Mercurial > octave-nkf
annotate libcruft/arpack/src/ssaupd.f @ 12274:9f5d2ef078e8 release-3-4-x
import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 28 Jan 2011 14:04:33 -0500 |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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1 c----------------------------------------------------------------------- |
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2 c\BeginDoc |
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3 c |
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4 c\Name: ssaupd |
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5 c |
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6 c\Description: |
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7 c |
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8 c Reverse communication interface for the Implicitly Restarted Arnoldi |
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9 c Iteration. For symmetric problems this reduces to a variant of the Lanczos |
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10 c method. This method has been designed to compute approximations to a |
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11 c few eigenpairs of a linear operator OP that is real and symmetric |
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12 c with respect to a real positive semi-definite symmetric matrix B, |
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13 c i.e. |
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14 c |
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15 c B*OP = (OP`)*B. |
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16 c |
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17 c Another way to express this condition is |
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18 c |
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19 c < x,OPy > = < OPx,y > where < z,w > = z`Bw . |
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20 c |
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21 c In the standard eigenproblem B is the identity matrix. |
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22 c ( A` denotes transpose of A) |
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23 c |
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24 c The computed approximate eigenvalues are called Ritz values and |
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25 c the corresponding approximate eigenvectors are called Ritz vectors. |
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26 c |
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27 c ssaupd is usually called iteratively to solve one of the |
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28 c following problems: |
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29 c |
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30 c Mode 1: A*x = lambda*x, A symmetric |
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31 c ===> OP = A and B = I. |
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32 c |
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33 c Mode 2: A*x = lambda*M*x, A symmetric, M symmetric positive definite |
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34 c ===> OP = inv[M]*A and B = M. |
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35 c ===> (If M can be factored see remark 3 below) |
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36 c |
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37 c Mode 3: K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite |
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38 c ===> OP = (inv[K - sigma*M])*M and B = M. |
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39 c ===> Shift-and-Invert mode |
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40 c |
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41 c Mode 4: K*x = lambda*KG*x, K symmetric positive semi-definite, |
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42 c KG symmetric indefinite |
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43 c ===> OP = (inv[K - sigma*KG])*K and B = K. |
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44 c ===> Buckling mode |
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45 c |
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46 c Mode 5: A*x = lambda*M*x, A symmetric, M symmetric positive semi-definite |
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47 c ===> OP = inv[A - sigma*M]*[A + sigma*M] and B = M. |
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48 c ===> Cayley transformed mode |
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49 c |
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50 c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v |
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51 c should be accomplished either by a direct method |
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52 c using a sparse matrix factorization and solving |
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53 c |
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54 c [A - sigma*M]*w = v or M*w = v, |
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55 c |
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56 c or through an iterative method for solving these |
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57 c systems. If an iterative method is used, the |
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58 c convergence test must be more stringent than |
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59 c the accuracy requirements for the eigenvalue |
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60 c approximations. |
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61 c |
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62 c\Usage: |
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63 c call ssaupd |
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64 c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, |
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65 c IPNTR, WORKD, WORKL, LWORKL, INFO ) |
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66 c |
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67 c\Arguments |
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68 c IDO Integer. (INPUT/OUTPUT) |
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69 c Reverse communication flag. IDO must be zero on the first |
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70 c call to ssaupd. IDO will be set internally to |
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71 c indicate the type of operation to be performed. Control is |
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72 c then given back to the calling routine which has the |
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73 c responsibility to carry out the requested operation and call |
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74 c ssaupd with the result. The operand is given in |
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75 c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)). |
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76 c (If Mode = 2 see remark 5 below) |
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77 c ------------------------------------------------------------- |
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78 c IDO = 0: first call to the reverse communication interface |
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79 c IDO = -1: compute Y = OP * X where |
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80 c IPNTR(1) is the pointer into WORKD for X, |
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81 c IPNTR(2) is the pointer into WORKD for Y. |
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82 c This is for the initialization phase to force the |
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83 c starting vector into the range of OP. |
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84 c IDO = 1: compute Y = OP * X where |
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85 c IPNTR(1) is the pointer into WORKD for X, |
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86 c IPNTR(2) is the pointer into WORKD for Y. |
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87 c In mode 3,4 and 5, the vector B * X is already |
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88 c available in WORKD(ipntr(3)). It does not |
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89 c need to be recomputed in forming OP * X. |
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90 c IDO = 2: compute Y = B * X where |
