mirror of
https://github.com/BelfrySCAD/BOSL2.git
synced 2024-12-29 16:29:40 +00:00
a5ae4879be
add cholesky fatorization (needed for above, also useful for solving symmetric linear systems.)
1319 lines
42 KiB
OpenSCAD
1319 lines
42 KiB
OpenSCAD
include <../std.scad>
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// Simple Calculations
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module test_quant() {
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assert_equal(quant(-4,3), -3);
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assert_equal(quant(-3,3), -3);
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assert_equal(quant(-2,3), -3);
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assert_equal(quant(-1,3), 0);
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assert_equal(quant(0,3), 0);
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assert_equal(quant(1,3), 0);
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assert_equal(quant(2,3), 3);
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assert_equal(quant(3,3), 3);
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assert_equal(quant(4,3), 3);
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assert_equal(quant(7,3), 6);
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assert_equal(quant(12,2.5), 12.5);
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assert_equal(quant(11,2.5), 10.0);
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assert_equal(quant([12,13,13.1,14,14.1,15,16],4), [12,12,12,16,16,16,16]);
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assert_equal(quant([9,10,10.4,10.5,11,12],3), [9,9,9,12,12,12]);
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assert_equal(quant([[9,10,10.4],[10.5,11,12]],3), [[9,9,9],[12,12,12]]);
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}
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test_quant();
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module test_quantdn() {
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assert_equal(quantdn(-4,3), -6);
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assert_equal(quantdn(-3,3), -3);
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assert_equal(quantdn(-2,3), -3);
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assert_equal(quantdn(-1,3), -3);
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assert_equal(quantdn(0,3), 0);
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assert_equal(quantdn(1,3), 0);
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assert_equal(quantdn(2,3), 0);
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assert_equal(quantdn(3,3), 3);
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assert_equal(quantdn(4,3), 3);
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assert_equal(quantdn(7,3), 6);
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assert_equal(quantdn(12,2.5), 10.0);
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assert_equal(quantdn(11,2.5), 10.0);
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assert_equal(quantdn([12,13,13.1,14,14.1,15,16],4), [12,12,12,12,12,12,16]);
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assert_equal(quantdn([9,10,10.4,10.5,11,12],3), [9,9,9,9,9,12]);
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assert_equal(quantdn([[9,10,10.4],[10.5,11,12]],3), [[9,9,9],[9,9,12]]);
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}
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test_quantdn();
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module test_quantup() {
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assert_equal(quantup(-4,3), -3);
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assert_equal(quantup(-3,3), -3);
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assert_equal(quantup(-2,3), 0);
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assert_equal(quantup(-1,3), 0);
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assert_equal(quantup(0,3), 0);
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assert_equal(quantup(1,3), 3);
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assert_equal(quantup(2,3), 3);
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assert_equal(quantup(3,3), 3);
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assert_equal(quantup(4,3), 6);
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assert_equal(quantup(7,3), 9);
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assert_equal(quantup(12,2.5), 12.5);
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assert_equal(quantup(11,2.5), 12.5);
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assert_equal(quantup([12,13,13.1,14,14.1,15,16],4), [12,16,16,16,16,16,16]);
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assert_equal(quantup([9,10,10.4,10.5,11,12],3), [9,12,12,12,12,12]);
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assert_equal(quantup([[9,10,10.4],[10.5,11,12]],3), [[9,12,12],[12,12,12]]);
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}
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test_quantup();
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module test_constrain() {
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assert_equal(constrain(-2,-1,1), -1);
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assert_equal(constrain(-1.75,-1,1), -1);
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assert_equal(constrain(-1,-1,1), -1);
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assert_equal(constrain(-0.75,-1,1), -0.75);
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assert_equal(constrain(0,-1,1), 0);
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assert_equal(constrain(0.75,-1,1), 0.75);
