mirror of
https://github.com/revarbat/BOSL2.git
synced 2025-08-29 16:59:49 +02:00
Move linear algebra to linalg.scad
columns->column because the multiindex case is handled by submatrix and also it never occurs in the code.
This commit is contained in:
Adrian Mariano
@@ -595,13 +595,13 @@ module test_mean() {
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}
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test_mean();
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/*
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module test_median() {
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assert_equal(median([2,3,7]), 4.5);
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assert_equal(median([[1,2,3], [3,4,5], [8,9,10]]), [4.5,5.5,6.5]);
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assert_equal(median([2,3,7]), 3);
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assert_equal(median([2,4,5,8]), 4.5);
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}
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test_median();
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*/
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module test_convolve() {
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@@ -618,40 +618,6 @@ test_convolve();
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module test_matrix_inverse() {
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assert_approx(matrix_inverse(rot([20,30,40])), [[0.663413948169,0.556670399226,-0.5,0],[-0.47302145844,0.829769465589,0.296198132726,0],[0.579769465589,0.0400087565481,0.813797681349,0],[0,0,0,1]]);
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}
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test_matrix_inverse();
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module test_det2() {
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assert_equal(det2([[6,-2], [1,8]]), 50);
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assert_equal(det2([[4,7], [3,2]]), -13);
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assert_equal(det2([[4,3], [3,4]]), 7);
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}
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test_det2();
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module test_det3() {
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M = [ [6,4,-2], [1,-2,8], [1,5,7] ];
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assert_equal(det3(M), -334);
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}
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test_det3();
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module test_determinant() {
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M = [ [6,4,-2,9], [1,-2,8,3], [1,5,7,6], [4,2,5,1] ];
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assert_equal(determinant(M), 2267);
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}
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test_determinant();
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module test_matrix_trace() {
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M = [ [6,4,-2,9], [1,-2,8,3], [1,5,7,6], [4,2,5,1] ];
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assert_equal(matrix_trace(M), 6-2+7+1);
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}
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test_matrix_trace();
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// Logic
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@@ -975,40 +941,6 @@ test_back_substitute();
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module test_norm_fro(){
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assert_approx(norm_fro([[2,3,4],[4,5,6]]), 10.29563014098700);
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} test_norm_fro();
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module test_linear_solve(){
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M = [[-2,-5,-1,3],
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[3,7,6,2],
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[6,5,-1,-6],
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[-7,1,2,3]];
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assert_approx(linear_solve(M, [-3,43,-11,13]), [1,2,3,4]);
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assert_approx(linear_solve(M, [[-5,8],[18,-61],[4,7],[-1,-12]]), [[1,-2],[1,-3],[1,-4],[1,-5]]);
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assert_approx(linear_solve([[2]],[4]), [2]);
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assert_approx(linear_solve([[2]],[[4,8]]), [[2, 4]]);
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assert_approx(linear_solve(select(M,0,2), [2,4,4]), [ 2.254871220604705e+00,
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-8.378819388897780e-01,
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2.330507118860985e-01,
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8.511278195488737e-01]);
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assert_approx(linear_solve(columns(M,[0:2]), [2,4,4,4]),
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[-2.457142857142859e-01,
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5.200000000000000e-01,
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7.428571428571396e-02]);
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assert_approx(linear_solve([[1,2,3,4]], [2]), [0.066666666666666, 0.13333333333, 0.2, 0.266666666666]);
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assert_approx(linear_solve([[1],[2],[3],[4]], [4,3,2,1]), [2/3]);
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rd = [[-2,-5,-1,3],
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[3,7,6,2],
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[3,7,6,2],
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[-7,1,2,3]];
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assert_equal(linear_solve(rd,[1,2,3,4]),[]);
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assert_equal(linear_solve(select(rd,0,2), [2,4,4]), []);
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assert_equal(linear_solve(transpose(select(rd,0,2)), [2,4,3,4]), []);
