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annotate libcruft/lapack/spbtrf.f @ 8596:8833c0b18eb2

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enable default settings queries in optim funcs
author Jaroslav Hajek <highegg@gmail.com>
date Tue, 27 Jan 2009 08:15:08 +0100
parents 82be108cc558
children
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1 SUBROUTINE SPBTRF( 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 * SPBTRF 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**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 * Arguments
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27 * =========
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28 *
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29 * UPLO (input) CHARACTER*1
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30 * = 'U': Upper triangle of A is stored;
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31 * = 'L': Lower triangle of A is stored.
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32 *
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33 * N (input) INTEGER
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34 * The order of the matrix A. N >= 0.
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35 *
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36 * KD (input) INTEGER
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37 * The number of superdiagonals of the matrix A if UPLO = 'U',
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38 * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
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39 *
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40 * AB (input/output) REAL array, dimension (LDAB,N)
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41 * On entry, the upper or lower triangle of the symmetric band
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42 * matrix A, stored in the first KD+1 rows of the array. The
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43 * j-th column of A is stored in the j-th column of the array AB
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44 * as follows:
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45 * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
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46 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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47 *
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48 * On exit, if INFO = 0, the triangular factor U or L from the
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49 * Cholesky factorization A = U**T*U or A = L*L**T of the band
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50 * matrix A, in the same storage format as A.
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51 *
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52 * LDAB (input) INTEGER
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53 * The leading dimension of the array AB. LDAB >= KD+1.
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54 *
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55 * INFO (output) INTEGER
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56 * = 0: successful exit
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57 * < 0: if INFO = -i, the i-th argument had an illegal value
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58 * > 0: if INFO = i, the leading minor of order i is not
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59 * positive definite, and the factorization could not be
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60 * completed.
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61 *
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62 * Further Details
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63 * ===============
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64 *
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65 * The band storage scheme is illustrated by the following example, when
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66 * N = 6, KD = 2, and UPLO = 'U':
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67 *
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68 * On entry: On exit:
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69 *
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70 * * * a13 a24 a35 a46 * * u13 u24 u35 u46
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71 * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
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72 * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
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73 *
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74 * Similarly, if UPLO = 'L' the format of A is as follows:
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75 *
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76 * On entry: On exit:
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77 *
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78 * a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
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79 * a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
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80 * a31 a42 a53 a64 * * l31 l42 l53 l64 * *
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81 *
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82 * Array elements marked * are not used by the routine.
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83 *
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84 * Contributed by
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85 * Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
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86 *
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87 * =====================================================================
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88 *
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89 * .. Parameters ..
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90 REAL ONE, ZERO
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91 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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92 INTEGER NBMAX, LDWORK
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93 PARAMETER ( NBMAX = 32, LDWORK = NBMAX+1 )
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94 * ..
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95 * .. Local Scalars ..
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96 INTEGER I, I2, I3, IB, II, J, JJ, NB
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97 * ..
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98 * .. Local Arrays ..
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99 REAL WORK( LDWORK, NBMAX )
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100 * ..
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101 * .. External Functions ..
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102 LOGICAL LSAME
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103 INTEGER ILAENV
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104 EXTERNAL LSAME, ILAENV
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105 * ..
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106 * .. External Subroutines ..
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107 EXTERNAL SGEMM, SPBTF2, SPOTF2, SSYRK, STRSM, XERBLA
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108 * ..
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109 * .. Intrinsic Functions ..
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110 INTRINSIC MIN
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111 * ..
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112 * .. Executable Statements ..
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113 *
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114 * Test the input parameters.
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115 *
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116 INFO = 0
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117 IF( ( .NOT.LSAME( UPLO, 'U' ) ) .AND.
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118 $ ( .NOT.LSAME( UPLO, 'L' ) ) ) THEN
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119 INFO = -1
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120 ELSE IF( N.LT.0 ) THEN
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121 INFO = -2
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122 ELSE IF( KD.LT.0 ) THEN
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123 INFO = -3
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124 ELSE IF( LDAB.LT.KD+1 ) THEN
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125 INFO = -5
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126 END IF
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127 IF( INFO.NE.0 ) THEN
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128 CALL XERBLA( 'SPBTRF', -INFO )
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129 RETURN
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130 END IF
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131 *
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132 * Quick return if possible
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133 *
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134 IF( N.EQ.0 )
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135 $ RETURN
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136 *
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137 * Determine the block size for this environment
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138 *
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139 NB = ILAENV( 1, 'SPBTRF', UPLO, N, KD, -1, -1 )
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140 *
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141 * The block size must not exceed the semi-bandwidth KD, and must not
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142 * exceed the limit set by the size of the local array WORK.
