meplib / binaries / bin / checkSimpleSolutions-01.pl @ master
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#! /usr/bin/perl |
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|
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# checkSimpleSolutions-01.pl - ST - 2006-01-24 |
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# |
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# Check the quality of a solution with the Maple infnorm. |
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# |
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# COMMAND LINE SYNTAX: |
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# checkSimpleSolutions-01.pl digitsNum decPointPos solutionsFile positionsFile |
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|
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# NOTE(S): |
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# This version checks the solutions produced by the "gp" PARI utility |
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# The number of chunks is given by the positionsFile |
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|
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############################################################################## |
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# PROGRAM DECLARATIONS |
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############################################################################## |
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|
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BEGIN |
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{
|
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# Modify @INC here if necessary |
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push(@INC, '../utils'); |
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}; |
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|
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# core modules |
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use strict; # must be first to force strict in all others |
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use Carp; |
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use Getopt::Long; |
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use Math::BigInt; |
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use Math::BigRat; |
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use Math::BigFloat; |
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|
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# custom modules |
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# Uncomment if you want to use standard exit error codes. |
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# the stdExitErrors.pm file must be available around. |
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use stdExitErrors; |
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|
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############################################################################## |
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# PROGRAM CONSTANT DECLARATIONS |
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############################################################################## |
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my $bigIntZero = Math::BigInt->new('0');
|
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my $debug = 1; |
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my $variableName = "x"; |
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my $mapleApplication = "/usr/local/maple/bin/maple"; |
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############################################################################## |
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# PROGRAM VARIABLE DECLARATIONS |
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############################################################################## |
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my $solutionsFileName = ""; |
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my $positionsFileName = ""; |
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my $numDigits = 0; |
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my $decPointPos = 0; |
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my $numChunks = 0; |
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my $function = ""; |
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my $lowerBound = ""; |
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my $upperBound = ""; |
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my $elem = ""; |
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my $line = ""; |
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my $lineNum = 0; |
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my @line = (); |
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my $powerOfTen = 0; |
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my $solutionVectorRef = 0; |
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my @solutionMatrix = (); |
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my @positionsVector = (); |
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my $powerIndex = 0; |
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my $polynomialDegree = 0; |
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my $mainDivisor = 0; |
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my @chunkMultipliers = (); |
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my $polynomialString = ""; |
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my @polynomials = (); |
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my $mapleProgram = (); |
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my $mapleResult = 0; |
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my $infNorm = ""; |
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my @infNorm = (); |
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my %sortHash = (); |
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my @sortedInfNorms = (); |
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# |
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# |
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# |
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############################################################################## |
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# TEST ENVIRONMENT AND CONFIGURATION VARIABLES |
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############################################################################## |
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|
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############################################################################## |
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# INITIALIZE DEBUG FILE |
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############################################################################## |
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|
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############################################################################## |
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# INITIALIZE LOG FILE |
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############################################################################## |
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|
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############################################################################## |
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# GET COMMAND LINE ARGUMENTS |
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############################################################################## |
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|
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############################################################################## |
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# PROGRAM MAIN |
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############################################################################## |
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&usage(); |
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# |
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# Check the command line parameters |
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# |
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# It's a TODO! |
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# |
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# Open the files |
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# |
