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annotate libcruft/lapack/cgelss.f @ 9409:ed392e13c117

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remove assertion in force_variable
author Jaroslav Hajek <highegg@gmail.com>
date Tue, 30 Jun 2009 08:18:26 +0200
parents 82be108cc558
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 SUBROUTINE CGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK,
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2 $ WORK, LWORK, RWORK, INFO )
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3 *
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4 * -- LAPACK driver routine (version 3.1) --
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5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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6 * November 2006
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7 *
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8 * .. Scalar Arguments ..
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9 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
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10 REAL RCOND
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11 * ..
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12 * .. Array Arguments ..
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13 REAL RWORK( * ), S( * )
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14 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
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15 * ..
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16 *
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17 * Purpose
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18 * =======
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19 *
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20 * CGELSS computes the minimum norm solution to a complex linear
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21 * least squares problem:
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22 *
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23 * Minimize 2-norm(| b - A*x |).
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24 *
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25 * using the singular value decomposition (SVD) of A. A is an M-by-N
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26 * matrix which may be rank-deficient.
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27 *
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28 * Several right hand side vectors b and solution vectors x can be
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29 * handled in a single call; they are stored as the columns of the
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30 * M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix
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31 * X.
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32 *
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33 * The effective rank of A is determined by treating as zero those
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34 * singular values which are less than RCOND times the largest singular
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35 * value.
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36 *
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37 * Arguments
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38 * =========
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39 *
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40 * M (input) INTEGER
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41 * The number of rows of the matrix A. M >= 0.
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42 *
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43 * N (input) INTEGER
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44 * The number of columns of the matrix A. N >= 0.
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45 *
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46 * NRHS (input) INTEGER
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47 * The number of right hand sides, i.e., the number of columns
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48 * of the matrices B and X. NRHS >= 0.
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49 *
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50 * A (input/output) COMPLEX array, dimension (LDA,N)
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51 * On entry, the M-by-N matrix A.
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52 * On exit, the first min(m,n) rows of A are overwritten with
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53 * its right singular vectors, stored rowwise.
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54 *
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55 * LDA (input) INTEGER
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56 * The leading dimension of the array A. LDA >= max(1,M).
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57 *
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58 * B (input/output) COMPLEX array, dimension (LDB,NRHS)
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59 * On entry, the M-by-NRHS right hand side matrix B.
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60 * On exit, B is overwritten by the N-by-NRHS solution matrix X.
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61 * If m >= n and RANK = n, the residual sum-of-squares for
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62 * the solution in the i-th column is given by the sum of
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63 * squares of the modulus of elements n+1:m in that column.
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64 *
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65 * LDB (input) INTEGER
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66 * The leading dimension of the array B. LDB >= max(1,M,N).
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67 *
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68 * S (output) REAL array, dimension (min(M,N))
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69 * The singular values of A in decreasing order.
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70 * The condition number of A in the 2-norm = S(1)/S(min(m,n)).
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71 *
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72 * RCOND (input) REAL
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73 * RCOND is used to determine the effective rank of A.
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74 * Singular values S(i) <= RCOND*S(1) are treated as zero.
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75 * If RCOND < 0, machine precision is used instead.
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76 *
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77 * RANK (output) INTEGER
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78 * The effective rank of A, i.e., the number of singular values
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79 * which are greater than RCOND*S(1).
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80 *
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81 * WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
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82 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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83 *
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84 * LWORK (input) INTEGER
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85 * The dimension of the array WORK. LWORK >= 1, and also:
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86 * LWORK >= 2*min(M,N) + max(M,N,NRHS)
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87 * For good performance, LWORK should generally be larger.
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88 *
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89 * If LWORK = -1, then a workspace query is assumed; the routine
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90 * only calculates the optimal size of the WORK array, returns
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91 * this value as the first entry of the WORK array, and no error
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92 * message related to LWORK is issued by XERBLA.
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93 *
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94 * RWORK (workspace) REAL array, dimension (5*min(M,N))
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95 *
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96 * INFO (output) INTEGER
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97 * = 0: successful exit
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98 * < 0: if INFO = -i, the i-th argument had an illegal value.
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99 * > 0: the algorithm for computing the SVD failed to converge;
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100 * if INFO = i, i off-diagonal elements of an intermediate
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101 * bidiagonal form did not converge to zero.
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102 *
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103 * =====================================================================
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104 *
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105 * .. Parameters ..
