Mercurial > octave-nkf
annotate libcruft/arpack/src/sgetv0.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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12274
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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----------------------------------------------------------------------- |
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2 c\BeginDoc |
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3 c |
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4 c\Name: sgetv0 |
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5 c |
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6 c\Description: |
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7 c Generate a random initial residual vector for the Arnoldi process. |
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8 c Force the residual vector to be in the range of the operator OP. |
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9 c |
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10 c\Usage: |
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11 c call sgetv0 |
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12 c ( IDO, BMAT, ITRY, INITV, N, J, V, LDV, RESID, RNORM, |
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13 c IPNTR, WORKD, IERR ) |
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14 c |
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15 c\Arguments |
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16 c IDO Integer. (INPUT/OUTPUT) |
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17 c Reverse communication flag. IDO must be zero on the first |
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18 c call to sgetv0. |
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19 c ------------------------------------------------------------- |
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20 c IDO = 0: first call to the reverse communication interface |
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21 c IDO = -1: compute Y = OP * X where |
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22 c IPNTR(1) is the pointer into WORKD for X, |
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23 c IPNTR(2) is the pointer into WORKD for Y. |
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24 c This is for the initialization phase to force the |
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25 c starting vector into the range of OP. |
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26 c IDO = 2: compute Y = B * X where |
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27 c IPNTR(1) is the pointer into WORKD for X, |
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28 c IPNTR(2) is the pointer into WORKD for Y. |
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29 c IDO = 99: done |
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30 c ------------------------------------------------------------- |
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31 c |
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32 c BMAT Character*1. (INPUT) |
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33 c BMAT specifies the type of the matrix B in the (generalized) |
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34 c eigenvalue problem A*x = lambda*B*x. |
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35 c B = 'I' -> standard eigenvalue problem A*x = lambda*x |
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36 c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x |
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37 c |
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38 c ITRY Integer. (INPUT) |
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39 c ITRY counts the number of times that sgetv0 is called. |
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40 c It should be set to 1 on the initial call to sgetv0. |
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41 c |
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42 c INITV Logical variable. (INPUT) |
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43 c .TRUE. => the initial residual vector is given in RESID. |
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44 c .FALSE. => generate a random initial residual vector. |
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45 c |
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46 c N Integer. (INPUT) |
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47 c Dimension of the problem. |
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48 c |
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49 c J Integer. (INPUT) |
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50 c Index of the residual vector to be generated, with respect to |
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51 c the Arnoldi process. J > 1 in case of a "restart". |
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52 c |
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53 c V Real N by J array. (INPUT) |
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54 c The first J-1 columns of V contain the current Arnoldi basis |
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55 c if this is a "restart". |
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56 c |
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57 c LDV Integer. (INPUT) |
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58 c Leading dimension of V exactly as declared in the calling |
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59 c program. |
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60 c |
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61 c RESID Real array of length N. (INPUT/OUTPUT) |
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62 c Initial residual vector to be generated. If RESID is |
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63 c provided, force RESID into the range of the operator OP. |
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64 c |
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65 c RNORM Real scalar. (OUTPUT) |
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66 c B-norm of the generated residual. |
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67 c |
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68 c IPNTR Integer array of length 3. (OUTPUT) |
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69 c |
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70 c WORKD Real work array of length 2*N. (REVERSE COMMUNICATION). |
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71 c On exit, WORK(1:N) = B*RESID to be used in SSAITR. |
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72 c |
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73 c IERR Integer. (OUTPUT) |
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74 c = 0: Normal exit. |
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75 c = -1: Cannot generate a nontrivial restarted residual vector |
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76 c in the range of the operator OP. |
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77 c |
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78 c\EndDoc |
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79 c |
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80 c----------------------------------------------------------------------- |
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81 c |
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82 c\BeginLib |
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83 c |
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84 c\Local variables: |
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85 c xxxxxx real |
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86 c |
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87 c\References: |
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88 c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in |
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89 c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), |
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90 c pp 357-385. |
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91 c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly |
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92 c Restarted Arnoldi Iteration", Rice University Technical Report |
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93 c TR95-13, Department of Computational and Applied Mathematics. |
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94 c |
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95 c\Routines called: |
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96 c arscnd ARPACK utility routine for timing. |
