Pooh program example 03-matrix-mult.p
Test 03-matrix-mult.p
Source of programm
# test work with two dimensional matrixes.
a = [
[ 1, 2, 3, 4 ],
[ 5, 6, 7, 8 ],
[ 9, 0, 1, 2 ],
[ 3, 4, 5, 6 ]
]
c = make_identity_matrix( ~rows 4 ~cols 4 )
print_matrix( ~matrix c )
println( ~msg 'matrix a' )
print_matrix( ~matrix a )
matrix_scale( ~factor 2 ~matrix a )
println( ~msg 'scale a by 2' )
print_matrix( ~matrix a )
println( ~msg 'matrix b' )
b = make_upper_triangle( ~rows 4 ~cols 4 )
print_matrix( ~matrix b )
d = matrix_mult( ~leftm a ~rightm b )
println( ~msg 'product of matrix a and b' )
print_matrix( ~matrix d )
sub matrix_scale( factor, matrix )
numrows = size( ~arg matrix )
numcols = size( ~arg matrix[ 1 ] )
for i range( ~from 1 ~to numrows )
for j range( ~from 1 ~to numcols )
matrix[i][j] = factor * matrix[ i ] [ j ]
end
end
end
sub matrix_mult( leftm, rightm )
numleftrows = size( ~arg leftm )
numleftcols = size( ~arg leftm[ 1 ] )
numrightrows = size( ~arg rightm )
numrightcols = size( ~arg rightm[ 1 ] )
if numleftcols != numrightrows
return []
end
c = []
for left_row range( ~from 1 ~to numleftrows )
for right_col range( ~from 1 ~to numrightcols )
s = 0
for n range( ~from 1 ~to numleftcols )
s = s + leftm[ left_row ] [ n ] * rightm[ n ] [ right_col ]
end
c[ left_row ] [ right_col ] = s
end
end
return c
end
sub print_matrix( matrix )
numrows = size( ~arg matrix )
numcols = size( ~arg matrix[ 1 ] )
for i range( ~from 1 ~to numrows )
for j range( ~from 1 ~to numcols )
print( ~msg matrix[i][j] .. ' ' )
end
println( ~msg ' ')
end
end
sub make_upper_triangle( rows, cols )
c = []
for i range( ~from 1 ~to rows )
for j range( ~from 1 ~to cols )
if i <= j
c[ i ] [ j ] = 1
else
c[ i ] [ j ] = 0
end
end
end
return c
end
sub make_identity_matrix( rows, cols )
c = []
for i range( ~from 1 ~to rows )
for j range( ~from 1 ~to cols )
if i == j
c[ i ] [ j ] = 1
else
c[ i ] [ j ] = 0
end
end
end
return c
end
Standard output for 03-matrix-mult.p
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
matrix a
1 2 3 4
5 6 7 8
9 0 1 2
3 4 5 6
scale a by 2
2 4 6 8
10 12 14 16
18 0 2 4
6 8 10 12
matrix b
1 1 1 1
0 1 1 1
0 0 1 1
0 0 0 1
product of matrix a and b
2 6 12 20
10 22 36 52
18 18 20 24
6 14 24 36
Trace output for 03-matrix-mult.p
003|a = [ [ 1 , 2 , 3 , 4] , [ 5 , 6 , 7 , 8] , [ 9 , 0 , 1 , 2] , [ 3 , 4 , 5 , 6] ]
010|... = make_identity_matrix( ~rows 4 ~cols 4 )...
099| c = [ ]
100| for ... range( ~from 1 ~to rows:4 )...
100| for i = 1
101| for ... range( ~from 1 ~to cols:4 )...
101| for j = 1
102| if (i:1 == j:1):true
103| c[i:1][j:1]:1 = 1
103| end # if
101| end
101| for ...
101| for j = 2
102| if (i:1 == j:2):false
103| else
105| c[i:1][j:2]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 3
102| if (i:1 == j:3):false
103| else
105| c[i:1][j:3]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 4
102| if (i:1 == j:4):false
103| else
105| c[i:1][j:4]:0 = 0
105| end # if
101| end
101| for ...
101| end # finish for loop
100| end
100| for ...
100| for i = 2
101| for ... range( ~from 1 ~to cols:4 )...
101| for j = 1
102| if (i:2 == j:1):false
103| else
105| c[i:2][j:1]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 2
102| if (i:2 == j:2):true
103| c[i:2][j:2]:1 = 1
103| end # if
101| end
101| for ...
101| for j = 3
102| if (i:2 == j:3):false
103| else
105| c[i:2][j:3]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 4
102| if (i:2 == j:4):false
103| else
105| c[i:2][j:4]:0 = 0
105| end # if
101| end
101| for ...