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assert_equal(constrain(1,-1,1), 1);
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assert_equal(constrain(1.75,-1,1), 1);
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assert_equal(constrain(2,-1,1), 1);
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}
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test_constrain();
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module test_is_matrix() {
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assert(is_matrix([[2,3,4],[5,6,7],[8,9,10]]));
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assert(is_matrix([[2,3],[5,6],[8,9]],3,2));
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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],[5,6],[8,9]],m=2,n=3));
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assert(!is_matrix([[2,3,4],[5,6,7]],m=3,n=2));
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assert(!is_matrix([ [2,[3,4]],
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[4,[5,6]]]));
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assert(!is_matrix([[3,4],[undef,3]]));
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assert(!is_matrix([[3,4],[3,"foo"]]));
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assert(!is_matrix([[3,4],[3,3,2]]));
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assert(!is_matrix([ [3,4],6]));
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assert(!is_matrix(undef));
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assert(!is_matrix(NAN));
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assert(!is_matrix(INF));
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assert(!is_matrix(-5));
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assert(!is_matrix(0));
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assert(!is_matrix(5));
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assert(!is_matrix(""));
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assert(!is_matrix("foo"));
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assert(!is_matrix([3,4,5]));
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assert(!is_matrix([]));
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}
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test_is_matrix();
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module test_all_zero() {
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assert(all_zero(0));
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assert(all_zero([0,0,0]));
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assert(all_zero([[0,0,0],[0,0]]));
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assert(all_zero([EPSILON/2,EPSILON/2,EPSILON/2]));
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assert(!all_zero(1e-3));
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assert(!all_zero([0,0,1e-3]));
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assert(!all_zero([EPSILON*10,0,0]));
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assert(!all_zero([0,EPSILON*10,0]));
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assert(!all_zero([0,0,EPSILON*10]));
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assert(!all_zero(true));
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assert(!all_zero(false));
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assert(!all_zero(INF));
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assert(!all_zero(-INF));
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assert(!all_zero(NAN));
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assert(!all_zero("foo"));
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assert(!all_zero([]));
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assert(!all_zero([0:1:2]));
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}
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test_all_zero();
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module test_all_nonzero() {
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assert(!all_nonzero(0));
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assert(!all_nonzero([0,0,0]));
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assert(!all_nonzero([[0,0,0],[0,0]]));
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assert(!all_nonzero([EPSILON/2,EPSILON/2,EPSILON/2]));
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assert(all_nonzero(1e-3));
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assert(!all_nonzero([0,0,1e-3]));
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assert(!all_nonzero([EPSILON*10,0,0]));
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assert(!all_nonzero([0,EPSILON*10,0]));
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assert(!all_nonzero([0,0,EPSILON*10]));
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assert(all_nonzero([1e-3,1e-3,1e-3]));
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assert(all_nonzero([EPSILON*10,EPSILON*10,EPSILON*10]));
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assert(!all_nonzero(true));
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assert(!all_nonzero(false));
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assert(!all_nonzero(INF));
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assert(!all_nonzero(-INF));
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assert(!all_nonzero(NAN));
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assert(!all_nonzero("foo"));
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assert(!all_nonzero([]));
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assert(!all_nonzero([0:1:2]));
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}
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test_all_nonzero();
