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annotate libcruft/lapack/slasda.f @ 7789:82be108cc558

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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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1 SUBROUTINE SLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
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2 $ DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
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3 $ PERM, GIVNUM, C, S, WORK, IWORK, INFO )
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4 *
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5 * -- LAPACK auxiliary routine (version 3.1) --
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6 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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7 * November 2006
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8 *
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9 * .. Scalar Arguments ..
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10 INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE
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11 * ..
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12 * .. Array Arguments ..
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13 INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ),
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14 $ K( * ), PERM( LDGCOL, * )
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15 REAL C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ),
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16 $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ),
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17 $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ),
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18 $ Z( LDU, * )
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19 * ..
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20 *
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21 * Purpose
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22 * =======
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23 *
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24 * Using a divide and conquer approach, SLASDA computes the singular
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25 * value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
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26 * B with diagonal D and offdiagonal E, where M = N + SQRE. The
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27 * algorithm computes the singular values in the SVD B = U * S * VT.
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28 * The orthogonal matrices U and VT are optionally computed in
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29 * compact form.
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30 *
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31 * A related subroutine, SLASD0, computes the singular values and
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32 * the singular vectors in explicit form.
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33 *
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34 * Arguments
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35 * =========
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36 *
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37 * ICOMPQ (input) INTEGER
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38 * Specifies whether singular vectors are to be computed
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39 * in compact form, as follows
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40 * = 0: Compute singular values only.
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41 * = 1: Compute singular vectors of upper bidiagonal
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42 * matrix in compact form.
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43 *
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44 * SMLSIZ (input) INTEGER
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45 * The maximum size of the subproblems at the bottom of the
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46 * computation tree.
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47 *
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48 * N (input) INTEGER
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49 * The row dimension of the upper bidiagonal matrix. This is
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50 * also the dimension of the main diagonal array D.
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51 *
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52 * SQRE (input) INTEGER
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53 * Specifies the column dimension of the bidiagonal matrix.
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54 * = 0: The bidiagonal matrix has column dimension M = N;
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55 * = 1: The bidiagonal matrix has column dimension M = N + 1.
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56 *
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57 * D (input/output) REAL array, dimension ( N )
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58 * On entry D contains the main diagonal of the bidiagonal
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59 * matrix. On exit D, if INFO = 0, contains its singular values.
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60 *
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61 * E (input) REAL array, dimension ( M-1 )
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62 * Contains the subdiagonal entries of the bidiagonal matrix.
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63 * On exit, E has been destroyed.
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64 *
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65 * U (output) REAL array,
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66 * dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
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67 * if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
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68 * singular vector matrices of all subproblems at the bottom
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69 * level.
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70 *
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71 * LDU (input) INTEGER, LDU = > N.
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72 * The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
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73 * GIVNUM, and Z.
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74 *
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75 * VT (output) REAL array,
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76 * dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
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77 * if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right
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78 * singular vector matrices of all subproblems at the bottom
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79 * level.
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80 *
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81 * K (output) INTEGER array, dimension ( N )
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82 * if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
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83 * If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
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84 * secular equation on the computation tree.
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85 *
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86 * DIFL (output) REAL array, dimension ( LDU, NLVL ),
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87 * where NLVL = floor(log_2 (N/SMLSIZ))).
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88 *
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89 * DIFR (output) REAL array,
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90 * dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
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91 * dimension ( N ) if ICOMPQ = 0.
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92 * If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
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93 * record distances between singular values on the I-th
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94 * level and singular values on the (I -1)-th level, and
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95 * DIFR(1:N, 2 * I ) contains the normalizing factors for
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96 * the right singular vector matrix. See SLASD8 for details.
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97 *
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98 * Z (output) REAL array,
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99 * dimension ( LDU, NLVL ) if ICOMPQ = 1 and
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100 * dimension ( N ) if ICOMPQ = 0.
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101 * The first K elements of Z(1, I) contain the components of
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102 * the deflation-adjusted updating row vector for subproblems
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103 * on the I-th level.
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104 *
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105 * POLES (output) REAL array,
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106 * dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
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107 * if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
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108 * POLES(1, 2*I) contain the new and old singular values
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109 * involved in the secular equations on the I-th level.
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110 *
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111 * GIVPTR (output) INTEGER array,
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112 * dimension ( N ) if ICOMPQ = 1, and not referenced if
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113 * ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
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114 * the number of Givens rotations performed on the I-th
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115 * problem on the computation tree.