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# First the solution vector file. |
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# |
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if (! open(SVF, "<$solutionsFileName")) |
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{
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print STDERR "\n\nCan't open $solutionsFileName. Aborting the program!\n\n"; |
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exit($EX_NOINPUT); |
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} |
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# Second the positions file. |
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# |
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if (! open(POF, "<$positionsFileName")) |
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{
|
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print STDERR "\n\nCan't open $positionsFileName. Aborting the program!\n\n"; |
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exit($EX_NOINPUT); |
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} |
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# |
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# Scan the solutions file. |
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# |
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while ($line = <SVF>) |
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{
|
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# Remove the '\n'. |
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chomp($line); |
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# Coalescing all consecutive spaces to one. |
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$line =~ s/(\s)+/ /g; |
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# Removing leading and trailling spaces. |
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$line =~ s/(^\s*)||(\s*$)//g; |
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# Only take into account the lines starting with "A[". |
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if (! ($line =~ /^A\[/)) |
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{
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next; |
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} |
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# Remove syntatic sugar. |
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$line =~ s/.*=\[//; |
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$line =~ s/\]://; |
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$solutionVectorRef = []; |
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@$solutionVectorRef = split(/,/, $line); |
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for (my $i = 0 ; $i < @$solutionVectorRef ; $i++) |
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{
|
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$$solutionVectorRef[$i] = Math::BigInt->new($$solutionVectorRef[$i]); |
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if($$solutionVectorRef[$i]->is_nan()) |
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{
|
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print STDERR "\n\n\"$line\" from the solution vector file holds an invalid"; |
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print STDERR " number at index $i."; |
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print STDERR " Aborting the program!\n\n"; |
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exit($EX_DATAERR); |
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} |
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} # End for |
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push(@solutionMatrix, $solutionVectorRef); |
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} # End while ($line = <SVF>) |
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# |
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# Read the positions file |
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# |
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$lineNum = 1; |
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while($line=<POF>) |
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{
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chomp($line); |
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# Coalescing all consecutive spaces to one. |
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$line =~ s/(\s)+/ /g; |
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# Removing leading and trailling spaces. |
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$line =~ s/(^\s*)||(\s*$)//g; |
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# The number of chunks is all by itself on the first line. |
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if ($lineNum == 1) |
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{
|
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$numChunks = $line; |
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} |
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# All the element are on line 2 |
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if ($lineNum == 2) |
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{
|
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@positionsVector = split(/ /, $line); |
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if (@positionsVector != $numChunks) |
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{
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print STDERR "\n\n\ The announced number of chunks($numChunks) "; |
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print STDERR "does not match the actual number of chuncks ", @positionsVector * 1; |
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print STDERR ". Aborting the program!\n\n"; |
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exit($EX_DATAERR); |
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} |
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last; # Only two data lines in positions file. |
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} |
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$lineNum++; |
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} # end scanning POF |
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# |
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# Degree of the polynomial |
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# |
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if ((@{$solutionMatrix[0]} % $numChunks) != 0)
|
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{
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print STDERR "\n\n\ The number of elements per solution (",(@{$solutionMatrix[0]} * 1);
|
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print STDERR ") and the number of chunks ($numChunks) do not match: "; |
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print STDERR "NumElemPerSols mod NumChunks should be zero.\n"; |
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print STDERR "Aborting the program!\n\n"; |
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exit($EX_DATAERR); |
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} |
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$polynomialDegree = @{$solutionMatrix[0]} / $numChunks - 1;
|
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# TODO: add a check on the degree (>=0) |
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$mainDivisor = "2^$decPointPos"; |
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# |
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# Compute the chunk multipliers |
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# |
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for (my $i = 0 ; $i < @positionsVector ; $i++) |
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{
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push(@chunkMultipliers, "2^$positionsVector[$i]"); |
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} # End for $i |
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# |
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# Shape a polynomial for Maple |
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# |
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for (my $i = 0 ; $i < @solutionMatrix ; $i++) |
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{
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$polynomialString = "P:=$variableName->"; |
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for (my $j = 0 ; $j <= $polynomialDegree ; $j++) |
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{
|
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if ($j != 0) |
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{
