mirror of
https://github.com/revarbat/BOSL2.git
synced 2025-09-01 07:43:14 +02:00
Revar Desmera
GitHub
@@ -76,6 +76,12 @@ module test_is_matrix() {
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assert(is_matrix([[2,3,4],[5,6,7],[8,9,10]],square=false));
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assert(is_matrix([[2,3],[5,6],[8,9]],m=3,n=2));
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assert(is_matrix([[2,3,4],[5,6,7]],m=2,n=3));
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assert(is_matrix([[2,3,4],[5,6,7]],2,3));
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assert(is_matrix([[2,3,4],[5,6,7]],m=2));
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assert(is_matrix([[2,3,4],[5,6,7]],2));
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assert(is_matrix([[2,3,4],[5,6,7]],n=3));
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assert(!is_matrix([[2,3,4],[5,6,7]],m=4));
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assert(!is_matrix([[2,3,4],[5,6,7]],n=5));
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assert(!is_matrix([[2,3,4],[5,6,7]],m=2,n=3,square=true));
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assert(is_matrix([[2,3,4],[5,6,7],[8,9,10]],square=false));
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assert(!is_matrix([[2,3],[5,6],[8,9]],m=2,n=3));
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@@ -181,6 +187,9 @@ module test_sqr() {
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assert_equal(sqr(2.5), 6.25);
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assert_equal(sqr(3), 9);
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assert_equal(sqr(16), 256);
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assert_equal(sqr([2,3,4]), [4,9,16]);
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assert_equal(sqr([[2,3,4],[3,5,7]]), [[4,9,16],[9,25,49]]);
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assert_equal(sqr([]),[]);
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}
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test_sqr();
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@@ -525,6 +534,9 @@ module test_any() {
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assert_equal(any([1,5,true]), true);
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assert_equal(any([[0,0], [0,0]]), false);
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assert_equal(any([[0,0], [1,0]]), true);
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assert_equal(any([[false,false],[[false,[false],[[[true]]]],false],[false,false]]), true);
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assert_equal(any([[false,false],[[false,[false],[[[false]]]],false],[false,false]]), false);
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assert_equal(any([]), false);
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}
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test_any();
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@@ -536,6 +548,9 @@ module test_all() {
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assert_equal(all([[0,0], [0,0]]), false);
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assert_equal(all([[0,0], [1,0]]), false);
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assert_equal(all([[1,1], [1,1]]), true);
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assert_equal(all([[true,true],[[true,[true],[[[true]]]],true],[true,true]]), true);
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assert_equal(all([[true,true],[[true,[true],[[[false]]]],true],[true,true]]), false);
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assert_equal(all([]), true);
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}
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test_all();
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@@ -554,6 +569,7 @@ test_count_true();
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module test_factorial() {
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assert_equal(factorial(0), 1);
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assert_equal(factorial(1), 1);
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assert_equal(factorial(2), 2);
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assert_equal(factorial(3), 6);
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@@ -562,6 +578,8 @@ module test_factorial() {
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assert_equal(factorial(6), 720);
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assert_equal(factorial(7), 5040);
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assert_equal(factorial(8), 40320);
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assert_equal(factorial(25,21), 303600);
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assert_equal(factorial(25,25), 1);
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}
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test_factorial();
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@@ -570,6 +588,11 @@ module test_gcd() {
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assert_equal(gcd(15,25), 5);
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assert_equal(gcd(15,27), 3);
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assert_equal(gcd(270,405), 135);
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assert_equal(gcd(39, 101),1);
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assert_equal(gcd(15,-25), 5);
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assert_equal(gcd(-15,25), 5);
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assert_equal(gcd(5,0),5);
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assert_equal(gcd(0,5),5);
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}
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test_gcd();
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@@ -578,9 +601,306 @@ module test_lcm() {
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assert_equal(lcm(15,25), 75);
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assert_equal(lcm(15,27), 135);
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assert_equal(lcm(270,405), 810);
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assert_equal(lcm([3,5,15,25,35]),525);
