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annotate libcruft/arpack/src/snapps.f @ 12274:9f5d2ef078e8 release-3-4-x

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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
author John W. Eaton <jwe@octave.org>
date Fri, 28 Jan 2011 14:04:33 -0500
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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: snapps
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5 c
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6 c\Description:
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7 c Given the Arnoldi factorization
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8 c
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9 c A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T,
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10 c
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11 c apply NP implicit shifts resulting in
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12 c
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13 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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14 c
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15 c where Q is an orthogonal matrix which is the product of rotations
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16 c and reflections resulting from the NP bulge chage sweeps.
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17 c The updated Arnoldi factorization becomes:
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18 c
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19 c A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T.
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20 c
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21 c\Usage:
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22 c call snapps
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23 c ( N, KEV, NP, SHIFTR, SHIFTI, V, LDV, H, LDH, RESID, Q, LDQ,
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24 c WORKL, WORKD )
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25 c
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26 c\Arguments
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27 c N Integer. (INPUT)
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28 c Problem size, i.e. size of matrix A.
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29 c
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30 c KEV Integer. (INPUT/OUTPUT)
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31 c KEV+NP is the size of the input matrix H.
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32 c KEV is the size of the updated matrix HNEW. KEV is only
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33 c updated on ouput when fewer than NP shifts are applied in
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34 c order to keep the conjugate pair together.
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35 c
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36 c NP Integer. (INPUT)
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37 c Number of implicit shifts to be applied.
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38 c
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39 c SHIFTR, Real array of length NP. (INPUT)
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40 c SHIFTI Real and imaginary part of the shifts to be applied.
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41 c Upon, entry to snapps, the shifts must be sorted so that the
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42 c conjugate pairs are in consecutive locations.
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43 c
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44 c V Real N by (KEV+NP) array. (INPUT/OUTPUT)
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45 c On INPUT, V contains the current KEV+NP Arnoldi vectors.
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46 c On OUTPUT, V contains the updated KEV Arnoldi vectors
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47 c in the first KEV columns of V.
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48 c
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49 c LDV Integer. (INPUT)
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50 c Leading dimension of V exactly as declared in the calling
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51 c program.
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52 c
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53 c H Real (KEV+NP) by (KEV+NP) array. (INPUT/OUTPUT)
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54 c On INPUT, H contains the current KEV+NP by KEV+NP upper
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55 c Hessenber matrix of the Arnoldi factorization.
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56 c On OUTPUT, H contains the updated KEV by KEV upper Hessenberg
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57 c matrix in the KEV leading submatrix.
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58 c
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59 c LDH Integer. (INPUT)
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60 c Leading dimension of H exactly as declared in the calling
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61 c program.
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62 c
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63 c RESID Real array of length N. (INPUT/OUTPUT)
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64 c On INPUT, RESID contains the the residual vector r_{k+p}.
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65 c On OUTPUT, RESID is the update residual vector rnew_{k}
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66 c in the first KEV locations.
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67 c
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68 c Q Real KEV+NP by KEV+NP work array. (WORKSPACE)
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69 c Work array used to accumulate the rotations and reflections
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70 c during the bulge chase sweep.
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71 c
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72 c LDQ Integer. (INPUT)
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73 c Leading dimension of Q exactly as declared in the calling
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74 c program.
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75 c
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76 c WORKL Real work array of length (KEV+NP). (WORKSPACE)
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77 c Private (replicated) array on each PE or array allocated on
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78 c the front end.
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79 c
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80 c WORKD Real work array of length 2*N. (WORKSPACE)
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81 c Distributed array used in the application of the accumulated
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82 c orthogonal matrix Q.
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83 c
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84 c\EndDoc
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85 c
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86 c-----------------------------------------------------------------------
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87 c
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88 c\BeginLib
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89 c
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90 c\Local variables:
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91 c xxxxxx real
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92 c
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93 c\References:
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94 c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in
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95 c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992),
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96 c pp 357-385.