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$polynomialString .= " + $variableName * (("
|
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} |
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for (my $k = 0 ; $k < @chunkMultipliers ; $k++) |
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{
|
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if (${$solutionMatrix[$i]}[$j] < 0)
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{
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$polynomialString .= "((${$solutionMatrix[$i]}[$j * $numChunks + $k])";
|
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} |
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else |
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{
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$polynomialString .= "(${$solutionMatrix[$i]}[$j * $numChunks + $k]";
|
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} |
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$polynomialString .= "*$chunkMultipliers[$k])"; |
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$polynomialString .= "/$mainDivisor"; |
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if ($k != (@chunkMultipliers - 1)) |
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{
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$polynomialString .= "+"; |
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} |
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} # End for $k $so |
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if ($j != 0) |
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{
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$polynomialString .= ") "; |
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} |
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} # End or $j |
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$polynomialString .= (')' x $polynomialDegree);
|
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$polynomialString .= ";"; |
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push(@polynomials, $polynomialString); |
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} # End for $i |
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#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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#exit(0); |
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#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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# |
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if ($debug) |
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{
|
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print STDERR "\nNum digits: $numDigits\n"; |
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print STDERR "\nDecimal point position: $decPointPos\n"; |
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print STDERR "\n Solutions:\n"; |
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for (my $i = 0 ; $i < @solutionMatrix ; $i++) |
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{
|
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for (my $j = 0 ; $j < @{$solutionMatrix[$i]} ; $j++)
|
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{
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print STDERR "${$solutionMatrix[$i]}[$j] ";
|
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} # End for $j |
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print STDERR "\n" |
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} # End for $i |
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print STDERR "\n"; |
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print STDERR "$numChunks chunk(s) at position(s): "; |
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for (my $i = 0 ; $i < @positionsVector ; $i++) |
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{
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print STDERR "$positionsVector[$i] "; |
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} # End for $i |
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print STDERR "\n"; |
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print STDERR "Degree of the polynomial: $polynomialDegree"; |
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print STDERR "\n"; |
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print STDERR "Main divisor: $mainDivisor"; |
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print STDERR "\n"; |
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print STDERR "Chunk multipliers:"; |
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for (my $i = 0 ; $i < @chunkMultipliers ; $i++) |
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{
|
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print STDERR "$chunkMultipliers[$i] "; |
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} # End for $i |
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print STDERR "Polynomials:\n"; |
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foreach $elem (@polynomials) |
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{
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print STDERR "$elem\n" |
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} |
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print STDERR "\n\n"; |
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} # End debug |
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# |
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# Run Maple and analyse the output. |
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# |
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# |
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# The interesting part is made of the three last lines. |
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# The last line is made of a simple prompt at the begining of the line: ">" |
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# |
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for (my $i = 0 ; $i < @polynomials ; $i++) |
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{
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$mapleProgram = "with(numapprox);"; |
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$mapleProgram .= $polynomials[$i]; |
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$mapleProgram .= "infnorm(($function-P(x)), x=$lowerBound..$upperBound, 'xmax');"; |
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$mapleResult = &runMaple($mapleProgram); |
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for (my $j = 0 ; $j < @$mapleResult; $j++) |
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{
|
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if ($$mapleResult[$j] =~ /^> quit/) |
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{
|
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# |
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# Removing leading and trailling spacesi for the exponent line. |
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$$mapleResult[$j - 3] =~ s/(^\s*)||(\s*$)//g; |
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if ($$mapleResult[$j - 3] ne "") |
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{
|
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$infNorm = $$mapleResult[$j - 3]; |
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$powerOfTen = '(' . $$mapleResult[$j - 3] . '))';
|
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} |
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else |
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{
|
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$infNorm = ""; |
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$powerOfTen = ""; |
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} |
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# Removing leading and trailling spaces. |
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$$mapleResult[$j - 2] =~ s/(^\s*)||(\s*$)//g; |
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print STDERR '.'; |
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if (length($powerOfTen) > 0) |
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{
|
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@infNorm = split(/ /, $$mapleResult[$j - 2]); |
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$infNorm = eval("$infNorm[0] * ($infNorm[1]**".$powerOfTen);
|
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} |
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else |
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{
|
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$infNorm = $$mapleResult[$j - 2]; |
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} |