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}
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test_lcm();
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module test_C_times() {
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assert_equal(C_times([4,5],[9,-4]), [56,29]);
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assert_equal(C_times([-7,2],[24,3]), [-174, 27]);
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}
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test_C_times();
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module test_C_div() {
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assert_equal(C_div([56,29],[9,-4]), [4,5]);
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assert_equal(C_div([-174,27],[-7,2]), [24,3]);
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}
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test_C_div();
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module test_back_substitute(){
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R = [[12,4,3,2],
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[0,2,-4,2],
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[0,0,4,5],
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[0,0,0,15]];
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assert_approx(back_substitute(R, [1,2,3,3]), [-0.675, 1.8, 0.5, 0.2]);
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assert_approx(back_substitute(R, [6, 3, 3.5, 37], transpose=true), [0.5, 0.5, 1, 2]);
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assert_approx(back_substitute(R, [[38,101],[-6,-16], [31, 71], [45, 105]]), [[1, 4],[2,3],[4,9],[3,7]]);
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assert_approx(back_substitute(R, [[12,48],[8,22],[11,36],[71,164]],transpose=true), [[1, 4],[2,3],[4,9],[3,7]]);
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assert_approx(back_substitute([[2]], [4]), [2]);
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sing1 =[[0,4,3,2],
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[0,3,-4,2],
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[0,0,4,5],
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[0,0,0,15]];
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sing2 =[[12,4,3,2],
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[0,0,-4,2],
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[0,0,4,5],
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[0,0,0,15]];
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sing3 = [[12,4,3,2],
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[0,2,-4,2],
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[0,0,4,5],
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[0,0,0,0]];
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assert_approx(back_substitute(sing1, [1,2,3,4]), []);
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assert_approx(back_substitute(sing2, [1,2,3,4]), []);
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assert_approx(back_substitute(sing3, [1,2,3,4]), []);
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}
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test_back_substitute();
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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(subindex(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_outer_product(){
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assert_equal(outer_product([1,2,3],[4,5,6]), [[4,5,6],[8,10,12],[12,15,18]]);
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assert_equal(outer_product([9],[7]), [[63]]);
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}
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test_outer_product();
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module test_deriv(){
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pent = [for(x=[0:70:359]) [cos(x), sin(x)]];
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assert_approx(deriv(pent,closed=true),
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[[-0.321393804843,0.556670399226],
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[-0.883022221559,0.321393804843],
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[-0.604022773555,-0.719846310393],
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[0.469846310393,-0.813797681349],
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[0.925416578398,0.163175911167],
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[0.413175911167,0.492403876506]]);
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assert_approx(deriv(pent,closed=true,h=2),
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0.5*[[-0.321393804843,0.556670399226],
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[-0.883022221559,0.321393804843],
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[-0.604022773555,-0.719846310393],
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[0.469846310393,-0.813797681349],
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[0.925416578398,0.163175911167],
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[0.413175911167,0.492403876506]]);
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assert_approx(deriv(pent,closed=false),
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[[-0.432937491789,1.55799143673],
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[-0.883022221559,0.321393804843],
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[-0.604022773555,-0.719846310393],
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[0.469846310393,-0.813797681349],
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[0.925416578398,0.163175911167],
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[0.696902572292,1.45914323952]]);
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spent = yscale(8,pent);
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lens = path_segment_lengths(spent,closed=true);
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assert_approx(deriv(spent, closed=true, h=lens),
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[[-0.0381285841663,0.998065839726],
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[-0.254979378104,0.0449763331253],