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91 c IPNTR(1) is the pointer into WORKD for X, |
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92 c IPNTR(2) is the pointer into WORKD for Y. |
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93 c IDO = 3: compute the IPARAM(8) shifts where |
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94 c IPNTR(11) is the pointer into WORKL for |
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95 c placing the shifts. See remark 6 below. |
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96 c IDO = 99: done |
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97 c ------------------------------------------------------------- |
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98 c |
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99 c BMAT Character*1. (INPUT) |
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100 c BMAT specifies the type of the matrix B that defines the |
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101 c semi-inner product for the operator OP. |
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102 c B = 'I' -> standard eigenvalue problem A*x = lambda*x |
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103 c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x |
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104 c |
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105 c N Integer. (INPUT) |
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106 c Dimension of the eigenproblem. |
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107 c |
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108 c WHICH Character*2. (INPUT) |
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109 c Specify which of the Ritz values of OP to compute. |
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110 c |
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111 c 'LA' - compute the NEV largest (algebraic) eigenvalues. |
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112 c 'SA' - compute the NEV smallest (algebraic) eigenvalues. |
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113 c 'LM' - compute the NEV largest (in magnitude) eigenvalues. |
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114 c 'SM' - compute the NEV smallest (in magnitude) eigenvalues. |
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115 c 'BE' - compute NEV eigenvalues, half from each end of the |
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116 c spectrum. When NEV is odd, compute one more from the |
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117 c high end than from the low end. |
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118 c (see remark 1 below) |
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119 c |
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120 c NEV Integer. (INPUT) |
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121 c Number of eigenvalues of OP to be computed. 0 < NEV < N. |
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122 c |
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123 c TOL Real scalar. (INPUT) |
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124 c Stopping criterion: the relative accuracy of the Ritz value |
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125 c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)). |
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126 c If TOL .LE. 0. is passed a default is set: |
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127 c DEFAULT = SLAMCH('EPS') (machine precision as computed |
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128 c by the LAPACK auxiliary subroutine SLAMCH). |
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129 c |
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130 c RESID Real array of length N. (INPUT/OUTPUT) |
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131 c On INPUT: |
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132 c If INFO .EQ. 0, a random initial residual vector is used. |
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133 c If INFO .NE. 0, RESID contains the initial residual vector, |
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134 c possibly from a previous run. |
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135 c On OUTPUT: |
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136 c RESID contains the final residual vector. |
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137 c |
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138 c NCV Integer. (INPUT) |
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139 c Number of columns of the matrix V (less than or equal to N). |
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140 c This will indicate how many Lanczos vectors are generated |
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141 c at each iteration. After the startup phase in which NEV |
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142 c Lanczos vectors are generated, the algorithm generates |
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143 c NCV-NEV Lanczos vectors at each subsequent update iteration. |
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144 c Most of the cost in generating each Lanczos vector is in the |
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145 c matrix-vector product OP*x. (See remark 4 below). |
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146 c |
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147 c V Real N by NCV array. (OUTPUT) |
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148 c The NCV columns of V contain the Lanczos basis vectors. |
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149 c |
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150 c LDV Integer. (INPUT) |
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151 c Leading dimension of V exactly as declared in the calling |
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152 c program. |
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153 c |
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154 c IPARAM Integer array of length 11. (INPUT/OUTPUT) |
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155 c IPARAM(1) = ISHIFT: method for selecting the implicit shifts. |
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156 c The shifts selected at each iteration are used to restart |
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157 c the Arnoldi iteration in an implicit fashion. |
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158 c ------------------------------------------------------------- |
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159 c ISHIFT = 0: the shifts are provided by the user via |
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160 c reverse communication. The NCV eigenvalues of |
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161 c the current tridiagonal matrix T are returned in |
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162 c the part of WORKL array corresponding to RITZ. |
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163 c See remark 6 below. |
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164 c ISHIFT = 1: exact shifts with respect to the reduced |
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165 c tridiagonal matrix T. This is equivalent to |
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166 c restarting the iteration with a starting vector |
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167 c that is a linear combination of Ritz vectors |
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168 c associated with the "wanted" Ritz values. |
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169 c ------------------------------------------------------------- |
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170 c |
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171 c IPARAM(2) = LEVEC |
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172 c No longer referenced. See remark 2 below. |
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173 c |
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174 c IPARAM(3) = MXITER |
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175 c On INPUT: maximum number of Arnoldi update iterations allowed. |
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176 c On OUTPUT: actual number of Arnoldi update iterations taken. |
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177 c |
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178 c IPARAM(4) = NB: blocksize to be used in the recurrence. |
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179 c The code currently works only for NB = 1. |
