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annotate libcruft/arpack/src/cneigh.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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12274
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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1 c\BeginDoc
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2 c
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3 c\Name: cneigh
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4 c
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5 c\Description:
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6 c Compute the eigenvalues of the current upper Hessenberg matrix
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7 c and the corresponding Ritz estimates given the current residual norm.
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8 c
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9 c\Usage:
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10 c call cneigh
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11 c ( RNORM, N, H, LDH, RITZ, BOUNDS, Q, LDQ, WORKL, RWORK, IERR )
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12 c
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13 c\Arguments
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14 c RNORM Real scalar. (INPUT)
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15 c Residual norm corresponding to the current upper Hessenberg
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16 c matrix H.
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17 c
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18 c N Integer. (INPUT)
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19 c Size of the matrix H.
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20 c
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21 c H Complex N by N array. (INPUT)
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22 c H contains the current upper Hessenberg matrix.
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23 c
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24 c LDH Integer. (INPUT)
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25 c Leading dimension of H exactly as declared in the calling
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26 c program.
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27 c
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28 c RITZ Complex array of length N. (OUTPUT)
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29 c On output, RITZ(1:N) contains the eigenvalues of H.
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30 c
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31 c BOUNDS Complex array of length N. (OUTPUT)
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32 c On output, BOUNDS contains the Ritz estimates associated with
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33 c the eigenvalues held in RITZ. This is equal to RNORM
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34 c times the last components of the eigenvectors corresponding
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35 c to the eigenvalues in RITZ.
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36 c
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37 c Q Complex N by N array. (WORKSPACE)
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38 c Workspace needed to store the eigenvectors of H.
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39 c
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40 c LDQ Integer. (INPUT)
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41 c Leading dimension of Q exactly as declared in the calling
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42 c program.
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43 c
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44 c WORKL Complex work array of length N**2 + 3*N. (WORKSPACE)
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45 c Private (replicated) array on each PE or array allocated on
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46 c the front end. This is needed to keep the full Schur form
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47 c of H and also in the calculation of the eigenvectors of H.
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48 c
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49 c RWORK Real work array of length N (WORKSPACE)
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50 c Private (replicated) array on each PE or array allocated on
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51 c the front end.
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52 c
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53 c IERR Integer. (OUTPUT)
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54 c Error exit flag from clahqr or ctrevc.
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55 c
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56 c\EndDoc
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57 c
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58 c-----------------------------------------------------------------------
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59 c
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60 c\BeginLib
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61 c
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62 c\Local variables:
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63 c xxxxxx Complex
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64 c
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65 c\Routines called:
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66 c ivout ARPACK utility routine that prints integers.
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67 c arscnd ARPACK utility routine for timing.
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68 c cmout ARPACK utility routine that prints matrices
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69 c cvout ARPACK utility routine that prints vectors.
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70 c svout ARPACK utility routine that prints vectors.
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71 c clacpy LAPACK matrix copy routine.
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72 c clahqr LAPACK routine to compute the Schur form of an
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73 c upper Hessenberg matrix.
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74 c claset LAPACK matrix initialization routine.
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75 c ctrevc LAPACK routine to compute the eigenvectors of a matrix
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76 c in upper triangular form
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77 c ccopy Level 1 BLAS that copies one vector to another.
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78 c csscal Level 1 BLAS that scales a complex vector by a real number.
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79 c scnrm2 Level 1 BLAS that computes the norm of a vector.
