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BOSL2/tests/test_math.scad
Adrian Mariano 054052144e sum/product optimizations
2024-06-25 19:24:48 -04:00

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include <../std.scad>
// Simple Calculations
module test_quant() {
assert_equal(quant(-4,3), -3);
assert_equal(quant(-3,3), -3);
assert_equal(quant(-2,3), -3);
assert_equal(quant(-1,3), 0);
assert_equal(quant(0,3), 0);
assert_equal(quant(1,3), 0);
assert_equal(quant(2,3), 3);
assert_equal(quant(3,3), 3);
assert_equal(quant(4,3), 3);
assert_equal(quant(7,3), 6);
assert_equal(quant(12,2.5), 12.5);
assert_equal(quant(11,2.5), 10.0);
assert_equal(quant([12,13,13.1,14,14.1,15,16],4), [12,12,12,16,16,16,16]);
assert_equal(quant([9,10,10.4,10.5,11,12],3), [9,9,9,12,12,12]);
assert_equal(quant([[9,10,10.4],[10.5,11,12]],3), [[9,9,9],[12,12,12]]);
}
test_quant();
module test_quantdn() {
assert_equal(quantdn(-4,3), -6);
assert_equal(quantdn(-3,3), -3);
assert_equal(quantdn(-2,3), -3);
assert_equal(quantdn(-1,3), -3);
assert_equal(quantdn(0,3), 0);
assert_equal(quantdn(1,3), 0);
assert_equal(quantdn(2,3), 0);
assert_equal(quantdn(3,3), 3);
assert_equal(quantdn(4,3), 3);
assert_equal(quantdn(7,3), 6);
assert_equal(quantdn(12,2.5), 10.0);
assert_equal(quantdn(11,2.5), 10.0);
assert_equal(quantdn([12,13,13.1,14,14.1,15,16],4), [12,12,12,12,12,12,16]);
assert_equal(quantdn([9,10,10.4,10.5,11,12],3), [9,9,9,9,9,12]);
assert_equal(quantdn([[9,10,10.4],[10.5,11,12]],3), [[9,9,9],[9,9,12]]);
}
test_quantdn();
module test_quantup() {
assert_equal(quantup(-4,3), -3);
assert_equal(quantup(-3,3), -3);
assert_equal(quantup(-2,3), 0);
assert_equal(quantup(-1,3), 0);
assert_equal(quantup(0,3), 0);
assert_equal(quantup(1,3), 3);
assert_equal(quantup(2,3), 3);
assert_equal(quantup(3,3), 3);
assert_equal(quantup(4,3), 6);
assert_equal(quantup(7,3), 9);
assert_equal(quantup(12,2.5), 12.5);
assert_equal(quantup(11,2.5), 12.5);
assert_equal(quantup([12,13,13.1,14,14.1,15,16],4), [12,16,16,16,16,16,16]);
assert_equal(quantup([9,10,10.4,10.5,11,12],3), [9,12,12,12,12,12]);
assert_equal(quantup([[9,10,10.4],[10.5,11,12]],3), [[9,12,12],[12,12,12]]);
}
test_quantup();
module test_constrain() {
assert_equal(constrain(-2,-1,1), -1);
assert_equal(constrain(-1.75,-1,1), -1);
assert_equal(constrain(-1,-1,1), -1);
assert_equal(constrain(-0.75,-1,1), -0.75);
assert_equal(constrain(0,-1,1), 0);
assert_equal(constrain(0.75,-1,1), 0.75);
assert_equal(constrain(1,-1,1), 1);
assert_equal(constrain(1.75,-1,1), 1);
assert_equal(constrain(2,-1,1), 1);
}
test_constrain();
module test_all_integer() {
assert(!all_integer(undef));
assert(!all_integer(true));
assert(!all_integer(false));
assert(!all_integer(4.3));
assert(!all_integer("foo"));
assert(!all_integer([]));
assert(!all_integer([3,4.1,5,7]));
assert(!all_integer([[1,2,3],[4,5,6],[7,8]]));
assert(all_integer(-4));
assert(all_integer(0));
assert(all_integer(5));
assert(all_integer([-3]));
