Pascal matrix generation: Difference between revisions
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But since the builtin function MatrixExp works by first computing eigenvalues this is |
But since the builtin function MatrixExp works by first computing eigenvalues this is |
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likely to be slower for large Pascal matrices |
likely to be slower for large Pascal matrices |
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=={{header|MATLAB}}== |
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{{trans|Mathematica/Wolfram_Language}} |
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<syntaxhighlight lang="MATLAB"> |
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clear all;close all;clc; |
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size = 5; % size of Pascal matrix |
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% Generate the symmetric Pascal matrix |
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symPascalMatrix = symPascal(size); |
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% Generate the upper triangular Pascal matrix |
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upperPascalMatrix = upperPascal(size); |
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% Generate the lower triangular Pascal matrix |
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lowerPascalMatrix = lowerPascal(size); |
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% Display the matrices |
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disp('Upper Pascal Matrix:'); |
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disp(upperPascalMatrix); |
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disp('Lower Pascal Matrix:'); |
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disp(lowerPascalMatrix); |
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disp('Symmetric Pascal Matrix:'); |
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disp(symPascalMatrix); |
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function symPascal = symPascal(size) |
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% Generates a symmetric Pascal matrix of given size |
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row = ones(1, size); |
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symPascal = row; |
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for k = 2:size |
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row = cumsum(row); |
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symPascal = [symPascal; row]; |
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end |
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end |
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function upperPascal = upperPascal(size) |
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% Generates an upper triangular Pascal matrix using Cholesky decomposition |
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upperPascal = chol(symPascal(size)); |
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end |
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function lowerPascal = lowerPascal(size) |
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% Generates a lower triangular Pascal matrix using Cholesky decomposition |
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lowerPascal = chol(symPascal(size))'; |
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end |
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</syntaxhighlight> |
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{{out}} |
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<pre> |
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Upper Pascal Matrix: |
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1 1 1 1 1 |
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0 1 2 3 4 |
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0 0 1 3 6 |
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0 0 0 1 4 |
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0 0 0 0 1 |
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Lower Pascal Matrix: |
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1 0 0 0 0 |
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1 1 0 0 0 |
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1 2 1 0 0 |
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1 3 3 1 0 |
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1 4 6 4 1 |
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Symmetric Pascal Matrix: |
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1 1 1 1 1 |
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1 2 3 4 5 |
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1 3 6 10 15 |
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1 4 10 20 35 |
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1 5 15 35 70 |
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</pre> |
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=={{header|Maxima}}== |
=={{header|Maxima}}== |
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