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106 REAL ZERO, ONE
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107 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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108 COMPLEX CZERO, CONE
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109 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
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110 $ CONE = ( 1.0E+0, 0.0E+0 ) )
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111 * ..
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112 * .. Local Scalars ..
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113 LOGICAL LQUERY
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114 INTEGER BL, CHUNK, I, IASCL, IBSCL, IE, IL, IRWORK,
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115 $ ITAU, ITAUP, ITAUQ, IWORK, LDWORK, MAXMN,
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116 $ MAXWRK, MINMN, MINWRK, MM, MNTHR
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117 REAL ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM, THR
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118 * ..
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119 * .. Local Arrays ..
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120 COMPLEX VDUM( 1 )
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121 * ..
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122 * .. External Subroutines ..
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123 EXTERNAL CBDSQR, CCOPY, CGEBRD, CGELQF, CGEMM, CGEMV,
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124 $ CGEQRF, CLACPY, CLASCL, CLASET, CSRSCL, CUNGBR,
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125 $ CUNMBR, CUNMLQ, CUNMQR, SLABAD, SLASCL, SLASET,
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126 $ XERBLA
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127 * ..
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128 * .. External Functions ..
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129 INTEGER ILAENV
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130 REAL CLANGE, SLAMCH
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131 EXTERNAL ILAENV, CLANGE, SLAMCH
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132 * ..
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133 * .. Intrinsic Functions ..
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134 INTRINSIC MAX, MIN
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135 * ..
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136 * .. Executable Statements ..
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137 *
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138 * Test the input arguments
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139 *
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140 INFO = 0
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141 MINMN = MIN( M, N )
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142 MAXMN = MAX( M, N )
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143 LQUERY = ( LWORK.EQ.-1 )
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144 IF( M.LT.0 ) THEN
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145 INFO = -1
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146 ELSE IF( N.LT.0 ) THEN
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147 INFO = -2
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148 ELSE IF( NRHS.LT.0 ) THEN
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149 INFO = -3
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150 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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151 INFO = -5
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152 ELSE IF( LDB.LT.MAX( 1, MAXMN ) ) THEN
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153 INFO = -7
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154 END IF
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155 *
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156 * Compute workspace
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157 * (Note: Comments in the code beginning "Workspace:" describe the
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158 * minimal amount of workspace needed at that point in the code,
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159 * as well as the preferred amount for good performance.
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160 * CWorkspace refers to complex workspace, and RWorkspace refers
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161 * to real workspace. NB refers to the optimal block size for the
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parents:
diff changeset
162 * immediately following subroutine, as returned by ILAENV.)
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163 *
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164 IF( INFO.EQ.0 ) THEN
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165 MINWRK = 1
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166 MAXWRK = 1
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167 IF( MINMN.GT.0 ) THEN
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168 MM = M
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169 MNTHR = ILAENV( 6, 'CGELSS', ' ', M, N, NRHS, -1 )
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170 IF( M.GE.N .AND. M.GE.MNTHR ) THEN
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171 *
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172 * Path 1a - overdetermined, with many more rows than
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173 * columns
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174 *
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175 MM = N
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176 MAXWRK = MAX( MAXWRK, N + N*ILAENV( 1, 'CGEQRF', ' ', M,
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177 $ N, -1, -1 ) )
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178 MAXWRK = MAX( MAXWRK, N + NRHS*ILAENV( 1, 'CUNMQR', 'LC',
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179 $ M, NRHS, N, -1 ) )
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180 END IF
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181 IF( M.GE.N ) THEN
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182 *
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183 * Path 1 - overdetermined or exactly determined
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184 *
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185 MAXWRK = MAX( MAXWRK, 2*N + ( MM + N )*ILAENV( 1,
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186 $ 'CGEBRD', ' ', MM, N, -1, -1 ) )
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187 MAXWRK = MAX( MAXWRK, 2*N + NRHS*ILAENV( 1, 'CUNMBR',
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188 $ 'QLC', MM, NRHS, N, -1 ) )
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189 MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1,
