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package ICC::Support::nPINT; |
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use strict; |
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use Carp; |
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our $VERSION = 0.72; |
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# revised 2018-09-08 |
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# |
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# Copyright © 2004-2020 by William B. Birkett |
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# inherit from Shared |
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use parent qw(ICC::Shared); |
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# support modules |
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use POSIX (); |
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=encoding utf-8 |
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n-channel polynomial interpolation engine (nPINT), inspired by Francois Lekien, Chad Coulliette and Jerry |
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Marsden, authors of "Tricubic interpolation in three dimensions" and "Tricubic Engine Technical Notes and |
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Full Matrix". |
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create new nPINT object parameter hash structure: |
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{'pda' => [polynomial_degree_array], 'coef' => [nPINT_coefficients]} |
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the polynomial_degree_array contains the polynomial degree for each input channel, e.g. [3, 3, 3, 3] => 4 |
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channels, each of degree 3 |
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the nPINT coefficients define the behavior of the model. they are normally obtained using the 'fit' |
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method, which uses linear least squares to fit the model to the supplied data. the number of rows in the |
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coefficient array is equal to the product of each channel's degree + 1, e.g. if the pda is [3, 3, 3, 3], |
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there are 256 coefficient rows. the number columns in the coefficient array is equal to the number of |
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output channels. |
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=cut |
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# optional usage forms: |
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# parameters: () |
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# parameters: (ref_to_parameter_hash) |
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# parameters: (path_to_storable_file) |
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# returns: (object_reference) |
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sub new { |
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# get object class |
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my $class = shift(); |
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# create empty nPINT object |
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my $self = [ |
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{}, # object header |
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[], # input polynomial degree array |
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[], # output coefficient array |
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undef # cached output coefficient array |
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]; |
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# if one parameter, a hash reference |
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if (@_ == 1 && ref($_[0]) eq 'HASH') { |
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# create new object from parameter hash |
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_new_from_hash($self, @_); |
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# if any parameters |
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} elsif (@_) { |
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# create new object from Storable file |
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_new_from_storable($self, @_) or carp("couldn't read Storable file: $_[0]"); |
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} |
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# bless object |
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bless($self, $class); |
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# return object reference |
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return($self); |
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} |
