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Added norm_fro, quadratic_roots and pivoting to qr_factor and

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linear_solve.  Added tests.
This commit is contained in:
Adrian Mariano
2020-09-01 17:57:31 -04:00
parent 8f6c2e8538
commit 3caeeff2cd
3 changed files with 108 additions and 24 deletions
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34
tests/test_math.scad
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@@ -781,6 +781,12 @@ 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],
@@ -954,6 +960,15 @@ module test_real_roots(){
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_qr_factor() {
// Check that R is upper triangular
function is_ut(R) =
@@ -962,7 +977,15 @@ module test_qr_factor() {
// 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);
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]));
// Test the R is upper trianglar, Q is orthogonal, R diagonal non-increasing and qrp=M
function qrokpiv(qr,M) =
is_ut(qr[1])
&& approx(qr[0]*transpose(qr[0]), ident(len(qr[0])))
&& approx(qr[0]*qr[1]*transpose(qr[2]),M)
&& list_decreasing([for(i=[0:1:min(len(qr[1]),len(qr[1][0]))-1]) abs(qr[1][i][i])]);
M = [[1,2,9,4,5],
[6,7,8,19,10],
@@ -991,6 +1014,15 @@ module test_qr_factor() {
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]]));
assert(qrokpiv(qr_factor(M,pivot=true),M));
assert(qrokpiv(qr_factor(select(M,0,3),pivot=true),select(M,0,3)));
assert(qrokpiv(qr_factor(transpose(select(M,0,3)),pivot=true),transpose(select(M,0,3))));
assert(qrokpiv(qr_factor(B,pivot=true),B));
assert(qrokpiv(qr_factor([[7]],pivot=true), [[7]]));
assert(qrokpiv(qr_factor([[1,2,3]],pivot=true), [[1,2,3]]));
assert(qrokpiv(qr_factor([[1],[2],[3]],pivot=true), [[1],[2],[3]]));
}
test_qr_factor();