Mercurial > octave
annotate libcruft/arpack/src/znapps.f @ 12274:9f5d2ef078e8 release-3-4-x
import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 28 Jan 2011 14:04:33 -0500 |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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1 c\BeginDoc |
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2 c |
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3 c\Name: znapps |
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4 c |
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5 c\Description: |
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6 c Given the Arnoldi factorization |
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7 c |
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8 c A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T, |
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9 c |
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10 c apply NP implicit shifts resulting in |
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11 c |
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12 c A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q |
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13 c |
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14 c where Q is an orthogonal matrix which is the product of rotations |
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15 c and reflections resulting from the NP bulge change sweeps. |
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16 c The updated Arnoldi factorization becomes: |
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17 c |
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18 c A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T. |
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19 c |
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20 c\Usage: |
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21 c call znapps |
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22 c ( N, KEV, NP, SHIFT, V, LDV, H, LDH, RESID, Q, LDQ, |
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23 c WORKL, WORKD ) |
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24 c |
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25 c\Arguments |
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26 c N Integer. (INPUT) |
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27 c Problem size, i.e. size of matrix A. |
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28 c |
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29 c KEV Integer. (INPUT/OUTPUT) |
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30 c KEV+NP is the size of the input matrix H. |
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31 c KEV is the size of the updated matrix HNEW. |
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32 c |
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33 c NP Integer. (INPUT) |
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34 c Number of implicit shifts to be applied. |
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35 c |
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36 c SHIFT Complex*16 array of length NP. (INPUT) |
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37 c The shifts to be applied. |
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38 c |
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39 c V Complex*16 N by (KEV+NP) array. (INPUT/OUTPUT) |
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40 c On INPUT, V contains the current KEV+NP Arnoldi vectors. |
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41 c On OUTPUT, V contains the updated KEV Arnoldi vectors |
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42 c in the first KEV columns of V. |
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43 c |
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44 c LDV Integer. (INPUT) |
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45 c Leading dimension of V exactly as declared in the calling |
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46 c program. |
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47 c |
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48 c H Complex*16 (KEV+NP) by (KEV+NP) array. (INPUT/OUTPUT) |
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49 c On INPUT, H contains the current KEV+NP by KEV+NP upper |
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50 c Hessenberg matrix of the Arnoldi factorization. |
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51 c On OUTPUT, H contains the updated KEV by KEV upper Hessenberg |
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52 c matrix in the KEV leading submatrix. |
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53 c |
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54 c LDH Integer. (INPUT) |
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55 c Leading dimension of H exactly as declared in the calling |
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56 c program. |
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57 c |
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58 c RESID Complex*16 array of length N. (INPUT/OUTPUT) |
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59 c On INPUT, RESID contains the the residual vector r_{k+p}. |
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60 c On OUTPUT, RESID is the update residual vector rnew_{k} |
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61 c in the first KEV locations. |
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62 c |
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63 c Q Complex*16 KEV+NP by KEV+NP work array. (WORKSPACE) |
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64 c Work array used to accumulate the rotations and reflections |
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65 c during the bulge chase sweep. |
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66 c |
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67 c LDQ Integer. (INPUT) |
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68 c Leading dimension of Q exactly as declared in the calling |
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69 c program. |
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70 c |
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71 c WORKL Complex*16 work array of length (KEV+NP). (WORKSPACE) |
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72 c Private (replicated) array on each PE or array allocated on |
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73 c the front end. |
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74 c |
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75 c WORKD Complex*16 work array of length 2*N. (WORKSPACE) |
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76 c Distributed array used in the application of the accumulated |
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77 c orthogonal matrix Q. |
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78 c |
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79 c\EndDoc |
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80 c |
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81 c----------------------------------------------------------------------- |
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82 c |
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83 c\BeginLib |
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84 c |
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85 c\Local variables: |
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86 c xxxxxx Complex*16 |
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87 c |
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88 c\References: |
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89 c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in |
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90 c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), |
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91 c pp 357-385. |
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92 c |
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93 c\Routines called: |
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94 c ivout ARPACK utility routine that prints integers. |
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95 c arscnd ARPACK utility routine for timing. |
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96 c zmout ARPACK utility routine that prints matrices |
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97 c zvout ARPACK utility routine that prints vectors. |
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98 c zlacpy LAPACK matrix copy routine. |
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99 c zlanhs LAPACK routine that computes various norms of a matrix. |
