Solver Guide to Multiplying Matrices

Source code of 'Guide to Multiplying Matrices'

This Solver (Guide to Multiplying Matrices) was created by by jim_thompson5910(35256)

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==section input

This solver will guide you through multiplying two matrices. Given two matrices A and B, the solver will compute AB (ie the product of the matrices A and B).

Enter the numerical entries (numbers only) for each matrix. Separate each entry with a comma. When a new row is needed, use a semicolon. For example, to enter the matrix {{{(matrix(3,3,1,2,3,4,5,6,7,8,9))}}}, enter the following: 1,2,3;4,5,6;7,8,9

Entries for matrix A *[input 30 matrix_list1=1,2,3;4,5,6;7,8,9]

Entries for matrix B *[input 30 matrix_list2=4,7,9;8,2,5;1,6,3]

Note: Remember that the number of columns of matrix A must equal the number of rows of matrix B. Also, remember that matrix multiplication is NOT commutative. In other words, {{{AB<>BA}}} in general. So make sure you enter the values in the correct order.

Please keep in mind that this solver doesn't do much error checking. So make sure that you read the instructions and enter the values in carefully. Also, be sure to verify the answer.

==section solution

perl

##num_ordinate example: 1st, 2nd, 3rd
sub num_ordinate {
my ($number, $suffix);
$number=abs(shift);

my $last_two_digits;

if($number>10)
{$last_two_digits=$1 if $number=~m/(\d{2})$/;}
else
{$last_two_digits=$number;}

if($last_two_digits=~m/1$/)
 {$suffix="st";}
elsif($last_two_digits=~m/2$/)
 {$suffix="nd";}
elsif($last_two_digits=~m/3$/)
 {$suffix="rd";}
else
 {$suffix="th";}

if(($last_two_digits>10)&&($last_two_digits<20))
{$suffix="th";}

$number.="$suffix" ;

return $number;}

## convert multidimensional array to list form
sub matrix_list
{
 my $array_ref=$_[0];
 my $list="";
 for(my $i=0;$i< @{$array_ref}; $i++)
 {
 for(my $j=0;$j< @{$array_ref->[$i]}; $j++)
 {
 #print "$array_ref->[$i][$j],";
 $list.="$array_ref->[$i][$j],";
 }
 }
 $list=~s/,$//;
 #print "\nLIST: $list\n";
 return $list;
 #print "SUB matrix_list: @{$array_ref->[2]}...$array_ref->[1][1] \n";
}

# pass in an array ref and row number to be highlighted and the result is the string (w/ highlighted row)
sub matrix_highlight_row
{
 die "Needs two arguments" if @_!=2;
 my ($array_ref,$row_num)=@_;
 my $list="";
 for(my $i=0;$i< @{$array_ref}; $i++)
 {
 for(my $j=0;$j< @{$array_ref->[$i]}; $j++)
 {
 #print "$array_ref->[$i][$j],";
 if ($i==$row_num)
 {
 $list.="highlight($array_ref->[$i][$j]),";
 }
 else
 {
 $list.="$array_ref->[$i][$j],";
 }
 }
 }
 $list=~s/,$//;
 #print "\nLIST: $list\n";
 return $list;
 #print "SUB matrix_list: @{$array_ref->[2]}...$array_ref->[1][1] \n";
}

# pass in an array ref and column number to be highlighted and the result is the string (w/ highlighted column)
sub matrix_highlight_col
{
 die "Needs two arguments" if @_!=2;
 my ($array_ref,$col_num)=@_;
 my $list="";
 for(my $i=0;$i< @{$array_ref}; $i++)
 {
 for(my $j=0;$j< @{$array_ref->[$i]}; $j++)
 {
 #print "$array_ref->[$i][$j],";
 if ($j==$col_num)
 {
 $list.="highlight($array_ref->[$i][$j]),";
 }
 else
 {
 $list.="$array_ref->[$i][$j],";
 }
 }
 }
 $list=~s/,$//;
 #print "\nLIST: $list\n";
 return $list;
 #print "SUB matrix_list: @{$array_ref->[2]}...$array_ref->[1][1] \n";
}