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#print STDERR $infNorm; |
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while(defined($sortHash{$infNorm}))
|
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{
|
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$infNorm .= ' '; |
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} |
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$sortHash{$infNorm} = $solutionMatrix[$i];
|
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} # End if ($$mapleResult[$j] =~ /^> quit/) |
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} # End for $j |
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} # End for $i |
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print STDERR "\n"; |
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@sortedInfNorms = sort(keys(%sortHash)); |
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foreach $elem (@sortedInfNorms) |
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{
|
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for (my $i = 0 ; $i < @{$sortHash{$elem}} ; $i ++)
|
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{
|
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print "${$sortHash{$elem}}[$i] ";
|
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} |
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print "-\> "; |
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print "$elem\n"; |
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} |
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|
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# Uncomment this line and remove the next one if using stdExitErrors. |
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exit($EX_OK); |
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|
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############################################################################## |
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# PROGRAM SUBS |
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############################################################################## |
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# |
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############################################################################## |
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# sub runMaple |
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############################################################################## |
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# Performed task: runs Maple with a program and returns the answer |
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# |
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# input : $mapleProgram |
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# output : $mapleResultRef |
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# globals : none |
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# uses : none |
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# notes : none |
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# |
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sub runMaple {
|
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my ($mapleProgram) = @_; |
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if (! defined($mapleProgram)) |
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{
|
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my @call_info = caller(0); |
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print "\n\n", $call_info[3], " missing parameter. Aborting program!\n\n"; |
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# Uncomment this line and remove the next one if using stdExitErrors. |
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#exit($EX_SOFTWARE); |
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exit(1); |
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} |
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my $line = ""; |
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my $mapleResult = []; |
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#print STDERR $mapleProgram, "\n"; |
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open(MR, "echo \"$mapleProgram\" | $mapleApplication |"); |
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while($line = <MR>) |
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{
|
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chomp($line); |
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push(@$mapleResult,$line); |
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} |
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return($mapleResult); |
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} # End runMaple |
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############################################################################## |
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# sub mySub |
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############################################################################## |
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# Performed task: |
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# |
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# input : |
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# output : |
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# globals : |
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# uses : |
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# notes : |
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# |
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sub mySub {
|
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my ($someParameter) = @_; |
| 398 |
if (! defined($someParameter)) |
| 399 |
{
|
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my @call_info = caller(0); |
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print "\n\n", $call_info[3], " missing parameter. Aborting program!\n\n"; |
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# Uncomment this line and remove the next one if using stdExitErrors. |
| 403 |
#exit($EX_SOFTWARE); |
| 404 |
exit(1); |
| 405 |
} |
| 406 |
} # End mySub |
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############################################################################## |
| 408 |
# sub $retv = _privateSubName($argv) |
| 409 |
############################################################################## |
| 410 |
|
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sub _privateSubName |
| 412 |
{
|
| 413 |
my $argv = shift(); |
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my $retv = undef; |
| 415 |
return($retv); |
| 416 |
}; |
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# |
| 418 |
############################################################################## |
| 419 |
# sub usage |
| 420 |
############################################################################## |
| 421 |
# Performed task: checks the command line parameters |
| 422 |
# |
| 423 |
# input : none |
| 424 |
# output : none |
| 425 |
# globals : $ARGV,others... |
| 426 |
# uses : none |
| 427 |
# notes : |
| 428 |
# |
| 429 |
sub usage {
|
| 430 |
if (! defined($ARGV[6])) |
| 431 |
{
|
| 432 |
my $scriptName = `basename $0`; |
| 433 |
chomp $scriptName; |
| 434 |
print STDERR "\n\nUsage: $scriptName numDigits decPointPos solutionsFile \n"; |
| 435 |
print STDERR " " , (" " x length("$scriptName ")), "positionsVectorFile";
|
| 436 |
print STDERR " function lowerBound upperBound\n\n"; |
| 437 |
print STDERR " - numDigits: the number of digits of the coefficients;\n"; |
| 438 |
print STDERR " - decPointPos: the positions of the decimal point;\n"; |
| 439 |
print STDERR " - solutionFile: the name of the solution vector file;\n"; |
| 440 |
print STDERR " - positionsFile: the name of the positions (of chunks in\n"; |
| 441 |
print STDERR " coefficient) vector file;\n"; |
| 442 |
print STDERR " - function (e.g. \"cos(x)\", don't forget quoting);\n"; |
| 443 |
print STDERR " - lowerBound (e.g. 0, don't forget quoting for complex expressions;\n"; |
| 444 |
print STDERR " - upperBound (e.g. \"Pi/4\" , don't forget quoting for complex expressions;\n"; |
| 445 |
# Uncomment this line and remove the next one if using stdExitErrors. |
| 446 |
#exit($EX_USAGE); |
| 447 |
exit(1); |
| 448 |
} # End if |
| 449 |
# Some initializations |
| 450 |
$numDigits = $ARGV[0]; |
| 451 |
$decPointPos = $ARGV[1]; |
| 452 |
$solutionsFileName = $ARGV[2]; |
| 453 |
$positionsFileName = $ARGV[3]; |
| 454 |
$function = $ARGV[4]; |
| 455 |
$lowerBound = $ARGV[5]; |
| 456 |
$upperBound = $ARGV[6]; |
| 457 |
} # End usage |
| 458 |
|
| 459 |
|
| 460 |
__END__ |
| 461 |
|