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97 c
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98 c\Routines called:
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99 c ivout ARPACK utility routine that prints integers.
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100 c arscnd ARPACK utility routine for timing.
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101 c smout ARPACK utility routine that prints matrices.
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102 c svout ARPACK utility routine that prints vectors.
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103 c slabad LAPACK routine that computes machine constants.
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104 c slacpy LAPACK matrix copy routine.
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105 c slamch LAPACK routine that determines machine constants.
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106 c slanhs LAPACK routine that computes various norms of a matrix.
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107 c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully.
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108 c slarf LAPACK routine that applies Householder reflection to
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109 c a matrix.
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110 c slarfg LAPACK Householder reflection construction routine.
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111 c slartg LAPACK Givens rotation construction routine.
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112 c slaset LAPACK matrix initialization routine.
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113 c sgemv Level 2 BLAS routine for matrix vector multiplication.
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114 c saxpy Level 1 BLAS that computes a vector triad.
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115 c scopy Level 1 BLAS that copies one vector to another .
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116 c sscal Level 1 BLAS that scales a vector.
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117 c
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118 c\Author
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119 c Danny Sorensen Phuong Vu
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120 c Richard Lehoucq CRPC / Rice University
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121 c Dept. of Computational & Houston, Texas
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122 c Applied Mathematics
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123 c Rice University
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124 c Houston, Texas
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125 c
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126 c\Revision history:
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127 c xx/xx/92: Version ' 2.4'
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128 c
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129 c\SCCS Information: @(#)
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130 c FILE: napps.F SID: 2.4 DATE OF SID: 3/28/97 RELEASE: 2
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131 c
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132 c\Remarks
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133 c 1. In this version, each shift is applied to all the sublocks of
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134 c the Hessenberg matrix H and not just to the submatrix that it
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135 c comes from. Deflation as in LAPACK routine slahqr (QR algorithm
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136 c for upper Hessenberg matrices ) is used.
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137 c The subdiagonals of H are enforced to be non-negative.
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138 c
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139 c\EndLib
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140 c
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141 c-----------------------------------------------------------------------
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142 c
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143 subroutine snapps
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144 & ( n, kev, np, shiftr, shifti, v, ldv, h, ldh, resid, q, ldq,
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145 & workl, workd )
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146 c
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147 c %----------------------------------------------------%
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148 c | Include files for debugging and timing information |
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149 c %----------------------------------------------------%
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150 c
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151 include 'debug.h'
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152 include 'stat.h'
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153 c
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154 c %------------------%
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155 c | Scalar Arguments |
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156 c %------------------%
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157 c
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158 integer kev, ldh, ldq, ldv, n, np
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159 c
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160 c %-----------------%
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161 c | Array Arguments |
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162 c %-----------------%
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163 c
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164 Real
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165 & h(ldh,kev+np), resid(n), shifti(np), shiftr(np),
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166 & v(ldv,kev+np), q(ldq,kev+np), workd(2*n), workl(kev+np)
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167 c
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168 c %------------%
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169 c | Parameters |
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170 c %------------%
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171 c
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172 Real
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173 & one, zero
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174 parameter (one = 1.0E+0, zero = 0.0E+0)
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175 c
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176 c %------------------------%
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177 c | Local Scalars & Arrays |
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178 c %------------------------%
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179 c
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180 integer i, iend, ir, istart, j, jj, kplusp, msglvl, nr
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181 logical cconj, first
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182 Real
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183 & c, f, g, h11, h12, h21, h22, h32, ovfl, r, s, sigmai,
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184 & sigmar, smlnum, ulp, unfl, u(3), t, tau, tst1
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185 save first, ovfl, smlnum, ulp, unfl
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186 c
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187 c %----------------------%
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188 c | External Subroutines |
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189 c %----------------------%
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190 c
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191 external saxpy, scopy, sscal, slacpy, slarfg, slarf,
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192 & slaset, slabad, arscnd, slartg
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193 c
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194 c %--------------------%
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195 c | External Functions |
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196 c %--------------------%
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197 c
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198 Real
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199 & slamch, slanhs, slapy2
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200 external slamch, slanhs, slapy2
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201 c
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202 c %----------------------%
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203 c | Intrinsics Functions |
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204 c %----------------------%
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205 c
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206 intrinsic abs, max, min
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207 c
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208 c %----------------%
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209 c | Data statments |
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210 c %----------------%
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211 c
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212 data first / .true. /
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213 c
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214 c %-----------------------%
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215 c | Executable Statements |
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216 c %-----------------------%
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217 c
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218 if (first) then
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219 c
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220 c %-----------------------------------------------%
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221 c | Set machine-dependent constants for the |
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222 c | stopping criterion. If norm(H) <= sqrt(OVFL), |
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223 c | overflow should not occur. |
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224 c | REFERENCE: LAPACK subroutine slahqr |
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225 c %-----------------------------------------------%
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226 c
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227 unfl = slamch( 'safe minimum' )
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228 ovfl = one / unfl
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229 call slabad( unfl, ovfl )
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230 ulp = slamch( 'precision' )
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231 smlnum = unfl*( n / ulp )
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232 first = .false.