101| end # finish for loop
100| end
100| for ...
100| for i = 3
101| for ... range( ~from 1 ~to cols:4 )...
101| for j = 1
102| if (i:3 == j:1):false
103| else
105| c[i:3][j:1]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 2
102| if (i:3 == j:2):false
103| else
105| c[i:3][j:2]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 3
102| if (i:3 == j:3):true
103| c[i:3][j:3]:1 = 1
103| end # if
101| end
101| for ...
101| for j = 4
102| if (i:3 == j:4):false
103| else
105| c[i:3][j:4]:0 = 0
105| end # if
101| end
101| for ...
101| end # finish for loop
100| end
100| for ...
100| for i = 4
101| for ... range( ~from 1 ~to cols:4 )...
101| for j = 1
102| if (i:4 == j:1):false
103| else
105| c[i:4][j:1]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 2
102| if (i:4 == j:2):false
103| else
105| c[i:4][j:2]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 3
102| if (i:4 == j:3):false
103| else
105| c[i:4][j:3]:0 = 0
105| end # if
101| end
101| for ...
101| for j = 4
102| if (i:4 == j:4):true
103| c[i:4][j:4]:1 = 1
103| end # if
101| end
101| for ...
101| end # finish for loop
100| end
100| for ...
100| end # finish for loop
109| return c:[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]
010|c = make_identity_matrix( ~rows 4 ~cols 4 ):[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]
011|print_matrix( ~matrix c:[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] )...
072| ... = size( ~arg matrix:-> [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] )...
072| numrows = size( ~arg matrix:-> [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ):4
073| ... = size( ~arg matrix[1]:[ 1, 0, 0, 0 ] )...
073| numcols = size( ~arg matrix[1]:[ 1, 0, 0, 0 ] ):4
075| for ... range( ~from 1 ~to numrows:4 )...
075| for i = 1
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:1][j:1]:1 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:1][j:2]:0 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:1][j:3]:0 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:1][j:4]:0 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 2
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:2][j:1]:0 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:2][j:2]:1 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:2][j:3]:0 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:2][j:4]:0 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 3
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:3][j:1]:0 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:3][j:2]:0 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:3][j:3]:1 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:3][j:4]:0 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 4
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:4][j:1]:0 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:4][j:2]:0 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:4][j:3]:0 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:4][j:4]:1 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| end # finish for loop
013|println( ~msg 'matrix a' )...
014|print_matrix( ~matrix a:[ -> [ -> 1, -> 2, -> 3, -> 4 ], -> [ -> 5, -> 6, -> 7, -> 8 ], -> [ -> 9, -> 0, -> 1, -> 2 ], -> [ -> 3, -> 4, -> 5, -> 6 ] ] )...
072| ... = size( ~arg matrix:-> [ -> [ -> 1, -> 2, -> 3, -> 4 ], -> [ -> 5, -> 6, -> 7, -> 8 ], -> [ -> 9, -> 0, -> 1, -> 2 ], -> [ -> 3, -> 4, -> 5, -> 6 ] ] )...
072| numrows = size( ~arg matrix:-> [ -> [ -> 1, -> 2, -> 3, -> 4 ], -> [ -> 5, -> 6, -> 7, -> 8 ], -> [ -> 9, -> 0, -> 1, -> 2 ], -> [ -> 3, -> 4, -> 5, -> 6 ] ] ):4
073| ... = size( ~arg matrix[1]:[ -> 1, -> 2, -> 3, -> 4 ] )...
073| numcols = size( ~arg matrix[1]:[ -> 1, -> 2, -> 3, -> 4 ] ):4
075| for ... range( ~from 1 ~to numrows:4 )...
075| for i = 1
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:1][j:1]:1 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:1][j:2]:2 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:1][j:3]:3 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:1][j:4]:4 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 2
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:2][j:1]:5 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:2][j:2]:6 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:2][j:3]:7 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:2][j:4]:8 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 3
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:3][j:1]:9 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:3][j:2]:0 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:3][j:3]:1 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:3][j:4]:2 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 4
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:4][j:1]:3 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:4][j:2]:4 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:4][j:3]:5 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:4][j:4]:6 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| end # finish for loop
016|matrix_scale( ~factor 2 ~matrix a:[ -> [ -> 1, -> 2, -> 3, -> 4 ], -> [ -> 5, -> 6, -> 7, -> 8 ], -> [ -> 9, -> 0, -> 1, -> 2 ], -> [ -> 3, -> 4, -> 5, -> 6 ] ] )...