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# fit nPINT object to data |
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# uses LAPACK dgels function to perform a least-squares fit |
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# parameters: (ref_to_pda_array, ref_to_input_array, ref_to_output_array) |
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# returns: (dgels_info_value) |
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sub fit { |
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# get parameters |
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my ($self, $pda, $in, $out) = @_; |
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# local variables |
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my ($info, $cols, $coef); |
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# get number of coefficients |
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$cols = ICC::Support::Lapack::xcols($pda); |
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# verify input is an array or Math::Matrix object |
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(ref($in) eq 'ARRAY' || UNIVERSAL::isa($in, 'Math::Matrix')) or croak('improper input array type'); |
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# verify input structure |
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(ref($in->[0]) eq 'ARRAY' && ! ref($in->[0][0])) or croak('improper input array structure'); |
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# verify output is an array or Math::Matrix object |
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(ref($out) eq 'ARRAY' || UNIVERSAL::isa($out, 'Math::Matrix')) or croak('improper output array type'); |
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# verify output structure |
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(ref($out->[0]) eq 'ARRAY' && ! ref($out->[0][0])) or croak('improper output array structure'); |
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# verify array dimensions |
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($#{$in} == $#{$out}) or croak('fit input and output arrays have different number of rows'); |
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# fit nPINT model |
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($info, $coef) = ICC::Support::Lapack::nPINT_fit($pda, $in, $out); |
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# check result |
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carp('fit failed - bad parameter when calling dgels') if ($info < 0); |
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carp('fit failed - A matrix not full rank') if ($info > 0); |
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# copy pda to object |
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$self->[1] = [@{$pda}]; |
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# copy coefficients to object |
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$self->[2] = [@{$coef}[0 .. $cols - 1]]; |
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# update cache |
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$self->[3] = ICC::Support::Lapack::cache_2D($self->[2]); |
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# return info value |
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return($info); |
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} |
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# get/set reference to header hash |
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# parameters: ([ref_to_new_hash]) |
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# returns: (ref_to_hash) |
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sub header { |
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# get object reference |
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my $self = shift(); |
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# if there are parameters |
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if (@_) { |
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# if one parameter, a hash reference |
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if (@_ == 1 && ref($_[0]) eq 'HASH') { |
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# set header to new hash |
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$self->[0] = {%{shift()}}; |
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} else { |
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# error |
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croak('parameter must be a hash reference'); |
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} |
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} |
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# return reference |
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return($self->[0]); |
