X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_matrices.cpp;h=cb8e64bf4f6fe1370613e95794723d8a20ed786b;hp=88bc5816b602d1d78dcfda5a045d1f1aca0811e3;hb=1256fb73b64a1cdfb0838df06facbc1e8b2d5f83;hpb=619d77d2676f7f1a562fb9fefc0ba6754fe2d750 diff --git a/check/exam_matrices.cpp b/check/exam_matrices.cpp index 88bc5816..cb8e64bf 100644 --- a/check/exam_matrices.cpp +++ b/check/exam_matrices.cpp @@ -1,9 +1,10 @@ + /** @file exam_matrices.cpp * * Here we examine manipulations on GiNaC's symbolic matrices. */ /* - * GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2020 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -20,8 +21,12 @@ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ +#include "ginac.h" +using namespace GiNaC; + +#include #include -#include "exams.h" +using namespace std; static unsigned matrix_determinants() { @@ -33,7 +38,7 @@ static unsigned matrix_determinants() symbol g("g"), h("h"), i("i"); // check symbolic trivial matrix determinant - m1.set(0,0,a); + m1 = matrix{{a}}; det = m1.determinant(); if (det != a) { clog << "determinant of 1x1 matrix " << m1 @@ -42,8 +47,8 @@ static unsigned matrix_determinants() } // check generic dense symbolic 2x2 matrix determinant - m2.set(0,0,a).set(0,1,b); - m2.set(1,0,c).set(1,1,d); + m2 = matrix{{a, b}, + {c, d}}; det = m2.determinant(); if (det != (a*d-b*c)) { clog << "determinant of 2x2 matrix " << m2 @@ -52,9 +57,9 @@ static unsigned matrix_determinants() } // check generic dense symbolic 3x3 matrix determinant - m3.set(0,0,a).set(0,1,b).set(0,2,c); - m3.set(1,0,d).set(1,1,e).set(1,2,f); - m3.set(2,0,g).set(2,1,h).set(2,2,i); + m3 = matrix{{a, b, c}, + {d, e, f}, + {g, h, i}}; det = m3.determinant(); if (det != (a*e*i - a*f*h - d*b*i + d*c*h + g*b*f - g*c*e)) { clog << "determinant of 3x3 matrix " << m3 @@ -63,9 +68,9 @@ static unsigned matrix_determinants() } // check dense numeric 3x3 matrix determinant - m3.set(0,0,numeric(0)).set(0,1,numeric(-1)).set(0,2,numeric(3)); - m3.set(1,0,numeric(3)).set(1,1,numeric(-2)).set(1,2,numeric(2)); - m3.set(2,0,numeric(3)).set(2,1,numeric(4)).set(2,2,numeric(-2)); + m3 = matrix{{0, -1, 3}, + {3, -2, 2}, + {3, 4, -2}}; det = m3.determinant(); if (det != 42) { clog << "determinant of 3x3 matrix " << m3 @@ -74,8 +79,8 @@ static unsigned matrix_determinants() } // check dense symbolic 2x2 matrix determinant - m2.set(0,0,a/(a-b)).set(0,1,1); - m2.set(1,0,b/(a-b)).set(1,1,1); + m2 = matrix{{a/(a-b), 1}, + {b/(a-b), 1}}; det = m2.determinant(); if (det != 1) { if (det.normal() == 1) // only half wrong @@ -97,9 +102,9 @@ static unsigned matrix_determinants() } // check characteristic polynomial - m3.set(0,0,a).set(0,1,-2).set(0,2,2); - m3.set(1,0,3).set(1,1,a-1).set(1,2,2); - m3.set(2,0,3).set(2,1,4).set(2,2,a-3); + m3 = matrix{{a, -2, 2}, + {3, a-1, 2}, + {3, 4, a-3}}; ex p = m3.charpoly(a); if (p != 0) { clog << "charpoly of 3x3 matrix " << m3 @@ -131,17 +136,16 @@ static unsigned matrix_invert1() static unsigned matrix_invert2() { unsigned result = 0; - matrix m(2,2); symbol a("a"), b("b"), c("c"), d("d"); - m.set(0,0,a).set(0,1,b); - m.set(1,0,c).set(1,1,d); + matrix m = {{a, b}, + {c, d}}; matrix