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module test_all_positive() {
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assert(!all_positive(-2));
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assert(!all_positive(0));
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assert(all_positive(2));
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assert(!all_positive([0,0,0]));
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assert(!all_positive([0,1,2]));
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assert(all_positive([3,1,2]));
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assert(!all_positive([3,-1,2]));
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assert(!all_positive([]));
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assert(!all_positive(true));
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assert(!all_positive(false));
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assert(!all_positive("foo"));
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assert(!all_positive([0:1:2]));
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}
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test_all_positive();
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module test_all_negative() {
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assert(all_negative(-2));
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assert(!all_negative(0));
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assert(!all_negative(2));
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assert(!all_negative([0,0,0]));
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assert(!all_negative([0,1,2]));
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assert(!all_negative([3,1,2]));
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assert(!all_negative([3,-1,2]));
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assert(all_negative([-3,-1,-2]));
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assert(!all_negative([-3,1,-2]));
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assert(all_negative([[-5,-7],[-3,-1,-2]]));
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assert(!all_negative([[-5,-7],[-3,1,-2]]));
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assert(!all_negative([]));
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assert(!all_negative(true));
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assert(!all_negative(false));
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assert(!all_negative("foo"));
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assert(!all_negative([0:1:2]));
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}
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test_all_negative();
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module test_all_nonpositive() {
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assert(all_nonpositive(-2));
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assert(all_nonpositive(0));
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assert(!all_nonpositive(2));
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assert(all_nonpositive([0,0,0]));
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assert(!all_nonpositive([0,1,2]));
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assert(all_nonpositive([0,-1,-2]));
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assert(!all_nonpositive([3,1,2]));
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assert(!all_nonpositive([3,-1,2]));
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assert(!all_nonpositive([]));
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assert(!all_nonpositive(true));
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assert(!all_nonpositive(false));
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assert(!all_nonpositive("foo"));
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assert(!all_nonpositive([0:1:2]));
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}
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test_all_nonpositive();
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module test_all_nonnegative() {
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assert(!all_nonnegative(-2));
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assert(all_nonnegative(0));
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assert(all_nonnegative(2));
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assert(all_nonnegative([0,0,0]));
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assert(all_nonnegative([0,1,2]));
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assert(all_nonnegative([3,1,2]));
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assert(!all_nonnegative([3,-1,2]));
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assert(!all_nonnegative([-3,-1,-2]));
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assert(!all_nonnegative([[-5,-7],[-3,-1,-2]]));
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assert(!all_nonnegative([[-5,-7],[-3,1,-2]]));
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assert(!all_nonnegative([[5,7],[3,-1,2]]));
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assert(all_nonnegative([[5,7],[3,1,2]]));
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assert(!all_nonnegative([]));
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assert(!all_nonnegative(true));
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assert(!all_nonnegative(false));
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assert(!all_nonnegative("foo"));
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assert(!all_nonnegative([0:1:2]));
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}