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143 *
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144 NB = MIN( NB, NBMAX )
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145 *
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146 IF( NB.LE.1 .OR. NB.GT.KD ) THEN
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147 *
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148 * Use unblocked code
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149 *
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150 CALL SPBTF2( UPLO, N, KD, AB, LDAB, INFO )
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151 ELSE
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152 *
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153 * Use blocked code
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154 *
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155 IF( LSAME( UPLO, 'U' ) ) THEN
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156 *
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157 * Compute the Cholesky factorization of a symmetric band
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158 * matrix, given the upper triangle of the matrix in band
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159 * storage.
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160 *
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161 * Zero the upper triangle of the work array.
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162 *
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163 DO 20 J = 1, NB
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164 DO 10 I = 1, J - 1
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165 WORK( I, J ) = ZERO
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166 10 CONTINUE
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167 20 CONTINUE
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168 *
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diff changeset
169 * Process the band matrix one diagonal block at a time.
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diff changeset
170 *
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diff changeset
171 DO 70 I = 1, N, NB
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172 IB = MIN( NB, N-I+1 )
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173 *
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diff changeset
174 * Factorize the diagonal block
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diff changeset
175 *
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176 CALL SPOTF2( UPLO, IB, AB( KD+1, I ), LDAB-1, II )
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177 IF( II.NE.0 ) THEN
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178 INFO = I + II - 1
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179 GO TO 150
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180 END IF
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181 IF( I+IB.LE.N ) THEN
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diff changeset
182 *
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diff changeset
183 * Update the relevant part of the trailing submatrix.
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diff changeset
184 * If A11 denotes the diagonal block which has just been
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diff changeset
185 * factorized, then we need to update the remaining
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186 * blocks in the diagram:
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187 *
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188 * A11 A12 A13
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189 * A22 A23
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diff changeset
190 * A33
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diff changeset
191 *
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192 * The numbers of rows and columns in the partitioning
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193 * are IB, I2, I3 respectively. The blocks A12, A22 and
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194 * A23 are empty if IB = KD. The upper triangle of A13
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195 * lies outside the band.
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196 *
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197 I2 = MIN( KD-IB, N-I-IB+1 )
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198 I3 = MIN( IB, N-I-KD+1 )
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199 *
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200 IF( I2.GT.0 ) THEN
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201 *
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202 * Update A12
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203 *
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204 CALL STRSM( 'Left', 'Upper', 'Transpose',
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205 $ 'Non-unit', IB, I2, ONE, AB( KD+1, I ),
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206 $ LDAB-1, AB( KD+1-IB, I+IB ), LDAB-1 )
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207 *
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208 * Update A22
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209 *
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210 CALL SSYRK( 'Upper', 'Transpose', I2, IB, -ONE,
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211 $ AB( KD+1-IB, I+IB ), LDAB-1, ONE,
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212 $ AB( KD+1, I+IB ), LDAB-1 )
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213 END IF
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214 *
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215 IF( I3.GT.0 ) THEN
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216 *
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217 * Copy the lower triangle of A13 into the work array.
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218 *
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219 DO 40 JJ = 1, I3
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220 DO 30 II = JJ, IB
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221 WORK( II, JJ ) = AB( II-JJ+1, JJ+I+KD-1 )
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222 30 CONTINUE
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223 40 CONTINUE
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224 *
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diff changeset
225 * Update A13 (in the work array).
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226 *
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227 CALL STRSM( 'Left', 'Upper', 'Transpose',
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228 $ 'Non-unit', IB, I3, ONE, AB( KD+1, I ),
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229 $ LDAB-1, WORK, LDWORK )
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230 *
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diff changeset
231 * Update A23
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diff changeset
232 *
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233 IF( I2.GT.0 )
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234 $ CALL SGEMM( 'Transpose', 'No Transpose', I2, I3,
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235 $ IB, -ONE, AB( KD+1-IB, I+IB ),
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diff changeset
236 $ LDAB-1, WORK, LDWORK, ONE,
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237 $ AB( 1+IB, I+KD ), LDAB-1 )
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238 *
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diff changeset
239 * Update A33
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240 *
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241 CALL SSYRK( 'Upper', 'Transpose', I3, IB, -ONE,
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242 $ WORK, LDWORK, ONE, AB( KD+1, I+KD ),
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243 $ LDAB-1 )
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244 *
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diff changeset
245 * Copy the lower triangle of A13 back into place.
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diff changeset
246 *
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247 DO 60 JJ = 1, I3
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diff changeset
248 DO 50 II = JJ, IB
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249 AB( II-JJ+1, JJ+I+KD-1 ) = WORK( II, JJ )
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250 50 CONTINUE
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251 60 CONTINUE
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252 END IF
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diff changeset
253 END IF
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254 70 CONTINUE
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255 ELSE
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diff changeset
256 *
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diff changeset
257 * Compute the Cholesky factorization of a symmetric band
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258 * matrix, given the lower triangle of the matrix in band
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diff changeset
259 * storage.
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diff changeset
260 *
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diff changeset
261 * Zero the lower triangle of the work array.