031| ... = size( ~arg matrix:-> [ -> [ -> 1, -> 2, -> 3, -> 4 ], -> [ -> 5, -> 6, -> 7, -> 8 ], -> [ -> 9, -> 0, -> 1, -> 2 ], -> [ -> 3, -> 4, -> 5, -> 6 ] ] )...
031| numrows = size( ~arg matrix:-> [ -> [ -> 1, -> 2, -> 3, -> 4 ], -> [ -> 5, -> 6, -> 7, -> 8 ], -> [ -> 9, -> 0, -> 1, -> 2 ], -> [ -> 3, -> 4, -> 5, -> 6 ] ] ):4
032| ... = size( ~arg matrix[1]:[ -> 1, -> 2, -> 3, -> 4 ] )...
032| numcols = size( ~arg matrix[1]:[ -> 1, -> 2, -> 3, -> 4 ] ):4
035| for ... range( ~from 1 ~to numrows:4 )...
035| for i = 1
036| for ... range( ~from 1 ~to numcols:4 )...
036| for j = 1
037| matrix[i:1][j:1]:2 = (factor:2 * matrix[i:1][j:1]:1):2
036| end
036| for ...
036| for j = 2
037| matrix[i:1][j:2]:4 = (factor:2 * matrix[i:1][j:2]:2):4
036| end
036| for ...
036| for j = 3
037| matrix[i:1][j:3]:6 = (factor:2 * matrix[i:1][j:3]:3):6
036| end
036| for ...
036| for j = 4
037| matrix[i:1][j:4]:8 = (factor:2 * matrix[i:1][j:4]:4):8
036| end
036| for ...
036| end # finish for loop
035| end
035| for ...
035| for i = 2
036| for ... range( ~from 1 ~to numcols:4 )...
036| for j = 1
037| matrix[i:2][j:1]:10 = (factor:2 * matrix[i:2][j:1]:5):10
036| end
036| for ...
036| for j = 2
037| matrix[i:2][j:2]:12 = (factor:2 * matrix[i:2][j:2]:6):12
036| end
036| for ...
036| for j = 3
037| matrix[i:2][j:3]:14 = (factor:2 * matrix[i:2][j:3]:7):14
036| end
036| for ...
036| for j = 4
037| matrix[i:2][j:4]:16 = (factor:2 * matrix[i:2][j:4]:8):16
036| end
036| for ...
036| end # finish for loop
035| end
035| for ...
035| for i = 3
036| for ... range( ~from 1 ~to numcols:4 )...
036| for j = 1
037| matrix[i:3][j:1]:18 = (factor:2 * matrix[i:3][j:1]:9):18
036| end
036| for ...
036| for j = 2
037| matrix[i:3][j:2]:0 = (factor:2 * matrix[i:3][j:2]:0):0
036| end
036| for ...
036| for j = 3
037| matrix[i:3][j:3]:2 = (factor:2 * matrix[i:3][j:3]:1):2
036| end
036| for ...
036| for j = 4
037| matrix[i:3][j:4]:4 = (factor:2 * matrix[i:3][j:4]:2):4
036| end
036| for ...
036| end # finish for loop
035| end
035| for ...
035| for i = 4
036| for ... range( ~from 1 ~to numcols:4 )...
036| for j = 1
037| matrix[i:4][j:1]:6 = (factor:2 * matrix[i:4][j:1]:3):6
036| end
036| for ...
036| for j = 2
037| matrix[i:4][j:2]:8 = (factor:2 * matrix[i:4][j:2]:4):8
036| end
036| for ...
036| for j = 3
037| matrix[i:4][j:3]:10 = (factor:2 * matrix[i:4][j:3]:5):10
036| end
036| for ...
036| for j = 4
037| matrix[i:4][j:4]:12 = (factor:2 * matrix[i:4][j:4]:6):12
036| end
036| for ...
036| end # finish for loop
035| end
035| for ...
035| end # finish for loop
017|println( ~msg 'scale a by 2' )...
018|print_matrix( ~matrix a:[ -> [ -> 2, -> 4, -> 6, -> 8 ], -> [ -> 10, -> 12, -> 14, -> 16 ], -> [ -> 18, -> 0, -> 2, -> 4 ], -> [ -> 6, -> 8, -> 10, -> 12 ] ] )...
072| ... = size( ~arg matrix:-> [ -> [ -> 2, -> 4, -> 6, -> 8 ], -> [ -> 10, -> 12, -> 14, -> 16 ], -> [ -> 18, -> 0, -> 2, -> 4 ], -> [ -> 6, -> 8, -> 10, -> 12 ] ] )...