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233 end if
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234 c
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235 c %-------------------------------%
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236 c | Initialize timing statistics |
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237 c | & message level for debugging |
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238 c %-------------------------------%
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239 c
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240 call arscnd (t0)
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241 msglvl = mnapps
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242 kplusp = kev + np
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243 c
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244 c %--------------------------------------------%
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245 c | Initialize Q to the identity to accumulate |
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246 c | the rotations and reflections |
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247 c %--------------------------------------------%
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248 c
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249 call slaset ('All', kplusp, kplusp, zero, one, q, ldq)
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250 c
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251 c %----------------------------------------------%
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252 c | Quick return if there are no shifts to apply |
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253 c %----------------------------------------------%
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254 c
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255 if (np .eq. 0) go to 9000
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256 c
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257 c %----------------------------------------------%
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258 c | Chase the bulge with the application of each |
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259 c | implicit shift. Each shift is applied to the |
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260 c | whole matrix including each block. |
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261 c %----------------------------------------------%
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262 c
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263 cconj = .false.
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264 do 110 jj = 1, np
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265 sigmar = shiftr(jj)
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266 sigmai = shifti(jj)
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267 c
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268 if (msglvl .gt. 2 ) then
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269 call ivout (logfil, 1, jj, ndigit,
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270 & '_napps: shift number.')
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271 call svout (logfil, 1, sigmar, ndigit,
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272 & '_napps: The real part of the shift ')
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273 call svout (logfil, 1, sigmai, ndigit,
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274 & '_napps: The imaginary part of the shift ')
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275 end if
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276 c
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277 c %-------------------------------------------------%
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278 c | The following set of conditionals is necessary |
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279 c | in order that complex conjugate pairs of shifts |
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280 c | are applied together or not at all. |
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281 c %-------------------------------------------------%
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282 c
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283 if ( cconj ) then
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284 c
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285 c %-----------------------------------------%
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286 c | cconj = .true. means the previous shift |
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287 c | had non-zero imaginary part. |
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288 c %-----------------------------------------%
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289 c
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290 cconj = .false.
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291 go to 110
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292 else if ( jj .lt. np .and. abs( sigmai ) .gt. zero ) then
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293 c
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294 c %------------------------------------%
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295 c | Start of a complex conjugate pair. |
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296 c %------------------------------------%
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297 c
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298 cconj = .true.