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180 c |
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181 c IPARAM(5) = NCONV: number of "converged" Ritz values. |
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182 c This represents the number of Ritz values that satisfy |
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183 c the convergence criterion. |
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184 c |
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185 c IPARAM(6) = IUPD |
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186 c No longer referenced. Implicit restarting is ALWAYS used. |
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187 c |
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188 c IPARAM(7) = MODE |
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189 c On INPUT determines what type of eigenproblem is being solved. |
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190 c Must be 1,2,3,4,5; See under \Description of ssaupd for the |
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191 c five modes available. |
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192 c |
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193 c IPARAM(8) = NP |
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194 c When ido = 3 and the user provides shifts through reverse |
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195 c communication (IPARAM(1)=0), ssaupd returns NP, the number |
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196 c of shifts the user is to provide. 0 < NP <=NCV-NEV. See Remark |
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197 c 6 below. |
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198 c |
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199 c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, |
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200 c OUTPUT: NUMOP = total number of OP*x operations, |
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201 c NUMOPB = total number of B*x operations if BMAT='G', |
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202 c NUMREO = total number of steps of re-orthogonalization. |
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203 c |
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204 c IPNTR Integer array of length 11. (OUTPUT) |
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205 c Pointer to mark the starting locations in the WORKD and WORKL |
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206 c arrays for matrices/vectors used by the Lanczos iteration. |
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207 c ------------------------------------------------------------- |
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208 c IPNTR(1): pointer to the current operand vector X in WORKD. |
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209 c IPNTR(2): pointer to the current result vector Y in WORKD. |
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210 c IPNTR(3): pointer to the vector B * X in WORKD when used in |
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211 c the shift-and-invert mode. |
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212 c IPNTR(4): pointer to the next available location in WORKL |
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213 c that is untouched by the program. |
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214 c IPNTR(5): pointer to the NCV by 2 tridiagonal matrix T in WORKL. |
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215 c IPNTR(6): pointer to the NCV RITZ values array in WORKL. |
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216 c IPNTR(7): pointer to the Ritz estimates in array WORKL associated |
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217 c with the Ritz values located in RITZ in WORKL. |
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218 c IPNTR(11): pointer to the NP shifts in WORKL. See Remark 6 below. |
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219 c |
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220 c Note: IPNTR(8:10) is only referenced by sseupd. See Remark 2. |
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221 c IPNTR(8): pointer to the NCV RITZ values of the original system. |
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222 c IPNTR(9): pointer to the NCV corresponding error bounds. |
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223 c IPNTR(10): pointer to the NCV by NCV matrix of eigenvectors |
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224 c of the tridiagonal matrix T. Only referenced by |
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225 c sseupd if RVEC = .TRUE. See Remarks. |
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226 c ------------------------------------------------------------- |
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227 c |
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228 c WORKD Real work array of length 3*N. (REVERSE COMMUNICATION) |
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229 c Distributed array to be used in the basic Arnoldi iteration |
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230 c for reverse communication. The user should not use WORKD |
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231 c as temporary workspace during the iteration. Upon termination |
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232 c WORKD(1:N) contains B*RESID(1:N). If the Ritz vectors are desired |
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233 c subroutine sseupd uses this output. |
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234 c See Data Distribution Note below. |
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235 c |
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236 c WORKL Real work array of length LWORKL. (OUTPUT/WORKSPACE) |
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237 c Private (replicated) array on each PE or array allocated on |
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238 c the front end. See Data Distribution Note below. |
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239 c |
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240 c LWORKL Integer. (INPUT) |
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241 c LWORKL must be at least NCV**2 + 8*NCV . |
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242 c |
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243 c INFO Integer. (INPUT/OUTPUT) |
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244 c If INFO .EQ. 0, a randomly initial residual vector is used. |
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245 c If INFO .NE. 0, RESID contains the initial residual vector, |
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246 c possibly from a previous run. |
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247 c Error flag on output. |
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248 c = 0: Normal exit. |
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249 c = 1: Maximum number of iterations taken. |
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250 c All possible eigenvalues of OP has been found. IPARAM(5) |
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251 c returns the number of wanted converged Ritz values. |
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252 c = 2: No longer an informational error. Deprecated starting |
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253 c with release 2 of ARPACK. |
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254 c = 3: No shifts could be applied during a cycle of the |
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255 c Implicitly restarted Arnoldi iteration. One possibility |
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256 c is to increase the size of NCV relative to NEV. |
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257 c See remark 4 below. |
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258 c = -1: N must be positive. |
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259 c = -2: NEV must be positive. |
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260 c = -3: NCV must be greater than NEV and less than or equal to N. |
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261 c = -4: The maximum number of Arnoldi update iterations allowed |
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262 c must be greater than zero. |
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263 c = -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'. |
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264 c = -6: BMAT must be one of 'I' or 'G'. |