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116 *
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117 * GIVCOL (output) INTEGER array,
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118 * dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
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119 * referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
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120 * GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
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121 * of Givens rotations performed on the I-th level on the
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122 * computation tree.
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123 *
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124 * LDGCOL (input) INTEGER, LDGCOL = > N.
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125 * The leading dimension of arrays GIVCOL and PERM.
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126 *
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127 * PERM (output) INTEGER array, dimension ( LDGCOL, NLVL )
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128 * if ICOMPQ = 1, and not referenced
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129 * if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
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130 * permutations done on the I-th level of the computation tree.
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131 *
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132 * GIVNUM (output) REAL array,
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133 * dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not
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134 * referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
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135 * GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
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136 * values of Givens rotations performed on the I-th level on
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137 * the computation tree.
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138 *
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139 * C (output) REAL array,
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140 * dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
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141 * If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
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142 * C( I ) contains the C-value of a Givens rotation related to
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143 * the right null space of the I-th subproblem.
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144 *
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145 * S (output) REAL array, dimension ( N ) if
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146 * ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
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147 * and the I-th subproblem is not square, on exit, S( I )
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148 * contains the S-value of a Givens rotation related to
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149 * the right null space of the I-th subproblem.
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150 *
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151 * WORK (workspace) REAL array, dimension
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152 * (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
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153 *
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154 * IWORK (workspace) INTEGER array, dimension (7*N).
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155 *
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156 * INFO (output) INTEGER
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157 * = 0: successful exit.
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158 * < 0: if INFO = -i, the i-th argument had an illegal value.
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159 * > 0: if INFO = 1, an singular value did not converge
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160 *
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161 * Further Details
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162 * ===============
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163 *
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164 * Based on contributions by
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165 * Ming Gu and Huan Ren, Computer Science Division, University of
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166 * California at Berkeley, USA
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167 *
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168 * =====================================================================
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169 *
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170 * .. Parameters ..
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171 REAL ZERO, ONE
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172 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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173 * ..
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174 * .. Local Scalars ..
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175 INTEGER I, I1, IC, IDXQ, IDXQI, IM1, INODE, ITEMP, IWK,
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176 $ J, LF, LL, LVL, LVL2, M, NCC, ND, NDB1, NDIML,
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177 $ NDIMR, NL, NLF, NLP1, NLVL, NR, NRF, NRP1, NRU,
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178 $ NWORK1, NWORK2, SMLSZP, SQREI, VF, VFI, VL, VLI
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179 REAL ALPHA, BETA
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180 * ..
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181 * .. External Subroutines ..
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182 EXTERNAL SCOPY, SLASD6, SLASDQ, SLASDT, SLASET, XERBLA
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183 * ..
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184 * .. Executable Statements ..
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185 *
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186 * Test the input parameters.
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187 *
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188 INFO = 0
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189 *
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190 IF( ( ICOMPQ.LT.0 ) .OR. ( ICOMPQ.GT.1 ) ) THEN
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191 INFO = -1
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192 ELSE IF( SMLSIZ.LT.3 ) THEN
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193 INFO = -2
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194 ELSE IF( N.LT.0 ) THEN
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195 INFO = -3
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196 ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
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197 INFO = -4
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198 ELSE IF( LDU.LT.( N+SQRE ) ) THEN
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199 INFO = -8
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200 ELSE IF( LDGCOL.LT.N ) THEN
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201 INFO = -17
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202 END IF
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203 IF( INFO.NE.0 ) THEN
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204 CALL XERBLA( 'SLASDA', -INFO )
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205 RETURN
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206 END IF
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207 *
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208 M = N + SQRE
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209 *
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210 * If the input matrix is too small, call SLASDQ to find the SVD.
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211 *
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212 IF( N.LE.SMLSIZ ) THEN
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213 IF( ICOMPQ.EQ.0 ) THEN
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214 CALL SLASDQ( 'U', SQRE, N, 0, 0, 0, D, E, VT, LDU, U, LDU,
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215 $ U, LDU, WORK, INFO )
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216 ELSE
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217 CALL SLASDQ( 'U', SQRE, N, M, N, 0, D, E, VT, LDU, U, LDU,
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218 $ U, LDU, WORK, INFO )
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219 END IF
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220 RETURN
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221 END IF
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222 *
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223 * Book-keeping and set up the computation tree.
