF( INFO.NE.0 ) THEN
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126 CALL XERBLA( 'SPBTF2', -INFO )
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127 RETURN
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128 END IF
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129 *
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130 * Quick return if possible
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131 *
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132 IF( N.EQ.0 )
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133 $ RETURN
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134 *
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135 KLD = MAX( 1, LDAB-1 )
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136 *
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137 IF( UPPER ) THEN
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138 *
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139 * Compute the Cholesky factorization A = U'*U.
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140 *
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141 DO 10 J = 1, N
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142 *
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143 * Compute U(J,J) and test for non-positive-definiteness.
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144 *
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145 AJJ = AB( KD+1, J )
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146 IF( AJJ.LE.ZERO )
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147 $ GO TO 30
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148 AJJ = SQRT( AJJ )
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149 AB( KD+1, J ) = AJJ
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150 *
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151 * Compute elements J+1:J+KN of row J and update the
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152 * trailing submatrix within the band.
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153 *
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154 KN = MIN( KD, N-J )
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155 IF( KN.GT.0 ) THEN
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156 CALL SSCAL( KN, ONE / AJJ, AB( KD, J+1 ), KLD )
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157 CALL SSYR( 'Upper', KN, -ONE, AB( KD, J+1 ), KLD,
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158 $ AB( KD+1, J+1 ), KLD )
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159 END IF
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160 10 CONTINUE
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161 ELSE
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162 *
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163 * Compute the Cholesky factorization A = L*L'.
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164 *
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165 DO 20 J = 1, N
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166 *
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167 * Compute L(J,J) and test for non-positive-definiteness.
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168 *
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169 AJJ = AB( 1, J )
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170 IF( AJJ.LE.ZERO )
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171 $ GO TO 30
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172 AJJ = SQRT( AJJ )
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173 AB( 1, J ) = AJJ
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174 *
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175 * Compute elements J+1:J+KN of column J and update the
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176 * trailing submatrix within the band.
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177 *
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178 KN = MIN( KD, N-J )
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179 IF( KN.GT.0 ) THEN
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180 CALL SSCAL( KN, ONE / AJJ, AB( 2, J ), 1 )
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181 CALL SSYR( 'Lower', KN, -ONE, AB( 2, J ), 1,
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182 $ AB( 1, J+1 ), KLD )
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183 END IF
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184 20 CONTINUE
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185 END IF
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186 RETURN
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187 *
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188 30 CONTINUE
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189 INFO = J
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190 RETURN
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191 *
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192 * End of SPBTF2
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193 *
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194 END