assert(all_integer([0]));
assert(all_integer([3]));
assert(all_integer([2,-4,0,5,7,9876543210]));
}
test_all_integer();
module test_posmod() {
assert_equal(posmod(-5,3), 1);
assert_equal(posmod(-4,3), 2);
assert_equal(posmod(-3,3), 0);
assert_equal(posmod(-2,3), 1);
assert_equal(posmod(-1,3), 2);
assert_equal(posmod(0,3), 0);
assert_equal(posmod(1,3), 1);
assert_equal(posmod(2,3), 2);
assert_equal(posmod(3,3), 0);
}
test_posmod();
module test_modang() {
assert_equal(modang(-700), 20);
assert_equal(modang(-270), 90);
assert_equal(modang(-120), -120);
assert_equal(modang(120), 120);
assert_equal(modang(270), -90);
assert_equal(modang(700), -20);
}
test_modang();
module test_sqr() {
assert_equal(sqr(-3), 9);
assert_equal(sqr(0), 0);
assert_equal(sqr(1), 1);
assert_equal(sqr(2), 4);
assert_equal(sqr(2.5), 6.25);
assert_equal(sqr(3), 9);
assert_equal(sqr(16), 256);
assert_equal(sqr([2,3,4]), 29);
assert_equal(sqr([[2,3,4],[3,5,7],[3,5,1]]), [[25,41,33],[42,69,54],[24,39,48]]);
}
test_sqr();
module test_log2() {
assert_equal(log2(0.125), -3);
assert_equal(log2(16), 4);
assert_equal(log2(256), 8);
}
test_log2();
module test_rand_int() {
nums = rand_int(-100,100,1000,seed=2134);
assert_equal(len(nums), 1000);
for (num = nums) {
assert(num>=-100);
assert(num<=100);
assert_equal(num, floor(num));
}
}
test_rand_int();
module test_gaussian_rands() {
nums1 = gaussian_rands(1000,0,10,seed=2132);
nums2 = gaussian_rands(1000,0,10,seed=2130);
nums3 = gaussian_rands(1000,0,10,seed=2132);
assert_equal(len(nums1), 1000);
assert_equal(len(nums2), 1000);
assert_equal(len(nums3), 1000);
assert_equal(nums1, nums3);
assert(nums1!=nums2);
R = [[4,2],[2,17]];
data = gaussian_rands(100000,[0,0],R,seed=49);
assert(approx(mean(data), [0,0], eps=1e-2));
assert(approx(transpose(data)*data/len(data), R, eps=2e-2));
R2 = [[4,2,-1],[2,17,4],[-1,4,11]];
data3 = gaussian_rands(100000,[1,2,3],R2,seed=97);
assert(approx(mean(data3),[1,2,3], eps=1e-2));
cdata = move(-mean(data3),data3);
assert(approx(transpose(cdata)*cdata/len(cdata),R2,eps=.1));
}
test_gaussian_rands();
module test_lerp() {
assert_equal(lerp(-20,20,0), -20);
assert_equal(lerp(-20,20,0.25), -10);
assert_equal(lerp(-20,20,0.5), 0);
assert_equal(lerp(-20,20,0.75), 10);
assert_equal(lerp(-20,20,1), 20);
assert_equal(lerp(-20,20,[0,0.25,0.5,0.75,1]), [-20,-10,0,10,20]);
assert_equal(lerp(-20,20,[0:0.25:1]), [-20,-10,0,10,20]);
assert_equal(lerp([10,10],[30,-10],0.5), [20,0]);
}
test_lerp();
module test_u_add() {
assert_equal(u_add(1,2),3);
assert_equal(u_add(1,-2),-1);
assert_equal(u_add(-1,2),1);
assert_equal(u_add(-1,-2),-3);
assert_equal(u_add(243,-27),216);
assert_equal(u_add([2,3,4],[8,7,9]),[10,10,13]);
assert_equal(u_add(undef,27),undef);
assert_equal(u_add(undef,-27),undef);
assert_equal(u_add(243,undef),undef);
assert_equal(u_add(-43,undef),undef);
assert_equal(u_add(undef,[8,7,9]),undef);
assert_equal(u_add([2,3,4],undef),undef);
}
test_u_add();
module test_u_sub() {