## go through each row and make sure each row has same number of elements
sub check_column_consistency
{
 my @matrix_rows=@_;
 my $column_count;
 for(my $i=0;$i<@matrix_rows;$i++)
 {
 my @temp_array=split(/,/,$matrix_rows[$i]);
 if($i==0)
 {
 $column_count=@temp_array;
 }
 my $temp_count=@temp_array;
 #die "Column Counts of the matrix @matrix_rows are INCONSISTENT!!" if $temp_count!=$column_count;
 
 if($temp_count!=$column_count)
 {
 print "Error: There is an inconsistency in the number of elements in each row (ie one row has more or less than another).";
 goto end;
 }
 }
 return $column_count;
}

# multiply row i of matrix 1 and column j of matrix 2
sub dot_product
{
 die "Needs two arguments" if @_!=2;
 my ($row_ref1,$col_ref2)=@_; ## 2 ref of arrays
 my $sum=0;
 my $list;
 my @partial;
 for(my $i=0; $i<@{$row_ref1}; $i++)
 {
 $sum=($row_ref1->[$i])*($col_ref2->[$i]);
 push(@partial,$sum);
 $list.="($row_ref1->[$i])*($col_ref2->[$i])+";
 $sum=0;
 }
 $sum=0;
 for(my $i=0;$i<@partial; $i++)
 {
 $sum+=$partial[$i];
 }

$list=~s/\+$//;
  $list="$list=".join("+",@partial)."=$sum";
  #print "$list";
  return ($list,$sum);

}

#sub multiply_matrices
#{
# die "Needs two arguments" if @_!=2;
# my ($matrix1_ref,$matrix2_ref)=@_;
# print "$matrix1_ref->[0][0]";
#
#}

############################## Input

##### Error Checking

#die "No variables allowed" if $matrix_list1=~m/[a-z]/ or $matrix_list2=~m/[a-z]/;

if($matrix_list1=~m/[a-z]/ or $matrix_list2=~m/[a-z]/)
{
 print "Error: Enter numbers only (no variables).";
 goto end;
}

if($matrix_list1=~m/\// or $matrix_list2=~m/\//)
{
 print "Error: This solver doesn't support fractions at this time. Please convert all fractions to decimal form.";
 goto end;
}

#### End Error Checking

#chomp(my $matrix_list1=<>);
#chomp(my $matrix_list2=<>);
#my $matrix_list1="2, -1, 0;-1, 1, -2";
#my $matrix_list2="1, -1, 2;-3, -2, 4;-1, 1, 1";

# remove whitespace
($matrix_list1,$matrix_list2)=map{s/\s//g; $_} ($matrix_list1,$matrix_list2);

#my $new_matrix_list1=$matrix_list1;
#my $new_matrix_list2=$matrix_list2;

#($new_matrix_list1,$new_matrix_list2)=map{s/;/,/g; $_} ($new_matrix_list1,$new_matrix_list2);

# generate row arrays
my @matrix1_rows=split(/;/,$matrix_list1);
my @matrix2_rows=split(/;/,$matrix_list2);

# get number of rows for both matrices
my $matrix1_row_count=@matrix1_rows;
my $matrix2_row_count=@matrix2_rows;

# go through each row of matrix 1 and make sure each row has same number of elements
my $matrix1_col_count=check_column_consistency(@matrix1_rows);

# go through each row of matrix 2 and make sure each row has same number of elements
my $matrix2_col_count=check_column_consistency(@matrix2_rows);

my @blank_array;

for(my $i=0;$i<$matrix2_col_count; $i++)
{
 push(@blank_array,"x");
}
my @blank_matrix=();

## need to make sure that inner dimensions match
##die "Matrix 1 column count != Matrix 2 row count " if $matrix1_col_count!=$matrix2_row_count;

if($matrix1_col_count!=$matrix2_row_count)
{
 print "Error: The number of columns of matrix A MUST equal the number of rows in matrix B.";
 goto end;
}

# store matrix 1 in multidimensional array
my @matrix1;
for(my $i=0;$i<@matrix1_rows;$i++)
{
 my @temp_row=split(/,/,$matrix1_rows[$i]);
 push @matrix1, [@temp_row];
 push @blank_matrix, [@blank_array];
}

# store matrix 2 in multidimensional array
my @matrix2;
for(my $i=0;$i<@matrix2_rows;$i++)
{
 my @temp_row=split(/,/,$matrix2_rows[$i]);
 push @matrix2, [@temp_row];
}

my $matrix_display1=matrix_list(\@matrix1);
my $matrix_display2=matrix_list(\@matrix2);
my $blank_matrix=matrix_list(\@blank_matrix);

print "Since the first matrix is a $matrix1_row_count by $matrix1_col_count matrix and the second matrix is a $matrix2_row_count by $matrix2_col_count matrix, this means that the resulting matrix will be a $matrix1_row_count by $matrix2_col_count matrix. The final matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.