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265 c = -7: Length of private work array WORKL is not sufficient. |
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266 c = -8: Error return from trid. eigenvalue calculation; |
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267 c Informatinal error from LAPACK routine ssteqr. |
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268 c = -9: Starting vector is zero. |
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269 c = -10: IPARAM(7) must be 1,2,3,4,5. |
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270 c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatable. |
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271 c = -12: IPARAM(1) must be equal to 0 or 1. |
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272 c = -13: NEV and WHICH = 'BE' are incompatable. |
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273 c = -9999: Could not build an Arnoldi factorization. |
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274 c IPARAM(5) returns the size of the current Arnoldi |
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275 c factorization. The user is advised to check that |
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276 c enough workspace and array storage has been allocated. |
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277 c |
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278 c |
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279 c\Remarks |
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280 c 1. The converged Ritz values are always returned in ascending |
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281 c algebraic order. The computed Ritz values are approximate |
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282 c eigenvalues of OP. The selection of WHICH should be made |
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283 c with this in mind when Mode = 3,4,5. After convergence, |
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284 c approximate eigenvalues of the original problem may be obtained |
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285 c with the ARPACK subroutine sseupd. |
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286 c |
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287 c 2. If the Ritz vectors corresponding to the converged Ritz values |
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288 c are needed, the user must call sseupd immediately following completion |
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289 c of ssaupd. This is new starting with version 2.1 of ARPACK. |
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290 c |
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291 c 3. If M can be factored into a Cholesky factorization M = LL` |
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292 c then Mode = 2 should not be selected. Instead one should use |
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293 c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular |
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294 c linear systems should be solved with L and L` rather |
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295 c than computing inverses. After convergence, an approximate |
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296 c eigenvector z of the original problem is recovered by solving |
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297 c L`z = x where x is a Ritz vector of OP. |
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298 c |
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299 c 4. At present there is no a-priori analysis to guide the selection |
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300 c of NCV relative to NEV. The only formal requrement is that NCV > NEV. |
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301 c However, it is recommended that NCV .ge. 2*NEV. If many problems of |
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302 c the same type are to be solved, one should experiment with increasing |
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303 c NCV while keeping NEV fixed for a given test problem. This will |
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304 c usually decrease the required number of OP*x operations but it |
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305 c also increases the work and storage required to maintain the orthogonal |
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306 c basis vectors. The optimal "cross-over" with respect to CPU time |
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307 c is problem dependent and must be determined empirically. |
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308 c |
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309 c 5. If IPARAM(7) = 2 then in the Reverse commuication interface the user |
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310 c must do the following. When IDO = 1, Y = OP * X is to be computed. |
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311 c When IPARAM(7) = 2 OP = inv(B)*A. After computing A*X the user |
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312 c must overwrite X with A*X. Y is then the solution to the linear set |
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313 c of equations B*Y = A*X. |
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314 c |
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315 c 6. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the |
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316 c NP = IPARAM(8) shifts in locations: |
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317 c 1 WORKL(IPNTR(11)) |
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318 c 2 WORKL(IPNTR(11)+1) |
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319 c . |
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320 c . |
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321 c . |
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322 c NP WORKL(IPNTR(11)+NP-1). |
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323 c |
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324 c The eigenvalues of the current tridiagonal matrix are located in |
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325 c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1). They are in the |
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326 c order defined by WHICH. The associated Ritz estimates are located in |
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327 c WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8)+NCV-1). |
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328 c |
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329 c----------------------------------------------------------------------- |
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330 c |
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331 c\Data Distribution Note: |
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332 c |
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333 c Fortran-D syntax: |
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334 c ================ |
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335 c REAL RESID(N), V(LDV,NCV), WORKD(3*N), WORKL(LWORKL) |
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336 c DECOMPOSE D1(N), D2(N,NCV) |
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337 c ALIGN RESID(I) with D1(I) |
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338 c ALIGN V(I,J) with D2(I,J) |
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339 c ALIGN WORKD(I) with D1(I) range (1:N) |
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340 c ALIGN WORKD(I) with D1(I-N) range (N+1:2*N) |
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341 c ALIGN WORKD(I) with D1(I-2*N) range (2*N+1:3*N) |
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342 c DISTRIBUTE D1(BLOCK), D2(BLOCK,:) |
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343 c REPLICATED WORKL(LWORKL) |
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344 c |
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345 c Cray MPP syntax: |
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346 c =============== |
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347 c REAL RESID(N), V(LDV,NCV), WORKD(N,3), WORKL(LWORKL) |
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348 c SHARED RESID(BLOCK), V(BLOCK,:), WORKD(BLOCK,:) |
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349 c REPLICATED WORKL(LWORKL) |
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350 c |