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224 *
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225 INODE = 1
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226 NDIML = INODE + N
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227 NDIMR = NDIML + N
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228 IDXQ = NDIMR + N
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229 IWK = IDXQ + N
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230 *
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231 NCC = 0
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232 NRU = 0
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233 *
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234 SMLSZP = SMLSIZ + 1
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235 VF = 1
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236 VL = VF + M
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237 NWORK1 = VL + M
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238 NWORK2 = NWORK1 + SMLSZP*SMLSZP
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239 *
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240 CALL SLASDT( N, NLVL, ND, IWORK( INODE ), IWORK( NDIML ),
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241 $ IWORK( NDIMR ), SMLSIZ )
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242 *
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243 * for the nodes on bottom level of the tree, solve
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244 * their subproblems by SLASDQ.
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245 *
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246 NDB1 = ( ND+1 ) / 2
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247 DO 30 I = NDB1, ND
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248 *
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249 * IC : center row of each node
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250 * NL : number of rows of left subproblem
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251 * NR : number of rows of right subproblem
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252 * NLF: starting row of the left subproblem
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253 * NRF: starting row of the right subproblem
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254 *
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255 I1 = I - 1
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256 IC = IWORK( INODE+I1 )
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257 NL = IWORK( NDIML+I1 )
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258 NLP1 = NL + 1
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259 NR = IWORK( NDIMR+I1 )
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260 NLF = IC - NL
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261 NRF = IC + 1
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262 IDXQI = IDXQ + NLF - 2
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263 VFI = VF + NLF - 1
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264 VLI = VL + NLF - 1
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265 SQREI = 1
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266 IF( ICOMPQ.EQ.0 ) THEN
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267 CALL SLASET( 'A', NLP1, NLP1, ZERO, ONE, WORK( NWORK1 ),
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268 $ SMLSZP )
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269 CALL SLASDQ( 'U', SQREI, NL, NLP1, NRU, NCC, D( NLF ),
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270 $ E( NLF ), WORK( NWORK1 ), SMLSZP,
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271 $ WORK( NWORK2 ), NL, WORK( NWORK2 ), NL,
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272 $ WORK( NWORK2 ), INFO )
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273 ITEMP = NWORK1 + NL*SMLSZP
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274 CALL SCOPY( NLP1, WORK( NWORK1 ), 1, WORK( VFI ), 1 )
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275 CALL SCOPY( NLP1, WORK( ITEMP ), 1, WORK( VLI ), 1 )
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276 ELSE
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277 CALL SLASET( 'A', NL, NL, ZERO, ONE, U( NLF, 1 ), LDU )
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278 CALL SLASET( 'A', NLP1, NLP1, ZERO, ONE, VT( NLF, 1 ), LDU )
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279 CALL SLASDQ( 'U', SQREI, NL, NLP1, NL, NCC, D( NLF ),
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280 $ E( NLF ), VT( NLF, 1 ), LDU, U( NLF, 1 ), LDU,
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281 $ U( NLF, 1 ), LDU, WORK( NWORK1 ), INFO )
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282 CALL SCOPY( NLP1, VT( NLF, 1 ), 1, WORK( VFI ), 1 )
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283 CALL SCOPY( NLP1, VT( NLF, NLP1 ), 1, WORK( VLI ), 1 )
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284 END IF
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285 IF( INFO.NE.0 ) THEN
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286 RETURN
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287 END IF
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288 DO 10 J = 1, NL
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289 IWORK( IDXQI+J ) = J
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290 10 CONTINUE
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291 IF( ( I.EQ.ND ) .AND. ( SQRE.EQ.0 ) ) THEN
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292 SQREI = 0
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293 ELSE
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294 SQREI = 1
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295 END IF
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296 IDXQI = IDXQI + NLP1
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297 VFI = VFI + NLP1
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298 VLI = VLI + NLP1
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299 NRP1 = NR + SQREI
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300 IF( ICOMPQ.EQ.0 ) THEN
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301 CALL SLASET( 'A', NRP1, NRP1, ZERO, ONE, WORK( NWORK1 ),
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302 $ SMLSZP )
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303 CALL SLASDQ( 'U', SQREI, NR, NRP1, NRU, NCC, D( NRF ),
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304 $ E( NRF ), WORK( NWORK1 ), SMLSZP,
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305 $ WORK( NWORK2 ), NR, WORK( NWORK2 ), NR,