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100 c zlartg LAPACK Givens rotation construction routine. |
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101 c zlaset LAPACK matrix initialization routine. |
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102 c dlabad LAPACK routine for defining the underflow and overflow |
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103 c limits. |
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104 c dlamch LAPACK routine that determines machine constants. |
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105 c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. |
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106 c zgemv Level 2 BLAS routine for matrix vector multiplication. |
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107 c zaxpy Level 1 BLAS that computes a vector triad. |
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108 c zcopy Level 1 BLAS that copies one vector to another. |
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109 c zscal Level 1 BLAS that scales a vector. |
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110 c |
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111 c\Author |
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112 c Danny Sorensen Phuong Vu |
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113 c Richard Lehoucq CRPC / Rice University |
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114 c Dept. of Computational & Houston, Texas |
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115 c Applied Mathematics |
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116 c Rice University |
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117 c Houston, Texas |
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118 c |
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119 c\SCCS Information: @(#) |
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120 c FILE: napps.F SID: 2.3 DATE OF SID: 3/28/97 RELEASE: 2 |
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121 c |
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122 c\Remarks |
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123 c 1. In this version, each shift is applied to all the sublocks of |
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124 c the Hessenberg matrix H and not just to the submatrix that it |
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125 c comes from. Deflation as in LAPACK routine zlahqr (QR algorithm |
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126 c for upper Hessenberg matrices ) is used. |
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127 c Upon output, the subdiagonals of H are enforced to be non-negative |
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128 c real numbers. |
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129 c |
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130 c\EndLib |
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131 c |
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132 c----------------------------------------------------------------------- |
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133 c |
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134 subroutine znapps |
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135 & ( n, kev, np, shift, v, ldv, h, ldh, resid, q, ldq, |
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136 & workl, workd ) |
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137 c |
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138 c %----------------------------------------------------% |
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139 c | Include files for debugging and timing information | |
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140 c %----------------------------------------------------% |
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141 c |
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142 include 'debug.h' |
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143 include 'stat.h' |
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144 c |
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145 c %------------------% |
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146 c | Scalar Arguments | |
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147 c %------------------% |
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148 c |
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149 integer kev, ldh, ldq, ldv, n, np |
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150 c |
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151 c %-----------------% |
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152 c | Array Arguments | |
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153 c %-----------------% |
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154 c |
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155 Complex*16 |
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156 & h(ldh,kev+np), resid(n), shift(np), |
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157 & v(ldv,kev+np), q(ldq,kev+np), workd(2*n), workl(kev+np) |
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158 c |
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159 c %------------% |
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160 c | Parameters | |
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161 c %------------% |
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162 c |
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163 Complex*16 |
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164 & one, zero |
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165 Double precision |
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166 & rzero |
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167 parameter (one = (1.0D+0, 0.0D+0), zero = (0.0D+0, 0.0D+0), |
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168 & rzero = 0.0D+0) |
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169 c |
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170 c %------------------------% |
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171 c | Local Scalars & Arrays | |
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172 c %------------------------% |
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173 c |
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174 integer i, iend, istart, j, jj, kplusp, msglvl |
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175 logical first |
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176 Complex*16 |
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177 & cdum, f, g, h11, h21, r, s, sigma, t |
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178 Double precision |
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179 & c, ovfl, smlnum, ulp, unfl, tst1 |
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180 save first, ovfl, smlnum, ulp, unfl |
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181 c |
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182 c %----------------------% |
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183 c | External Subroutines | |
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184 c %----------------------% |
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185 c |
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186 external zaxpy, zcopy, zgemv, zscal, zlacpy, zlartg, |
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187 & zvout, zlaset, dlabad, zmout, arscnd, ivout |
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188 c |
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189 c %--------------------% |
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190 c | External Functions | |
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191 c %--------------------% |
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192 c |
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193 Double precision |
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194 & zlanhs, dlamch, dlapy2 |
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195 external zlanhs, dlamch, dlapy2 |
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196 c |
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197 c %----------------------% |
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198 c | Intrinsics Functions | |
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199 c %----------------------% |
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200 c |
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201 intrinsic abs, dimag, conjg, dcmplx, max, min, dble |
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202 c |
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203 c %---------------------% |