072| numrows = size( ~arg matrix:-> [ -> [ -> 2, -> 4, -> 6, -> 8 ], -> [ -> 10, -> 12, -> 14, -> 16 ], -> [ -> 18, -> 0, -> 2, -> 4 ], -> [ -> 6, -> 8, -> 10, -> 12 ] ] ):4
073| ... = size( ~arg matrix[1]:[ -> 2, -> 4, -> 6, -> 8 ] )...
073| numcols = size( ~arg matrix[1]:[ -> 2, -> 4, -> 6, -> 8 ] ):4
075| for ... range( ~from 1 ~to numrows:4 )...
075| for i = 1
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:1][j:1]:2 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:1][j:2]:4 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:1][j:3]:6 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:1][j:4]:8 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 2
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:2][j:1]:10 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:2][j:2]:12 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:2][j:3]:14 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:2][j:4]:16 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 3
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:3][j:1]:18 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:3][j:2]:0 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:3][j:3]:2 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:3][j:4]:4 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 4
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:4][j:1]:6 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:4][j:2]:8 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:4][j:3]:10 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:4][j:4]:12 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| end # finish for loop
020|println( ~msg 'matrix b' )...
021|... = make_upper_triangle( ~rows 4 ~cols 4 )...
085| c = [ ]
086| for ... range( ~from 1 ~to rows:4 )...
086| for i = 1
087| for ... range( ~from 1 ~to cols:4 )...
087| for j = 1
088| if (i:1 <= j:1):true
089| c[i:1][j:1]:1 = 1
089| end # if
087| end
087| for ...
087| for j = 2
088| if (i:1 <= j:2):true
089| c[i:1][j:2]:1 = 1
089| end # if
087| end
087| for ...
087| for j = 3
088| if (i:1 <= j:3):true
089| c[i:1][j:3]:1 = 1
089| end # if
087| end
087| for ...
087| for j = 4
088| if (i:1 <= j:4):true
089| c[i:1][j:4]:1 = 1
089| end # if
087| end
087| for ...
087| end # finish for loop
086| end
086| for ...
086| for i = 2
087| for ... range( ~from 1 ~to cols:4 )...
087| for j = 1
088| if (i:2 <= j:1):false
089| else
091| c[i:2][j:1]:0 = 0
091| end # if
087| end
087| for ...
087| for j = 2
088| if (i:2 <= j:2):true
089| c[i:2][j:2]:1 = 1
089| end # if
087| end
087| for ...
087| for j = 3
088| if (i:2 <= j:3):true
089| c[i:2][j:3]:1 = 1
089| end # if
087| end
087| for ...
087| for j = 4
088| if (i:2 <= j:4):true
089| c[i:2][j:4]:1 = 1
089| end # if
087| end
087| for ...
087| end # finish for loop
086| end
086| for ...
086| for i = 3
087| for ... range( ~from 1 ~to cols:4 )...
087| for j = 1
088| if (i:3 <= j:1):false
089| else
091| c[i:3][j:1]:0 = 0
091| end # if
087| end
087| for ...
087| for j = 2
088| if (i:3 <= j:2):false
089| else
091| c[i:3][j:2]:0 = 0
091| end # if
087| end
087| for ...
087| for j = 3
088| if (i:3 <= j:3):true
089| c[i:3][j:3]:1 = 1
089| end # if
087| end
087| for ...
087| for j = 4
088| if (i:3 <= j:4):true
089| c[i:3][j:4]:1 = 1
089| end # if
087| end
087| for ...
087| end # finish for loop
086| end
086| for ...
086| for i = 4
087| for ... range( ~from 1 ~to cols:4 )...
087| for j = 1
088| if (i:4 <= j:1):false
089| else
091| c[i:4][j:1]:0 = 0
091| end # if
087| end
087| for ...
087| for j = 2
088| if (i:4 <= j:2):false
089| else
091| c[i:4][j:2]:0 = 0
091| end # if
087| end
087| for ...
087| for j = 3
088| if (i:4 <= j:3):false
089| else
091| c[i:4][j:3]:0 = 0
091| end # if
087| end
087| for ...
087| for j = 4
088| if (i:4 <= j:4):true
089| c[i:4][j:4]:1 = 1
089| end # if
087| end
087| for ...
087| end # finish for loop
086| end
086| for ...
086| end # finish for loop
095| return c:[ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ]
021|b = make_upper_triangle( ~rows 4 ~cols 4 ):[ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ]
022|print_matrix( ~matrix b:[ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] )...
072| ... = size( ~arg matrix:-> [ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] )...