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306 $ WORK( NWORK2 ), INFO )
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307 ITEMP = NWORK1 + ( NRP1-1 )*SMLSZP
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308 CALL SCOPY( NRP1, WORK( NWORK1 ), 1, WORK( VFI ), 1 )
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309 CALL SCOPY( NRP1, WORK( ITEMP ), 1, WORK( VLI ), 1 )
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310 ELSE
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311 CALL SLASET( 'A', NR, NR, ZERO, ONE, U( NRF, 1 ), LDU )
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312 CALL SLASET( 'A', NRP1, NRP1, ZERO, ONE, VT( NRF, 1 ), LDU )
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313 CALL SLASDQ( 'U', SQREI, NR, NRP1, NR, NCC, D( NRF ),
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314 $ E( NRF ), VT( NRF, 1 ), LDU, U( NRF, 1 ), LDU,
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315 $ U( NRF, 1 ), LDU, WORK( NWORK1 ), INFO )
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316 CALL SCOPY( NRP1, VT( NRF, 1 ), 1, WORK( VFI ), 1 )
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317 CALL SCOPY( NRP1, VT( NRF, NRP1 ), 1, WORK( VLI ), 1 )
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318 END IF
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319 IF( INFO.NE.0 ) THEN
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320 RETURN
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321 END IF
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322 DO 20 J = 1, NR
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323 IWORK( IDXQI+J ) = J
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324 20 CONTINUE
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325 30 CONTINUE
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326 *
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327 * Now conquer each subproblem bottom-up.
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328 *
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329 J = 2**NLVL
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330 DO 50 LVL = NLVL, 1, -1
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331 LVL2 = LVL*2 - 1
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332 *
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333 * Find the first node LF and last node LL on
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334 * the current level LVL.
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335 *
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336 IF( LVL.EQ.1 ) THEN
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337 LF = 1
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338 LL = 1
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339 ELSE
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340 LF = 2**( LVL-1 )
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341 LL = 2*LF - 1
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342 END IF
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343 DO 40 I = LF, LL
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344 IM1 = I - 1
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345 IC = IWORK( INODE+IM1 )
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346 NL = IWORK( NDIML+IM1 )
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347 NR = IWORK( NDIMR+IM1 )
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348 NLF = IC - NL
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349 NRF = IC + 1
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350 IF( I.EQ.LL ) THEN
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351 SQREI = SQRE
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352 ELSE
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353 SQREI = 1
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354 END IF
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355 VFI = VF + NLF - 1
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356 VLI = VL + NLF - 1
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357 IDXQI = IDXQ + NLF - 1
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358 ALPHA = D( IC )
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359 BETA = E( IC )
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360 IF( ICOMPQ.EQ.0 ) THEN
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361 CALL SLASD6( ICOMPQ, NL, NR, SQREI, D( NLF ),
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362 $ WORK( VFI ), WORK( VLI ), ALPHA, BETA,
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363 $ IWORK( IDXQI ), PERM, GIVPTR( 1 ), GIVCOL,
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364 $ LDGCOL, GIVNUM, LDU, POLES, DIFL, DIFR, Z,
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365 $ K( 1 ), C( 1 ), S( 1 ), WORK( NWORK1 ),
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366 $ IWORK( IWK ), INFO )
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367 ELSE
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368 J = J - 1
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369 CALL SLASD6( ICOMPQ, NL, NR, SQREI, D( NLF ),
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370 $ WORK( VFI ), WORK( VLI ), ALPHA, BETA,
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371 $ IWORK( IDXQI ), PERM( NLF, LVL ),
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372 $ GIVPTR( J ), GIVCOL( NLF, LVL2 ), LDGCOL,
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373 $ GIVNUM( NLF, LVL2 ), LDU,
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374 $ POLES( NLF, LVL2 ), DIFL( NLF, LVL ),
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375 $ DIFR( NLF, LVL2 ), Z( NLF, LVL ), K( J ),
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376 $ C( J ), S( J ), WORK( NWORK1 ),
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377 $ IWORK( IWK ), INFO )
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378 END IF
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379 IF( INFO.NE.0 ) THEN
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380 RETURN
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381 END IF
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382 40 CONTINUE
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383 50 CONTINUE
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384 *
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385 RETURN
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386 *
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387 * End of SLASDA
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388 *
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389 END