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} |
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# get/set reference to pda array |
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# parameters: ([ref_to_new_array]) |
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# returns: (ref_to_array) |
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sub pda { |
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# get object reference |
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my $self = shift(); |
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# if there are parameters |
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if (@_) { |
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# if one parameter, an array reference |
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if (@_ == 1 && ref($_[0]) eq 'ARRAY') { |
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# set CLUT to new array |
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$self->[1] = [@{shift()}]; |
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} else { |
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# error |
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croak('parameter must be an array reference'); |
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} |
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} |
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# return reference |
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return($self->[1]); |
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} |
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# get/set reference to coefficient array |
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# parameters: ([ref_to_new_array]) |
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# returns: (ref_to_array) |
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sub array { |
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# get object reference |
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my $self = shift(); |
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# if there are parameters |
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if (@_) { |
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# if one parameter, an array or a Math::Matrix object |
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if (@_ == 1 && (ref($_[0]) eq 'ARRAY' || UNIVERSAL::isa($_[0], 'Math::Matrix'))) { |
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# verify array structure |
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(ref($_[0][0]) eq 'ARRAY' && ! ref($_[0][0][0])) or croak('improper coefficient array structure'); |
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# set CLUT to new array |
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$self->[2] = bless(Storable::dclone(shift()), 'Math::Matrix'); |
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# update cache |
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$self->[3] = ICC::Support::Lapack::cache_2D($self->[2]); |
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} else { |
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# error |
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croak('improper coefficient array type'); |
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} |
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} |
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# return reference |
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return($self->[2]); |
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} |
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# transform data |
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# nominal input range is (0 - 1) |
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# hash key 'ubox' enables unit box extrapolation |
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# supported input types: |
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# parameters: (list, [hash]) |
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# parameters: (vector, [hash]) |
235
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# parameters: (matrix, [hash]) |
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# parameters: (Math::Matrix_object, [hash]) |
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# parameters: (structure, [hash]) |
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# returns: (same_type_as_input) |
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sub transform { |
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# set hash value (0 or 1) |
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my $h = ref($_[-1]) eq 'HASH' ? 1 : 0; |
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# if input a 'Math::Matrix' object |