072| numrows = size( ~arg matrix:-> [ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] ):4
073| ... = size( ~arg matrix[1]:[ 1, 1, 1, 1 ] )...
073| numcols = size( ~arg matrix[1]:[ 1, 1, 1, 1 ] ):4
075| for ... range( ~from 1 ~to numrows:4 )...
075| for i = 1
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:1][j:1]:1 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:1][j:2]:1 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:1][j:3]:1 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:1][j:4]:1 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 2
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:2][j:1]:0 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:2][j:2]:1 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:2][j:3]:1 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:2][j:4]:1 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 3
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:3][j:1]:0 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:3][j:2]:0 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:3][j:3]:1 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:3][j:4]:1 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 4
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:4][j:1]:0 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:4][j:2]:0 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:4][j:3]:0 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:4][j:4]:1 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| end # finish for loop
024|... = matrix_mult( ~leftm a:[ -> [ -> 2, -> 4, -> 6, -> 8 ], -> [ -> 10, -> 12, -> 14, -> 16 ], -> [ -> 18, -> 0, -> 2, -> 4 ], -> [ -> 6, -> 8, -> 10, -> 12 ] ] ~rightm b:[ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] )...
044| ... = size( ~arg leftm:-> [ -> [ -> 2, -> 4, -> 6, -> 8 ], -> [ -> 10, -> 12, -> 14, -> 16 ], -> [ -> 18, -> 0, -> 2, -> 4 ], -> [ -> 6, -> 8, -> 10, -> 12 ] ] )...
044| numleftrows = size( ~arg leftm:-> [ -> [ -> 2, -> 4, -> 6, -> 8 ], -> [ -> 10, -> 12, -> 14, -> 16 ], -> [ -> 18, -> 0, -> 2, -> 4 ], -> [ -> 6, -> 8, -> 10, -> 12 ] ] ):4
045| ... = size( ~arg leftm[1]:[ -> 2, -> 4, -> 6, -> 8 ] )...
045| numleftcols = size( ~arg leftm[1]:[ -> 2, -> 4, -> 6, -> 8 ] ):4
047| ... = size( ~arg rightm:-> [ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] )...
047| numrightrows = size( ~arg rightm:-> [ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] ):4
048| ... = size( ~arg rightm[1]:[ 1, 1, 1, 1 ] )...
048| numrightcols = size( ~arg rightm[1]:[ 1, 1, 1, 1 ] ):4
050| if (numleftcols:4 != numrightrows:4):false
051| end # if
054| c = [ ]
056| for ... range( ~from 1 ~to numleftrows:4 )...
056| for left_row = 1
057| for ... range( ~from 1 ~to numrightcols:4 )...
057| for right_col = 1
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:1][n:1]:2 * rightm[n:1][right_col:1]:1):2):2
060| end
060| for ...
060| for n = 2
061| s = (s:2 + (leftm[left_row:1][n:2]:4 * rightm[n:2][right_col:1]:0):0):2
060| end
060| for ...
060| for n = 3
061| s = (s:2 + (leftm[left_row:1][n:3]:6 * rightm[n:3][right_col:1]:0):0):2
060| end
060| for ...
060| for n = 4
061| s = (s:2 + (leftm[left_row:1][n:4]:8 * rightm[n:4][right_col:1]:0):0):2
060| end
060| for ...
060| end # finish for loop
063| c[left_row:1][right_col:1]:2 = s:2
057| end
057| for ...
057| for right_col = 2
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:1][n:1]:2 * rightm[n:1][right_col:2]:1):2):2
060| end
060| for ...
060| for n = 2
061| s = (s:2 + (leftm[left_row:1][n:2]:4 * rightm[n:2][right_col:2]:1):4):6
060| end
060| for ...
060| for n = 3
061| s = (s:6 + (leftm[left_row:1][n:3]:6 * rightm[n:3][right_col:2]:0):0):6
060| end
060| for ...
060| for n = 4
061| s = (s:6 + (leftm[left_row:1][n:4]:8 * rightm[n:4][right_col:2]:0):0):6
060| end
060| for ...
060| end # finish for loop
063| c[left_row:1][right_col:2]:6 = s:6
057| end
057| for ...
057| for right_col = 3
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:1][n:1]:2 * rightm[n:1][right_col:3]:1):2):2
060| end
060| for ...
060| for n = 2
061| s = (s:2 + (leftm[left_row:1][n:2]:4 * rightm[n:2][right_col:3]:1):4):6
060| end
060| for ...
060| for n = 3
061| s = (s:6 + (leftm[left_row:1][n:3]:6 * rightm[n:3][right_col:3]:1):6):12
060| end
060| for ...