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}
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test_linear_solve();
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module test_cumprod(){
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@@ -1186,85 +1118,6 @@ module test_quadratic_roots(){
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test_quadratic_roots();
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module test_null_space(){
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assert_equal(null_space([[3,2,1],[3,6,3],[3,9,-3]]),[]);
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function nullcheck(A,dim) =
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let(v=null_space(A))
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len(v)==dim && all_zero(A*transpose(v),eps=1e-12);
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A = [[-1, 2, -5, 2],[-3,-1,3,-3],[5,0,5,0],[3,-4,11,-4]];
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assert(nullcheck(A,1));
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B = [
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[ 4, 1, 8, 6, -2, 3],
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[ 10, 5, 10, 10, 0, 5],
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[ 8, 1, 8, 8, -6, 1],
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[ -8, -8, 6, -1, -8, -1],
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[ 2, 2, 0, 1, 2, 1],
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[ 2, -3, 10, 6, -8, 1],
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];
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assert(nullcheck(B,3));
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}
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test_null_space();
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module test_qr_factor() {
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// Check that R is upper triangular
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function is_ut(R) =
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let(bad = [for(i=[1:1:len(R)-1], j=[0:min(i-1, len(R[0])-1)]) if (!approx(R[i][j],0)) 1])
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bad == [];
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// Test the R is upper trianglar, Q is orthogonal and qr=M
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function qrok(qr,M) =
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is_ut(qr[1]) && approx(qr[0]*transpose(qr[0]), ident(len(qr[0]))) && approx(qr[0]*qr[1],M) && qr[2]==ident(len(qr[2]));
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// Test the R is upper trianglar, Q is orthogonal, R diagonal non-increasing and qrp=M
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function qrokpiv(qr,M) =
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is_ut(qr[1])
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&& approx(qr[0]*transpose(qr[0]), ident(len(qr[0])))
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&& approx(qr[0]*qr[1]*transpose(qr[2]),M)
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&& is_decreasing([for(i=[0:1:min(len(qr[1]),len(qr[1][0]))-1]) abs(qr[1][i][i])]);
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M = [[1,2,9,4,5],
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[6,7,8,19,10],
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[11,12,13,14,15],
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[1,17,18,19,20],
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[21,22,10,24,25]];
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assert(qrok(qr_factor(M),M));
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assert(qrok(qr_factor(select(M,0,3)),select(M,0,3)));
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assert(qrok(qr_factor(transpose(select(M,0,3))),transpose(select(M,0,3))));
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A = [[1,2,9,4,5],
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[6,7,8,19,10],
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[0,0,0,0,0],
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[1,17,18,19,20],
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[21,22,10,24,25]];
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assert(qrok(qr_factor(A),A));
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B = [[1,2,0,4,5],
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[6,7,0,19,10],
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[0,0,0,0,0],
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[1,17,0,19,20],
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[21,22,0,24,25]];
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assert(qrok(qr_factor(B),B));
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assert(qrok(qr_factor([[7]]), [[7]]));
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assert(qrok(qr_factor([[1,2,3]]), [[1,2,3]]));
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assert(qrok(qr_factor([[1],[2],[3]]), [[1],[2],[3]]));
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assert(qrokpiv(qr_factor(M,pivot=true),M));
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assert(qrokpiv(qr_factor(select(M,0,3),pivot=true),select(M,0,3)));
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assert(qrokpiv(qr_factor(transpose(select(M,0,3)),pivot=true),transpose(select(M,0,3))));
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assert(qrokpiv(qr_factor(B,pivot=true),B));
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assert(qrokpiv(qr_factor([[7]],pivot=true), [[7]]));
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assert(qrokpiv(qr_factor([[1,2,3]],pivot=true), [[1,2,3]]));
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assert(qrokpiv(qr_factor([[1],[2],[3]],pivot=true), [[1],[2],[3]]));
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}
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test_qr_factor();
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module test_poly_mult(){
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assert_equal(poly_mult([3,2,1],[4,5,6,7]),[12,23,32,38,20,7]);
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