assert_equal(u_sub(1,2),-1);
assert_equal(u_sub(1,-2),3);
assert_equal(u_sub(-1,2),-3);
assert_equal(u_sub(-1,-2),1);
assert_equal(u_sub(243,-27),270);
assert_equal(u_sub([2,3,4],[8,7,9]),[-6,-4,-5]);
assert_equal(u_sub(undef,27),undef);
assert_equal(u_sub(undef,-27),undef);
assert_equal(u_sub(243,undef),undef);
assert_equal(u_sub(-43,undef),undef);
assert_equal(u_sub(undef,[8,7,9]),undef);
assert_equal(u_sub([2,3,4],undef),undef);
}
test_u_sub();
module test_u_mul() {
assert_equal(u_mul(3,2),6);
assert_equal(u_mul(3,-2),-6);
assert_equal(u_mul(-3,2),-6);
assert_equal(u_mul(-3,-2),6);
assert_equal(u_mul(243,-27),-6561);
assert_equal(u_mul([2,3,4],[8,7,9]),[16,21,36]);
assert_equal(u_mul(undef,27),undef);
assert_equal(u_mul(undef,-27),undef);
assert_equal(u_mul(243,undef),undef);
assert_equal(u_mul(-43,undef),undef);
assert_equal(u_mul(undef,[8,7,9]),undef);
assert_equal(u_mul([2,3,4],undef),undef);
}
test_u_mul();
module test_u_div() {
assert_equal(u_div(1,2),1/2);
assert_equal(u_div(1,-2),-1/2);
assert_equal(u_div(-1,2),-1/2);
assert_equal(u_div(-1,-2),1/2);
assert_equal(u_div(243,-27),-9);
assert_equal(u_div([8,7,9],[2,3,4]),[4,7/3,9/4]);
assert_equal(u_div(undef,27),undef);
assert_equal(u_div(undef,-27),undef);
assert_equal(u_div(243,undef),undef);
assert_equal(u_div(-43,undef),undef);
assert_equal(u_div(undef,[8,7,9]),undef);
assert_equal(u_div([2,3,4],undef),undef);
}
test_u_div();
module test_hypot() {
assert_approx(hypot(20,30), norm([20,30]));
}
test_hypot();
module test_sinh() {
assert_approx(sinh(-2), -3.6268604078);
assert_approx(sinh(-1), -1.1752011936);
assert_approx(sinh(0), 0);
assert_approx(sinh(1), 1.1752011936);
assert_approx(sinh(2), 3.6268604078);
}
test_sinh();
module test_cosh() {
assert_approx(cosh(-2), 3.7621956911);
assert_approx(cosh(-1), 1.5430806348);
assert_approx(cosh(0), 1);
assert_approx(cosh(1), 1.5430806348);
assert_approx(cosh(2), 3.7621956911);
}
test_cosh();
module test_tanh() {
assert_approx(tanh(-2), -0.9640275801);
assert_approx(tanh(-1), -0.761594156);
assert_approx(tanh(0), 0);
assert_approx(tanh(1), 0.761594156);
assert_approx(tanh(2), 0.9640275801);
}
test_tanh();
module test_asinh() {
assert_approx(asinh(sinh(-2)), -2);
assert_approx(asinh(sinh(-1)), -1);
assert_approx(asinh(sinh(0)), 0);
assert_approx(asinh(sinh(1)), 1);
assert_approx(asinh(sinh(2)), 2);
}
test_asinh();
module test_acosh() {
assert_approx(acosh(cosh(-2)), 2);
assert_approx(acosh(cosh(-1)), 1);
assert_approx(acosh(cosh(0)), 0);
assert_approx(acosh(cosh(1)), 1);
assert_approx(acosh(cosh(2)), 2);
}
test_acosh();
module test_atanh() {
assert_approx(atanh(tanh(-2)), -2);
assert_approx(atanh(tanh(-1)), -1);
assert_approx(atanh(tanh(0)), 0);
assert_approx(atanh(tanh(1)), 1);
assert_approx(atanh(tanh(2)), 2);
}
test_atanh();
module test_sum() {
assert_equal(sum([]), 0);
assert_equal(sum([],dflt=undef), undef);
assert_equal(sum([1,2,3]), 6);
assert_equal(sum([-2,-1,0,1,2]), 0);
