X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_matrices.cpp;h=b163386fe4f22b5d3e8af952f16401649637b65d;hp=81fed94ed2265fd49d8314e10eaa0d586bc6c0c6;hb=8cffcdf13d817a47f217f1a1043317d95969e070;hpb=f4ea690a3f118bf364190f0ef3c3f6d2ccdf6206 diff --git a/check/exam_matrices.cpp b/check/exam_matrices.cpp index 81fed94e..b163386f 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) 1999-2000 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2019 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 @@ -17,229 +18,388 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * 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() +{ + unsigned result = 0; + ex det; + matrix m1(1,1), m2(2,2), m3(3,3), m4(4,4); + symbol a("a"), b("b"), c("c"); + symbol d("d"), e("e"), f("f"); + symbol g("g"), h("h"), i("i"); + + // check symbolic trivial matrix determinant + m1 = matrix{{a}}; + det = m1.determinant(); + if (det != a) { + clog << "determinant of 1x1 matrix " << m1 + << " erroneously returned " << det << endl; + ++result; + } + + // check generic dense symbolic 2x2 matrix determinant + m2 = matrix{{a, b}, + {c, d}}; + det = m2.determinant(); + if (det != (a*d-b*c)) { + clog << "determinant of 2x2 matrix " << m2 + << " erroneously returned " << det << endl; + ++result; + } + + // check generic dense symbolic 3x3 matrix determinant + 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 + << " erroneously returned " << det << endl; + ++result; + } + + // check dense numeric 3x3 matrix determinant + m3 = matrix{{0, -1, 3}, + {3, -2, 2}, + {3, 4, -2}}; + det = m3.determinant(); + if (det != 42) { + clog << "determinant of 3x3 matrix " << m3 + << " erroneously returned " << det << endl; + ++result; + } + + // check dense symbolic 2x2 matrix determinant + m2 = matrix{{a/(a-b), 1}, + {b/(a-b), 1}}; + det = m2.determinant(); + if (det != 1) { + if (det.normal() == 1) // only half wrong + clog << "determinant of 2x2 matrix " << m2 + << " was returned unnormalized as " << det << endl; + else // totally wrong + clog << "determinant of 2x2 matrix " << m2 + << " erroneously returned " << det << endl; + ++result; + } + + // check sparse symbolic 4x4 matrix determinant + m4.set(0,1,a).set(1,0,b).set(3,2,c).set(2,3,d); + det = m4.determinant(); + if (det != a*b*c*d) { + clog << "determinant of 4x4 matrix " << m4 + << " erroneously returned " << det << endl; + ++result; + } + + // check characteristic polynomial + 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 + << " erroneously returned " << p << endl; + ++result; + } + + return result; +} + +static unsigned matrix_invert1() +{ + unsigned result = 0; + matrix m(1,1); + symbol a("a"); + + m.set(0,0,a); + matrix m_i = m.inverse(); + + if (m_i(0,0) != pow(a,-1)) { + clog << "inversion of 1x1 matrix " << m + << " erroneously returned " << m_i << endl; + ++result; + } + + return result; +} -static unsigned matrix_determinants(void) +static unsigned matrix_invert2() { - unsigned result = 0; - ex det; - matrix m1(1,1), m2(2,2), m3(3,3), m4(4,4); - symbol a("a"), b("b"), c("c"); - symbol d("d"), e("e"), f("f"); - symbol g("g"), h("h"), i("i"); - - // check symbolic trivial matrix determinant - m1.set(0,0,a); - det = m1.determinant(); - if (det != a) { - clog << "determinant of 1x1 matrix " << m1 - << " erroneously returned " << det << endl; - ++result; - } - - // 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); - det = m2.determinant(); - if (det != (a*d-b*c)) { - clog << "determinant of 2x2 matrix " << m2 - << " erroneously returned " << det << endl; - ++result; - } - - // 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); - det = m3.determinant().expand(); - 