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190 $ 'CUNGBR', 'P', N, N, N, -1 ) )
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191 MAXWRK = MAX( MAXWRK, N*NRHS )
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192 MINWRK = 2*N + MAX( NRHS, M )
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193 END IF
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194 IF( N.GT.M ) THEN
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195 MINWRK = 2*M + MAX( NRHS, N )
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196 IF( N.GE.MNTHR ) THEN
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197 *
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198 * Path 2a - underdetermined, with many more columns
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199 * than rows
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200 *
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201 MAXWRK = M + M*ILAENV( 1, 'CGELQF', ' ', M, N, -1,
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202 $ -1 )
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203 MAXWRK = MAX( MAXWRK, 3*M + M*M + 2*M*ILAENV( 1,
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204 $ 'CGEBRD', ' ', M, M, -1, -1 ) )
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205 MAXWRK = MAX( MAXWRK, 3*M + M*M + NRHS*ILAENV( 1,
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206 $ 'CUNMBR', 'QLC', M, NRHS, M, -1 ) )
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207 MAXWRK = MAX( MAXWRK, 3*M + M*M + ( M - 1 )*ILAENV( 1,
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208 $ 'CUNGBR', 'P', M, M, M, -1 ) )
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209 IF( NRHS.GT.1 ) THEN
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210 MAXWRK = MAX( MAXWRK, M*M + M + M*NRHS )
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211 ELSE
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212 MAXWRK = MAX( MAXWRK, M*M + 2*M )
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213 END IF
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214 MAXWRK = MAX( MAXWRK, M + NRHS*ILAENV( 1, 'CUNMLQ',
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215 $ 'LC', N, NRHS, M, -1 ) )
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216 ELSE
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217 *
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218 * Path 2 - underdetermined
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219 *
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220 MAXWRK = 2*M + ( N + M )*ILAENV( 1, 'CGEBRD', ' ', M,
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221 $ N, -1, -1 )
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222 MAXWRK = MAX( MAXWRK, 2*M + NRHS*ILAENV( 1, 'CUNMBR',
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223 $ 'QLC', M, NRHS, M, -1 ) )
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224 MAXWRK = MAX( MAXWRK, 2*M + M*ILAENV( 1, 'CUNGBR',
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225 $ 'P', M, N, M, -1 ) )
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226 MAXWRK = MAX( MAXWRK, N*NRHS )
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227 END IF
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228 END IF
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229 MAXWRK = MAX( MINWRK, MAXWRK )
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230 END IF
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231 WORK( 1 ) = MAXWRK
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232 *
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233 IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
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234 $ INFO = -12
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235 END IF
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236 *
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237 IF( INFO.NE.0 ) THEN
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238 CALL XERBLA( 'CGELSS', -INFO )
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239 RETURN
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240 ELSE IF( LQUERY ) THEN
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241 RETURN
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242 END IF
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243 *
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244 * Quick return if possible
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245 *
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246 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
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247 RANK = 0
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248 RETURN
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249 END IF
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250 *
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251 * Get machine parameters
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diff changeset
252 *
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253 EPS = SLAMCH( 'P' )
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254 SFMIN = SLAMCH( 'S' )
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255 SMLNUM = SFMIN / EPS
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256 BIGNUM = ONE / SMLNUM
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257 CALL SLABAD( SMLNUM, BIGNUM )
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258 *
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259 * Scale A if max element outside range [SMLNUM,BIGNUM]
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260 *
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261 ANRM = CLANGE( 'M', M, N, A, LDA, RWORK )
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262 IASCL = 0
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263 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
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264 *
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265 * Scale matrix norm up to SMLNUM
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266 *
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267 CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO )
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268 IASCL = 1
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269 ELSE IF( ANRM.GT.BIGNUM ) THEN
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270 *
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271 * Scale matrix norm down to BIGNUM
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272 *
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273 CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO )
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274 IASCL = 2
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275 ELSE IF( ANRM.EQ.ZERO ) THEN
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276 *
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277 * Matrix all zero. Return zero solution.