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test_all_nonnegative();
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module test_all_integer() {
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assert(!all_integer(undef));
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assert(!all_integer(true));
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assert(!all_integer(false));
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assert(!all_integer(4.3));
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assert(!all_integer("foo"));
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assert(!all_integer([]));
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assert(!all_integer([3,4.1,5,7]));
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assert(!all_integer([[1,2,3],[4,5,6],[7,8]]));
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assert(all_integer(-4));
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assert(all_integer(0));
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assert(all_integer(5));
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assert(all_integer([-3]));
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assert(all_integer([0]));
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assert(all_integer([3]));
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assert(all_integer([2,-4,0,5,7,9876543210]));
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}
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test_all_integer();
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module test_approx() {
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assert_equal(approx(PI, 3.141592653589793236), true);
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assert_equal(approx(PI, 3.1415926), false);
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assert_equal(approx(PI, 3.1415926, eps=1e-6), true);
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assert_equal(approx(-PI, -3.141592653589793236), true);
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assert_equal(approx(-PI, -3.1415926), false);
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assert_equal(approx(-PI, -3.1415926, eps=1e-6), true);
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assert_equal(approx(1/3, 0.3333333333), true);
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assert_equal(approx(-1/3, -0.3333333333), true);
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assert_equal(approx(10*[cos(30),sin(30)], 10*[sqrt(3)/2, 1/2]), true);
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assert_equal(approx([1,[1,undef]], [1+1e-12,[1,true]]), false);
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assert_equal(approx([1,[1,undef]], [1+1e-12,[1,undef]]), true);
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}
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test_approx();
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module test_min_index() {
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vals = rands(-100,100,100,seed=75);
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minval = min(vals);
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minidx = min_index(vals);
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assert_equal(vals[minidx], minval);
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assert_equal(min_index([3,4,5,6]), 0);
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assert_equal(min_index([4,3,5,6]), 1);
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assert_equal(min_index([4,5,3,6]), 2);
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assert_equal(min_index([4,5,6,3]), 3);
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assert_equal(min_index([6,5,4,3]), 3);
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assert_equal(min_index([6,3,4,5]), 1);
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assert_equal(min_index([-56,72,-874,5]), 2);
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}
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test_min_index();
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module test_max_index() {
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vals = rands(-100,100,100,seed=97);
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maxval = max(vals);
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maxidx = max_index(vals);
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assert_equal(vals[maxidx], maxval);
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assert_equal(max_index([3,4,5,6]), 3);
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assert_equal(max_index([3,4,6,5]), 2);
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assert_equal(max_index([3,6,4,5]), 1);
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assert_equal(max_index([6,3,4,5]), 0);
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assert_equal(max_index([5,6,4,3]), 1);
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assert_equal(max_index([-56,72,-874,5]), 1);
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}
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test_max_index();
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module test_posmod() {
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assert_equal(posmod(-5,3), 1);
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assert_equal(posmod(-4,3), 2);
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assert_equal(posmod(-3,3), 0);
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assert_equal(posmod(-2,3), 1);
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assert_equal(posmod(-1,3), 2);
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assert_equal(posmod(0,3), 0);