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if (@_ == $h + 2 && UNIVERSAL::isa($_[1], 'Math::Matrix')) { |
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# call matrix transform |
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&_trans2; |
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# if input an array reference |
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} elsif (@_ == $h + 2 && ref($_[1]) eq 'ARRAY') { |
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# if array contains numbers (vector) |
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if (! ref($_[1][0]) && @{$_[1]} == grep {Scalar::Util::looks_like_number($_)} @{$_[1]}) { |
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255
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256
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# call vector transform |
257
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&_trans1; |
258
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# if array contains vectors (2-D array) |
260
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} elsif (ref($_[1][0]) eq 'ARRAY' && @{$_[1]} == grep {ref($_) eq 'ARRAY' && Scalar::Util::looks_like_number($_->[0])} @{$_[1]}) { |
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261
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262
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# call matrix transform |
263
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&_trans2; |
264
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265
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} else { |
266
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267
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# call structure transform |
268
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&_trans3; |
269
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270
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} |
271
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272
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# if input a list (of numbers) |
273
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0
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} elsif (@_ == $h + 1 + grep {Scalar::Util::looks_like_number($_)} @_) { |
274
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275
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# call list transform |
276
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0
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&_trans0; |
277
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278
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} else { |
279
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280
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# error |
281
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0
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croak('invalid transform input'); |
282
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283
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} |
284
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285
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} |
286
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287
|
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|
# inverse transform |
288
|
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|
# note: number of undefined output values must equal number of defined input values |
289
|
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|
# note: the input and output vectors contain the final solution on return |
290
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|
# hash key 'init' specifies initial value vector |
291
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|
# hash key 'ubox' enables unit box extrapolation |
292
|
|
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|
# parameters: (input_vector, output_vector, [hash]) |
293
|
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|
# returns: (RMS_error_value) |
294
|
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|
sub inverse { |
295
|
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296
|
|
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|
# get parameters |
297
|
0
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0
|
0
|
|
my ($self, $in, $out, $hash) = @_; |
298
|
|
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|
|
299
|
|
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|
|
# local variables |
300
|
0
|
|
|
|
|
|
my ($i, $j, @si, @so, $init); |
301
|
0
|
|
|
|
|
|
my ($int, $jac, $mat, $delta); |
302
|
0
|
|
|
|
|
|
my ($max, $elim, $dlim, $accum, $error); |
303
|
|
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|
304
|
|
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|
|
# initialize indices |
305
|
0
|
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|
|
|
$i = $j = -1; |