060| for n = 4
061| s = (s:12 + (leftm[left_row:1][n:4]:8 * rightm[n:4][right_col:3]:0):0):12
060| end
060| for ...
060| end # finish for loop
063| c[left_row:1][right_col:3]:12 = s:12
057| end
057| for ...
057| for right_col = 4
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:1][n:1]:2 * rightm[n:1][right_col:4]:1):2):2
060| end
060| for ...
060| for n = 2
061| s = (s:2 + (leftm[left_row:1][n:2]:4 * rightm[n:2][right_col:4]:1):4):6
060| end
060| for ...
060| for n = 3
061| s = (s:6 + (leftm[left_row:1][n:3]:6 * rightm[n:3][right_col:4]:1):6):12
060| end
060| for ...
060| for n = 4
061| s = (s:12 + (leftm[left_row:1][n:4]:8 * rightm[n:4][right_col:4]:1):8):20
060| end
060| for ...
060| end # finish for loop
063| c[left_row:1][right_col:4]:20 = s:20
057| end
057| for ...
057| end # finish for loop
056| end
056| for ...
056| for left_row = 2
057| for ... range( ~from 1 ~to numrightcols:4 )...
057| for right_col = 1
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:2][n:1]:10 * rightm[n:1][right_col:1]:1):10):10
060| end
060| for ...
060| for n = 2
061| s = (s:10 + (leftm[left_row:2][n:2]:12 * rightm[n:2][right_col:1]:0):0):10
060| end
060| for ...
060| for n = 3
061| s = (s:10 + (leftm[left_row:2][n:3]:14 * rightm[n:3][right_col:1]:0):0):10
060| end
060| for ...
060| for n = 4
061| s = (s:10 + (leftm[left_row:2][n:4]:16 * rightm[n:4][right_col:1]:0):0):10
060| end
060| for ...
060| end # finish for loop
063| c[left_row:2][right_col:1]:10 = s:10
057| end
057| for ...
057| for right_col = 2
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:2][n:1]:10 * rightm[n:1][right_col:2]:1):10):10
060| end
060| for ...
060| for n = 2
061| s = (s:10 + (leftm[left_row:2][n:2]:12 * rightm[n:2][right_col:2]:1):12):22
060| end
060| for ...
060| for n = 3
061| s = (s:22 + (leftm[left_row:2][n:3]:14 * rightm[n:3][right_col:2]:0):0):22
060| end
060| for ...
060| for n = 4
061| s = (s:22 + (leftm[left_row:2][n:4]:16 * rightm[n:4][right_col:2]:0):0):22
060| end
060| for ...
060| end # finish for loop
063| c[left_row:2][right_col:2]:22 = s:22
057| end
057| for ...
057| for right_col = 3
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:2][n:1]:10 * rightm[n:1][right_col:3]:1):10):10
060| end
060| for ...
060| for n = 2
061| s = (s:10 + (leftm[left_row:2][n:2]:12 * rightm[n:2][right_col:3]:1):12):22
060| end
060| for ...
060| for n = 3
061| s = (s:22 + (leftm[left_row:2][n:3]:14 * rightm[n:3][right_col:3]:1):14):36
060| end
060| for ...
060| for n = 4
061| s = (s:36 + (leftm[left_row:2][n:4]:16 * rightm[n:4][right_col:3]:0):0):36
060| end
060| for ...
060| end # finish for loop
063| c[left_row:2][right_col:3]:36 = s:36
057| end
057| for ...
057| for right_col = 4
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:2][n:1]:10 * rightm[n:1][right_col:4]:1):10):10
060| end
060| for ...
060| for n = 2
061| s = (s:10 + (leftm[left_row:2][n:2]:12 * rightm[n:2][right_col:4]:1):12):22
060| end
060| for ...
060| for n = 3
061| s = (s:22 + (leftm[left_row:2][n:3]:14 * rightm[n:3][right_col:4]:1):14):36
060| end
060| for ...
060| for n = 4
061| s = (s:36 + (leftm[left_row:2][n:4]:16 * rightm[n:4][right_col:4]:1):16):52
060| end
060| for ...
060| end # finish for loop
063| c[left_row:2][right_col:4]:52 = s:52
057| end
057| for ...
057| end # finish for loop
056| end
056| for ...
056| for left_row = 3
057| for ... range( ~from 1 ~to numrightcols:4 )...
057| for right_col = 1
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:3][n:1]:18 * rightm[n:1][right_col:1]:1):18):18
060| end
060| for ...