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assert_equal(posmod(1,3), 1);
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assert_equal(posmod(2,3), 2);
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assert_equal(posmod(3,3), 0);
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}
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test_posmod();
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module test_modang() {
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assert_equal(modang(-700), 20);
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assert_equal(modang(-270), 90);
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assert_equal(modang(-120), -120);
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assert_equal(modang(120), 120);
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assert_equal(modang(270), -90);
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assert_equal(modang(700), -20);
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}
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test_modang();
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module test_sqr() {
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assert_equal(sqr(-3), 9);
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assert_equal(sqr(0), 0);
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assert_equal(sqr(1), 1);
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assert_equal(sqr(2), 4);
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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]), 29);
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assert_equal(sqr([[2,3,4],[3,5,7],[3,5,1]]), [[25,41,33],[42,69,54],[24,39,48]]);
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}
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test_sqr();
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module test_log2() {
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assert_equal(log2(0.125), -3);
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assert_equal(log2(16), 4);
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assert_equal(log2(256), 8);
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}
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test_log2();
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module test_rand_int() {
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nums = rand_int(-100,100,1000,seed=2134);
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assert_equal(len(nums), 1000);
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for (num = nums) {
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assert(num>=-100);
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assert(num<=100);
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assert_equal(num, floor(num));
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}
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}
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test_rand_int();
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module test_gaussian_rands() {
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nums1 = gaussian_rands(1000,0,10,seed=2132);
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nums2 = gaussian_rands(1000,0,10,seed=2130);
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nums3 = gaussian_rands(1000,0,10,seed=2132);
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assert_equal(len(nums1), 1000);
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assert_equal(len(nums2), 1000);
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assert_equal(len(nums3), 1000);
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assert_equal(nums1, nums3);
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assert(nums1!=nums2);
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}
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test_gaussian_rands();
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module test_segs() {
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assert_equal(segs(50,$fn=8), 8);
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assert_equal(segs(50,$fa=2,$fs=2), 158);
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}
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test_segs();
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module test_lerp() {
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assert_equal(lerp(-20,20,0), -20);
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assert_equal(lerp(-20,20,0.25), -10);
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assert_equal(lerp(-20,20,0.5), 0);
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assert_equal(lerp(-20,20,0.75), 10);
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assert_equal(lerp(-20,20,1), 20);
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assert_equal(lerp(-20,20,[0,0.25,0.5,0.75,1]), [-20,-10,0,10,20]);
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assert_equal(lerp(-20,20,[0:0.25:1]), [-20,-10,0,10,20]);
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assert_equal(lerp([10,10],[30,-10],0.5), [20,0]);
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}
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test_lerp();
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module test_u_add() {
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assert_equal(u_add(1,2),3);
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assert_equal(u_add(1,-2),-1);
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assert_equal(u_add(-1,2),1);
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assert_equal(u_add(-1,-2),-3);
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assert_equal(u_add(243,-27),216);