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 - << " erroneously returned " << det << endl; - ++result; - } - - // 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)); - det = m3.determinant(); - if (det != 42) { - clog << "determinant of 3x3 matrix " << m3 - << " erroneously returned " << det << endl; - ++result; - } - - // check dense symbolic 2x2 matrix determinant - m2.set(0,0,a/(a-b)).set(0,1,numeric(1)); - m2.set(1,0,b/(a-b)).set(1,1,numeric(1)); - det = m2.determinant(true); - if (det != 1) { - clog << "determinant of 2x2 matrix " << m2 - << " erroneously returned " << det << endl; - ++result; - } - - // check sparse symbolic 4x4 matrix determinant - m4.set(0,1,a).set(1,0,b).set(3,2,c).set(2,3,d); - det = m4.determinant(); - if (det != a*b*c*d) { - clog << "determinant of 4x4 matrix " << m4 - << " erroneously returned " << det << endl; - ++result; - } - - // 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); - ex p = m3.charpoly(a); - if (p != 0) { - clog << "charpoly of 3x3 matrix " << m3 - << " erroneously returned " << p << endl; - ++result; - } - - return result; + unsigned result = 0; + symbol a("a"), b("b"), c("c"), d("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)) { + clog << "inversion of 2x2 matrix " << m + << " erroneously returned " << m_i << endl; + ++result; + } + + return result; +} + +static unsigned matrix_invert3() +{ + unsigned result = 0; + symbol a("a"), b("b"), c("c"); + symbol d("d"), e("e"), f("f"); + symbol g("g"), h("h"), i("i"); + matrix m = {{a, b, c}, + {d, e, f}, + {g, h, i}}; + matrix m_i = m.inverse(); + ex det = m.determinant(); + + if ((normal(m_i(0,0)*det) != (e*i-f*h)) || + (normal(m_i(0,1)*det) != (c*h-b*i)) || + (normal(m_i(0,2)*det) != (b*f-c*e)) || + (normal(m_i(1,0)*det) != (f*g-d*i)) || + (normal(m_i(1,1)*det) != (a*i-c*g)) || + (normal(m_i(1,2)*det) != (c*d-a*f)) || + (normal(m_i(2,0)*det) != (d*h-e*g)) || + (normal(m_i(2,1)*det) != (b*g-a*h)) || + (normal(m_i(2,2)*det) != (a*e-b*d))) { + clog << "inversion of 3x3 matrix " << m + << " erroneously returned " << m_i << endl; + ++result; + } + + return result; +} + +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 ] + unsigned result = 0; + symbol a("a"); + symbol x0("x0"), x1("x1"), x2("x2"); + symbol y0("y0"), y1("y1"), y2("y2"); + 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)); + if (cmp != sol) { + clog << "Solving " << A << " * " << X << " == " << B << endl + << "erroneously returned " << sol << endl; + result = 1; + } + + return result; } -static unsigned matrix_invert1(void) +static unsigned matrix_solve3() { - matrix m(1,1); - symbol a("a"); - - m.set(0,0,a); - matrix m_i = m.inverse(); - - if (m_i(0,0) != pow(a,-1)) { - clog << "inversion of 1x1 matrix " << m - << " erroneously returned " << m_i << endl; - return 1; - } - return 0; + 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; +} + +static unsigned matrix_evalm() +{ + unsigned result = 0; + + 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(); + if (!f.is_equal(R)) { + clog << "Evaluating " << e << " erroneously returned " << f << " instead of " << R << endl; + result++; + } + + return result; +} + +static unsigned matrix_rank() +{ + unsigned result = 0; + symbol x("x"), y("y"); + matrix m(3,3); + + // the zero matrix always has rank 0 + if (m.rank() != 0) { + clog << "The rank of " << m << " was not computed correctly." << endl; + ++result; + } + + // a trivial rank one example + 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}}; + if (m.rank() != 2) { + clog << "The rank of " << m << " was not computed correctly." << endl; + ++result; + } + + // the 3x3 unit matrix has rank 3 + m = ex_to(unit_matrix(3,3)); + if (m.rank() != 3) { + clog << "The rank of " << m << " was not computed correctly." << endl; + ++result; + } + + return result; } -static unsigned matrix_invert2(void) +unsigned matrix_solve_nonnormal() { - 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_i = m.inverse(); - ex det = m.determinant().expand(); - - 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)) { - clog << "inversion of 2x2 matrix " << m - << " erroneously returned " << m_i << endl; - return 1; - } - return 0; + 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_invert3(void) +static unsigned matrix_misc() { - 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_i = m.inverse(); - ex det = m.determinant().normal().expand(); - - if ((normal(m_i(0,0)*det) != (e*i-f*h)) || - (normal(m_i(0,1)*det) != (c*h-b*i)) || - (normal(m_i(0,2)*det) != (b*f-c*e)) || - (normal(m_i(1,0)*det) != (f*g-d*i)) || - (normal(m_i(1,1)*det) != (a*i-c*g)) || - (normal(m_i(1,2)*det) != (c*d-a*f)) || - (normal(m_i(2,0)*det) != (d*h-e*g)) || - (normal(m_i(2,1)*det) != (b*g-a*h)) || - (normal(m_i(2,2)*det) != (a*e-b*d))) { - clog << "inversion of 3x3 matrix " << m - << " erroneously returned " << m_i << endl; - return 1; - } - return 0; + unsigned result = 0; + symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f"); + matrix m1 = {{a, b}, + {c, d}}; + ex tr = trace(m1); + + // check a simple trace + if (tr.compare(a+d)) { + clog << "trace of 2x2 matrix " << m1 + << " erroneously returned " << tr << endl; + ++result; + } + + // and two simple transpositions + matrix m2 = transpose(m1); + if (m2(0,0) != a || m2(0,1) != c || m2(1,0) != b || m2(1,1) != d) { + clog << "transpose of 2x2 matrix " << m1 + << " erroneously returned " << m2 << endl; + ++result; + } + 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; + ++result; + } + + // produce a runtime-error by inverting a singular matrix and catch it + matrix m4(2,2); + matrix m5; + bool caught = false; + try { + m5 = inverse(m4); + } catch (std::runtime_error err) { + caught = true; + } + if (!caught) { + cerr << "singular 2x2 matrix " << m4 + << " erroneously inverted to " << m5 << endl; + ++result; + } + + return result; } -static unsigned matrix_misc(void) +unsigned exam_matrices() { - 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); - ex tr = trace(m1); - - // check a simple trace - if (tr.compare(a+d)) { - clog << "trace of 2x2 matrix " << m1 - << " erroneously returned " << tr << endl; - ++result; - } - - // and two simple transpositions - matrix m2 = transpose(m1); - if (m2(0,0) != a || m2(0,1) != c || m2(1,0) != b || m2(1,1) != d) { - clog << "transpose of 2x2 matrix " << m1 - << " 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); - if (transpose(transpose(m3)) != m3) { - clog << "transposing 3x2 matrix " << m3 << " twice" - << " erroneously returned " << transpose(transpose(m3)) << endl; - ++result; - } - - // produce a runtime-error by inverting a singular matrix and catch it - matrix m4(2,2); - matrix m5; - bool caught=false; - try { - m5 = inverse(m4); - } catch (std::runtime_error err) { - caught=true; - } - if (!caught) { - cerr << "singular 2x2 matrix " << m4 - << " erroneously inverted to " << m5 << endl; - ++result; - } - - return result; + unsigned result = 0; + + cout << "examining symbolic matrix manipulations" << flush; + + 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; + + return result; } -unsigned exam_matrices(void) +int main(int argc, char** argv) { - 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_misc(); cout << '.' << flush; - - if (!result) { - cout << " passed " << endl; - clog << "(no output)" << endl; - } else { - cout << " failed " << endl; - } - - return result; + return exam_matrices(); }