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[-0.216850793938,-0.953089506601],
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[0.123993253223,-0.982919228715],
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[0.191478335034,0.0131898128456],
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[0.0674850818111,0.996109041561]]);
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assert_approx(deriv(spent, closed=false, h=select(lens,0,-2)),
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[[-0.0871925973657,0.996191473044],
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[-0.254979378104,0.0449763331253],
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[-0.216850793938,-0.953089506601],
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[0.123993253223,-0.982919228715],
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[0.191478335034,0.0131898128456],
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[0.124034734589,0.992277876714]]);
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}
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test_deriv();
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module test_deriv2(){
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oct = [for(x=[0:45:359]) [cos(x), sin(x)]];
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assert_approx(deriv2(oct),
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[[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
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[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
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[0,0.585786437627],[-0.636634192232,0.534938683021]]);
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assert_approx(deriv2(oct,closed=false),
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[[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
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[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
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[0,0.585786437627],[-0.636634192232,0.534938683021]]);
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assert_approx(deriv2(oct,closed=true),
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[[-0.585786437627,0],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
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[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
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[0,0.585786437627],[-0.414213562373,0.414213562373]]);
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assert_approx(deriv2(oct,closed=false,h=2),
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0.25*[[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
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[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
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[0,0.585786437627],[-0.636634192232,0.534938683021]]);
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assert_approx(deriv2(oct,closed=true,h=2),
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0.25* [[-0.585786437627,0],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
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[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
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[0,0.585786437627],[-0.414213562373,0.414213562373]]);
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}
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test_deriv2();
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module test_deriv3(){
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oct = [for(x=[0:45:359]) [cos(x), sin(x)]];
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assert_approx(deriv3(oct),
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[[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
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[0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
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[-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]);
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assert_approx(deriv3(oct,closed=false),
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[[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
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[0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
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[-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]);
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assert_approx(deriv3(oct,closed=false,h=2),
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[[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
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[0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
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[-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]/8);
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assert_approx(deriv3(oct,closed=true),
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[[0,-0.414213562373],[0.292893218813,-0.292893218813],[0.414213562373,0],[0.292893218813,0.292893218813],
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[0,0.414213562373],[-0.292893218813,0.292893218813],[-0.414213562373,0],[-0.292893218813,-0.292893218813]]);
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assert_approx(deriv3(oct,closed=true,h=2),
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[[0,-0.414213562373],[0.292893218813,-0.292893218813],[0.414213562373,0],[0.292893218813,0.292893218813],
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[0,0.414213562373],[-0.292893218813,0.292893218813],[-0.414213562373,0],[-0.292893218813,-0.292893218813]]/8);
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}
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test_deriv3();
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module test_polynomial(){
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assert_equal(polynomial([],12),0);
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assert_equal(polynomial([],[12,4]),[0,0]);
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assert_equal(polynomial([1,2,3,4],3),58);