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97 c svout ARPACK utility routine for vector output. |
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98 c slarnv LAPACK routine for generating a random vector. |
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99 c sgemv Level 2 BLAS routine for matrix vector multiplication. |
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100 c scopy Level 1 BLAS that copies one vector to another. |
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101 c sdot Level 1 BLAS that computes the scalar product of two vectors. |
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102 c snrm2 Level 1 BLAS that computes the norm of a vector. |
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103 c |
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104 c\Author |
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105 c Danny Sorensen Phuong Vu |
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106 c Richard Lehoucq CRPC / Rice University |
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107 c Dept. of Computational & Houston, Texas |
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108 c Applied Mathematics |
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109 c Rice University |
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110 c Houston, Texas |
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111 c |
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112 c\SCCS Information: @(#) |
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113 c FILE: getv0.F SID: 2.7 DATE OF SID: 04/07/99 RELEASE: 2 |
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114 c |
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115 c\EndLib |
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116 c |
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117 c----------------------------------------------------------------------- |
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118 c |
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119 subroutine sgetv0 |
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120 & ( ido, bmat, itry, initv, n, j, v, ldv, resid, rnorm, |
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121 & ipntr, workd, ierr ) |
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122 c |
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123 c %----------------------------------------------------% |
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124 c | Include files for debugging and timing information | |
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125 c %----------------------------------------------------% |
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126 c |
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127 include 'debug.h' |
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128 include 'stat.h' |
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129 c |
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130 c %------------------% |
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131 c | Scalar Arguments | |
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132 c %------------------% |
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133 c |
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134 character bmat*1 |
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135 logical initv |
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136 integer ido, ierr, itry, j, ldv, n |
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137 Real |
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138 & rnorm |
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139 c |
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140 c %-----------------% |
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141 c | Array Arguments | |
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142 c %-----------------% |
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143 c |
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144 integer ipntr(3) |
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145 Real |
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146 & resid(n), v(ldv,j), workd(2*n) |
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147 c |
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148 c %------------% |
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149 c | Parameters | |
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150 c %------------% |
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151 c |
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152 Real |
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153 & one, zero |
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154 parameter (one = 1.0E+0, zero = 0.0E+0) |
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155 c |
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156 c %------------------------% |
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157 c | Local Scalars & Arrays | |
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158 c %------------------------% |
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159 c |
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160 logical first, inits, orth |
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161 integer idist, iseed(4), iter, msglvl, jj |
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162 Real |
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163 & rnorm0 |
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164 save first, iseed, inits, iter, msglvl, orth, rnorm0 |
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165 c |
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166 c %----------------------% |
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167 c | External Subroutines | |
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168 c %----------------------% |
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169 c |
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170 external slarnv, svout, scopy, sgemv, arscnd |
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171 c |
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172 c %--------------------% |
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173 c | External Functions | |
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174 c %--------------------% |
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175 c |
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176 Real |
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177 & sdot, snrm2 |
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178 external sdot, snrm2 |
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179 c |
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180 c %---------------------% |
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181 c | Intrinsic Functions | |
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182 c %---------------------% |
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183 c |
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184 intrinsic abs, sqrt |
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185 c |
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186 c %-----------------% |
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187 c | Data Statements | |
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188 c %-----------------% |
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189 c |
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190 data inits /.true./ |
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191 c |
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192 c %-----------------------% |
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193 c | Executable Statements | |
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194 c %-----------------------% |
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195 c |
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196 c |
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197 c %-----------------------------------% |
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198 c | Initialize the seed of the LAPACK | |
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199 c | random number generator | |
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200 c %-----------------------------------% |
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201 c |
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202 if (inits) then |
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203 iseed(1) = 1 |
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204 iseed(2) = 3 |
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205 iseed(3) = 5 |