So the final resulting matrix will look like:

{{{(matrix($matrix1_row_count,$matrix2_col_count,$blank_matrix))}}}

note: the \"x\"s are just placeholders for now

print " -------------------------------------------------- ";

my $matrix1_ref=\@matrix1;
my $matrix2_ref=\@matrix2;

my @matrix_ans;
my @temp_ans_array=();

my $font1="";
my $font2="";
my $back="";

for(my $i=0;$i<$matrix1_row_count;$i++)
{

for(my $j=0;$j<$matrix2_col_count;$j++)
 {
 my $array_ref1=$matrix1[$i];
 my @temp_array=();

for(my $k=0;$k<$matrix2_row_count;$k++)
 {
 push(@temp_array,$matrix2[$k][$j]);
 }

my $array_ref2=\@temp_array;
 my ($intermediate_list,$sum)=dot_product($array_ref1,$array_ref2);
 push(@temp_ans_array,$sum);
 #print " TEMP ANS: @temp_ans_array ";
 print " ";
 print " Multiply the corresponding entries from the $font1",num_ordinate($i+1),"$back row of the first matrix by the $font2",num_ordinate($j+1),"$back column of the second matrix. After multiplying, add the values: ";
 print " $font1",num_ordinate($i+1),"$back row, $font2",num_ordinate($j+1),"$back column: ";
 my $row1=matrix_highlight_row(\@matrix1,$i);
 my $col1=matrix_highlight_col(\@matrix2,$j);
 print "{{{(matrix($matrix1_row_count,$matrix1_col_count,$row1))(matrix($matrix2_row_count,$matrix2_col_count,$col1))}}} ";

print "{{{$intermediate_list}}} ";

print " So the element in the $font1",num_ordinate($i+1),"$back row, $font2",num_ordinate($j+1),"$back column of the resulting matrix is {{{$sum}}}. ";
 print "Now let's update the matrix: ";
 $blank_matrix[$i][$j]=$sum;
 my $temp_ans=matrix_list(\@blank_matrix);
 print " {{{(matrix($matrix1_row_count,$matrix2_col_count,$temp_ans))}}} ";
 print '-' x 50 if $j!=$matrix2_col_count-1;
 print " ";
 }
 push @matrix_ans, [@temp_ans_array];
 @temp_ans_array=();
 print " ";
 print '=' x 80 if $i!=$matrix1_row_count-1;
 print " ";

}

my $matrix_ans_list=matrix_list(\@matrix_ans);

#my $row1=matrix_highlight_row(\@matrix_ans,0);
#my $col1=matrix_highlight_col(\@matrix_ans,0);

#multiply_matrices($matrix1_ref,$matrix2_ref);

#dot_product([1,2,3],[4,5,6]);

#print " Matrix 1: {{{(matrix($matrix1_row_count,$matrix1_col_count,$new_matrix_list1))}}} ";

#print " Matrix 2: {{{(matrix($matrix2_row_count,$matrix2_col_count,$new_matrix_list2))}}} ";

print " ============================================================================== ";

print " Answer: ";

print " So the solution is {{{(matrix($matrix1_row_count,$matrix2_col_count,$matrix_ans_list))}}}

In other words,

{{{(matrix($matrix1_row_count,$matrix1_col_count,$matrix_display1))*(matrix($matrix2_row_count,$matrix2_col_count,$matrix_display2))=(matrix($matrix1_row_count,$matrix2_col_count,$matrix_ans_list))}}}

#print " HIGHLIGHT ROW 1: {{{(matrix($matrix1_row_count,$matrix2_col_count,$row1))}}} ";
#print " HIGHLIGHT COL 1: {{{(matrix($matrix1_row_count,$matrix2_col_count,$col1))}}} ";
#print "$matrix2[0][2]";

end:

==section output

==section check