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204 c | Statement Functions | |
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205 c %---------------------% |
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206 c |
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207 Double precision |
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208 & zabs1 |
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209 zabs1( cdum ) = abs( dble( cdum ) ) + abs( dimag( cdum ) ) |
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210 c |
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211 c %----------------% |
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212 c | Data statments | |
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213 c %----------------% |
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214 c |
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215 data first / .true. / |
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216 c |
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217 c %-----------------------% |
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218 c | Executable Statements | |
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219 c %-----------------------% |
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220 c |
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221 if (first) then |
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222 c |
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223 c %-----------------------------------------------% |
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224 c | Set machine-dependent constants for the | |
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225 c | stopping criterion. If norm(H) <= sqrt(OVFL), | |
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226 c | overflow should not occur. | |
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227 c | REFERENCE: LAPACK subroutine zlahqr | |
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228 c %-----------------------------------------------% |
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229 c |
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230 unfl = dlamch( 'safe minimum' ) |
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231 ovfl = dble(one / unfl) |
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232 call dlabad( unfl, ovfl ) |
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233 ulp = dlamch( 'precision' ) |
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234 smlnum = unfl*( n / ulp ) |
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235 first = .false. |
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236 end if |
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237 c |
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238 c %-------------------------------% |
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239 c | Initialize timing statistics | |
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240 c | & message level for debugging | |
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241 c %-------------------------------% |
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242 c |
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243 call arscnd (t0) |
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244 msglvl = mcapps |
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245 c |
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246 kplusp = kev + np |
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247 c |
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248 c %--------------------------------------------% |
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249 c | Initialize Q to the identity to accumulate | |
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250 c | the rotations and reflections | |
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251 c %--------------------------------------------% |
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252 c |
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253 call zlaset ('All', kplusp, kplusp, zero, one, q, ldq) |
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254 c |
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255 c %----------------------------------------------% |
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256 c | Quick return if there are no shifts to apply | |
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257 c %----------------------------------------------% |
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258 c |
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259 if (np .eq. 0) go to 9000 |
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260 c |
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261 c %----------------------------------------------% |
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262 c | Chase the bulge with the application of each | |
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263 c | implicit shift. Each shift is applied to the | |
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264 c | whole matrix including each block. | |
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265 c %----------------------------------------------% |
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266 c |
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267 do 110 jj = 1, np |
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268 sigma = shift(jj) |
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269 c |
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270 if (msglvl .gt. 2 ) then |
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271 call ivout (logfil, 1, jj, ndigit, |
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272 & '_napps: shift number.') |
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273 call zvout (logfil, 1, sigma, ndigit, |
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274 & '_napps: Value of the shift ') |
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275 end if |
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276 c |
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277 istart = 1 |
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278 20 continue |
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279 c |
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280 do 30 i = istart, kplusp-1 |
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281 c |
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282 c %----------------------------------------% |
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283 c | Check for splitting and deflation. Use | |
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284 c | a standard test as in the QR algorithm | |
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285 c | REFERENCE: LAPACK subroutine zlahqr | |
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286 c %----------------------------------------% |
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287 c |
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288 tst1 = zabs1( h( i, i ) ) + zabs1( h( i+1, i+1 ) ) |
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289 if( tst1.eq.rzero ) |
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290 & tst1 = zlanhs( '1', kplusp-jj+1, h, ldh, workl ) |
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291 if ( abs(dble(h(i+1,i))) |
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292 & .le. max(ulp*tst1, smlnum) ) then |
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293 if (msglvl .gt. 0) then |
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294 call ivout (logfil, 1, i, ndigit, |
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295 & '_napps: matrix splitting at row/column no.') |
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296 call ivout (logfil, 1, jj, ndigit, |
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297 & '_napps: matrix splitting with shift number.') |
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298 call zvout (logfil, 1, h(i+1,i), ndigit, |
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299 & '_napps: off diagonal element.') |
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300 end if |
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301 iend = i |
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302 h(i+1,i) = zero |
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303 go to 40 |
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304 end if |
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305 30 continue |
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306 iend = kplusp |
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307 40 continue |
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308 c |