assert_equal(sum([[1,2,3], [3,4,5], [5,6,7]]), [9,12,15]);
}
test_sum();
module test_cumsum() {
assert_equal(cumsum([]), []);
assert_equal(cumsum([1,1,1]), [1,2,3]);
assert_equal(cumsum([2,2,2]), [2,4,6]);
assert_equal(cumsum([1,2,3]), [1,3,6]);
assert_equal(cumsum([-2,-1,0,1,2]), [-2,-3,-3,-2,0]);
assert_equal(cumsum([[1,2,3], [3,4,5], [5,6,7]]), [[1,2,3],[4,6,8],[9,12,15]]);
}
test_cumsum();
module test_sum_of_sines() {
assert_equal(sum_of_sines(0, [[3,4,0],[2,2,0]]), 0);
assert_equal(sum_of_sines(45, [[3,4,0],[2,2,0]]), 2);
assert_equal(sum_of_sines(90, [[3,4,0],[2,2,0]]), 0);
assert_equal(sum_of_sines(135, [[3,4,0],[2,2,0]]), -2);
assert_equal(sum_of_sines(180, [[3,4,0],[2,2,0]]), 0);
}
test_sum_of_sines();
module test_deltas() {
assert_equal(deltas([2,5,9,17]), [3,4,8]);
assert_equal(deltas([2,5,9,17],wrap=true), [3,4,8,-15]);
assert_equal(deltas([[1,2,3], [3,6,8], [4,8,11]]), [[2,4,5], [1,2,3]]);
assert_equal(deltas([[1,2,3], [3,6,8], [4,8,11]],wrap=true), [[2,4,5], [1,2,3], [-3,-6,-8]]);
}
test_deltas();
module test_product() {
assert_equal(product([]),[]);
assert_equal(product([2,3,4]), 24);
assert_equal(product([[1,2,3], [3,4,5], [5,6,7]]), [15, 48, 105]);
m1 = [[2,3,4],[4,5,6],[6,7,8]];
m2 = [[4,1,2],[3,7,2],[8,7,4]];
m3 = [[3,7,8],[9,2,4],[5,8,3]];
assert_equal(product([m1,m2,m3]), m1*m2*m3);
}
test_product();
module test_mean() {
assert_equal(mean([2,3,4]), 3);
assert_equal(mean([[1,2,3], [3,4,5], [5,6,7]]), [3,4,5]);
}
test_mean();
module test_median() {
assert_equal(median([2,3,7]), 3);
assert_equal(median([2,4,5,8]), 4.5);
}
test_median();
module test_convolve() {
assert_equal(convolve([],[1,2,1]), []);
assert_equal(convolve([1,1],[]), []);
assert_equal(convolve([1,1],[1,2,1]), [1,3,3,1]);
assert_equal(convolve([1,2,3],[1,2,1]), [1,4,8,8,3]);
assert_equal(convolve([1,2,3],[[1],[2],[1]]), [[1], [4], [8], [8], [3]]);
assert_equal(convolve([[1],[2],[3]],[[1],[2],[1]]), [1,4,8,8,3]);
assert_equal(convolve([[1,0],[2,1],[3,2]],[[1,0],[2,1],[1,2]]), [1,4,9,12,7]);
assert_equal(convolve([1,2,3],[[1,0],[2,1],[1,2]]), [[1,0],[4,1],[8,4],[8,7],[3,6]]);
}
test_convolve();
// Logic
module test_any() {
assert_equal(any([0,false,undef]), false);
assert_equal(any([1,false,undef]), true);
assert_equal(any([1,5,true]), true);
assert_equal(any([[0,0], [0,0]]), true);
assert_equal(any([[0,0], [1,0]]), true);
assert_equal(any([[false,false],[[false,[false],[[[true]]]],false],[false,false]]), true);
assert_equal(any([[false,false],[[false,[false],[[[false]]]],false],[false,false]]), true);
assert_equal(any([]), false);
assert_equal(any([1,3,5,7,9], function (a) a%2==0),false);
assert_equal(any([1,3,6,7,9], function (a) a%2==0),true);
assert_equal(any([1,3,5,7,9], function (a) a%2!=0),true);
}
test_any();
module test_all() {
assert_equal(all([0,false,undef]), false);
assert_equal(all([1,false,undef]), false);
assert_equal(all([1,5,true]), true);
assert_equal(all([[0,0], [0,0]]), true);
assert_equal(all([[0,0], [1,0]]), true);