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351 c |
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352 c\BeginLib |
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353 c |
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354 c\References: |
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355 c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in |
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356 c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), |
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357 c pp 357-385. |
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358 c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly |
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359 c Restarted Arnoldi Iteration", Rice University Technical Report |
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360 c TR95-13, Department of Computational and Applied Mathematics. |
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361 c 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, |
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362 c 1980. |
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363 c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", |
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364 c Computer Physics Communications, 53 (1989), pp 169-179. |
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365 c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to |
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366 c Implement the Spectral Transformation", Math. Comp., 48 (1987), |
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367 c pp 663-673. |
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368 c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos |
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369 c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", |
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370 c SIAM J. Matr. Anal. Apps., January (1993). |
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371 c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines |
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372 c for Updating the QR decomposition", ACM TOMS, December 1990, |
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373 c Volume 16 Number 4, pp 369-377. |
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374 c 8. R.B. Lehoucq, D.C. Sorensen, "Implementation of Some Spectral |
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375 c Transformations in a k-Step Arnoldi Method". In Preparation. |
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376 c |
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377 c\Routines called: |
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378 c ssaup2 ARPACK routine that implements the Implicitly Restarted |
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379 c Arnoldi Iteration. |
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380 c sstats ARPACK routine that initialize timing and other statistics |
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381 c variables. |
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382 c ivout ARPACK utility routine that prints integers. |
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383 c arscnd ARPACK utility routine for timing. |
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384 c svout ARPACK utility routine that prints vectors. |
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385 c slamch LAPACK routine that determines machine constants. |
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386 c |
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387 c\Authors |
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388 c Danny Sorensen Phuong Vu |
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389 c Richard Lehoucq CRPC / Rice University |
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390 c Dept. of Computational & Houston, Texas |
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391 c Applied Mathematics |
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392 c Rice University |
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393 c Houston, Texas |
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394 c |
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395 c\Revision history: |
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396 c 12/15/93: Version ' 2.4' |
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397 c |
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398 c\SCCS Information: @(#) |
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399 c FILE: saupd.F SID: 2.8 DATE OF SID: 04/10/01 RELEASE: 2 |
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400 c |
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401 c\Remarks |
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402 c 1. None |
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403 c |
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404 c\EndLib |
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405 c |
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406 c----------------------------------------------------------------------- |
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407 c |
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408 subroutine ssaupd |
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409 & ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, |
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410 & ipntr, workd, workl, lworkl, info ) |
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411 c |
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412 c %----------------------------------------------------% |
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413 c | Include files for debugging and timing information | |
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414 c %----------------------------------------------------% |
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415 c |
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416 include 'debug.h' |
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417 include 'stat.h' |
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418 c |
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419 c %------------------% |
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420 c | Scalar Arguments | |
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421 c %------------------% |
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422 c |
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423 character bmat*1, which*2 |
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424 integer ido, info, ldv, lworkl, n, ncv, nev |
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425 Real |
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426 & tol |
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427 c |
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428 c %-----------------% |
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429 c | Array Arguments | |
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430 c %-----------------% |
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431 c |
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432 integer iparam(11), ipntr(11) |
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433 Real |
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434 & resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) |
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435 c |
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436 c %------------% |
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437 c | Parameters | |
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438 c %------------% |
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439 c |
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440 Real |
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441 & one, zero |
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442 parameter (one = 1.0E+0 , zero = 0.0E+0 ) |
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443 c |
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444 c %---------------% |
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445 c | Local Scalars | |
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446 c %---------------% |
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447 c |
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448 integer bounds, ierr, ih, iq, ishift, iupd, iw, |
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449 & ldh, ldq, msglvl, mxiter, mode, nb, |
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450 & nev0, next, np, ritz, j |