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309 if (msglvl .gt. 2) then |
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310 call ivout (logfil, 1, istart, ndigit, |
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311 & '_napps: Start of current block ') |
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312 call ivout (logfil, 1, iend, ndigit, |
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313 & '_napps: End of current block ') |
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314 end if |
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315 c |
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316 c %------------------------------------------------% |
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317 c | No reason to apply a shift to block of order 1 | |
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318 c | or if the current block starts after the point | |
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319 c | of compression since we'll discard this stuff | |
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320 c %------------------------------------------------% |
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321 c |
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322 if ( istart .eq. iend .or. istart .gt. kev) go to 100 |
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323 c |
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324 h11 = h(istart,istart) |
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325 h21 = h(istart+1,istart) |
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326 f = h11 - sigma |
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327 g = h21 |
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328 c |
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329 do 80 i = istart, iend-1 |
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330 c |
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331 c %------------------------------------------------------% |
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332 c | Construct the plane rotation G to zero out the bulge | |
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333 c %------------------------------------------------------% |
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334 c |
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335 call zlartg (f, g, c, s, r) |
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336 if (i .gt. istart) then |
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337 h(i,i-1) = r |
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338 h(i+1,i-1) = zero |
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339 end if |
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340 c |
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341 c %---------------------------------------------% |
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342 c | Apply rotation to the left of H; H <- G'*H | |
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343 c %---------------------------------------------% |
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344 c |
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345 do 50 j = i, kplusp |
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346 t = c*h(i,j) + s*h(i+1,j) |
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347 h(i+1,j) = -conjg(s)*h(i,j) + c*h(i+1,j) |
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348 h(i,j) = t |
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349 50 continue |
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350 c |
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351 c %---------------------------------------------% |
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352 c | Apply rotation to the right of H; H <- H*G | |
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353 c %---------------------------------------------% |
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354 c |
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355 do 60 j = 1, min(i+2,iend) |
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356 t = c*h(j,i) + conjg(s)*h(j,i+1) |
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357 h(j,i+1) = -s*h(j,i) + c*h(j,i+1) |
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358 h(j,i) = t |
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359 60 continue |
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360 c |
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361 c %-----------------------------------------------------% |
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362 c | Accumulate the rotation in the matrix Q; Q <- Q*G' | |
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363 c %-----------------------------------------------------% |
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364 c |
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365 do 70 j = 1, min(i+jj, kplusp) |
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366 t = c*q(j,i) + conjg(s)*q(j,i+1) |
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367 q(j,i+1) = - s*q(j,i) + c*q(j,i+1) |
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368 q(j,i) = t |
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369 70 continue |
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370 c |
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371 c %---------------------------% |
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372 c | Prepare for next rotation | |
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373 c %---------------------------% |
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374 c |
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375 if (i .lt. iend-1) then |
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376 f = h(i+1,i) |
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377 g = h(i+2,i) |
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378 end if |
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379 80 continue |
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380 c |
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381 c %-------------------------------% |
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382 c | Finished applying the shift. | |
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383 c %-------------------------------% |
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384 c |
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385 100 continue |
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386 c |
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387 c %---------------------------------------------------------% |
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388 c | Apply the same shift to the next block if there is any. | |
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389 c %---------------------------------------------------------% |
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390 c |
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391 istart = iend + 1 |
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392 if (iend .lt. kplusp) go to 20 |
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393 c |
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394 c %---------------------------------------------% |
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395 c | Loop back to the top to get the next shift. | |
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396 c %---------------------------------------------% |
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397 c |
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398 110 continue |
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399 c |
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400 c %---------------------------------------------------% |
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401 c | Perform a similarity transformation that makes | |
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402 c | sure that the compressed H will have non-negative | |
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403 c | real subdiagonal elements. | |
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404 c %---------------------------------------------------% |
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405 c |
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406 do 120 j=1,kev |
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407 if ( dble( h(j+1,j) ) .lt. rzero .or. |
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408 & dimag( h(j+1,j) ) .ne. rzero ) then |
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409 t = h(j+1,j) / dlapy2(dble(h(j+1,j)),dimag(h(j+1,j))) |
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410 call zscal( kplusp-j+1, conjg(t), h(j+1,j), ldh ) |