assert_equal(all([[1,1], [1,1]]), true);
assert_equal(all([[true,true],[[true,[true],[[[true]]]],true],[true,true]]), true);
assert_equal(all([[true,true],[[true,[true],[[[false]]]],true],[true,true]]), true);
assert_equal(all([]), true);
assert_equal(all([1,3,5,7,9], function (a) a%2==0),false);
assert_equal(all([1,3,6,8,9], function (a) a%2==0),false);
assert_equal(all([1,3,5,7,9], function (a) a%2!=0),true);
}
test_all();
module test_factorial() {
assert_equal(factorial(0), 1);
assert_equal(factorial(1), 1);
assert_equal(factorial(2), 2);
assert_equal(factorial(3), 6);
assert_equal(factorial(4), 24);
assert_equal(factorial(5), 120);
assert_equal(factorial(6), 720);
assert_equal(factorial(7), 5040);
assert_equal(factorial(8), 40320);
assert_equal(factorial(25,21), 303600);
assert_equal(factorial(25,25), 1);
}
test_factorial();
module test_binomial() {
assert_equal(binomial(1), [1,1]);
assert_equal(binomial(2), [1,2,1]);
assert_equal(binomial(3), [1,3,3,1]);
assert_equal(binomial(5), [1,5,10,10,5,1]);
}
test_binomial();
module test_binomial_coefficient() {
assert_equal(binomial_coefficient(2,1), 2);
assert_equal(binomial_coefficient(3,2), 3);
assert_equal(binomial_coefficient(4,2), 6);
assert_equal(binomial_coefficient(10,7), 120);
assert_equal(binomial_coefficient(10,7), binomial(10)[7]);
assert_equal(binomial_coefficient(15,4), binomial(15)[4]);
}
test_binomial_coefficient();
module test_gcd() {
assert_equal(gcd(15,25), 5);
assert_equal(gcd(15,27), 3);
assert_equal(gcd(270,405), 135);
assert_equal(gcd(39, 101),1);
assert_equal(gcd(15,-25), 5);
assert_equal(gcd(-15,25), 5);
assert_equal(gcd(5,0), 5);
assert_equal(gcd(0,5), 5);
}
test_gcd();
module test_lcm() {
assert_equal(lcm(15,25), 75);
assert_equal(lcm(15,27), 135);
assert_equal(lcm(270,405), 810);
assert_equal(lcm([3,5,15,25,35]),525);
}
test_lcm();
module test_rational_approx()
{
pq1 = rational_approx(PI,10); // Returns: [22,7]
pq2 = rational_approx(PI,10000); // Returns: [355, 113]
pq3 = rational_approx(221/323,500); // Returns: [13,19]
pq4 = rational_approx(0,50); // Returns: [0,1]
assert_equal(pq1,[22,7]);
assert_equal(pq2,[355,113]);
assert_equal(pq3,[13,19]);
assert_equal(pq4,[0,1]);
assert_equal(rational_approx(-PI,10),[-22,7]);
assert_equal(rational_approx(7,10), [7,1]);
}
test_rational_approx();
module test_complex(){
assert_equal( complex(ident(4)), c_ident(4));
assert_equal( complex(3), [3,0]);
assert_equal( complex([1,2]), [[1,0],[2,0]]);
assert_equal( complex([[1,2],[3,4]]), [[ [1,0],[2,0] ], [ [3,0],[4,0]]]);
}
test_complex();
module test_c_mul() {
assert_equal(c_mul([4,5],[9,-4]), [56,29]);
assert_equal(c_mul([-7,2],[24,3]), [-174, 27]);
assert_equal(c_mul([3,4], [[3,-7], [4,9], [4,8]]), [[37,-9],[-24,43], [-20,40]]);
assert_equal(c_mul([[3,-7], [4,9], [4,8]], [[1,1],[3,4],[-3,4]]), [-58,31]);
M = [
[ [3,4], [9,-1], [4,3] ],
[ [2,9], [4,9], [3,-1] ]
];
assert_equal(c_mul(M, [ [3,4], [4,4],[5,5]]), [[38,91], [-30, 97]]);