m_i = m.inverse(); ex det = m.determinant(); if ((normal(m_i(0,0)*det) != d) || - (normal(m_i(0,1)*det) != -b) || - (normal(m_i(1,0)*det) != -c) || - (normal(m_i(1,1)*det) != a)) { + (normal(m_i(0,1)*det) != -b) || + (normal(m_i(1,0)*det) != -c) || + (normal(m_i(1,1)*det) != a)) { clog << "inversion of 2x2 matrix " << m << " erroneously returned " << m_i << endl; ++result; @@ -153,13 +157,12 @@ static unsigned matrix_invert2() static unsigned matrix_invert3() { unsigned result = 0; - matrix m(3,3); symbol a("a"), b("b"), c("c"); symbol d("d"), e("e"), f("f"); symbol g("g"), h("h"), i("i"); - m.set(0,0,a).set(0,1,b).set(0,2,c); - m.set(1,0,d).set(1,1,e).set(1,2,f); - m.set(2,0,g).set(2,1,h).set(2,2,i); + matrix m = {{a, b, c}, + {d, e, f}, + {g, h, i}}; matrix m_i = m.inverse(); ex det = m.determinant(); @@ -183,36 +186,57 @@ static unsigned matrix_invert3() static unsigned matrix_solve2() { // check the solution of the multiple system A*X = B: - // [ 1 2 -1 ] [ x0 y0 ] [ 4 0 ] - // [ 1 4 -2 ]*[ x1 y1 ] = [ 7 0 ] - // [ a -2 2 ] [ x2 y2 ] [ a 4 ] + // [ 1 2 -1 ] [ x0 y0 ] [ 4 0 ] + // [ 1 4 -2 ]*[ x1 y1 ] = [ 7 0 ] + // [ a -2 2 ] [ x2 y2 ] [ a 4 ] unsigned result = 0; symbol a("a"); symbol x0("x0"), x1("x1"), x2("x2"); symbol y0("y0"), y1("y1"), y2("y2"); - matrix A(3,3); - A.set(0,0,1).set(0,1,2).set(0,2,-1); - A.set(1,0,1).set(1,1,4).set(1,2,-2); - A.set(2,0,a).set(2,1,-2).set(2,2,2); - matrix B(3,2); - B.set(0,0,4).set(1,0,7).set(2,0,a); - B.set(0,1,0).set(1,1,0).set(2,1,4); - matrix X(3,2); - X.set(0,0,x0).set(1,0,x1).set(2,0,x2); - X.set(0,1,y0).set(1,1,y1).set(2,1,y2); - matrix cmp(3,2); - cmp.set(0,0,1).set(1,0,3).set(2,0,3); - cmp.set(0,1,0).set(1,1,2).set(2,1,4); + matrix A = {{1, 2, -1}, + {1, 4, -2}, + {a, -2, 2}}; + matrix B = {{4, 0}, + {7, 0}, + {a, 4}}; + matrix X = {{x0 ,y0}, + {x1, y1}, + {x2, y2}}; + matrix cmp = {{1, 0}, + {3, 2}, + {3, 4}}; matrix sol(A.solve(X, B)); - for (unsigned ro=0; ro<3; ++ro) - for (unsigned co=0; co<2; ++co) - if (cmp(ro,co) != sol(ro,co)) - result = 1; - if (result) { + if (cmp != sol) { clog << "Solving " << A << " * " << X << " == " << B << endl << "erroneously returned " << sol << endl; + result = 1; + } + + return result; +} + +static unsigned matrix_solve3() +{ + unsigned result = 0; + symbol x("x"); + symbol t1("t1"), t2("t2"), t3("t3"); + matrix A = { + {3+6*x, 6*(x+x*x)/(2+3*x), 0}, + {-(2+7*x+6*x*x)/x, -2-2*x, 0}, + {-2*(2+3*x)/(1+2*x), -6*x/(1+2*x), 1+4*x} + }; + matrix B = {{0}, {0}, {0}}; + matrix X = {{t1}, {t2}, {t3}}; + for (auto algo : vector({ + solve_algo::gauss, solve_algo::divfree, solve_algo::bareiss, solve_algo::markowitz + })) { + matrix sol(A.solve(X, B, algo)); + if (!normal((A*sol - B).evalm()).is_zero_matrix()) { + clog << "Solving " << A << " * " << X << " == " << B << " with algo=" << algo << endl + << "erroneously returned " << sol << endl; + result += 1; + } } - return result; } @@ -220,16 +244,12 @@ static unsigned matrix_evalm() { unsigned result = 0; - matrix S(2, 2, lst( - 1, 2, - 3, 4 - )), T(2, 2, lst( - 1, 1, - 2, -1 - )), R(2, 2, lst( - 27, 14, - 36, 26 - )); + matrix S {{1, 2}, + {3, 4}}; + matrix T {{1, 