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411 call zscal( min(j+2, kplusp), t, h(1,j+1), 1 ) |
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412 call zscal( min(j+np+1,kplusp), t, q(1,j+1), 1 ) |
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413 h(j+1,j) = dcmplx( dble( h(j+1,j) ), rzero ) |
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414 end if |
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415 120 continue |
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416 c |
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417 do 130 i = 1, kev |
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418 c |
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419 c %--------------------------------------------% |
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420 c | Final check for splitting and deflation. | |
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421 c | Use a standard test as in the QR algorithm | |
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422 c | REFERENCE: LAPACK subroutine zlahqr. | |
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423 c | Note: Since the subdiagonals of the | |
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424 c | compressed H are nonnegative real numbers, | |
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425 c | we take advantage of this. | |
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426 c %--------------------------------------------% |
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427 c |
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428 tst1 = zabs1( h( i, i ) ) + zabs1( h( i+1, i+1 ) ) |
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429 if( tst1 .eq. rzero ) |
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430 & tst1 = zlanhs( '1', kev, h, ldh, workl ) |
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431 if( dble( h( i+1,i ) ) .le. max( ulp*tst1, smlnum ) ) |
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432 & h(i+1,i) = zero |
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433 130 continue |
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434 c |
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435 c %-------------------------------------------------% |
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436 c | Compute the (kev+1)-st column of (V*Q) and | |
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437 c | temporarily store the result in WORKD(N+1:2*N). | |
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438 c | This is needed in the residual update since we | |
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439 c | cannot GUARANTEE that the corresponding entry | |
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440 c | of H would be zero as in exact arithmetic. | |
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441 c %-------------------------------------------------% |
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442 c |
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443 if ( dble( h(kev+1,kev) ) .gt. rzero ) |
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444 & call zgemv ('N', n, kplusp, one, v, ldv, q(1,kev+1), 1, zero, |
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445 & workd(n+1), 1) |
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446 c |
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447 c %----------------------------------------------------------% |
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448 c | Compute column 1 to kev of (V*Q) in backward order | |
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449 c | taking advantage of the upper Hessenberg structure of Q. | |
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450 c %----------------------------------------------------------% |
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451 c |
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452 do 140 i = 1, kev |
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453 call zgemv ('N', n, kplusp-i+1, one, v, ldv, |
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454 & q(1,kev-i+1), 1, zero, workd, 1) |
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455 call zcopy (n, workd, 1, v(1,kplusp-i+1), 1) |
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456 140 continue |
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457 c |
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458 c %-------------------------------------------------% |
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459 c | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). | |
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460 c %-------------------------------------------------% |
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461 c |
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462 call zlacpy ('A', n, kev, v(1,kplusp-kev+1), ldv, v, ldv) |
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463 c |
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464 c %--------------------------------------------------------------% |
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465 c | Copy the (kev+1)-st column of (V*Q) in the appropriate place | |
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466 c %--------------------------------------------------------------% |
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467 c |
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468 if ( dble( h(kev+1,kev) ) .gt. rzero ) |
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469 & call zcopy (n, workd(n+1), 1, v(1,kev+1), 1) |
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470 c |
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471 c %-------------------------------------% |
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472 c | Update the residual vector: | |
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473 c | r <- sigmak*r + betak*v(:,kev+1) | |
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474 c | where | |
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475 c | sigmak = (e_{kev+p}'*Q)*e_{kev} | |
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476 c | betak = e_{kev+1}'*H*e_{kev} | |
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477 c %-------------------------------------% |
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478 c |
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479 call zscal (n, q(kplusp,kev), resid, 1) |
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480 if ( dble( h(kev+1,kev) ) .gt. rzero ) |
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481 & call zaxpy (n, h(kev+1,kev), v(1,kev+1), 1, resid, 1) |
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482 c |
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483 if (msglvl .gt. 1) then |
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484 call zvout (logfil, 1, q(kplusp,kev), ndigit, |
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485 & '_napps: sigmak = (e_{kev+p}^T*Q)*e_{kev}') |
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486 call zvout (logfil, 1, h(kev+1,kev), ndigit, |
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487 & '_napps: betak = e_{kev+1}^T*H*e_{kev}') |
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488 call ivout (logfil, 1, kev, ndigit, |
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489 & '_napps: Order of the final Hessenberg matrix ') |
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490 if (msglvl .gt. 2) then |
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491 call zmout (logfil, kev, kev, h, ldh, ndigit, |
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492 & '_napps: updated Hessenberg matrix H for next iteration') |
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493 end if |
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494 c |
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495 end if |
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496 c |
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497 9000 continue |
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498 call arscnd (t1) |
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499 tcapps = tcapps + (t1 - t0) |
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500 c |
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501 return |
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502 c |
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503 c %---------------% |
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504 c | End of znapps | |
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505 c %---------------% |
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506 c |
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507 end |