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299 else if ( jj .eq. np .and. abs( sigmai ) .gt. zero ) then
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300 c
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301 c %----------------------------------------------%
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302 c | The last shift has a nonzero imaginary part. |
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303 c | Don't apply it; thus the order of the |
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304 c | compressed H is order KEV+1 since only np-1 |
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305 c | were applied. |
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306 c %----------------------------------------------%
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307 c
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308 kev = kev + 1
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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309 go to 110
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310 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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311 istart = 1
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diff changeset
312 20 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
313 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
314 c %--------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
315 c | if sigmai = 0 then |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
316 c | Apply the jj-th shift ... |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
317 c | else |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
318 c | Apply the jj-th and (jj+1)-th together ... |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
319 c | (Note that jj < np at this point in the code) |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
320 c | end |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
321 c | to the current block of H. The next do loop |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
322 c | determines the current block ; |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
323 c %--------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
324 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
325 do 30 i = istart, kplusp-1
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
326 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
327 c %----------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
328 c | Check for splitting and deflation. Use |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
329 c | a standard test as in the QR algorithm |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
330 c | REFERENCE: LAPACK subroutine slahqr |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
331 c %----------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
332 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
333 tst1 = abs( h( i, i ) ) + abs( h( i+1, i+1 ) )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
334 if( tst1.eq.zero )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
335 & tst1 = slanhs( '1', kplusp-jj+1, h, ldh, workl )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
336 if( abs( h( i+1,i ) ).le.max( ulp*tst1, smlnum ) ) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
337 if (msglvl .gt. 0) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
338 call ivout (logfil, 1, i, ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
339 & '_napps: matrix splitting at row/column no.')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
340 call ivout (logfil, 1, jj, ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
341 & '_napps: matrix splitting with shift number.')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
342 call svout (logfil, 1, h(i+1,i), ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
343 & '_napps: off diagonal element.')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
344 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
345 iend = i
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
346 h(i+1,i) = zero
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
347 go to 40
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
348 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
349 30 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
350 iend = kplusp
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
351 40 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
352 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
353 if (msglvl .gt. 2) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
354 call ivout (logfil, 1, istart, ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
355 & '_napps: Start of current block ')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
356 call ivout (logfil, 1, iend, ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
357 & '_napps: End of current block ')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
358 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
359 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
360 c %------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
361 c | No reason to apply a shift to block of order 1 |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
362 c %------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
363 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
364 if ( istart .eq. iend ) go to 100
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
365 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
366 c %------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
367 c | If istart + 1 = iend then no reason to apply a |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
368 c | complex conjugate pair of shifts on a 2 by 2 matrix. |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
369 c %------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
370 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
371 if ( istart + 1 .eq. iend .and. abs( sigmai ) .gt. zero )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
372 & go to 100
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
373 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
374 h11 = h(istart,istart)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
375 h21 = h(istart+1,istart)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
376 if ( abs( sigmai ) .le. zero ) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
377 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
378 c %---------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
379 c | Real-valued shift ==> apply single shift QR |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
380 c %---------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
381 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
382 f = h11 - sigmar
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
383 g = h21
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
384 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
385 do 80 i = istart, iend-1
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
386 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
387 c %-----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
388 c | Contruct the plane rotation G to zero out the bulge |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
389 c %-----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
390 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
391 call slartg (f, g, c, s, r)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
392 if (i .gt. istart) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
393 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
394 c %-------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
395 c | The following ensures that h(1:iend-1,1), |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
396 c | the first iend-2 off diagonal of elements |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
397 c | H, remain non negative. |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
398 c %-------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
399 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
400 if (r .lt. zero) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
401 r = -r
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
402 c = -c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
403 s = -s
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
404 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
405 h(i,i-1) = r
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
406 h(i+1,i-1) = zero
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
407 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
408 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
409 c %---------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
410 c | Apply rotation to the left of H; H <- G'*H |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
411 c %---------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
412 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
