| … | |
… | |
| 22 | } |
22 | } |
| 23 | $A_lr = $A->decompose_LR(); |
23 | $A_lr = $A->decompose_LR(); |
| 24 | $det = $A_lr->det_LR(); |
24 | $det = $A_lr->det_LR(); |
| 25 | } |
25 | } |
| 26 | return $A; |
26 | return $A; |
|
|
27 | } |
|
|
28 | |
|
|
29 | =head4 random_diag_matrix |
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30 | |
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|
31 | This method returns a random nxn diagonal matrix. |
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32 | |
|
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33 | =cut |
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|
34 | |
|
|
35 | sub random_diag_matrix{ ## Builds and returns a random diagonal \$n by \$n matrix |
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36 | |
|
|
37 | warn "Usage: \$new_matrix = random_diag_matrix(\$n)" if (@_ != 1); |
|
|
38 | |
|
|
39 | my $D = new Matrix($_[0],$_[0]); |
|
|
40 | my $norm = 0; |
|
|
41 | while( $norm == 0 ){ |
|
|
42 | foreach my $i (1..$_[0]){ |
|
|
43 | foreach my $j (1..$_[0]){ |
|
|
44 | if( $i != $j ){ |
|
|
45 | $D->assign($i,$j,0); |
|
|
46 | }else{ |
|
|
47 | $D->assign($i,$j,random(-9,9,1)); |
|
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48 | } |
|
|
49 | } |
|
|
50 | } |
|
|
51 | $norm = abs($D); |
|
|
52 | } |
|
|
53 | return $D; |
| 27 | } |
54 | } |
| 28 | |
55 | |
| 29 | sub swap_rows{ |
56 | sub swap_rows{ |
| 30 | |
57 | |
| 31 | warn "Usage: \$new_matrix = swap_rows(\$matrix,\$row1,\$row2);" |
58 | warn "Usage: \$new_matrix = swap_rows(\$matrix,\$row1,\$row2);" |
| … | |
… | |
| 610 | }else{ |
637 | }else{ |
| 611 | 1; |
638 | 1; |
| 612 | } |
639 | } |
| 613 | } |
640 | } |
| 614 | |
641 | |
|
|
642 | sub is_diagonal{ |
|
|
643 | my $matrix = shift; |
|
|
644 | my %options = @_; |
|
|
645 | my $process_ans_hash = ( ref( $matrix ) eq 'AnswerHash' ) ? 1 : 0 ; |
|
|
646 | my ($rh_ans); |
|
|
647 | if ($process_ans_hash) { |
|
|
648 | $rh_ans = $matrix; |
|
|
649 | $matrix = $rh_ans->{ra_student_ans}; |
|
|
650 | } |
|
|
651 | |
|
|
652 | return 0 unless defined($matrix); |
|
|
653 | |
|
|
654 | if( ref($matrix) eq 'ARRAY' ){ |
|
|
655 | my @matrix = @{$matrix}; |
|
|
656 | @matrix = @{$matrix[0]} if ref($matrix[0][0]) eq 'ARRAY'; |
|
|
657 | if( ref($matrix[0]) ne 'ARRAY' or scalar( @matrix ) != scalar( @{$matrix[0]} ) ){ |
|
|
658 | warn "It is impossible for a non-square matrix to be diagonal, if you are a student, please tell your professor that there is a problem."; |
|
|
659 | } |
|
|
660 | |
|
|
661 | for( my $i = 0; $i < scalar( @matrix ) ; $i++ ){ |
|
|
662 | for( my $j = 0; $j < scalar( @{$matrix[0]} ); $j++ ){ |
|
|
663 | if( $matrix[$i][$j] != 0 and $i != $j ) |
|
|
664 | { |
|
|
665 | if ($process_ans_hash){ |
|
|
666 | $rh_ans->throw_error('EVAL'); |
|
|
667 | return $rh_ans; |
|
|
668 | } else { |
|
|
669 | return 0; |
|
|
670 | } |
|