1}, + {2, -1}}; + matrix R {{27, 14}, + {36, 26}}; ex e = ((S + T) * (S + 2*T)); ex f = e.evalm(); @@ -254,18 +274,18 @@ static unsigned matrix_rank() } // a trivial rank one example - m = 1, 0, 0, - 2, 0, 0, - 3, 0, 0; + m = {{1, 0, 0}, + {2, 0, 0}, + {3, 0, 0}}; if (m.rank() != 1) { clog << "The rank of " << m << " was not computed correctly." << endl; ++result; } // an example from Maple's help with rank two - m = x, 1, 0, - 0, 0, 1, - x*y, y, 1; + m = {{x, 1, 0}, + {0, 0, 1}, + {x*y, y, 1}}; if (m.rank() != 2) { clog << "The rank of " << m << " was not computed correctly." << endl; ++result; @@ -281,13 +301,41 @@ static unsigned matrix_rank() return result; } +unsigned matrix_solve_nonnormal() +{ + symbol a("a"), b("b"), c("c"), x("x"); + // This matrix has a non-normal zero element! + matrix mx {{1,0,0}, + {0,1/(x+1)-(x-1)/(x*x-1),1}, + {0,0,0}}; + matrix zero {{0}, {0}, {0}}; + matrix vars {{a}, {b}, {c}}; + try { + matrix sol_gauss = mx.solve(vars, zero, solve_algo::gauss); + matrix sol_divfree = mx.solve(vars, zero, solve_algo::divfree); + matrix sol_bareiss = mx.solve(vars, zero, solve_algo::bareiss); + if (sol_gauss != sol_divfree || sol_gauss != sol_bareiss) { + clog << "different solutions while solving " + << mx << " * " << vars << " == " << zero << endl + << "gauss: " << sol_gauss << endl + << "divfree: " << sol_divfree << endl + << "bareiss: " << sol_bareiss << endl; + return 1; + } + } catch (const exception & e) { + clog << "exception thrown while solving " + << mx << " * " << vars << " == " << zero << endl; + return 1; + } + return 0; +} + static unsigned matrix_misc() { unsigned result = 0; - matrix m1(2,2); symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f"); - m1.set(0,0,a).set(0,1,b); - m1.set(1,0,c).set(1,1,d); + matrix m1 = {{a, b}, + {c, d}}; ex tr = trace(m1); // check a simple trace @@ -304,10 +352,9 @@ static unsigned matrix_misc() << " erroneously returned " << m2 << endl; ++result; } - matrix m3(3,2); - m3.set(0,0,a).set(0,1,b); - m3.set(1,0,c).set(1,1,d); - m3.set(2,0,e).set(2,1,f); + matrix m3 = {{a, b}, + {c, d}, + {e, f}}; if (transpose(transpose(m3)) != m3) { clog << "transposing 3x2 matrix " << m3 << " twice" << " erroneously returned " << transpose(transpose(m3)) << endl; @@ -337,23 +384,22 @@ unsigned exam_matrices() unsigned result = 0; cout << "examining symbolic matrix manipulations" << flush; - clog << "----------symbolic matrix manipulations:" << endl; result += matrix_determinants(); cout << '.' << flush; result += matrix_invert1(); cout << '.' << flush; result += matrix_invert2(); cout << '.' << flush; result += matrix_invert3(); cout << '.' << flush; result += matrix_solve2(); cout << '.' << flush; + result += matrix_solve3(); cout << '.' << flush; result += matrix_evalm(); cout << "." << flush; result += matrix_rank(); cout << "." << flush; + result += matrix_solve_nonnormal(); cout << "." << flush; result += matrix_misc(); cout << '.' << flush; - if (!result) { - cout << " passed " << endl; - clog << "(no output)" << endl; - } else { - cout << " failed " << endl; - } - return result; } + +int main(int argc, char** argv) +{ + return exam_matrices(); +}