306
|
|
|
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|
|
307
|
|
|
|
|
|
|
# build slice arrays while validating input and output arrays |
308
|
0
|
0
|
|
|
|
|
((grep {$i++; defined() && push(@si, $i)} @{$in}) == (grep {$j++; ! defined() && push(@so, $j)} @{$out})) or croak('wrong number of undefined values'); |
|
0
|
0
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|
|
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|
|
0
|
0
|
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0
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0
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0
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0
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309
|
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|
310
|
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|
|
# get init array |
311
|
0
|
|
|
|
|
|
$init = $hash->{'init'}; |
312
|
|
|
|
|
|
|
|
313
|
|
|
|
|
|
|
# for each undefined output value |
314
|
0
|
|
|
|
|
|
for my $i (@so) { |
315
|
|
|
|
|
|
|
|
316
|
|
|
|
|
|
|
# set to supplied initial value or 0.5 |
317
|
0
|
0
|
|
|
|
|
$out->[$i] = defined($init->[$i]) ? $init->[$i] : 0.5; |
318
|
|
|
|
|
|
|
|
319
|
|
|
|
|
|
|
} |
320
|
|
|
|
|
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|
|
321
|
|
|
|
|
|
|
# set maximum loop count |
322
|
0
|
|
0
|
|
|
|
$max = $hash->{'inv_max'} || 10; |
323
|
|
|
|
|
|
|
|
324
|
|
|
|
|
|
|
# loop error limit |
325
|
0
|
|
0
|
|
|
|
$elim = $hash->{'inv_elim'} || 1E-6; |
326
|
|
|
|
|
|
|
|
327
|
|
|
|
|
|
|
# set delta limit |
328
|
0
|
|
0
|
|
|
|
$dlim = $hash->{'inv_dlim'} || 0.5; |
329
|
|
|
|
|
|
|
|
330
|
|
|
|
|
|
|
# create empty solution matrix |
331
|
0
|
|
|
|
|
|
$mat = Math::Matrix->new([]); |
332
|
|
|
|
|
|
|
|
333
|
|
|
|
|
|
|
# compute initial transform values |
334
|
0
|
|
|
|
|
|
($jac, $int) = jacobian($self, $out, $hash); |
335
|
|
|
|
|
|
|
|
336
|
|
|
|
|
|
|
# solution loop |
337
|
0
|
|
|
|
|
|
for (1 .. $max) { |
338
|
|
|
|
|
|
|
|
339
|
|
|
|
|
|
|
# for each input |
340
|
0
|
|
|
|
|
|
for my $i (0 .. $#si) { |
341
|
|
|
|
|
|
|
|
342
|
|
|
|
|
|
|
# for each output |
343
|
0
|
|
|
|
|
|
for my $j (0 .. $#so) { |
344
|
|
|
|
|
|
|
|
345
|
|
|
|
|
|
|
# copy Jacobian value to solution matrix |
346
|
0
|
|
|
|
|
|
$mat->[$i][$j] = $jac->[$si[$i]][$so[$j]]; |
347
|
|
|
|
|
|
|
|
348
|
|
|
|
|
|
|
} |
349
|
|
|
|
|
|
|
|
350
|
|
|
|
|
|
|
# save residual value to solution matrix |
351
|
0
|
|
|
|
|
|
$mat->[$i][$#si + 1] = $in->[$si[$i]] - $int->[$si[$i]]; |
352
|
|
|
|
|
|
|
|
353
|
|
|
|
|
|
|
} |
354
|
|
|
|
|
|
|
|
355
|
|
|
|
|
|
|
# solve for delta values |
356
|
0
|
|
|
|
|
|
$delta = $mat->solve; |
357
|
|
|
|
|
|
|
|
358
|
|
|
|
|
|
|
# for each output value |
359
|
0
|
|
|
|
|
|
for my $i (0 .. $#so) { |
360
|
|
|
|
|
|
|
|
361
|
|
|
|
|
|
|
# add delta (limited using hyperbolic tangent) |
362
|
0
|
|
|
|
|
|
$out->[$so[$i]] += POSIX::tanh($delta->[$i][0]/$dlim) * $dlim; |
363
|
|
|
|
|
|
|
|
364
|
|
|
|
|
|
|
} |
365
|
|
|
|
|
|
|
|
366
|
|
|
|
|
|
|
# compute updated transform values |
367
|
0
|
|
|
|
|
|
($jac, $int) = jacobian($self, $out, $hash); |
368
|
|
|
|
|
|
|
|
369
|
|
|
|
|
|
|
# initialize error accumulator |
370
|
0
|
|
|
|
|
|
$accum = 0; |
371
|
|
|
|
|
|
|
|
372
|
|
|
|
|
|
|
# for each input |
373
|
0
|
|
|
|
|
|
for my $i (0 .. $#si) { |
374
|
|
|
|
|
|
|
|
375
|
|
|
|
|
|
|
# accumulate delta squared |
376
|
0
|
|
|
|
|
|
$accum += ($in->[$si[$i]] - $int->[$si[$i]])**2; |
377
|
|
|
|
|
|
|
|
378
|
|
|
|
|
|
|
} |
379
|
|
|
|
|
|
|
|
380
|
|
|
|
|
|
|
# compute RMS error |
381
|
0
|
|
|
|
|
|
$error = sqrt($accum/@si); |
382
|
|
|
|
|
|
|
|
383
|
|
|
|
|
|
|
# if error less than limit |
384
|
0
|
0
|
|
|
|
|
last if ($error < $elim); |
385
|
|
|
|
|
|
|
|
386
|
|
|
|
|
|
|
} |
387
|
|
|
|
|
|
|
|
388
|
|
|
|
|
|
|
# update input vector with final values |
389
|
0
|
|
|
|
|
|
@{$in} = @{$int}; |
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
390
|
|
|
|
|
|
|
|
391
|
|
|
|
|
|
|
# return |
392
|
0
|
|
|
|
|
|
return($error); |
393
|
|
|
|
|
|
|
|
394
|
|
|
|
|
|
|
} |
395
|
|
|
|
|
|
|
|
396
|
|
|
|
|
|
|
# compute Jacobian matrix |
397
|
|
|
|
|
|
|
# nominal input range is (0 - 1) |
398
|
|
|
|
|
|
|
# hash key 'ubox' enables unit box extrapolation |
399
|
|
|
|
|
|
|
# parameters: (input_vector, [hash]) |
400
|
|
|
|
|
|
|
# returns: (Jacobian_matrix, [output_vector]) |
401
|
|
|
|
|
|
|
sub jacobian { |
402
|
|
|
|
|
|
|
|
403
|
|
|
|
|
|
|
# get parameters |
404
|
0
|
|
|
0
|
0
|
|
my ($self, $in, $hash) = @_; |
405
|
|
|
|
|
|
|
|
406
|
|
|
|
|
|
|
# local variables |
407
|
0
|
|
|
|
|
|
my ($xflag, $ext, $ubox, $jac, $delta, $out); |
408
|
|
|
|
|
|
|
|
409
|
|
|
|
|
|
|
# verify input vector |
410
|
0
|
0
|
0
|
|
|
|
(ref($in) eq 'ARRAY' && @{$in} == @{$self->[1]} && @{$in} == grep {! ref()} @{$in}) or croak('invalid jacobian input'); |