assert_equal(c_mul([[4,4],[9,1]], M), [[5,111],[67,117], [32,22]]);
assert_equal(c_mul(M,transpose(M)), [ [[80,30], [30, 117]], [[30,117], [-134, 102]]]);
assert_equal(c_mul(transpose(M),M), [ [[-84,60],[-42,87],[15,50]], [[-42,87],[15,54],[60,46]], [[15,50],[60,46],[15,18]]]);
}
test_c_mul();
module test_c_div() {
assert_equal(c_div([56,29],[9,-4]), [4,5]);
assert_equal(c_div([-174,27],[-7,2]), [24,3]);
}
test_c_div();
module test_c_conj(){
assert_equal(c_conj([3,4]), [3,-4]);
assert_equal(c_conj( [ [2,9], [4,9], [3,-1] ]), [ [2,-9], [4,-9], [3,1] ]);
M = [
[ [3,4], [9,-1], [4,3] ],
[ [2,9], [4,9], [3,-1] ]
];
Mc = [
[ [3,-4], [9,1], [4,-3] ],
[ [2,-9], [4,-9], [3,1] ]
];
assert_equal(c_conj(M), Mc);
}
test_c_conj();
module test_c_real(){
M = [
[ [3,4], [9,-1], [4,3] ],
[ [2,9], [4,9], [3,-1] ]
];
assert_equal(c_real(M), [[3,9,4],[2,4,3]]);
assert_equal(c_real( [ [3,4], [9,-1], [4,3] ]), [3,9,4]);
assert_equal(c_real([3,4]),3);
}
test_c_real();
module test_c_imag(){
M = [
[ [3,4], [9,-1], [4,3] ],
[ [2,9], [4,9], [3,-1] ]
];
assert_equal(c_imag(M), [[4,-1,3],[9,9,-1]]);
assert_equal(c_imag( [ [3,4], [9,-1], [4,3] ]), [4,-1,3]);
assert_equal(c_imag([3,4]),4);
}
test_c_imag();
module test_c_ident(){
assert_equal(c_ident(3), [[[1, 0], [0, 0], [0, 0]], [[0, 0], [1, 0], [0, 0]], [[0, 0], [0, 0], [1, 0]]]);
}
test_c_ident();
module test_c_norm(){
assert_equal(c_norm([3,4]), 5);
assert_approx(c_norm([[3,4],[5,6]]), 9.273618495495704);
}
test_c_norm();
module test_cumprod(){
assert_equal(cumprod([1,2,3,4]), [1,2,6,24]);
assert_equal(cumprod([4]), [4]);
assert_equal(cumprod([]),[]);
assert_equal(cumprod([[2,3],[4,5],[6,7]]), [[2,3],[8,15],[48,105]]);
assert_equal(cumprod([[5,6,7]]),[[5,6,7]]);
assert_equal(cumprod([up(5),down(5)]), [up(5),IDENT]);
assert_equal(cumprod([
[[1,2],[3,4]],
[[-4,5],[6,4]],
[[9,-3],[4,3]]
]),
[
[[1,2],[3,4]],
[[11,12],[18,28]],
[[45,24],[98,132]]
]);
assert_equal(cumprod([
[[1,2],[3,4]],
[[-4,5],[6,4]],
[[9,-3],[4,3]]
],right=true),
[
[[1,2],[3,4]],
[[8, 13],[12,31]],
[[124, 15],[232,57]]
]);
assert_equal(cumprod([[[1,2],[3,4]]]), [[[1,2],[3,4]]]);
}
test_cumprod();
module test_deriv(){
pent = [for(x=[0:70:359]) [cos(x), sin(x)]];
assert_approx(deriv(pent,closed=true),
[[-0.321393804843,0.556670399226],
[-0.883022221559,0.321393804843],
[-0.604022773555,-0.719846310393],
[0.469846310393,-0.813797681349],
[0.925416578398,0.163175911167],
[0.413175911167,0.492403876506]]);
assert_approx(deriv(pent,closed=true,h=2),
0.5*[[-0.321393804843,0.556670399226],
[-0.883022221559,0.321393804843],
[-0.604022773555,-0.719846310393],
[0.469846310393,-0.813797681349],
[0.925416578398,0.163175911167],
[0.413175911167,0.492403876506]]);
assert_approx(deriv(pent,closed=false),
[[-0.432937491789,1.55799143673],
[-0.883022221559,0.321393804843],
[-0.604022773555,-0.719846310393],
[0.469846310393,-0.813797681349],
[0.925416578398,0.163175911167],
[0.696902572292,1.45914323952]]);
spent = yscale(8,p=pent);