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206 iseed(4) = 7 |
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207 inits = .false. |
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208 end if |
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209 c |
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210 if (ido .eq. 0) then |
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211 c |
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212 c %-------------------------------% |
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213 c | Initialize timing statistics | |
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214 c | & message level for debugging | |
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215 c %-------------------------------% |
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216 c |
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217 call arscnd (t0) |
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218 msglvl = mgetv0 |
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219 c |
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220 ierr = 0 |
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221 iter = 0 |
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222 first = .FALSE. |
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223 orth = .FALSE. |
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224 c |
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225 c %-----------------------------------------------------% |
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226 c | Possibly generate a random starting vector in RESID | |
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227 c | Use a LAPACK random number generator used by the | |
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228 c | matrix generation routines. | |
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229 c | idist = 1: uniform (0,1) distribution; | |
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230 c | idist = 2: uniform (-1,1) distribution; | |
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231 c | idist = 3: normal (0,1) distribution; | |
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232 c %-----------------------------------------------------% |
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233 c |
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234 if (.not.initv) then |
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235 idist = 2 |
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236 call slarnv (idist, iseed, n, resid) |
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237 end if |
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238 c |
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239 c %----------------------------------------------------------% |
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240 c | Force the starting vector into the range of OP to handle | |
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241 c | the generalized problem when B is possibly (singular). | |
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242 c %----------------------------------------------------------% |
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243 c |
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244 call arscnd (t2) |
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245 if (bmat .eq. 'G') then |
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246 nopx = nopx + 1 |
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247 ipntr(1) = 1 |
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248 ipntr(2) = n + 1 |
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249 call scopy (n, resid, 1, workd, 1) |
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250 ido = -1 |
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251 go to 9000 |
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252 end if |
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253 end if |
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254 c |
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255 c %-----------------------------------------% |
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256 c | Back from computing OP*(initial-vector) | |
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257 c %-----------------------------------------% |
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258 c |
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259 if (first) go to 20 |
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260 c |
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261 c %-----------------------------------------------% |
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262 c | Back from computing B*(orthogonalized-vector) | |
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263 c %-----------------------------------------------% |
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264 c |
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265 if (orth) go to 40 |
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266 c |
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267 if (bmat .eq. 'G') then |
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268 call arscnd (t3) |
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269 tmvopx = tmvopx + (t3 - t2) |
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270 end if |
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271 c |
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272 c %------------------------------------------------------% |
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273 c | Starting vector is now in the range of OP; r = OP*r; | |
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274 c | Compute B-norm of starting vector. | |
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275 c %------------------------------------------------------% |
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276 c |
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277 call arscnd (t2) |
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278 first = .TRUE. |
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279 if (bmat .eq. 'G') then |
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280 nbx = nbx + 1 |
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281 call scopy (n, workd(n+1), 1, resid, 1) |
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282 ipntr(1) = n + 1 |
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283 ipntr(2) = 1 |
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284 ido = 2 |
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285 go to 9000 |
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286 else if (bmat .eq. 'I') then |
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287 call scopy (n, resid, 1, workd, 1) |
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288 end if |
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289 c |
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290 20 continue |
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291 c |
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292 if (bmat .eq. 'G') then |
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293 call arscnd (t3) |
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294 tmvbx = tmvbx + (t3 - t2) |
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295 end if |
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296 c |
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297 first = .FALSE. |
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298 if (bmat .eq. 'G') then |
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299 rnorm0 = sdot (n, resid, 1, workd, 1) |
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300 rnorm0 = sqrt(abs(rnorm0)) |
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301 else if (bmat .eq. 'I') then |
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302 rnorm0 = snrm2(n, resid, 1) |
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303 end if |
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304 rnorm = rnorm0 |
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305 c |
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306 c %---------------------------------------------% |
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307 c | Exit if this is the very first Arnoldi step | |
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308 c %---------------------------------------------% |
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309 c |
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310 if (j .eq. 1) go to 50 |
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311 c |
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312 c %---------------------------------------------------------------- |
