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=9e8d90c754cce32f2302a9dcb41d6103587be129;hb=1193f765c62171a4267ef0138ecc22c875a7daf4;hpb=383d5eb3b0f0506810d9105a268f939125bfc347

diff --git a/check/exam_matrices.cpp b/check/exam_matrices.cpp
index 9e8d90c7..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) 1999-2001 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
@@ -17,13 +18,17 @@
  *
  *  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 <iostream>
 #include <stdexcept>
-#include "exams.h"
+using namespace std;
 
-static unsigned matrix_determinants(void)
+static unsigned matrix_determinants()
 {
 	unsigned result = 0;
 	ex det;
@@ -33,7 +38,7 @@ static unsigned matrix_determinants(void)
 	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(void)
 	}
 	
 	// 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(void)
 	}
 	
 	// 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(void)
 	}
 	
 	// 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(void)
 	}
 	
 	// 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(void)
 	}
 	
 	// 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
@@ -110,7 +115,7 @@ static unsigned matrix_determinants(void)
 	return result;
 }
 
-static unsigned matrix_invert1(void)
+static unsigned matrix_invert1()
 {
 	unsigned result = 0;
 	matrix m(1,1);
@@ -128,20 +133,19 @@ static unsigned matrix_invert1(void)
 	return result;
 }
 
-static unsigned matrix_invert2(void)
+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;
@@ -150,16 +154,15 @@ static unsigned matrix_invert2(void)
 	return result;
 }
 
-static unsigned matrix_invert3(void)
+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();
 	
@@ -180,49 +183,159 @@ static unsigned matrix_invert3(void)
 	return result;
 }
 
-static unsigned matrix_solve2(void)
+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<int>({
+		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_misc(void)
+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<matrix>(unit_matrix(3,3));
+	if (m.rank() != 3) {
+		clog << "The rank of " << m << " was not computed correctly." << endl;
+		++result;
+	}
+
+	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
@@ -239,10 +352,9 @@ static unsigned matrix_misc(void)
 			 << " 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;
@@ -267,26 +379,27 @@ static unsigned matrix_misc(void)
 	return result;
 }
 
-unsigned exam_matrices(void)
+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();
+}