lens = path_segment_lengths(spent,closed=true);
assert_approx(deriv(spent, closed=true, h=lens),
[[-0.0381285841663,0.998065839726],
[-0.254979378104,0.0449763331253],
[-0.216850793938,-0.953089506601],
[0.123993253223,-0.982919228715],
[0.191478335034,0.0131898128456],
[0.0674850818111,0.996109041561]]);
assert_approx(deriv(spent, closed=false, h=select(lens,0,-2)),
[[-0.0871925973657,0.996191473044],
[-0.254979378104,0.0449763331253],
[-0.216850793938,-0.953089506601],
[0.123993253223,-0.982919228715],
[0.191478335034,0.0131898128456],
[0.124034734589,0.992277876714]]);
}
test_deriv();
module test_deriv2(){
oct = [for(x=[0:45:359]) [cos(x), sin(x)]];
assert_approx(deriv2(oct),
[[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
[0,0.585786437627],[-0.636634192232,0.534938683021]]);
assert_approx(deriv2(oct,closed=false),
[[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
[0,0.585786437627],[-0.636634192232,0.534938683021]]);
assert_approx(deriv2(oct,closed=true),
[[-0.585786437627,0],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
[0,0.585786437627],[-0.414213562373,0.414213562373]]);
assert_approx(deriv2(oct,closed=false,h=2),
0.25*[[-0.828427124746,0.0719095841794],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
[0,0.585786437627],[-0.636634192232,0.534938683021]]);
assert_approx(deriv2(oct,closed=true,h=2),
0.25* [[-0.585786437627,0],[-0.414213562373,-0.414213562373],[0,-0.585786437627],
[0.414213562373,-0.414213562373],[0.585786437627,0],[0.414213562373,0.414213562373],
[0,0.585786437627],[-0.414213562373,0.414213562373]]);
}
test_deriv2();
module test_deriv3(){
oct = [for(x=[0:45:359]) [cos(x), sin(x)]];
assert_approx(deriv3(oct),
[[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
[0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
[-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]);
assert_approx(deriv3(oct,closed=false),
[[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
[0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
[-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]);
assert_approx(deriv3(oct,closed=false,h=2),
[[0.414213562373,-0.686291501015],[0.414213562373,-0.343145750508],[0.414213562373,0],
[0.292893218813,0.292893218813],[0,0.414213562373],[-0.292893218813,0.292893218813],
[-0.535533905933,0.0502525316942],[-0.778174593052,-0.192388155425]]/8);
assert_approx(deriv3(oct,closed=true),
[[0,-0.414213562373],[0.292893218813,-0.292893218813],[0.414213562373,0],[0.292893218813,0.292893218813],
[0,0.414213562373],[-0.292893218813,0.292893218813],[-0.414213562373,0],[-0.292893218813,-0.292893218813]]);
assert_approx(deriv3(oct,closed=true,h=2),
[[0,-0.414213562373],[0.292893218813,-0.292893218813],[0.414213562373,0],[0.292893218813,0.292893218813],
[0,0.414213562373],[-0.292893218813,0.292893218813],[-0.414213562373,0],[-0.292893218813,-0.292893218813]]/8);
}
test_deriv3();
module test_polynomial(){
assert_equal(polynomial([0],12),0);