413 do 50 j = i, kplusp
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
414 t = c*h(i,j) + s*h(i+1,j)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
415 h(i+1,j) = -s*h(i,j) + c*h(i+1,j)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
416 h(i,j) = t
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
417 50 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
418 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
419 c %---------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
420 c | Apply rotation to the right of H; H <- H*G |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
421 c %---------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
422 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
423 do 60 j = 1, min(i+2,iend)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
424 t = c*h(j,i) + s*h(j,i+1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
425 h(j,i+1) = -s*h(j,i) + c*h(j,i+1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
426 h(j,i) = t
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
427 60 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
428 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
429 c %----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
430 c | Accumulate the rotation in the matrix Q; Q <- Q*G |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
431 c %----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
432 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
433 do 70 j = 1, min( i+jj, kplusp )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
434 t = c*q(j,i) + s*q(j,i+1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
435 q(j,i+1) = - s*q(j,i) + c*q(j,i+1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
436 q(j,i) = t
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
437 70 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
438 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
439 c %---------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
440 c | Prepare for next rotation |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
441 c %---------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
442 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
443 if (i .lt. iend-1) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
444 f = h(i+1,i)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
445 g = h(i+2,i)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
446 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
447 80 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
448 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
449 c %-----------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
450 c | Finished applying the real shift. |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
451 c %-----------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
452 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
453 else
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
454 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
455 c %----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
456 c | Complex conjugate shifts ==> apply double shift QR |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
457 c %----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
458 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
459 h12 = h(istart,istart+1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
460 h22 = h(istart+1,istart+1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
461 h32 = h(istart+2,istart+1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
462 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
463 c %---------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
464 c | Compute 1st column of (H - shift*I)*(H - conj(shift)*I) |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
465 c %---------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
466 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
467 s = 2.0*sigmar
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
468 t = slapy2 ( sigmar, sigmai )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
469 u(1) = ( h11 * (h11 - s) + t * t ) / h21 + h12
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
470 u(2) = h11 + h22 - s
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
471 u(3) = h32
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
472 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
473 do 90 i = istart, iend-1
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
474 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
475 nr = min ( 3, iend-i+1 )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
476 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
477 c %-----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
478 c | Construct Householder reflector G to zero out u(1). |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
479 c | G is of the form I - tau*( 1 u )' * ( 1 u' ). |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
480 c %-----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
481 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
482 call slarfg ( nr, u(1), u(2), 1, tau )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
483 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
484 if (i .gt. istart) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
485 h(i,i-1) = u(1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
486 h(i+1,i-1) = zero
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
487 if (i .lt. iend-1) h(i+2,i-1) = zero
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
488 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
489 u(1) = one
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
490 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
491 c %--------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
492 c | Apply the reflector to the left of H |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
493 c %--------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
494 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
495 call slarf ('Left', nr, kplusp-i+1, u, 1, tau,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
496 & h(i,i), ldh, workl)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
497 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
498 c %---------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
499 c | Apply the reflector to the right of H |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
500 c %---------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
501 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
502 ir = min ( i+3, iend )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
503 call slarf ('Right', ir, nr, u, 1, tau,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
504 & h(1,i), ldh, workl)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
505 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
506 c %-----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
507 c | Accumulate the reflector in the matrix Q; Q <- Q*G |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
508 c %-----------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
509 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
510 call slarf ('Right', kplusp, nr, u, 1, tau,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
511 & q(1,i), ldq, workl)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
512 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
513 c %----------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
514 c | Prepare for next reflector |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
515 c %----------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
516 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
517 if (i .lt. iend-1) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
518 u(1) = h(i+1,i)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
519 u(2) = h(i+2,i)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
520 if (i .lt. iend-2) u(3) = h(i+3,i)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
521 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
522 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
523 90 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
524 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
525 c %--------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
526 c | Finished applying a complex pair of shifts |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
527 c | to the current block |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
528 c %--------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
529 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
530 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
531 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
532 100 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
533 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
534 c %---------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