|
0
|
|
0
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
411
|
|
|
|
|
|
|
|
412
|
|
|
|
|
|
|
# if extrapolation required (any input outside the unit box) |
413
|
0
|
0
|
0
|
|
|
|
if ($xflag = $hash->{'ubox'} && grep {$_ < 0 || $_ > 1} @{$in}) { |
414
|
|
|
|
|
|
|
|
415
|
|
|
|
|
|
|
# get unit box intersection values |
416
|
0
|
|
|
|
|
|
($ext, $ubox) = _intersect($in); |
417
|
|
|
|
|
|
|
|
418
|
|
|
|
|
|
|
# get Jacobian (at unit box surface) |
419
|
0
|
|
|
|
|
|
$jac = ICC::Support::Lapack::nPINT_jacobian($self->[1], $ubox, $self->[3]); |
420
|
|
|
|
|
|
|
|
421
|
|
|
|
|
|
|
} else { |
422
|
|
|
|
|
|
|
|
423
|
|
|
|
|
|
|
# get Jacobian (at input values) |
424
|
0
|
|
|
|
|
|
$jac = ICC::Support::Lapack::nPINT_jacobian($self->[1], $in, $self->[3]); |
425
|
|
|
|
|
|
|
} |
426
|
|
|
|
|
|
|
|
427
|
|
|
|
|
|
|
# bless to Math::Matrix object |
428
|
0
|
|
|
|
|
|
bless($jac, 'Math::Matrix'); |
429
|
|
|
|
|
|
|
|
430
|
|
|
|
|
|
|
# if output values wanted |
431
|
0
|
0
|
|
|
|
|
if (wantarray) { |
432
|
|
|
|
|
|
|
|
433
|
|
|
|
|
|
|
# if extrapolation required |
434
|
0
|
0
|
|
|
|
|
if ($xflag) { |
435
|
|
|
|
|
|
|
|
436
|
|
|
|
|
|
|
# compute ouptut values (at unit box surface) |
437
|
0
|
|
|
|
|
|
$out = ICC::Support::Lapack::nPINT_vec_trans($self->[1], $ubox, $self->[3]); |
438
|
|
|
|
|
|
|
|
439
|
|
|
|
|
|
|
# for each output |
440
|
0
|
|
|
|
|
|
for my $i (0 .. $#{$out}) { |
|
0
|
|
|
|
|
|
|
441
|
|
|
|
|
|
|
|
442
|
|
|
|
|
|
|
# add delta value |
443
|
0
|
|
|
|
|
|
$out->[$i] += ICC::Shared::dotProduct($jac->[$i], $ext); |
444
|
|
|
|
|
|
|
|
445
|
|
|
|
|
|
|
} |
446
|
|
|
|
|
|
|
|
447
|
|
|
|
|
|
|
} else { |
448
|
|
|
|
|
|
|
|
449
|
|
|
|
|
|
|
# compute ouptut values (at input values) |
450
|
0
|
|
|
|
|
|
$out = ICC::Support::Lapack::nPINT_vec_trans($self->[1], $in, $self->[3]); |
451
|
|
|
|
|
|
|
|
452
|
|
|
|
|
|
|
} |
453
|
|
|
|
|
|
|
|
454
|
|
|
|
|
|
|
# return Jacobian and output values |
455
|
0
|
|
|
|
|
|
return($jac, $out); |
456
|
|
|
|
|
|
|
|
457
|
|
|
|
|
|
|
} else { |
458
|
|
|
|
|
|
|
|
459
|
|
|
|
|
|
|
# return Jacobian only |
460
|
0
|
|
|
|
|
|
return($jac); |
461
|
|
|
|
|
|
|
|
462
|
|
|
|
|
|
|
} |
463
|
|
|
|
|
|
|
|
464
|
|
|
|
|
|
|
} |
465
|
|
|
|
|
|
|
|
466
|
|
|
|
|
|
|
# print object contents to string |
467
|
|
|
|
|
|
|
# format is an array structure |
468
|
|
|
|
|
|
|
# parameter: ([format]) |
469
|
|
|
|
|
|
|
# returns: (string) |
470
|
|
|
|
|
|
|
sub sdump { |
471
|
|
|
|
|
|
|
|
472
|
|
|
|
|
|
|
# get parameters |
473
|
0
|
|
|
0
|
1
|
|
my ($self, $p) = @_; |
474
|
|
|
|
|
|
|
|
475
|
|
|
|
|
|
|
# local variables |
476
|
0
|
|
|
|
|
|
my ($s, $fmt); |
477
|
|
|
|
|
|
|
|
478
|
|
|
|
|
|
|
# resolve parameter to an array reference |
479
|
0
|
0
|
|
|
|
|
$p = defined($p) ? ref($p) eq 'ARRAY' ? $p : [$p] : []; |
|
|
0
|
|
|
|
|
|
480
|
|
|
|
|
|
|
|
481
|
|
|
|
|
|
|
# get format string |
482
|
0
|
0
|
0
|
|
|
|
$fmt = defined($p->[0]) && ! ref($p->[0]) ? $p->[0] : 'undef'; |
483
|
|
|
|
|
|
|
|
484
|
|
|
|
|
|
|
# set string to object ID |
485
|
0
|
|
|
|
|
|
$s = sprintf("'%s' object, (0x%x)\n", ref($self), $self); |
486
|
|
|
|
|
|
|
|
487
|
|
|
|
|
|
|
# return |
488
|
0
|
|
|
|
|
|
return($s); |
489
|
|
|
|
|
|
|
|
490
|
|
|
|
|
|
|
} |
491
|
|
|
|
|
|
|
|
492
|
|
|
|
|
|
|
# transform list |
493
|
|
|
|
|
|
|
# parameters: (object_reference, list, [hash]) |
494
|
|
|
|
|
|
|
# returns: (list) |
495
|
|
|
|
|
|
|
sub _trans0 { |
496
|
|
|
|
|
|
|
|
497
|
|
|
|
|
|
|
# local variables |
498
|
0
|
|
|
0
|
|
|
my ($self, $hash); |
499
|
|
|
|
|
|
|
|
500
|
|
|
|
|
|
|
# get object reference |
501
|
0
|
|
|
|
|
|
$self = shift(); |
502
|
|
|
|
|
|
|
|
503
|
|
|
|
|
|
|
# get optional hash |
504
|
0
|
0
|
|
|
|
|
$hash = pop() if (ref($_[-1]) eq 'HASH'); |
505
|
|
|
|
|
|
|
|
506
|
|
|
|
|
|
|
# call _trans1 |
507
|
0
|
|
|
|
|
|
return(@{_trans1($self, \@_, $hash)}); |
|
0
|
|
|
|
|
|
|
508
|
|
|
|
|
|
|
|
509
|
|
|
|
|
|
|
} |
510
|
|
|
|
|
|
|
|
511
|
|
|
|
|
|
|
# transform vector |
512
|
|
|
|
|
|
|
# parameters: (object_reference, vector, [hash]) |
513
|
|
|
|
|
|
|
# returns: (vector) |
514
|
|
|
|
|
|
|
sub _trans1 { |
515
|
|
|
|
|
|
|
|
516
|
|
|
|
|
|
|
# get parameters |
517
|
0
|
|
|
0
|
|
|
my ($self, $in, $hash) = @_; |
518
|
|
|
|
|
|
|
|
519
|
|
|
|
|
|
|
# local variables |
520
|
0
|
|
|
|
|
|
my ($ext, $ubox, $out, $jac); |
521
|
|
|
|
|
|
|
|
522
|
|
|
|
|
|
|
# if unit box extrapolation |
523
|
0
|
0
|
0
|
|
|
|
if ($hash->{'ubox'} && grep {$_ < 0.0 || $_ > 1.0} @{$in}) { |
|
0
|
0
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
524
|
|
|
|
|
|
|
|
525
|
|
|
|
|
|
|
# get unit box intersection values |
526
|
0
|
|
|
|
|
|
($ext, $ubox) = _intersect($in); |
527
|
|
|
|
|
|
|
|
528
|
|
|
|
|
|
|