assert_equal(polynomial([0],[12,4]),[0,0]);
// assert_equal(polynomial([],12),0);
// assert_equal(polynomial([],[12,4]),[0,0]);
assert_equal(polynomial([1,2,3,4],3),58);
assert_equal(polynomial([1,2,3,4],[3,-1]),[47,-41]);
assert_equal(polynomial([0,0,2],4),2);
}
test_polynomial();
module test_poly_roots(){
// Fifth roots of unity
assert_approx(
poly_roots([1,0,0,0,0,-1]),
[[1,0],[0.309016994375,0.951056516295],[-0.809016994375,0.587785252292],
[-0.809016994375,-0.587785252292],[0.309016994375,-0.951056516295]]);
assert_approx(poly_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50]])),
[[1, 1], [5, 5], [1, 2], [-3, 1], [-3, -1], [1, -1], [1, -2], [5, -5]]);
assert_approx(poly_roots([.124,.231,.942, -.334]),
[[0.3242874219074053,0],[-1.093595323856930,2.666477428660098], [-1.093595323856930,-2.666477428660098]]);
}
test_poly_roots();
module test_real_roots(){
// Wilkinson polynomial is a nasty test:
assert_approx(
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]]))),
count(10,1));
assert_equal(real_roots([3]), []);
assert_equal(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50]])),[]);
assert_equal(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50],[1,0,0]])),[0,0]);
assert_approx(real_roots(poly_mult([[1,-2,5],[12,-24,24],[-2, -12, -20],[1,-10,50],[1,4]])),[-4]);
assert(approx(real_roots([1,-10,25]),[5,5],eps=5e-6));
assert_approx(real_roots([4,-3]), [0.75]);
assert_approx(real_roots([0,0,0,4,-3]), [0.75]);
}
test_real_roots();
module test_quadratic_roots(){
assert_approx(quadratic_roots([1,4,4]),[[-2,0],[-2,0]]);
assert_approx(quadratic_roots([1,4,4],real=true),[-2,-2]);
assert_approx(quadratic_roots([1,-5,6],real=true), [2,3]);
assert_approx(quadratic_roots([1,-5,6]), [[2,0],[3,0]]);
}
test_quadratic_roots();
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([[1,2],[3,4],[5,6]]), [15,68,100,48]);
assert_equal(poly_mult([3,2,1],[0]),[0]);
assert_equal(poly_mult([[1,2],[0],[5,6]]), [0]);
assert_equal(poly_mult([[3,4,5],[0,0,0]]), [0]);
assert_equal(poly_mult([[0],[0,0,0]]),[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],[0]]);
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]]);
assert_equal(poly_div([0], [1,-3]), [[0],[0]]);
}
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]),[0]);
// assert_equal(poly_add([1,2,3],-[1,2,3]),[]);
}
test_poly_add();
module test_root_find(){
flist = [
function(x) x*x*x-2*x-5,
function(x) 1-1/x/x,
function(x) pow(x-3,3),
function(x) pow(x-2,5),
function(x) (let(xi=0.61489) -3062*(1-xi)*exp(-x)/(xi+(1-xi)*exp(-x)) -1013 + 1628/x),
function(x) exp(x)-2-.01/x/x + .000002/x/x/x,
];
fint=[
[0,4],
[1e-4, 4],
[0,6],
[0,4],
[1e-4,5],
[-1,4]
];
answers = [2.094551481542328,
1,
3,
2,
1.037536033287040,
0.7032048403631350
];
roots = [for(i=idx(flist)) root_find(flist[i], fint[i][0], fint[i][1])];
assert_approx(roots, answers, 1e-10);
}
test_root_find();
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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