535 c | Apply the same shift to the next block if there is any. |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
536 c %---------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
537 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
538 istart = iend + 1
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
539 if (iend .lt. kplusp) go to 20
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
540 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
541 c %---------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
542 c | Loop back to the top to get the next shift. |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
543 c %---------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
544 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
545 110 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
546 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
547 c %--------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
548 c | Perform a similarity transformation that makes |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
549 c | sure that H will have non negative sub diagonals |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
550 c %--------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
551 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
552 do 120 j=1,kev
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
553 if ( h(j+1,j) .lt. zero ) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
554 call sscal( kplusp-j+1, -one, h(j+1,j), ldh )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
555 call sscal( min(j+2, kplusp), -one, h(1,j+1), 1 )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
556 call sscal( min(j+np+1,kplusp), -one, q(1,j+1), 1 )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
557 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
558 120 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
559 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
560 do 130 i = 1, kev
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
561 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
562 c %--------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
563 c | Final check for splitting and deflation. |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
564 c | Use a standard test as in the QR algorithm |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
565 c | REFERENCE: LAPACK subroutine slahqr |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
566 c %--------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
567 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
568 tst1 = abs( h( i, i ) ) + abs( h( i+1, i+1 ) )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
569 if( tst1.eq.zero )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
570 & tst1 = slanhs( '1', kev, h, ldh, workl )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
571 if( h( i+1,i ) .le. max( ulp*tst1, smlnum ) )
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
572 & h(i+1,i) = zero
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
573 130 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
574 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
575 c %-------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
576 c | Compute the (kev+1)-st column of (V*Q) and |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
577 c | temporarily store the result in WORKD(N+1:2*N). |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
578 c | This is needed in the residual update since we |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
579 c | cannot GUARANTEE that the corresponding entry |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
580 c | of H would be zero as in exact arithmetic. |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
581 c %-------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
582 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
583 if (h(kev+1,kev) .gt. zero)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
584 & call sgemv ('N', n, kplusp, one, v, ldv, q(1,kev+1), 1, zero,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
585 & workd(n+1), 1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
586 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
587 c %----------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
588 c | Compute column 1 to kev of (V*Q) in backward order |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
589 c | taking advantage of the upper Hessenberg structure of Q. |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
590 c %----------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
591 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
592 do 140 i = 1, kev
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
593 call sgemv ('N', n, kplusp-i+1, one, v, ldv,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
594 & q(1,kev-i+1), 1, zero, workd, 1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
595 call scopy (n, workd, 1, v(1,kplusp-i+1), 1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
596 140 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
597 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
598 c %-------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
599 c | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
600 c %-------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
601 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
602 call slacpy ('A', n, kev, v(1,kplusp-kev+1), ldv, v, ldv)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
603 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
604 c %--------------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
605 c | Copy the (kev+1)-st column of (V*Q) in the appropriate place |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
606 c %--------------------------------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
607 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
608 if (h(kev+1,kev) .gt. zero)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
609 & call scopy (n, workd(n+1), 1, v(1,kev+1), 1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
610 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
611 c %-------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
612 c | Update the residual vector: |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
613 c | r <- sigmak*r + betak*v(:,kev+1) |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
614 c | where |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
615 c | sigmak = (e_{kplusp}'*Q)*e_{kev} |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
616 c | betak = e_{kev+1}'*H*e_{kev} |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
617 c %-------------------------------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
618 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
619 call sscal (n, q(kplusp,kev), resid, 1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
620 if (h(kev+1,kev) .gt. zero)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
621 & call saxpy (n, h(kev+1,kev), v(1,kev+1), 1, resid, 1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
622 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
623 if (msglvl .gt. 1) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
624 call svout (logfil, 1, q(kplusp,kev), ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
625 & '_napps: sigmak = (e_{kev+p}^T*Q)*e_{kev}')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
626 call svout (logfil, 1, h(kev+1,kev), ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
627 & '_napps: betak = e_{kev+1}^T*H*e_{kev}')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
628 call ivout (logfil, 1, kev, ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
629 & '_napps: Order of the final Hessenberg matrix ')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
630 if (msglvl .gt. 2) then
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
631 call smout (logfil, kev, kev, h, ldh, ndigit,
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
632 & '_napps: updated Hessenberg matrix H for next iteration')
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
633 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
634 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
635 end if
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
636 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
637 9000 continue
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
638 call arscnd (t1)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
639 tnapps = tnapps + (t1 - t0)
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
640 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
641 return
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
642 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
643 c %---------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
644 c | End of snapps |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
645 c %---------------%
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
646 c
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
diff changeset
647 end