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313 c | Otherwise need to B-orthogonalize the starting vector against | |
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314 c | the current Arnoldi basis using Gram-Schmidt with iter. ref. | |
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315 c | This is the case where an invariant subspace is encountered | |
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316 c | in the middle of the Arnoldi factorization. | |
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317 c | | |
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318 c | s = V^{T}*B*r; r = r - V*s; | |
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319 c | | |
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320 c | Stopping criteria used for iter. ref. is discussed in | |
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321 c | Parlett's book, page 107 and in Gragg & Reichel TOMS paper. | |
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322 c %---------------------------------------------------------------% |
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323 c |
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324 orth = .TRUE. |
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325 30 continue |
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326 c |
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327 call sgemv ('T', n, j-1, one, v, ldv, workd, 1, |
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328 & zero, workd(n+1), 1) |
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329 call sgemv ('N', n, j-1, -one, v, ldv, workd(n+1), 1, |
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330 & one, resid, 1) |
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331 c |
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332 c %----------------------------------------------------------% |
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333 c | Compute the B-norm of the orthogonalized starting vector | |
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334 c %----------------------------------------------------------% |
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335 c |
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336 call arscnd (t2) |
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337 if (bmat .eq. 'G') then |
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338 nbx = nbx + 1 |
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339 call scopy (n, resid, 1, workd(n+1), 1) |
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340 ipntr(1) = n + 1 |
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341 ipntr(2) = 1 |
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342 ido = 2 |
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343 go to 9000 |
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344 else if (bmat .eq. 'I') then |
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345 call scopy (n, resid, 1, workd, 1) |
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346 end if |
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347 c |
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348 40 continue |
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349 c |
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350 if (bmat .eq. 'G') then |
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351 call arscnd (t3) |
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352 tmvbx = tmvbx + (t3 - t2) |
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353 end if |
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354 c |
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355 if (bmat .eq. 'G') then |
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356 rnorm = sdot (n, resid, 1, workd, 1) |
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357 rnorm = sqrt(abs(rnorm)) |
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358 else if (bmat .eq. 'I') then |
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359 rnorm = snrm2(n, resid, 1) |
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360 end if |
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361 c |
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362 c %--------------------------------------% |
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363 c | Check for further orthogonalization. | |
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364 c %--------------------------------------% |
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365 c |
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366 if (msglvl .gt. 2) then |
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367 call svout (logfil, 1, rnorm0, ndigit, |
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368 & '_getv0: re-orthonalization ; rnorm0 is') |
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369 call svout (logfil, 1, rnorm, ndigit, |
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370 & '_getv0: re-orthonalization ; rnorm is') |
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371 end if |
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372 c |
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373 if (rnorm .gt. 0.717*rnorm0) go to 50 |
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374 c |
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375 iter = iter + 1 |
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376 if (iter .le. 5) then |
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377 c |
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378 c %-----------------------------------% |
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379 c | Perform iterative refinement step | |
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380 c %-----------------------------------% |
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381 c |
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382 rnorm0 = rnorm |
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383 go to 30 |
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384 else |
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385 c |
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386 c %------------------------------------% |
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387 c | Iterative refinement step "failed" | |
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388 c %------------------------------------% |
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389 c |
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390 do 45 jj = 1, n |
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391 resid(jj) = zero |
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392 45 continue |
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393 rnorm = zero |
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394 ierr = -1 |
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395 end if |
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396 c |
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397 50 continue |
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398 c |
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399 if (msglvl .gt. 0) then |
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400 call svout (logfil, 1, rnorm, ndigit, |
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401 & '_getv0: B-norm of initial / restarted starting vector') |
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402 end if |
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403 if (msglvl .gt. 3) then |
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404 call svout (logfil, n, resid, ndigit, |
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405 & '_getv0: initial / restarted starting vector') |
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406 end if |
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407 ido = 99 |
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408 c |
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409 call arscnd (t1) |
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410 tgetv0 = tgetv0 + (t1 - t0) |
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411 c |
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412 9000 continue |
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413 return |
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414 c |
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415 c %---------------% |
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416 c | End of sgetv0 | |
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417 c %---------------% |
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418 c |
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419 end |