# get transformed values (at unit box surface) |
529
|
0
|
|
|
|
|
|
$out = ICC::Support::Lapack::nPINT_vec_trans($self->[1], $ubox, $self->[3]); |
530
|
|
|
|
|
|
|
|
531
|
|
|
|
|
|
|
# get Jacobian (at unit box surface) |
532
|
0
|
|
|
|
|
|
$jac = ICC::Support::Lapack::nPINT_jacobian($self->[1], $ubox, $self->[3]); |
533
|
|
|
|
|
|
|
|
534
|
|
|
|
|
|
|
# for each output |
535
|
0
|
|
|
|
|
|
for my $i (0 .. $#{$out}) { |
|
0
|
|
|
|
|
|
|
536
|
|
|
|
|
|
|
|
537
|
|
|
|
|
|
|
# add delta value |
538
|
0
|
|
|
|
|
|
$out->[$i] += ICC::Shared::dotProduct($jac->[$i], $ext); |
539
|
|
|
|
|
|
|
|
540
|
|
|
|
|
|
|
} |
541
|
|
|
|
|
|
|
|
542
|
|
|
|
|
|
|
# return extrapolated value |
543
|
0
|
|
|
|
|
|
return($out); |
544
|
|
|
|
|
|
|
|
545
|
|
|
|
|
|
|
} else { |
546
|
|
|
|
|
|
|
|
547
|
|
|
|
|
|
|
# call BLAS-based vector transform function |
548
|
0
|
|
|
|
|
|
return(ICC::Support::Lapack::nPINT_vec_trans($self->[1], $in, $self->[3])); |
549
|
|
|
|
|
|
|
|
550
|
|
|
|
|
|
|
} |
551
|
|
|
|
|
|
|
|
552
|
|
|
|
|
|
|
} |
553
|
|
|
|
|
|
|
|
554
|
|
|
|
|
|
|
# transform matrix (2-D array -or- Math::Matrix object) |
555
|
|
|
|
|
|
|
# parameters: (object_reference, matrix, [hash]) |
556
|
|
|
|
|
|
|
# returns: (matrix) |
557
|
|
|
|
|
|
|
sub _trans2 { |
558
|
|
|
|
|
|
|
|
559
|
|
|
|
|
|
|
# get parameters |
560
|
0
|
|
|
0
|
|
|
my ($self, $in, $hash) = @_; |
561
|
|
|
|
|
|
|
|
562
|
|
|
|
|
|
|
# local variable |
563
|
0
|
|
|
|
|
|
my ($out); |
564
|
|
|
|
|
|
|
|
565
|
|
|
|
|
|
|
# if unit box extrapolation |
566
|
0
|
0
|
|
|
|
|
if ($hash->{'ubox'}) { |
567
|
|
|
|
|
|
|
|
568
|
|
|
|
|
|
|
# for each matrix row |
569
|
0
|
|
|
|
|
|
for my $i (0 .. $#{$in}) { |
|
0
|
|
|
|
|
|
|
570
|
|
|
|
|
|
|
|
571
|
|
|
|
|
|
|
# compute output vector |
572
|
0
|
|
|
|
|
|
$out->[$i] = _trans1($self, $in->[$i], $hash); |
573
|
|
|
|
|
|
|
|
574
|
|
|
|
|
|
|
} |
575
|
|
|
|
|
|
|
|
576
|
|
|
|
|
|
|
} else { |
577
|
|
|
|
|
|
|
|
578
|
|
|
|
|
|
|
# call BLAS-based vector transform function |
579
|
0
|
|
|
|
|
|
$out = ICC::Support::Lapack::nPINT_mat_trans($self->[1], $in, $self->[3]); |
580
|
|
|
|
|
|
|
|
581
|
|
|
|
|
|
|
} |
582
|
|
|
|
|
|
|
|
583
|
|
|
|
|
|
|
# return matrix, same form as input |
584
|
0
|
0
|
|
|
|
|
return(UNIVERSAL::isa($in, 'Math::Matrix') ? bless($out, 'Math::Matrix') : $out); |
585
|
|
|
|
|
|
|
|
586
|
|
|
|
|
|
|
} |
587
|
|
|
|
|
|
|
|
588
|
|
|
|
|
|
|
# transform structure |
589
|
|
|
|
|
|
|
# parameters: (object_reference, structure, [hash]) |
590
|
|
|
|
|
|
|
# returns: (structure) |
591
|
|
|
|
|
|
|
sub _trans3 { |
592
|
|
|
|
|
|
|
|
593
|
|
|
|
|
|
|
# get parameters |
594
|
0
|
|
|
0
|
|
|
my ($self, $in, $hash) = @_; |
595
|
|
|
|
|
|
|
|
596
|
|
|
|
|
|
|
# transform the array structure |
597
|
0
|
|
|
|
|
|
_crawl($self, $in, my $out = []); |
598
|
|
|
|
|
|
|
|
599
|
|
|
|
|
|
|
# return output array reference |
600
|
0
|
|
|
|
|
|
return($out); |
601
|
|
|
|
|
|
|
|
602
|
|
|
|
|
|
|
} |
603
|
|
|
|
|
|
|
|
604
|
|
|
|
|
|
|
# recursive transform |
605
|
|
|
|
|
|
|
# array structure is traversed until scalar arrays are found and transformed |
606
|
|
|
|
|
|
|
# parameters: (object_reference, input_array_reference, output_array_reference, hash) |
607
|
|
|
|
|
|
|
sub _crawl { |
608
|
|
|
|
|
|
|
|
609
|
|
|
|
|
|
|
# get parameters |
610
|
0
|
|
|
0
|
|
|
my ($self, $in, $out, $hash) = @_; |
611
|
|
|
|
|
|
|
|
612
|
|
|
|
|
|
|
# if input is a vector (reference to a scalar array) |
613
|
0
|
0
|
|
|
|
|
if (@{$in} == grep {! ref()} @{$in}) { |
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
614
|
|
|
|
|
|
|
|
615
|
|
|
|
|
|
|
# transform input vector and copy to output |
616
|
0
|
|
|
|
|
|
@{$out} = @{_trans1($self, $in, $hash)}; |
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
617
|
|
|
|
|
|
|
|
618
|
|
|
|
|
|
|
} else { |
619
|
|
|
|
|
|
|
|
620
|
|
|
|
|
|
|
# for each input element |
621
|
0
|
|
|
|
|
|
for my $i (0 .. $#{$in}) { |
|
0
|
|
|
|
|
|
|
622
|
|
|
|
|
|
|
|
623
|
|
|
|
|
|
|
# if an array reference |
624
|
0
|
0
|
|
|
|
|
if (ref($in->[$i]) eq 'ARRAY') { |
625
|
|
|
|
|
|
|
|
626
|
|
|
|
|
|
|
# transform next level |
627
|
0
|
|
|
|
|
|
_crawl($self, $in->[$i], $out->[$i] = [], $hash); |
628
|
|
|
|
|
|
|
|
629
|
|
|
|
|
|
|
} else { |
630
|
|
|
|
|
|
|
|
631
|
|
|
|
|
|
|
# error |
632
|
0
|
|
|
|
|
|
croak('invalid transform input'); |
633
|
|
|
|
|
|
|
|
634
|
|
|
|
|
|
|
} |
635
|
|
|
|
|
|
|
|
636
|
|
|
|
|
|
|
} |
637
|
|
|
|
|
|
|
|
638
|
|
|
|
|
|
|
} |
639
|
|
|
|
|
|
|
|
640
|
|
|
|
|
|
|
} |
641
|
|
|
|
|
|
|
|
642
|
|
|
|
|
|
|
# find unit box intersection |
643
|
|
|
|
|
|
|
# with line from input to box-center |
644
|
|
|
|
|
|
|
# parameters: (input_vector) |
645
|
|
|
|
|
|
|
# returns: (extrapolation_vector, unit_box_intersection) |
646
|
|
|
|
|
|
|
sub _intersect { |
647
|
|
|
|
|
|
|
|