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278 *
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279 CALL CLASET( 'F', MAX( M, N ), NRHS, CZERO, CZERO, B, LDB )
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280 CALL SLASET( 'F', MINMN, 1, ZERO, ZERO, S, MINMN )
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281 RANK = 0
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282 GO TO 70
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283 END IF
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284 *
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285 * Scale B if max element outside range [SMLNUM,BIGNUM]
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286 *
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287 BNRM = CLANGE( 'M', M, NRHS, B, LDB, RWORK )
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288 IBSCL = 0
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289 IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
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290 *
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291 * Scale matrix norm up to SMLNUM
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292 *
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293 CALL CLASCL( 'G', 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO )
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294 IBSCL = 1
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295 ELSE IF( BNRM.GT.BIGNUM ) THEN
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296 *
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297 * Scale matrix norm down to BIGNUM
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298 *
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299 CALL CLASCL( 'G', 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO )
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300 IBSCL = 2
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301 END IF
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302 *
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diff changeset
303 * Overdetermined case
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diff changeset
304 *
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305 IF( M.GE.N ) THEN
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306 *
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diff changeset
307 * Path 1 - overdetermined or exactly determined
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parents:
diff changeset
308 *
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309 MM = M
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310 IF( M.GE.MNTHR ) THEN
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311 *
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312 * Path 1a - overdetermined, with many more rows than columns
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diff changeset
313 *
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314 MM = N
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315 ITAU = 1
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316 IWORK = ITAU + N
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317 *
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318 * Compute A=Q*R
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319 * (CWorkspace: need 2*N, prefer N+N*NB)
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320 * (RWorkspace: none)
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321 *
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322 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
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diff changeset
323 $ LWORK-IWORK+1, INFO )
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324 *
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David Bateman <dbateman@free.fr>
parents:
diff changeset
325 * Multiply B by transpose(Q)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
326 * (CWorkspace: need N+NRHS, prefer N+NRHS*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
327 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
328 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
329 CALL CUNMQR( 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAU ), B,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
330 $ LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
331 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
332 * Zero out below R
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
333 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
334 IF( N.GT.1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
335 $ CALL CLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
336 $ LDA )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
337 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
338 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
339 IE = 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
340 ITAUQ = 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
341 ITAUP = ITAUQ + N
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
342 IWORK = ITAUP + N
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
343 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
344 * Bidiagonalize R in A
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
345 * (CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
346 * (RWorkspace: need N)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
347 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
348 CALL CGEBRD( MM, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
349 $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
350 $ INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
351 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
352 * Multiply B by transpose of left bidiagonalizing vectors of R
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
353 * (CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
354 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
355 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
356 CALL CUNMBR( 'Q', 'L', 'C', MM, NRHS, N, A, LDA, WORK( ITAUQ ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
357 $ B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
358 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
359 * Generate right bidiagonalizing vectors of R in A
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
360 * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
361 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
362 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
363 CALL CUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
364 $ WORK( IWORK ), LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
365 IRWORK = IE + N
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
366 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
367 * Perform bidiagonal QR iteration
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
368 * multiply B by transpose of left singular vectors
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
369 * compute right singular vectors in A
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
370 * (CWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
371 * (RWorkspace: need BDSPAC)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
372 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
373 CALL CBDSQR( 'U', N, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
374 $ 1, B, LDB, RWORK( IRWORK ), INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
375 IF( INFO.NE.0 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
376 $ GO TO 70
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
377 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
378 * Multiply B by reciprocals of singular values
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
379 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
380 THR = MAX( RCOND*S( 1 ), SFMIN )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
381 IF( RCOND.LT.ZERO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
382 $ THR = MAX( EPS*S( 1 ), SFMIN )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
383 RANK = 0
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
384 DO 10 I = 1, N
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
385 IF( S( I ).GT.THR ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
386 CALL CSRSCL( NRHS, S( I ), B( I, 1 ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
387 RANK = RANK + 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
388 ELSE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
389 CALL CLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
390 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
391 10 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
392 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
393 * Multiply B by right singular vectors
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
394 * (CWorkspace: need N, prefer N*NRHS)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
395 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
396 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
397 IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