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451 save bounds, ierr, ih, iq, ishift, iupd, iw, |
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452 & ldh, ldq, msglvl, mxiter, mode, nb, |
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453 & nev0, next, np, ritz |
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454 c |
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455 c %----------------------% |
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456 c | External Subroutines | |
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457 c %----------------------% |
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458 c |
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459 external ssaup2, svout, ivout, arscnd, sstats |
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|
460 c |
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|
461 c %--------------------% |
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462 c | External Functions | |
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463 c %--------------------% |
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464 c |
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465 Real |
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466 & slamch |
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467 external slamch |
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468 c |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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|
469 c %-----------------------% |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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470 c | Executable Statements | |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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471 c %-----------------------% |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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472 c |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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473 if (ido .eq. 0) then |
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474 c |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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|
475 c %-------------------------------% |
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476 c | Initialize timing statistics | |
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477 c | & message level for debugging | |
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478 c %-------------------------------% |
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479 c |
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480 call sstats |
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481 call arscnd (t0) |
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482 msglvl = msaupd |
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483 c |
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484 ierr = 0 |
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485 ishift = iparam(1) |
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486 mxiter = iparam(3) |
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487 c nb = iparam(4) |
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488 nb = 1 |
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489 c |
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490 c %--------------------------------------------% |
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491 c | Revision 2 performs only implicit restart. | |
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492 c %--------------------------------------------% |
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493 c |
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494 iupd = 1 |
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495 mode = iparam(7) |
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496 c |
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497 c %----------------% |
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498 c | Error checking | |
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499 c %----------------% |
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500 c |
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501 if (n .le. 0) then |
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502 ierr = -1 |
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503 else if (nev .le. 0) then |
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504 ierr = -2 |
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505 else if (ncv .le. nev .or. ncv .gt. n) then |
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506 ierr = -3 |
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507 end if |
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508 c |
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509 c %----------------------------------------------% |
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510 c | NP is the number of additional steps to | |
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511 c | extend the length NEV Lanczos factorization. | |
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512 c %----------------------------------------------% |
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513 c |
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514 np = ncv - nev |
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515 c |
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516 if (mxiter .le. 0) ierr = -4 |
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517 if (which .ne. 'LM' .and. |
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518 & which .ne. 'SM' .and. |
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519 & which .ne. 'LA' .and. |
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|
520 & which .ne. 'SA' .and. |
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|
521 & which .ne. 'BE') ierr = -5 |
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522 if (bmat .ne. 'I' .and. bmat .ne. 'G') ierr = -6 |
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523 c |
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524 if (lworkl .lt. ncv**2 + 8*ncv) ierr = -7 |
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|
525 if (mode .lt. 1 .or. mode .gt. 5) then |
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526 ierr = -10 |
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|
527 else if (mode .eq. 1 .and. bmat .eq. 'G') then |
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|
528 ierr = -11 |
9f5d2ef078e8
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|
529 else if (ishift .lt. 0 .or. ishift .gt. 1) then |
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John W. Eaton <jwe@octave.org>
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|
530 ierr = -12 |
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parents:
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changeset
|
531 else if (nev .eq. 1 .and. which .eq. 'BE') then |
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|
532 ierr = -13 |
9f5d2ef078e8
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parents:
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|
533 end if |
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John W. Eaton <jwe@octave.org>
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|
534 c |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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|
535 c %------------% |
9f5d2ef078e8
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John W. Eaton <jwe@octave.org>
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|
536 c | Error Exit | |
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John W. Eaton <jwe@octave.org>
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|
537 c %------------% |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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|
538 c |
9f5d2ef078e8
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John W. Eaton <jwe@octave.org>
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|
539 if (ierr .ne. 0) then |
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|
540 info = ierr |
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|
541 ido = 99 |
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John W. Eaton <jwe@octave.org>
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|
542 go to 9000 |
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|
543 end if |
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|
544 c |
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John W. Eaton <jwe@octave.org>
parents:
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|
545 c %------------------------% |
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parents:
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|
546 c | Set default parameters | |
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John W. Eaton <jwe@octave.org>
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|
547 c %------------------------% |
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changeset
|
548 c |
9f5d2ef078e8
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parents:
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changeset
|
549 if (nb .le. 0) nb = 1 |
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|
550 if (tol .le. zero) tol = slamch('EpsMach') |
9f5d2ef078e8
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John W. Eaton <jwe@octave.org>
parents:
diff
changeset
|
551 c |
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John W. Eaton <jwe@octave.org>
parents:
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|
552 c %----------------------------------------------% |
9f5d2ef078e8
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parents:
diff
changeset
|
553 c | NP is the number of additional steps to | |
9f5d2ef078e8
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John W. Eaton <jwe@octave.org>
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|
554 c | extend the length NEV Lanczos factorization. | |
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John W. Eaton <jwe@octave.org>
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555 c | NEV0 is the local variable designating the | |
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parents:
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556 c | size of the invariant subspace desired. | |
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John W. Eaton <jwe@octave.org>
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557 c %----------------------------------------------% |
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parents:
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|
558 c |
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John W. Eaton <jwe@octave.org>
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559 np = ncv - nev |
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John W. Eaton <jwe@octave.org>
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changeset
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560 nev0 = nev |
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John W. Eaton <jwe@octave.org>
parents:
diff
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561 c |
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John W. Eaton <jwe@octave.org>
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562 c %-----------------------------% |
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John W. Eaton <jwe@octave.org>
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|
563 c | Zero out internal workspace | |
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John W. Eaton <jwe@octave.org>
parents:
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564 c %-----------------------------% |
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565 c |
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parents:
diff
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|
566 do 10 j = 1, ncv**2 + 8*ncv |
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John W. Eaton <jwe@octave.org>
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changeset
|
567 workl(j) = zero |
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John W. Eaton <jwe@octave.org>
parents:
diff
changeset
|
568 10 continue |
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John W. Eaton <jwe@octave.org>
parents:
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|
569 c |
9f5d2ef078e8
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parents:
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changeset
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570 c %-------------------------------------------------------% |
9f5d2ef078e8
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John W. Eaton <jwe@octave.org>
parents:
diff
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571 c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | |
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John W. Eaton <jwe@octave.org>
parents:
diff
changeset
|
572 c | etc... and the remaining workspace. | |
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John W. Eaton <jwe@octave.org>
parents:
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573 c | Also update pointer to be used on output. | |
9f5d2ef078e8
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John W. Eaton <jwe@octave.org>
parents:
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|
574 c | Memory is laid out as follows: | |
9f5d2ef078e8
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John W. Eaton <jwe@octave.org>
parents:
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575 c | workl(1:2*ncv) := generated tridiagonal matrix | |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
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|
576 c | workl(2*ncv+1:2*ncv+ncv) := ritz values | |
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John W. Eaton <jwe@octave.org>
parents:
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changeset
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577 c | workl(3*ncv+1:3*ncv+ncv) := computed error bounds | |
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John W. Eaton <jwe@octave.org>
parents:
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578 c | workl(4*ncv+1:4*ncv+ncv*ncv) := rotation matrix Q | |
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John W. Eaton <jwe@octave.org>
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changeset
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579 c | workl(4*ncv+ncv*ncv+1:7*ncv+ncv*ncv) := workspace | |
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John W. Eaton <jwe@octave.org>
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changeset
|
580 c %-------------------------------------------------------% |
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|
581 c |
9f5d2ef078e8
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582 ldh = ncv |
9f5d2ef078e8
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583 ldq = ncv |
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584 ih = 1 |
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585 ritz = ih + 2*ldh |
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586 bounds = ritz + ncv |
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587 iq = bounds + ncv |
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588 iw = iq + ncv**2 |
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589 next = iw + 3*ncv |
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John W. Eaton <jwe@octave.org>
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590 c |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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591 ipntr(4) = next |
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592 ipntr(5) = ih |
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593 ipntr(6) = ritz |
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|
594 ipntr(7) = bounds |
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595 ipntr(11) = iw |
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John W. Eaton <jwe@octave.org>
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|
596 end if |
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John W. Eaton <jwe@octave.org>
parents:
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changeset
|
597 c |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
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changeset
|
598 c %-------------------------------------------------------% |
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John W. Eaton <jwe@octave.org>
parents:
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|
599 c | Carry out the Implicitly restarted Lanczos Iteration. | |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
parents:
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changeset
|
600 c %-------------------------------------------------------% |
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John W. Eaton <jwe@octave.org>
parents:
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changeset
|
601 c |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
John W. Eaton <jwe@octave.org>
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changeset