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assert_equal(u_add([2,3,4],[8,7,9]),[10,10,13]);
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assert_equal(u_add(undef,27),undef);
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assert_equal(u_add(undef,-27),undef);
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assert_equal(u_add(243,undef),undef);
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assert_equal(u_add(-43,undef),undef);
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assert_equal(u_add(undef,[8,7,9]),undef);
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assert_equal(u_add([2,3,4],undef),undef);
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}
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test_u_add();
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module test_u_sub() {
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assert_equal(u_sub(1,2),-1);
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assert_equal(u_sub(1,-2),3);
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assert_equal(u_sub(-1,2),-3);
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assert_equal(u_sub(-1,-2),1);
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assert_equal(u_sub(243,-27),270);
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assert_equal(u_sub([2,3,4],[8,7,9]),[-6,-4,-5]);
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assert_equal(u_sub(undef,27),undef);
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assert_equal(u_sub(undef,-27),undef);
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assert_equal(u_sub(243,undef),undef);
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assert_equal(u_sub(-43,undef),undef);
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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([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]), 4.5);
|
|
assert_equal(median([[1,2,3], [3,4,5], [8,9,10]]), [4.5,5.5,6.5]);
|
|
}
|
|
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();
|
|
|
|
|
|
|
|
module test_matrix_inverse() {
|
|
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]]);
|
|
}
|
|
test_matrix_inverse();
|
|
|
|
|
|
module test_det2() {
|
|
assert_equal(det2([[6,-2], [1,8]]), 50);
|
|
assert_equal(det2([[4,7], [3,2]]), -13);
|
|
assert_equal(det2([[4,3], [3,4]]), 7);
|
|
}
|
|
test_det2();
|
|
|
|
|
|
module test_det3() {
|
|
M = [ [6,4,-2], [1,-2,8], [1,5,7] ];
|
|
assert_equal(det3(M), -334);
|
|
}
|
|
test_det3();
|
|
|
|
|
|
module test_determinant() {
|
|
M = [ [6,4,-2,9], [1,-2,8,3], [1,5,7,6], [4,2,5,1] ];
|
|
assert_equal(determinant(M), 2267);
|
|
}
|
|
test_determinant();
|
|
|
|
|
|
module test_matrix_trace() {
|
|
M = [ [6,4,-2,9], [1,-2,8,3], [1,5,7,6], [4,2,5,1] ];
|
|
assert_equal(matrix_trace(M), 6-2+7+1);
|
|
}
|
|
test_matrix_trace();
|
|
|
|
|
|
// Logic
|
|
|
|
|
|
module test_compare_vals() {
|
|
assert(compare_vals(-10,0) < 0);
|
|
assert(compare_vals(10,0) > 0);
|
|
assert(compare_vals(10,10) == 0);
|
|
|
|
assert(compare_vals("abc","abcd") < 0);
|
|
assert(compare_vals("abcd","abc") > 0);
|
|
assert(compare_vals("abcd","abcd") == 0);
|
|
|
|
assert(compare_vals(false,false) == 0);
|
|
assert(compare_vals(true,false) > 0);
|
|
assert(compare_vals(false,true) < 0);
|
|
assert(compare_vals(true,true) == 0);
|
|
|
|
assert(compare_vals([2,3,4], [2,3,4,5]) < 0);
|
|
assert(compare_vals([2,3,4,5], [2,3,4,5]) == 0);
|
|
assert(compare_vals([2,3,4,5], [2,3,4]) > 0);
|
|
assert(compare_vals([2,3,4,5], [2,3,5,5]) < 0);
|
|
assert(compare_vals([[2,3,4,5]], [[2,3,5,5]]) < 0);
|
|
|
|
assert(compare_vals([[2,3,4],[3,4,5]], [[2,3,4], [3,4,5]]) == 0);
|
|
assert(compare_vals([[2,3,4],[3,4,5]], [[2,3,4,5], [3,4,5]]) < 0);
|
|
assert(compare_vals([[2,3,4],[3,4,5]], [[2,3,4], [3,4,5,6]]) < 0);
|
|
assert(compare_vals([[2,3,4,5],[3,4,5]], [[2,3,4], [3,4,5]]) > 0);
|
|
assert(compare_vals([[2,3,4],[3,4,5,6]], [[2,3,4], [3,4,5]]) > 0);
|
|
assert(compare_vals([[2,3,4],[3,5,5]], [[2,3,4], [3,4,5]]) > 0);
|
|
assert(compare_vals([[2,3,4],[3,4,5]], [[2,3,4], [3,5,5]]) < 0);
|
|
|
|
assert(compare_vals(undef, undef) == 0);
|
|
assert(compare_vals(undef, true) < 0);
|
|
assert(compare_vals(undef, 0) < 0);
|
|
assert(compare_vals(undef, "foo") < 0);
|
|
assert(compare_vals(undef, [2,3,4]) < 0);
|
|
assert(compare_vals(undef, [0:3]) < 0);
|
|
|
|
assert(compare_vals(true, undef) > 0);
|
|
assert(compare_vals(true, true) == 0);
|
|
assert(compare_vals(true, 0) < 0);
|
|
assert(compare_vals(true, "foo") < 0);
|
|
assert(compare_vals(true, [2,3,4]) < 0);
|
|
assert(compare_vals(true, [0:3]) < 0);
|
|
|
|
assert(compare_vals(0, undef) > 0);
|
|
assert(compare_vals(0, true) > 0);
|
|
assert(compare_vals(0, 0) == 0);
|
|
assert(compare_vals(0, "foo") < 0);
|
|
assert(compare_vals(0, [2,3,4]) < 0);
|
|
assert(compare_vals(0, [0:3]) < 0);
|
|
|
|
assert(compare_vals(1, undef) > 0);
|
|
assert(compare_vals(1, true) > 0);
|
|
assert(compare_vals(1, 1) == 0);
|
|
assert(compare_vals(1, "foo") < 0);
|
|
assert(compare_vals(1, [2,3,4]) < 0);
|
|
assert(compare_vals(1, [0:3]) < 0);
|
|
|
|
assert(compare_vals("foo", undef) > 0);
|
|
assert(compare_vals("foo", true) > 0);
|
|
assert(compare_vals("foo", 1) > 0);
|
|
assert(compare_vals("foo", "foo") == 0);
|
|
assert(compare_vals("foo", [2,3,4]) < 0);
|
|
assert(compare_vals("foo", [0:3]) < 0);
|
|
|
|
assert(compare_vals([2,3,4], undef) > 0);
|
|
assert(compare_vals([2,3,4], true) > 0);
|
|
assert(compare_vals([2,3,4], 1) > 0);
|
|
assert(compare_vals([2,3,4], "foo") > 0);
|
|
assert(compare_vals([2,3,4], [2,3,4]) == 0);
|
|
assert(compare_vals([2,3,4], [0:3]) < 0);
|
|
|
|
assert(compare_vals([0:3], undef) > 0);
|
|
assert(compare_vals([0:3], true) > 0);
|
|
assert(compare_vals([0:3], 1) > 0);
|
|
