Casio fx-CG50: Sparse Matrix Builder
Introduction
The programs can create a sparse matrix, a matrix where most of the entries have zero value. There are several ways to represent sparse matrix in a shortcut form. The most straight forward way is the COO (row-column-value) representation.
Mat A: three column matrix: (row-column-value representation)
Column 1: row number
Column 2: column number
Column 3: value
Mat S: sparse matrix
Casio fx-CG 50 Program: SPARSE
[ [ row, column, value ] ... ] → sparse matrix
"TO SPARSE MATRIX"
"EDWARD SHORE"
"[[ROW,COL,VALUE]]"
"MAT"?→Mat A
Mat→List(Mat A,1)→List 26
Max(List 26)→R
Mat→List(Mat A,2)→List 26
Max(List 26)→C
{R,C}→Dim Mat S
Dim Mat A→List 26
List 26[1]→N
For 1→I To N
Mat A[I,1]→J
Mat A[I,2]→K
Mat A[I,3]→Mat S[J,K]
Next
"SPARSE MATRIX:"⊿
Mat S
Casio fx-CG 50 Program: ISPARSE
sparse matrix → [ [ row, column, value ] ... ]
"INV SPARSE MATRIX"
"EDWARD SHORE"
"SPARSE"?→Mat S
Dim Mat S→List 26
List 26[1]→R
List 26[2]→C
0→N
For 1→I To R
For 1→J To C
Mat S[I,J] →V
[[I][J][V]]→Mat Z
(V≠0 And N=0)⇒Mat Z→Mat A
(V≠0 And N>0)⇒Augment(Mat A,Mat Z)→Mat A
(V≠0)⇒1+N→N
Next
Next
"COO FORMAT:"⊿
Trn Mat A→Mat A
Example
Example 1:
Row/Column/Value (COO) Format: (Mat A)
[ [ 1, 2, 8 ]
[ 2, 4, -3 ]
[ 3, 1, 2 ]
[ 3, 3, 6 ]
[ 4, 2, -1 ] ]
Sparse Matrix: (Mat S)
[ [ 0, 8, 0, 0 ]
[ 0, 0, 0, -3 ]
[ 2, 0, 6, 0 ]
[ 0, -1, 0, 0 ] ]
Example 2:
Row/Column/Value (COO) Format: (Mat A)
[ [ 1, 2, 1 ]
[ 1, 3, 2 ]
[ 2, 1, -1 ]
[ 2, 3, 3 ]
[ 3, 3, 4 ]
[ 4, 1, 5 ] ]
Sparse Matrix: (Mat S)
[ [ 0, 1, 2 ]
[-1, 0, 3 ]
[ 0, 0, 4 ]
[ 5, 0, 0 ] ]
Source:
"Sparse matrix" Wikipedia. Last edited March 11, 2022. Accessed May 9, 2022. https://en.wikipedia.org/wiki/Sparse_matrix
Eddie
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