398 CALL CGEMM( 'C', 'N', N, NRHS, N, CONE, A, LDA, B, LDB,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
399 $ CZERO, WORK, LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
400 CALL CLACPY( 'G', N, NRHS, WORK, LDB, B, LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
401 ELSE IF( NRHS.GT.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
402 CHUNK = LWORK / N
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
403 DO 20 I = 1, NRHS, CHUNK
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
404 BL = MIN( NRHS-I+1, CHUNK )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
405 CALL CGEMM( 'C', 'N', N, BL, N, CONE, A, LDA, B( 1, I ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
406 $ LDB, CZERO, WORK, N )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
407 CALL CLACPY( 'G', N, BL, WORK, N, B( 1, I ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
408 20 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
409 ELSE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
410 CALL CGEMV( 'C', N, N, CONE, A, LDA, B, 1, CZERO, WORK, 1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
411 CALL CCOPY( N, WORK, 1, B, 1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
412 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
413 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
414 ELSE IF( N.GE.MNTHR .AND. LWORK.GE.3*M+M*M+MAX( M, NRHS, N-2*M ) )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
415 $ THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
416 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
417 * Underdetermined case, M much less than N
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
418 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
419 * Path 2a - underdetermined, with many more columns than rows
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
420 * and sufficient workspace for an efficient algorithm
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
421 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
422 LDWORK = M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
423 IF( LWORK.GE.3*M+M*LDA+MAX( M, NRHS, N-2*M ) )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
424 $ LDWORK = LDA
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
425 ITAU = 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
426 IWORK = M + 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
427 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
428 * Compute A=L*Q
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
429 * (CWorkspace: need 2*M, prefer M+M*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
430 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
431 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
432 CALL CGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
433 $ LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
434 IL = IWORK
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
435 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
436 * Copy L to WORK(IL), zeroing out above it
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
437 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
438 CALL CLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWORK )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
439 CALL CLASET( 'U', M-1, M-1, CZERO, CZERO, WORK( IL+LDWORK ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
440 $ LDWORK )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
441 IE = 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
442 ITAUQ = IL + LDWORK*M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
443 ITAUP = ITAUQ + M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
444 IWORK = ITAUP + M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
445 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
446 * Bidiagonalize L in WORK(IL)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
447 * (CWorkspace: need M*M+4*M, prefer M*M+3*M+2*M*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
448 * (RWorkspace: need M)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
449 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
450 CALL CGEBRD( M, M, WORK( IL ), LDWORK, S, RWORK( IE ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
451 $ WORK( ITAUQ ), WORK( ITAUP ), WORK( IWORK ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
452 $ LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
453 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
454 * Multiply B by transpose of left bidiagonalizing vectors of L
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
455 * (CWorkspace: need M*M+3*M+NRHS, prefer M*M+3*M+NRHS*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
456 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
457 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
458 CALL CUNMBR( 'Q', 'L', 'C', M, NRHS, M, WORK( IL ), LDWORK,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
459 $ WORK( ITAUQ ), B, LDB, WORK( IWORK ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
460 $ LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
461 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
462 * Generate right bidiagonalizing vectors of R in WORK(IL)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
463 * (CWorkspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
464 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
465 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
466 CALL CUNGBR( 'P', M, M, M, WORK( IL ), LDWORK, WORK( ITAUP ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
467 $ WORK( IWORK ), LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
468 IRWORK = IE + M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
469 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
470 * Perform bidiagonal QR iteration, computing right singular
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
471 * vectors of L in WORK(IL) and multiplying B by transpose of
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
472 * left singular vectors
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
473 * (CWorkspace: need M*M)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
474 * (RWorkspace: need BDSPAC)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
475 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
476 CALL CBDSQR( 'U', M, M, 0, NRHS, S, RWORK( IE ), WORK( IL ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
477 $ LDWORK, A, LDA, B, LDB, RWORK( IRWORK ), INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
478 IF( INFO.NE.0 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
479 $ GO TO 70
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
480 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
481 * Multiply B by reciprocals of singular values
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
482 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
483 THR = MAX( RCOND*S( 1 ), SFMIN )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
484 IF( RCOND.LT.ZERO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
485 $ THR = MAX( EPS*S( 1 ), SFMIN )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
486 RANK = 0
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
487 DO 30 I = 1, M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
488 IF( S( I ).GT.THR ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
489 CALL CSRSCL( NRHS, S( I ), B( I, 1 ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
490 RANK = RANK + 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
491 ELSE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
492 CALL CLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
493 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
494 30 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
495 IWORK = IL + M*LDWORK
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
496 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
497 * Multiply B by right singular vectors of L in WORK(IL)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
498 * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NRHS)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
499 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
500 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
501 IF( LWORK.GE.LDB*NRHS+IWORK-1 .AND. NRHS.GT.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
502 CALL CGEMM( 'C', 'N', M, NRHS, M, CONE, WORK( IL ), LDWORK,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
503 $ B, LDB, CZERO, WORK( IWORK ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
504 CALL CLACPY( 'G', M, NRHS, WORK( IWORK ), LDB, B, LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
505 ELSE IF( NRHS.GT.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
506 CHUNK = ( LWORK-IWORK+1 ) / M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
507 DO 40 I = 1, NRHS, CHUNK
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
508 BL = MIN( NRHS-I+1, CHUNK )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
509 CALL CGEMM( 'C', 'N', M, BL, M, CONE, WORK( IL ), LDWORK,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
510 $ B( 1, I ), LDB, CZERO, WORK( IWORK ), M )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