|
671 | } |
|
|
672 | } |
|
|
673 | } |
|
|
674 | if ($process_ans_hash){ |
|
|
675 | return $rh_ans; |
|
|
676 | } else { |
|
|
677 | return 1; |
|
|
678 | } |
|
|
679 | }elsif( ref($matrix) eq 'Matrix' ){ |
|
|
680 | if( $matrix->[1] != $matrix->[2] ){ |
|
|
681 | warn "It is impossible for a non-square matrix to be diagonal, if you are a student, please tell your professor that there is a problem."; |
|
|
682 | if ($process_ans_hash){ |
|
|
683 | $rh_ans->throw_error('EVAL'); |
|
|
684 | return $rh_ans; |
|
|
685 | } else { |
|
|
686 | return 0; |
|
|
687 | } |
|
|
688 | } |
|
|
689 | for( my $i = 0; $i < $matrix->[1] ; $i++ ){ |
|
|
690 | for( my $j = 0; $j < $matrix->[2] ; $j++ ){ |
|
|
691 | if( $matrix->[0][$i][$j] != 0 and $i != $j ){ |
|
|
692 | if ($process_ans_hash){ |
|
|
693 | $rh_ans->throw_error('EVAL'); |
|
|
694 | return $rh_ans; |
|
|
695 | } else { |
|
|
696 | return 0; |
|
|
697 | } |
|
|
698 | } |
|
|
699 | } |
|
|
700 | } |
|
|
701 | if ($process_ans_hash){ |
|
|
702 | return $rh_ans; |
|
|
703 | } else { |
|
|
704 | return 1; |
|
|
705 | } |
|
|
706 | }else{ |
|
|
707 | warn "There is a problem with the problem, please alert your professor."; |
|
|
708 | if ($process_ans_hash){ |
|
|
709 | $rh_ans->throw_error('EVAL'); |
|
|
710 | return $rh_ans; |
|
|
711 | } else { |
|
|
712 | return 0; |
|
|
713 | } |
|
|
714 | } |
|
|
715 | |
|
|
716 | } |
|
|
717 | |
|
|
718 | |
| 615 | sub are_unit_vecs{ |
719 | sub are_unit_vecs{ |
| 616 | my ( $vec_ref,%opts ) = @_; |
720 | my ( $vec_ref,%opts ) = @_; |
| 617 | my @vecs = (); |
721 | my @vecs = (); |
| 618 | if( ref($vec_ref) eq 'AnswerHash' ) |
722 | if( ref($vec_ref) eq 'AnswerHash' ) |
| 619 | { |
723 | { |
| … | |
… | |
| 815 | $rh_ans->{rm_correct_ans} = Matrix->new_from_col_vecs(\@correct_space); |
919 | $rh_ans->{rm_correct_ans} = Matrix->new_from_col_vecs(\@correct_space); |
| 816 | $rh_ans->{ra_student_ans} = \@space; |
920 | $rh_ans->{ra_student_ans} = \@space; |
| 817 | return compare_basis( $rh_ans, %options ); |
921 | return compare_basis( $rh_ans, %options ); |
| 818 | } |
922 | } |
| 819 | } |
923 | } |
|
|
924 | |
|
|
925 | sub pretty_matrix{ |
|
|
926 | my $matrix = shift; |
| 820 | |
927 | |
|
|
928 | if( ref($matrix) ne 'Matrix' ){ |
|
|
929 | warn "Usage: \$pretty_matrix = pretty_matrix(\$matrix)"; |
|
|
930 | } |
|
|
931 | |
|
|
932 | for( my $i = 0; $i < $matrix->[1]; $i++ ){ |
|
|
933 | for( my $j = 0; $j < $matrix->[2]; $j++ ){ |
|
|
934 | if( $matrix->[0][$i][$j] - sprintf("%.0f", $matrix->[0][$i][$j] ) < $main::functZeroLevelTolDefault ){ |
|
|
935 | $matrix->[0][$i][$j] = sprintf("%.0f", $matrix->[0][$i][$j] ); |
|
|
936 | $matrix->[0][$i][$j] = 0 if( $matrix->[0][$i][$j] == 0); |
|
|
937 | } |
|
|
938 | } |
|
|
939 | } |
|
|
940 | $matrix; |
|
|
941 | } |
| 821 | |
942 | |
| 822 | 1; |
943 | 1; |
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