060| for n = 2
061| s = (s:18 + (leftm[left_row:3][n:2]:0 * rightm[n:2][right_col:1]:0):0):18
060| end
060| for ...
060| for n = 3
061| s = (s:18 + (leftm[left_row:3][n:3]:2 * rightm[n:3][right_col:1]:0):0):18
060| end
060| for ...
060| for n = 4
061| s = (s:18 + (leftm[left_row:3][n:4]:4 * rightm[n:4][right_col:1]:0):0):18
060| end
060| for ...
060| end # finish for loop
063| c[left_row:3][right_col:1]:18 = s:18
057| end
057| for ...
057| for right_col = 2
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:3][n:1]:18 * rightm[n:1][right_col:2]:1):18):18
060| end
060| for ...
060| for n = 2
061| s = (s:18 + (leftm[left_row:3][n:2]:0 * rightm[n:2][right_col:2]:1):0):18
060| end
060| for ...
060| for n = 3
061| s = (s:18 + (leftm[left_row:3][n:3]:2 * rightm[n:3][right_col:2]:0):0):18
060| end
060| for ...
060| for n = 4
061| s = (s:18 + (leftm[left_row:3][n:4]:4 * rightm[n:4][right_col:2]:0):0):18
060| end
060| for ...
060| end # finish for loop
063| c[left_row:3][right_col:2]:18 = s:18
057| end
057| for ...
057| for right_col = 3
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:3][n:1]:18 * rightm[n:1][right_col:3]:1):18):18
060| end
060| for ...
060| for n = 2
061| s = (s:18 + (leftm[left_row:3][n:2]:0 * rightm[n:2][right_col:3]:1):0):18
060| end
060| for ...
060| for n = 3
061| s = (s:18 + (leftm[left_row:3][n:3]:2 * rightm[n:3][right_col:3]:1):2):20
060| end
060| for ...
060| for n = 4
061| s = (s:20 + (leftm[left_row:3][n:4]:4 * rightm[n:4][right_col:3]:0):0):20
060| end
060| for ...
060| end # finish for loop
063| c[left_row:3][right_col:3]:20 = s:20
057| end
057| for ...
057| for right_col = 4
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:3][n:1]:18 * rightm[n:1][right_col:4]:1):18):18
060| end
060| for ...
060| for n = 2
061| s = (s:18 + (leftm[left_row:3][n:2]:0 * rightm[n:2][right_col:4]:1):0):18
060| end
060| for ...
060| for n = 3
061| s = (s:18 + (leftm[left_row:3][n:3]:2 * rightm[n:3][right_col:4]:1):2):20
060| end
060| for ...
060| for n = 4
061| s = (s:20 + (leftm[left_row:3][n:4]:4 * rightm[n:4][right_col:4]:1):4):24
060| end
060| for ...
060| end # finish for loop
063| c[left_row:3][right_col:4]:24 = s:24
057| end
057| for ...
057| end # finish for loop
056| end
056| for ...
056| for left_row = 4
057| for ... range( ~from 1 ~to numrightcols:4 )...
057| for right_col = 1
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:4][n:1]:6 * rightm[n:1][right_col:1]:1):6):6
060| end
060| for ...
060| for n = 2
061| s = (s:6 + (leftm[left_row:4][n:2]:8 * rightm[n:2][right_col:1]:0):0):6
060| end
060| for ...
060| for n = 3
061| s = (s:6 + (leftm[left_row:4][n:3]:10 * rightm[n:3][right_col:1]:0):0):6
060| end
060| for ...
060| for n = 4
061| s = (s:6 + (leftm[left_row:4][n:4]:12 * rightm[n:4][right_col:1]:0):0):6
060| end
060| for ...
060| end # finish for loop
063| c[left_row:4][right_col:1]:6 = s:6
057| end
057| for ...
057| for right_col = 2
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:4][n:1]:6 * rightm[n:1][right_col:2]:1):6):6
060| end
060| for ...
060| for n = 2
061| s = (s:6 + (leftm[left_row:4][n:2]:8 * rightm[n:2][right_col:2]:1):8):14
060| end
060| for ...
060| for n = 3
061| s = (s:14 + (leftm[left_row:4][n:3]:10 * rightm[n:3][right_col:2]:0):0):14
060| end
060| for ...
060| for n = 4
061| s = (s:14 + (leftm[left_row:4][n:4]:12 * rightm[n:4][right_col:2]:0):0):14
060| end
060| for ...
060| end # finish for loop
063| c[left_row:4][right_col:2]:14 = s:14
057| end
057| for ...