511 CALL CLACPY( 'G', M, BL, WORK( IWORK ), M, B( 1, I ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
512 $ LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
513 40 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
514 ELSE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
515 CALL CGEMV( 'C', M, M, CONE, WORK( IL ), LDWORK, B( 1, 1 ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
516 $ 1, CZERO, WORK( IWORK ), 1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
517 CALL CCOPY( M, WORK( IWORK ), 1, B( 1, 1 ), 1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
518 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
519 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
520 * Zero out below first M rows of B
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
521 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
522 CALL CLASET( 'F', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
523 IWORK = ITAU + M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
524 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
525 * Multiply transpose(Q) by B
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
526 * (CWorkspace: need M+NRHS, prefer M+NHRS*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
527 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
528 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
529 CALL CUNMLQ( 'L', 'C', N, NRHS, M, A, LDA, WORK( ITAU ), B,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
530 $ LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
531 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
532 ELSE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
533 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
534 * Path 2 - remaining underdetermined cases
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
535 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
536 IE = 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
537 ITAUQ = 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
538 ITAUP = ITAUQ + M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
539 IWORK = ITAUP + M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
540 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
541 * Bidiagonalize A
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
542 * (CWorkspace: need 3*M, prefer 2*M+(M+N)*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
543 * (RWorkspace: need N)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
544 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
545 CALL CGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
546 $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
547 $ INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
548 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
549 * Multiply B by transpose of left bidiagonalizing vectors
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
550 * (CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
551 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
552 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
553 CALL CUNMBR( 'Q', 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAUQ ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
554 $ B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
555 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
556 * Generate right bidiagonalizing vectors in A
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
557 * (CWorkspace: need 3*M, prefer 2*M+M*NB)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
558 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
559 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
560 CALL CUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
561 $ WORK( IWORK ), LWORK-IWORK+1, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
562 IRWORK = IE + M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
563 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
564 * Perform bidiagonal QR iteration,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
565 * computing right singular vectors of A in A and
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
566 * multiplying B by transpose of left singular vectors
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
567 * (CWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
568 * (RWorkspace: need BDSPAC)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
569 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
570 CALL CBDSQR( 'L', M, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
571 $ 1, B, LDB, RWORK( IRWORK ), INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
572 IF( INFO.NE.0 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
573 $ GO TO 70
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
574 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
575 * Multiply B by reciprocals of singular values
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
576 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
577 THR = MAX( RCOND*S( 1 ), SFMIN )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
578 IF( RCOND.LT.ZERO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
579 $ THR = MAX( EPS*S( 1 ), SFMIN )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
580 RANK = 0
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
581 DO 50 I = 1, M
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
582 IF( S( I ).GT.THR ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
583 CALL CSRSCL( NRHS, S( I ), B( I, 1 ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
584 RANK = RANK + 1
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
585 ELSE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
586 CALL CLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
587 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
588 50 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
589 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
590 * Multiply B by right singular vectors of A
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
591 * (CWorkspace: need N, prefer N*NRHS)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
592 * (RWorkspace: none)
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
593 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
594 IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
595 CALL CGEMM( 'C', 'N', N, NRHS, M, CONE, A, LDA, B, LDB,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
596 $ CZERO, WORK, LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
597 CALL CLACPY( 'G', N, NRHS, WORK, LDB, B, LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
598 ELSE IF( NRHS.GT.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
599 CHUNK = LWORK / N
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
600 DO 60 I = 1, NRHS, CHUNK
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
601 BL = MIN( NRHS-I+1, CHUNK )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
602 CALL CGEMM( 'C', 'N', N, BL, M, CONE, A, LDA, B( 1, I ),
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
603 $ LDB, CZERO, WORK, N )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
604 CALL CLACPY( 'F', N, BL, WORK, N, B( 1, I ), LDB )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
605 60 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
606 ELSE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
607 CALL CGEMV( 'C', M, N, CONE, A, LDA, B, 1, CZERO, WORK, 1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
608 CALL CCOPY( N, WORK, 1, B, 1 )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
609 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
610 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
611 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
612 * Undo scaling
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
613 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
614 IF( IASCL.EQ.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
615 CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
616 CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
617 $ INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
618 ELSE IF( IASCL.EQ.2 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
619 CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
620 CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
621 $ INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
622 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
623 IF( IBSCL.EQ.1 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
624 CALL CLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
625 ELSE IF( IBSCL.EQ.2 ) THEN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
626 CALL CLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO )
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
627 END IF
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
628 70 CONTINUE
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
629 WORK( 1 ) = MAXWRK
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
630 RETURN
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
631 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
632 * End of CGELSS
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
633 *
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff changeset
634 END