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parents:
diff changeset
262 *
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diff changeset
263 DO 90 J = 1, NB
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diff changeset
264 DO 80 I = J + 1, NB
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265 WORK( I, J ) = ZERO
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266 80 CONTINUE
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267 90 CONTINUE
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diff changeset
268 *
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diff changeset
269 * Process the band matrix one diagonal block at a time.
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parents:
diff changeset
270 *
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diff changeset
271 DO 140 I = 1, N, NB
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272 IB = MIN( NB, N-I+1 )
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273 *
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diff changeset
274 * Factorize the diagonal block
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diff changeset
275 *
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276 CALL SPOTF2( UPLO, IB, AB( 1, I ), LDAB-1, II )
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277 IF( II.NE.0 ) THEN
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278 INFO = I + II - 1
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279 GO TO 150
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280 END IF
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281 IF( I+IB.LE.N ) THEN
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diff changeset
282 *
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diff changeset
283 * Update the relevant part of the trailing submatrix.
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diff changeset
284 * If A11 denotes the diagonal block which has just been
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diff changeset
285 * factorized, then we need to update the remaining
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diff changeset
286 * blocks in the diagram:
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diff changeset
287 *
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diff changeset
288 * A11
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diff changeset
289 * A21 A22
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diff changeset
290 * A31 A32 A33
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parents:
diff changeset
291 *
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diff changeset
292 * The numbers of rows and columns in the partitioning
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diff changeset
293 * are IB, I2, I3 respectively. The blocks A21, A22 and
82be108cc558 First attempt at single precision tyeps
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diff changeset
294 * A32 are empty if IB = KD. The lower triangle of A31
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diff changeset
295 * lies outside the band.
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diff changeset
296 *
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297 I2 = MIN( KD-IB, N-I-IB+1 )
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298 I3 = MIN( IB, N-I-KD+1 )
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299 *
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diff changeset
300 IF( I2.GT.0 ) THEN
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parents:
diff changeset
301 *
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diff changeset
302 * Update A21
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diff changeset
303 *
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diff changeset
304 CALL STRSM( 'Right', 'Lower', 'Transpose',
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diff changeset
305 $ 'Non-unit', I2, IB, ONE, AB( 1, I ),
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306 $ LDAB-1, AB( 1+IB, I ), LDAB-1 )
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parents:
diff changeset
307 *
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diff changeset
308 * Update A22
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parents:
diff changeset
309 *
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diff changeset
310 CALL SSYRK( 'Lower', 'No Transpose', I2, IB, -ONE,
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diff changeset
311 $ AB( 1+IB, I ), LDAB-1, ONE,
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parents:
diff changeset
312 $ AB( 1, I+IB ), LDAB-1 )
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313 END IF
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parents:
diff changeset
314 *
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diff changeset
315 IF( I3.GT.0 ) THEN
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parents:
diff changeset
316 *
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diff changeset
317 * Copy the upper triangle of A31 into the work array.
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diff changeset
318 *
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diff changeset
319 DO 110 JJ = 1, IB
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diff changeset
320 DO 100 II = 1, MIN( JJ, I3 )
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diff changeset
321 WORK( II, JJ ) = AB( KD+1-JJ+II, JJ+I-1 )
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322 100 CONTINUE
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323 110 CONTINUE
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diff changeset
324 *
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diff changeset
325 * Update A31 (in the work array).
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diff changeset
326 *
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diff changeset
327 CALL STRSM( 'Right', 'Lower', 'Transpose',
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parents:
diff changeset
328 $ 'Non-unit', I3, IB, ONE, AB( 1, I ),
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parents:
diff changeset
329 $ LDAB-1, WORK, LDWORK )
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parents:
diff changeset
330 *
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diff changeset
331 * Update A32
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parents:
diff changeset
332 *
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diff changeset
333 IF( I2.GT.0 )
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diff changeset
334 $ CALL SGEMM( 'No transpose', 'Transpose', I3, I2,
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parents:
diff changeset
335 $ IB, -ONE, WORK, LDWORK,
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parents:
diff changeset
336 $ AB( 1+IB, I ), LDAB-1, ONE,
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337 $ AB( 1+KD-IB, I+IB ), LDAB-1 )
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338 *
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339 * Update A33
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340 *
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341 CALL SSYRK( 'Lower', 'No Transpose', I3, IB, -ONE,
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342 $ WORK, LDWORK, ONE, AB( 1, I+KD ),
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343 $ LDAB-1 )
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344 *
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345 * Copy the upper triangle of A31 back into place.
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346 *
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347 DO 130 JJ = 1, IB
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348 DO 120 II = 1, MIN( JJ, I3 )
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349 AB( KD+1-JJ+II, JJ+I-1 ) = WORK( II, JJ )
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350 120 CONTINUE
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351 130 CONTINUE
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352 END IF
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353 END IF
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354 140 CONTINUE
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355 END IF
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356 END IF
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357 RETURN
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358 *
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359 150 CONTINUE
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360 RETURN
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361 *
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362 * End of SPBTRF
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363 *
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364 END