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80 c
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81 c
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82 c\Author
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83 c Danny Sorensen Phuong Vu
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84 c Richard Lehoucq CRPC / Rice University
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85 c Dept. of Computational & Houston, Texas
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86 c Applied Mathematics
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87 c Rice University
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88 c Houston, Texas
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89 c
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90 c\SCCS Information: @(#)
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91 c FILE: neigh.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2
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92 c
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93 c\Remarks
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94 c None
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95 c
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96 c\EndLib
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97 c
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98 c-----------------------------------------------------------------------
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99 c
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100 subroutine cneigh (rnorm, n, h, ldh, ritz, bounds,
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101 & q, ldq, workl, rwork, ierr)
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102 c
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103 c %----------------------------------------------------%
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104 c | Include files for debugging and timing information |
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105 c %----------------------------------------------------%
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106 c
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107 include 'debug.h'
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108 include 'stat.h'
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109 c
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110 c %------------------%
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111 c | Scalar Arguments |
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112 c %------------------%
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113 c
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114 integer ierr, n, ldh, ldq
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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115 Real
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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116 & rnorm
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117 c
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118 c %-----------------%
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119 c | Array Arguments |
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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120 c %-----------------%
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121 c
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122 Complex
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123 & bounds(n), h(ldh,n), q(ldq,n), ritz(n),
9f5d2ef078e8 import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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124 & workl(n*(n+3))
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125 Real
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126 & rwork(n)
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127 c
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128 c %------------%
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129 c | Parameters |
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130 c %------------%
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131 c
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132 Complex
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133 & one, zero
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134 Real
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135 & rone
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136 parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0),
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137 & rone = 1.0E+0)
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138 c
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139 c %------------------------%
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140 c | Local Scalars & Arrays |
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141 c %------------------------%
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142 c
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143 logical select(1)
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144 integer j, msglvl
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145 Complex
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146 & vl(1)
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147 Real
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148 & temp
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149 c
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150 c %----------------------%
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151 c | External Subroutines |
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152 c %----------------------%
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153 c
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154 external clacpy, clahqr, ctrevc, ccopy,
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155 & csscal, cmout, cvout, arscnd
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156 c
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157 c %--------------------%
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158 c | External Functions |
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159 c %--------------------%
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160 c
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161 Real
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162 & scnrm2
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163 external scnrm2
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164 c
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165 c %-----------------------%
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166 c | Executable Statements |
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167 c %-----------------------%
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168 c
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169 c %-------------------------------%
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170 c | Initialize timing statistics |
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171 c | & message level for debugging |
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172 c %-------------------------------%
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173 c
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174 call arscnd (t0)
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175 msglvl = mceigh
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176 c
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177 if (msglvl .gt. 2) then
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178 call cmout (logfil, n, n, h, ldh, ndigit,
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179 & '_neigh: Entering upper Hessenberg matrix H ')
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180 end if
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181 c
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182 c %----------------------------------------------------------%
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183 c | 1. Compute the eigenvalues, the last components of the |
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184 c | corresponding Schur vectors and the full Schur form T |
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185 c | of the current upper Hessenberg matrix H. |
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186 c | clahqr returns the full Schur form of H |
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187 c | in WORKL(1:N**2), and the Schur vectors in q. |
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188 c %----------------------------------------------------------%
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189 c
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190 call clacpy ('All', n, n, h, ldh, workl, n)
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191 call claset ('All', n, n, zero, one, q, ldq)
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192 call clahqr (.true., .true., n, 1, n, workl, ldh, ritz,
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193 & 1, n, q, ldq, ierr)
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194 if (ierr .ne. 0) go to 9000
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195 c
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196 call ccopy (n, q(n-1,1), ldq, bounds, 1)
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197 if (msglvl .gt. 1) then
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198 call cvout (logfil, n, bounds, ndigit,
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199 & '_neigh: last row of the Schur matrix for H')
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200 end if
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201 c
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202 c %----------------------------------------------------------%
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203 c | 2. Compute the eigenvectors of the full Schur form T and |
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204 c | apply the Schur vectors to get the corresponding |
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205 c | eigenvectors. |
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206 c %----------------------------------------------------------%
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207 c
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208 call ctrevc ('Right', 'Back', select, n, workl, n, vl, n, q,
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209 & ldq, n, n, workl(n*n+1), rwork, ierr)
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210 c
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211 if (ierr .ne. 0) go to 9000
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212 c
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213 c %------------------------------------------------%
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214 c | Scale the returning eigenvectors so that their |
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215 c | Euclidean norms are all one. LAPACK subroutine |
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216 c | ctrevc returns each eigenvector normalized so |
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217 c | that the element of largest magnitude has |
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218 c | magnitude 1; here the magnitude of a complex |
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219 c | number (x,y) is taken to be |x| + |y|. |
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220 c %------------------------------------------------%
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221 c
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222 do 10 j=1, n
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223 temp = scnrm2( n, q(1,j), 1 )
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224 call csscal ( n, rone / temp, q(1,j), 1 )
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225 10 continue
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226 c
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227 if (msglvl .gt. 1) then
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228 call ccopy(n, q(n,1), ldq, workl, 1)
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229 call cvout (logfil, n, workl, ndigit,
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230 & '_neigh: Last row of the eigenvector matrix for H')
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231 end if
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232 c
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233 c %----------------------------%
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234 c | Compute the Ritz estimates |
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235 c %----------------------------%
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236 c
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237 call ccopy(n, q(n,1), n, bounds, 1)
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238 call csscal(n, rnorm, bounds, 1)
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239 c
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240 if (msglvl .gt. 2) then
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241 call cvout (logfil, n, ritz, ndigit,
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242 & '_neigh: The eigenvalues of H')
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243 call cvout (logfil, n, bounds, ndigit,
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244 & '_neigh: Ritz estimates for the eigenvalues of H')
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245 end if
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246 c
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247 call arscnd(t1)
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248 tceigh = tceigh + (t1 - t0)
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249 c
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250 9000 continue
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251 return
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252 c
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253 c %---------------%
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254 c | End of cneigh |
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255 c %---------------%
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256 c
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257 end