648
|
|
|
|
|
|
|
# get input vector |
649
|
0
|
|
|
0
|
|
|
my $in = shift(); |
650
|
|
|
|
|
|
|
|
651
|
|
|
|
|
|
|
# local variables |
652
|
0
|
|
|
|
|
|
my (@cin, $dmax, $ubox); |
653
|
|
|
|
|
|
|
|
654
|
|
|
|
|
|
|
# compute input to center difference |
655
|
0
|
|
|
|
|
|
@cin = map {$_ - 0.5} @{$in}; |
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
656
|
|
|
|
|
|
|
|
657
|
|
|
|
|
|
|
# initialize |
658
|
0
|
|
|
|
|
|
$dmax = 0; |
659
|
|
|
|
|
|
|
|
660
|
|
|
|
|
|
|
# for each difference |
661
|
0
|
|
|
|
|
|
for (@cin) { |
662
|
|
|
|
|
|
|
|
663
|
|
|
|
|
|
|
# if larger absolute value |
664
|
0
|
0
|
|
|
|
|
if (abs($_) > $dmax) { |
665
|
|
|
|
|
|
|
|
666
|
|
|
|
|
|
|
# new max difference |
667
|
0
|
|
|
|
|
|
$dmax = abs($_); |
668
|
|
|
|
|
|
|
|
669
|
|
|
|
|
|
|
} |
670
|
|
|
|
|
|
|
|
671
|
|
|
|
|
|
|
} |
672
|
|
|
|
|
|
|
|
673
|
|
|
|
|
|
|
# multiply max difference by 2 |
674
|
0
|
|
|
|
|
|
$dmax *= 2; |
675
|
|
|
|
|
|
|
|
676
|
|
|
|
|
|
|
# compute output values (on surface of unit box) |
677
|
0
|
|
|
|
|
|
$ubox = [map {$_/$dmax + 0.5} @cin]; |
|
0
|
|
|
|
|
|
|
678
|
|
|
|
|
|
|
|
679
|
|
|
|
|
|
|
# return extrapolation vector ($in - $ubox) and unit-box intersection vector |
680
|
0
|
|
|
|
|
|
return([map {$in->[$_] - $ubox->[$_]} (0 .. $#{$in})], $ubox); |
|
0
|
|
|
|
|
|
|
|
0
|
|
|
|
|
|
|
681
|
|
|
|
|
|
|
|
682
|
|
|
|
|
|
|
} |
683
|
|
|
|
|
|
|
|
684
|
|
|
|
|
|
|
# make nPINT object from parameter hash |
685
|
|
|
|
|
|
|
# parameters: (object_reference, ref_to_parameter_hash) |
686
|
|
|
|
|
|
|
sub _new_from_hash { |
687
|
|
|
|
|
|
|
|
688
|
|
|
|
|
|
|
# get parameters |
689
|
0
|
|
|
0
|
|
|
my ($self, $hash) = @_; |
690
|
|
|
|
|
|
|
|
691
|
|
|
|
|
|
|
# local variables |
692
|
0
|
|
|
|
|
|
my ($pda, $coef, $size); |
693
|
|
|
|
|
|
|
|
694
|
|
|
|
|
|
|
# get input polynomial degree array (pda) reference |
695
|
0
|
0
|
|
|
|
|
$pda = $hash->{'pda'} or croak('missing polynomial degree array'); |
696
|
|
|
|
|
|
|
|
697
|
|
|
|
|
|
|
# get output coefficient array reference |
698
|
0
|
0
|
|
|
|
|
$coef = $hash->{'coef'} or croak('missing coefficient array'); |
699
|
|
|
|
|
|
|
|
700
|
|
|
|
|
|
|
# verify pda structure |
701
|
0
|
0
|
0
|
|
|
|
(ref($pda) eq 'ARRAY' && ! ref($pda->[0])) or croak('improper polynomial degree array'); |
702
|
|
|
|
|
|
|
|
703
|
|
|
|
|
|
|
# copy pda to object |
704
|
0
|
|
|
|
|
|
$self->[1] = [@{$pda}]; |
|
0
|
|
|
|
|
|
|
705
|
|
|
|
|
|
|
|
706
|
|
|
|
|
|
|
# initialize coefficient array size |
707
|
0
|
|
|
|
|
|
$size = 1; |
708
|
|
|
|
|
|
|
|
709
|
|
|
|
|
|
|
# for each pda element |
710
|
0
|
|
|
|
|
|
for my $d (@{$pda}) { |
|
0
|
|
|
|
|
|
|
711
|
|
|
|
|
|
|
|
712
|
|
|
|
|
|
|
# multiply by (degree + 1) |
713
|
0
|
|
|
|
|
|
$size *= ($d + 1); |
714
|
|
|
|
|
|
|
|
715
|
|
|
|
|
|
|
} |
716
|
|
|
|
|
|
|
|
717
|
|
|
|
|
|
|
# verify coef is array or Math::Matrix object |
718
|
0
|
0
|
0
|
|
|
|
(ref($coef) eq 'ARRAY' || UNIVERSAL::isa($coef, 'Math::Matrix')) or croak('improper coefficient array type'); |
719
|
|
|
|
|
|
|
|
720
|
|
|
|
|
|
|
# verify coef structure |
721
|
0
|
0
|
0
|
|
|
|
(ref($coef->[0]) eq 'ARRAY' && ! ref($coef->[0][0]) && @{$coef} == $size) or croak('improper coefficient array structure'); |
|
0
|
|
0
|
|
|
|
|
722
|
|
|
|
|
|
|
|
723
|
|
|
|
|
|
|
# copy coefficient array to object |
724
|
0
|
|
|
|
|
|
$self->[2] = bless(Storable::dclone($coef), 'Math::Matrix'); |
725
|
|
|
|
|
|
|
|
726
|
|
|
|
|
|
|
# update cache |
727
|
0
|
|
|
|
|
|
$self->[3] = ICC::Support::Lapack::cache_2D($self->[2]); |
728
|
|
|
|
|
|
|
|
729
|
|
|
|
|
|
|
} |
730
|
|
|
|
|
|
|
|
731
|
|
|
|
|
|
|
# make nPINT object from Storable file |
732
|
|
|
|
|
|
|
# parameters: (object_reference, path_to_storable_file) |
733
|
|
|
|
|
|
|
sub _new_from_storable { |
734
|
|
|
|
|
|
|
|
735
|
|
|
|
|
|
|
# get parameters |
736
|
0
|
|
|
0
|
|
|
my ($self, $path) = @_; |
737
|
|
|
|
|
|
|
|
738
|
|
|
|
|
|
|
# local variables |
739
|
0
|
|
|
|
|
|
my ($hash, @files); |
740
|
|
|
|
|
|
|
|
741
|
|
|
|
|
|
|
# filter path |
742
|
0
|
|
|
|
|
|
ICC::Shared::filterPath($path); |
743
|
|
|
|
|
|
|
|
744
|
|
|
|
|
|
|
# retrieve hash reference |
745
|
0
|
|
|
|
|
|
$hash = Storable::retrieve($path); |
746
|
|
|
|
|
|
|
|
747
|
|
|
|
|
|
|
# if successful |
748
|
0
|
0
|
|
|
|
|
if (defined($hash)) { |
749
|
|
|
|
|
|
|
|
750
|
|
|
|
|
|
|
# create nPINT object from hash reference |
751
|
0
|
|
|
|
|
|
_new_from_hash($self, $hash); |
752
|
|
|
|
|
|
|
|
753
|
|
|
|
|
|
|
# return success flag |
754
|
0
|
|
|
|
|
|
return(1); |
755
|
|
|
|
|
|
|
|
756
|
|
|
|
|
|
|
} else { |
757
|
|
|
|
|
|
|
|
758
|
|
|
|
|
|
|
# return failure flag |
759
|
0
|
|
|
|
|
|
return(0); |
760
|
|
|
|
|
|
|
|
761
|
|
|
|
|
|
|
} |
762
|
|
|
|
|
|
|
|
763
|
|
|
|
|
|
|
} |
764
|
|
|
|
|
|
|
|
765
|
|
|
|
|
|
|
1; |