057| for right_col = 3
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:4][n:1]:6 * rightm[n:1][right_col:3]:1):6):6
060| end
060| for ...
060| for n = 2
061| s = (s:6 + (leftm[left_row:4][n:2]:8 * rightm[n:2][right_col:3]:1):8):14
060| end
060| for ...
060| for n = 3
061| s = (s:14 + (leftm[left_row:4][n:3]:10 * rightm[n:3][right_col:3]:1):10):24
060| end
060| for ...
060| for n = 4
061| s = (s:24 + (leftm[left_row:4][n:4]:12 * rightm[n:4][right_col:3]:0):0):24
060| end
060| for ...
060| end # finish for loop
063| c[left_row:4][right_col:3]:24 = s:24
057| end
057| for ...
057| for right_col = 4
059| s = 0
060| for ... range( ~from 1 ~to numleftcols:4 )...
060| for n = 1
061| s = (s:0 + (leftm[left_row:4][n:1]:6 * rightm[n:1][right_col:4]:1):6):6
060| end
060| for ...
060| for n = 2
061| s = (s:6 + (leftm[left_row:4][n:2]:8 * rightm[n:2][right_col:4]:1):8):14
060| end
060| for ...
060| for n = 3
061| s = (s:14 + (leftm[left_row:4][n:3]:10 * rightm[n:3][right_col:4]:1):10):24
060| end
060| for ...
060| for n = 4
061| s = (s:24 + (leftm[left_row:4][n:4]:12 * rightm[n:4][right_col:4]:1):12):36
060| end
060| for ...
060| end # finish for loop
063| c[left_row:4][right_col:4]:36 = s:36
057| end
057| for ...
057| end # finish for loop
056| end
056| for ...
056| end # finish for loop
066| return c:[ [ 2, 6, 12, 20 ], [ 10, 22, 36, 52 ], [ 18, 18, 20, 24 ], [ 6, 14, 24, 36 ] ]
024|d = matrix_mult( ~leftm a:[ -> [ -> 2, -> 4, -> 6, -> 8 ], -> [ -> 10, -> 12, -> 14, -> 16 ], -> [ -> 18, -> 0, -> 2, -> 4 ], -> [ -> 6, -> 8, -> 10, -> 12 ] ] ~rightm b:[ [ 1, 1, 1, 1 ], [ 0, 1, 1, 1 ], [ 0, 0, 1, 1 ], [ 0, 0, 0, 1 ] ] ):[ [ 2, 6, 12, 20 ], [ 10, 22, 36, 52 ], [ 18, 18, 20, 24 ], [ 6, 14, 24, 36 ] ]
025|println( ~msg 'product of matrix a and b' )...
026|print_matrix( ~matrix d:[ [ 2, 6, 12, 20 ], [ 10, 22, 36, 52 ], [ 18, 18, 20, 24 ], [ 6, 14, 24, 36 ] ] )...
072| ... = size( ~arg matrix:-> [ [ 2, 6, 12, 20 ], [ 10, 22, 36, 52 ], [ 18, 18, 20, 24 ], [ 6, 14, 24, 36 ] ] )...
072| numrows = size( ~arg matrix:-> [ [ 2, 6, 12, 20 ], [ 10, 22, 36, 52 ], [ 18, 18, 20, 24 ], [ 6, 14, 24, 36 ] ] ):4
073| ... = size( ~arg matrix[1]:[ 2, 6, 12, 20 ] )...
073| numcols = size( ~arg matrix[1]:[ 2, 6, 12, 20 ] ):4
075| for ... range( ~from 1 ~to numrows:4 )...
075| for i = 1
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:1][j:1]:2 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:1][j:2]:6 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:1][j:3]:12 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:1][j:4]:20 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 2
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:2][j:1]:10 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:2][j:2]:22 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:2][j:3]:36 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:2][j:4]:52 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 3
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:3][j:1]:18 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:3][j:2]:18 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:3][j:3]:20 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:3][j:4]:24 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| for i = 4
076| for ... range( ~from 1 ~to numcols:4 )...
076| for j = 1
077| print( ~msg matrix[i:4][j:1]:6 .. ' ' )...
076| end
076| for ...
076| for j = 2
077| print( ~msg matrix[i:4][j:2]:14 .. ' ' )...
076| end
076| for ...
076| for j = 3
077| print( ~msg matrix[i:4][j:3]:24 .. ' ' )...
076| end
076| for ...
076| for j = 4
077| print( ~msg matrix[i:4][j:4]:36 .. ' ' )...
076| end
076| for ...
076| end # finish for loop
079| println( ~msg ' ' )...
075| end
075| for ...
075| end # finish for loop