matrix-except-all ( matrix -- submatrices )
Matrix operations

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Vocabulary
math.matrices

Inputs

matrix

a matrix

Outputs

submatrices

a sequence of matrixs

Word description
Find every possible submatrix of matrix by using matrix-except for every value's row-column pair.

Examples
There are 9 possible 2x2 submatrices of a 3x3 matrix with 9 indices, because there are 9 indices to exclude creating a new submatrix.

USING: math.matrices prettyprint ; { { 0 1 2 } { 3 4 5 } { 6 7 8 } } matrix-except-all .
{ { { { 4 5 } { 7 8 } } { { 3 5 } { 6 8 } } { { 3 4 } { 6 7 } } } { { { 1 2 } { 7 8 } } { { 0 2 } { 6 8 } } { { 0 1 } { 6 7 } } } { { { 1 2 } { 4 5 } } { { 0 2 } { 3 5 } } { { 0 1 } { 3 4 } } } }

Definition

USING: kernel sequences sequences.private ;

IN: math.matrices

:: matrix-except-all ( matrix -- submatrices )
    matrix dimension [ <iota> ] map
    first2-unsafe cartesian-product
    [ [ matrix swap matrix-except ] map ] map ;