|
602 call ssaup2 |
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John W. Eaton <jwe@octave.org>
parents:
diff
changeset
|
603 & ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd, |
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John W. Eaton <jwe@octave.org>
parents:
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604 & ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritz), |
9f5d2ef078e8
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parents:
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605 & workl(bounds), workl(iq), ldq, workl(iw), ipntr, workd, |
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changeset
|
606 & info ) |
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changeset
|
607 c |
9f5d2ef078e8
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|
608 c %--------------------------------------------------% |
9f5d2ef078e8
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John W. Eaton <jwe@octave.org>
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609 c | ido .ne. 99 implies use of reverse communication | |
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changeset
|
610 c | to compute operations involving OP or shifts. | |
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changeset
|
611 c %--------------------------------------------------% |
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import ARPACK sources to libcruft from Debian package libarpack2 2.1+parpack96.dfsg-3+b1
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changeset
|
612 c |
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|
613 if (ido .eq. 3) iparam(8) = np |
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614 if (ido .ne. 99) go to 9000 |
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|
615 c |
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616 iparam(3) = mxiter |
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617 iparam(5) = np |
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618 iparam(9) = nopx |
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619 iparam(10) = nbx |
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620 iparam(11) = nrorth |
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621 c |
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622 c %------------------------------------% |
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623 c | Exit if there was an informational | |
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624 c | error within ssaup2. | |
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625 c %------------------------------------% |
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626 c |
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627 if (info .lt. 0) go to 9000 |
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628 if (info .eq. 2) info = 3 |
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629 c |
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630 if (msglvl .gt. 0) then |
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631 call ivout (logfil, 1, mxiter, ndigit, |
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632 & '_saupd: number of update iterations taken') |
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633 call ivout (logfil, 1, np, ndigit, |
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634 & '_saupd: number of "converged" Ritz values') |
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635 call svout (logfil, np, workl(Ritz), ndigit, |
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636 & '_saupd: final Ritz values') |
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637 call svout (logfil, np, workl(Bounds), ndigit, |
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638 & '_saupd: corresponding error bounds') |
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|
639 end if |
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|
640 c |
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641 call arscnd (t1) |
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642 tsaupd = t1 - t0 |
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|
643 c |
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644 if (msglvl .gt. 0) then |
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|
645 c |
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646 c %--------------------------------------------------------% |
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647 c | Version Number & Version Date are defined in version.h | |
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648 c %--------------------------------------------------------% |
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649 c |
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650 write (6,1000) |
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651 write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt, |
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652 & tmvopx, tmvbx, tsaupd, tsaup2, tsaitr, titref, |
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653 & tgetv0, tseigt, tsgets, tsapps, tsconv |
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654 1000 format (//, |
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655 & 5x, '==========================================',/ |
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656 & 5x, '= Symmetric implicit Arnoldi update code =',/ |
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657 & 5x, '= Version Number:', ' 2.4' , 19x, ' =',/ |
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658 & 5x, '= Version Date: ', ' 07/31/96' , 14x, ' =',/ |
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659 & 5x, '==========================================',/ |
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660 & 5x, '= Summary of timing statistics =',/ |
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661 & 5x, '==========================================',//) |
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662 1100 format ( |
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663 & 5x, 'Total number update iterations = ', i5,/ |
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664 & 5x, 'Total number of OP*x operations = ', i5,/ |
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665 & 5x, 'Total number of B*x operations = ', i5,/ |
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666 & 5x, 'Total number of reorthogonalization steps = ', i5,/ |
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667 & 5x, 'Total number of iterative refinement steps = ', i5,/ |
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668 & 5x, 'Total number of restart steps = ', i5,/ |
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669 & 5x, 'Total time in user OP*x operation = ', f12.6,/ |
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670 & 5x, 'Total time in user B*x operation = ', f12.6,/ |
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671 & 5x, 'Total time in Arnoldi update routine = ', f12.6,/ |
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672 & 5x, 'Total time in saup2 routine = ', f12.6,/ |
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673 & 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/ |
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674 & 5x, 'Total time in reorthogonalization phase = ', f12.6,/ |
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675 & 5x, 'Total time in (re)start vector generation = ', f12.6,/ |
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676 & 5x, 'Total time in trid eigenvalue subproblem = ', f12.6,/ |
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677 & 5x, 'Total time in getting the shifts = ', f12.6,/ |
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678 & 5x, 'Total time in applying the shifts = ', f12.6,/ |
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679 & 5x, 'Total time in convergence testing = ', f12.6) |
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680 end if |
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681 c |
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682 9000 continue |
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683 c |
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684 return |
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685 c |
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686 c %---------------% |
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687 c | End of ssaupd | |
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688 c %---------------% |
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689 c |
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690 end |