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assert_equal(polynomial([1,2,3,4],[3,-1]),[47,-41]);
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assert_equal(polynomial([0,0,2],4),2);
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}
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test_polynomial();
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module test_poly_roots(){
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// Fifth roots of unity
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assert_approx(
|
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poly_roots([1,0,0,0,0,-1]),
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[[1,0],[0.309016994375,0.951056516295],[-0.809016994375,0.587785252292],
|
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[-0.809016994375,-0.587785252292],[0.309016994375,-0.951056516295]]);
|
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assert_approx(poly_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50]])),
|
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[[1, 1], [5, 5], [1, 2], [-3, 1], [-3, -1], [1, -1], [1, -2], [5, -5]]);
|
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assert_approx(poly_roots([.124,.231,.942, -.334]),
|
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[[0.3242874219074053,0],[-1.093595323856930,2.666477428660098], [-1.093595323856930,-2.666477428660098]]);
|
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}
|
||||
test_poly_roots();
|
||||
|
||||
module test_real_roots(){
|
||||
// Wilkinson polynomial is a nasty test:
|
||||
assert_approx(
|
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sort(real_roots(poly_mult([[1,-1],[1,-2],[1,-3],[1,-4],[1,-5],[1,-6],[1,-7],[1,-8],[1,-9],[1,-10]]))),
|
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list_range(n=10,s=1));
|
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assert_equal(real_roots([3]), []);
|
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assert_equal(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50]])),[]);
|
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assert_equal(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50],[1,0,0]])),[0,0]);
|
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assert_approx(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50],[1,4]])),[-4]);
|
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assert(approx(real_roots([1,-10,25]),[5,5],eps=5e-6));
|
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assert_approx(real_roots([4,-3]), [0.75]);
|
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assert_approx(real_roots([0,0,0,4,-3]), [0.75]);
|
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}
|
||||
test_real_roots();
|
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|
||||
// Need decision about behavior for out of bounds ranges, empty ranges
|
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module test_submatrix(){
|
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M = [[1,2,3,4,5],
|
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[6,7,8,9,10],
|
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[11,12,13,14,15],
|
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[16,17,18,19,20],
|
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[21,22,23,24,25]];
|
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assert_equal(submatrix(M,[1:2], [3:4]), [[9,10],[14,15]]);
|
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assert_equal(submatrix(M,[1], [3,4]), [[9,10]]);
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assert_equal(submatrix(M,1, [3,4]), [[9,10]]);
|
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assert_equal(submatrix(M, [3,4],1), [[17],[22]]);
|
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assert_equal(submatrix(M, [1,3],[2,4]), [[8,10],[18,20]]);
|
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}
|
||||
test_submatrix();
|
||||
|
||||
|
||||
|
||||
module test_qr_factor() {
|
||||
// Check that R is upper triangular
|
||||
function is_ut(R) =
|
||||
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 == [];
|
||||
|
||||
// Test the R is upper trianglar, Q is orthogonal and qr=M
|
||||
function qrok(qr,M) =
|
||||
is_ut(qr[1]) && approx(qr[0]*transpose(qr[0]), ident(len(qr[0]))) && approx(qr[0]*qr[1],M);
|
||||
|
||||
M = [[1,2,9,4,5],
|
||||
[6,7,8,19,10],
|
||||
[11,12,13,14,15],
|
||||
[1,17,18,19,20],
|
||||
[21,22,10,24,25]];
|
||||
|
||||
assert(qrok(qr_factor(M),M));
|
||||
assert(qrok(qr_factor(select(M,0,3)),select(M,0,3)));
|
||||
assert(qrok(qr_factor(transpose(select(M,0,3))),transpose(select(M,0,3))));
|
||||
|
||||
A = [[1,2,9,4,5],
|
||||
[6,7,8,19,10],
|
||||
[0,0,0,0,0],
|
||||
[1,17,18,19,20],
|
||||
[21,22,10,24,25]];
|
||||
assert(qrok(qr_factor(A),A));
|
||||
|
||||
B = [[1,2,0,4,5],
|
||||
[6,7,0,19,10],
|
||||
[0,0,0,0,0],
|
||||
[1,17,0,19,20],
|
||||
[21,22,0,24,25]];
|
||||
|
||||
assert(qrok(qr_factor(B),B));
|
||||
assert(qrok(qr_factor([[7]]), [[7]]));
|
||||
assert(qrok(qr_factor([[1,2,3]]), [[1,2,3]]));
|
||||
assert(qrok(qr_factor([[1],[2],[3]]), [[1],[2],[3]]));
|
||||
}
|
||||
test_qr_factor();
|
||||
|
||||
|
||||
module test_poly_mult(){
|
||||
assert_equal(poly_mult([3,2,1],[4,5,6,7]),[12,23,32,38,20,7]);
|
||||
assert_equal(poly_mult([3,2,1],[]),[]);
|
||||
assert_equal(poly_mult([[1,2],[3,4],[5,6]]), [15,68,100,48]);
|
||||
assert_equal(poly_mult([[1,2],[],[5,6]]), []);
|
||||
assert_equal(poly_mult([[3,4,5],[0,0,0]]),[]);
|
||||
}
|
||||
test_poly_mult();
|
||||
|
||||
|
||||
module test_poly_div(){
|
||||
assert_equal(poly_div(poly_mult([4,3,3,2],[2,1,3]), [2,1,3]),[[4,3,3,2],[]]);
|
||||
assert_equal(poly_div([1,2,3,4],[1,2,3,4,5]), [[], [1,2,3,4]]);
|
||||
assert_equal(poly_div(poly_add(poly_mult([1,2,3,4],[2,0,2]), [1,1,2]), [1,2,3,4]), [[2,0,2],[1,1,2]]);
|
||||
assert_equal(poly_div([1,2,3,4], [1,-3]), [[1,5,18],[58]]);
|
||||
}
|
||||
test_poly_div();
|
||||
|
||||
|
||||
module test_poly_add(){
|
||||
assert_equal(poly_add([2,3,4],[3,4,5,6]),[3,6,8,10]);
|
||||
assert_equal(poly_add([1,2,3,4],[-1,-2,3,4]), [6,8]);
|
||||
assert_equal(poly_add([1,2,3],-[1,2,3]),[]);
|
||||
}
|
||||
test_poly_add();
|
||||
|
||||
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|
||||
|
||||
Reference in New Issue
Block a user