assert(compare_vals([0:3], "foo") > 0);
|
|
assert(compare_vals([0:3], [2,3,4]) > 0);
|
|
assert(compare_vals([0:3], [0:3]) == 0);
|
|
}
|
|
test_compare_vals();
|
|
|
|
|
|
module test_compare_lists() {
|
|
assert(compare_lists([2,3,4], [2,3,4,5]) < 0);
|
|
assert(compare_lists([2,3,4,5], [2,3,4,5]) == 0);
|
|
assert(compare_lists([2,3,4,5], [2,3,4]) > 0);
|
|
assert(compare_lists([2,3,4,5], [2,3,5,5]) < 0);
|
|
|
|
assert(compare_lists([[2,3,4],[3,4,5]], [[2,3,4], [3,4,5]]) == 0);
|
|
assert(compare_lists([[2,3,4],[3,4,5]], [[2,3,4,5], [3,4,5]]) < 0);
|
|
assert(compare_lists([[2,3,4],[3,4,5]], [[2,3,4], [3,4,5,6]]) < 0);
|
|
assert(compare_lists([[2,3,4,5],[3,4,5]], [[2,3,4], [3,4,5]]) > 0);
|
|
assert(compare_lists([[2,3,4],[3,4,5,6]], [[2,3,4], [3,4,5]]) > 0);
|
|
assert(compare_lists([[2,3,4],[3,5,5]], [[2,3,4], [3,4,5]]) > 0);
|
|
assert(compare_lists([[2,3,4],[3,4,5]], [[2,3,4], [3,5,5]]) < 0);
|
|
|
|
assert(compare_lists("cat", "bat") > 0);
|
|
assert(compare_lists(["cat"], ["bat"]) > 0);
|
|
}
|
|
test_compare_lists();
|
|
|
|
|
|
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_count_true() {
|
|
assert_equal(count_true([0,false,undef]), 0);
|
|
assert_equal(count_true([1,false,undef]), 1);
|
|
assert_equal(count_true([1,5,false]), 2);
|
|
assert_equal(count_true([1,5,true]), 3);
|
|
assert_equal(count_true([[0,0], [0,0]]), 2);
|
|
assert_equal(count_true([[0,0], [1,0]]), 2);
|
|
assert_equal(count_true([[1,1], [1,1]]), 2);
|
|
assert_equal(count_true([1,1,1,1,1], nmax=3), 3);
|
|
assert_equal(count_true([1,3,5,7,9], function (a) a%2==0),0);
|
|
assert_equal(count_true([1,3,6,8,9], function (a) a%2==0),2);
|
|
assert_equal(count_true([1,3,5,7,9], function (a) a%2!=0),5);
|
|
}
|
|
test_count_true();
|
|
|
|
|
|
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_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_back_substitute(){
|
|
R = [[12,4,3,2],
|
|
[0,2,-4,2],
|
|
[0,0,4,5],
|
|
[0,0,0,15]];
|
|
assert_approx(back_substitute(R, [1,2,3,3]), [-0.675, 1.8, 0.5, 0.2]);
|
|
assert_approx(back_substitute(R, [6, 3, 3.5, 37], transpose=true), [0.5, 0.5, 1, 2]);
|
|
assert_approx(back_substitute(R, [[38,101],[-6,-16], [31, 71], [45, 105]]), [[1, 4],[2,3],[4,9],[3,7]]);
|
|
assert_approx(back_substitute(R, [[12,48],[8,22],[11,36],[71,164]],transpose=true), [[1, 4],[2,3],[4,9],[3,7]]);
|
|
assert_approx(back_substitute([[2]], [4]), [2]);
|
|
sing1 =[[0,4,3,2],
|
|
[0,3,-4,2],
|
|
[0,0,4,5],
|
|
[0,0,0,15]];
|
|
sing2 =[[12,4,3,2],
|
|
[0,0,-4,2],
|
|
[0,0,4,5],
|
|
[0,0,0,15]];
|
|
sing3 = [[12,4,3,2],
|
|
[0,2,-4,2],
|
|
[0,0,4,5],
|
|
[0,0,0,0]];
|
|
assert_approx(back_substitute(sing1, [1,2,3,4]), []);
|
|
assert_approx(back_substitute(sing2, [1,2,3,4]), []);
|
|
assert_approx(back_substitute(sing3, [1,2,3,4]), []);
|
|
}
|
|
test_back_substitute();
|
|
|
|
|
|
|
|
module test_norm_fro(){
|
|
assert_approx(norm_fro([[2,3,4],[4,5,6]]), 10.29563014098700);
|
|
|
|
} test_norm_fro();
|
|
|
|
|
|
module test_linear_solve(){
|
|
M = [[-2,-5,-1,3],
|
|
[3,7,6,2],
|
|
[6,5,-1,-6],
|
|
[-7,1,2,3]];
|
|
assert_approx(linear_solve(M, [-3,43,-11,13]), [1,2,3,4]);
|
|
assert_approx(linear_solve(M, [[-5,8],[18,-61],[4,7],[-1,-12]]), [[1,-2],[1,-3],[1,-4],[1,-5]]);
|
|
assert_approx(linear_solve([[2]],[4]), [2]);
|
|
assert_approx(linear_solve([[2]],[[4,8]]), [[2, 4]]);
|
|
assert_approx(linear_solve(select(M,0,2), [2,4,4]), [ 2.254871220604705e+00,
|
|
-8.378819388897780e-01,
|
|
2.330507118860985e-01,
|
|
8.511278195488737e-01]);
|
|
assert_approx(linear_solve(subindex(M,[0:2]), [2,4,4,4]),
|
|
[-2.457142857142859e-01,
|
|
5.200000000000000e-01,
|
|
7.428571428571396e-02]);
|
|
assert_approx(linear_solve([[1,2,3,4]], [2]), [0.066666666666666, 0.13333333333, 0.2, 0.266666666666]);
|
|
assert_approx(linear_solve([[1],[2],[3],[4]], [4,3,2,1]), [2/3]);
|
|
rd = [[-2,-5,-1,3],
|
|
[3,7,6,2],
|
|
[3,7,6,2],
|
|
[-7,1,2,3]];
|
|
assert_equal(linear_solve(rd,[1,2,3,4]),[]);
|
|
assert_equal(linear_solve(select(rd,0,2), [2,4,4]), []);
|
|
assert_equal(linear_solve(transpose(select(rd,0,2)), [2,4,3,4]), []);
|
|
}
|
|
test_linear_solve();
|
|
|
|
|
|
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([
|
|
[[1,2],[3,4]],
|
|
[[-4,5],[6,4]],
|
|
[[9,-3],[4,3]]
|
|
]),
|
|
[
|
|
[[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_outer_product(){
|
|
assert_equal(outer_product([1,2,3],[4,5,6]), [[4,5,6],[8,10,12],[12,15,18]]);
|
|
assert_equal(outer_product([1,2],[4,5,6]), [[4,5,6],[8,10,12]]);
|
|
assert_equal(outer_product([9],[7]), [[63]]);
|
|
}
|
|
test_outer_product();
|
|
|
|
|
|
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();
|
|
|
|
|
|
|
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module test_quadratic_roots(){
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assert_approx(quadratic_roots([1,4,4]),[[-2,0],[-2,0]]);
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assert_approx(quadratic_roots([1,4,4],real=true),[-2,-2]);
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assert_approx(quadratic_roots([1,-5,6],real=true), [2,3]);
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assert_approx(quadratic_roots([1,-5,6]), [[2,0],[3,0]]);
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}
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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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&& list_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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|
|
|
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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]]));
|
|
}
|
|
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([[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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