Sunday, July 3, 2022

Casio fx-CG50: Sparse Matrix Builder

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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