X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fcheck_matrices.cpp;h=62b74ba2651ff5d4134dbed97c380b328cb409c3;hp=ec7efefc523132fae8b701c2864a674d26c3927e;hb=db5765dc91202851739e196ba11bfccb0b3fe7bc;hpb=f4ea690a3f118bf364190f0ef3c3f6d2ccdf6206

diff --git a/check/check_matrices.cpp b/check/check_matrices.cpp
index ec7efefc..62b74ba2 100644
--- a/check/check_matrices.cpp
+++ b/check/check_matrices.cpp
@@ -22,23 +22,91 @@
 
 #include "checks.h"
 
-// determinants of some sparse symbolic size x size matrices
-static unsigned matrix_determinants(void)
+/* determinants of some sparse symbolic matrices with coefficients in
+ * an integral domain. */
+static unsigned integdom_matrix_determinants(void)
 {
     unsigned result = 0;
     symbol a("a");
-
-    for (int size=3; size<16; ++size) {
+    
+    for (unsigned size=3; size<20; ++size) {
         matrix A(size,size);
-        for (int c=0; c<size; ++c) {
-            for (int r=0;r<size-1; ++r)
-                // populate 10 percent of the entries, the rest remains 0:
-                if (!(int)(10.0*rand()/(RAND_MAX+1.0)))
-                    A.set(r,c,dense_univariate_poly(a,5));
-            // set the last line to a linear combination of two other lines
-            // to guarantee that the determinant vanishes:
+        // populate one element in each row:
+        for (unsigned r=0; r<size-1; ++r)
+            A.set(r,unsigned(rand()%size),dense_univariate_poly(a,5));
+        // set the last row to a linear combination of two other lines
+        // to guarantee that the determinant is zero:
+        for (unsigned c=0; c<size; ++c)
             A.set(size-1,c,A(0,c)-A(size-2,c));
+        if (!A.determinant().is_zero()) {
+            clog << "Determinant of " << size << "x" << size << " matrix "
+                 << endl << A << endl
+                 << "was not found to vanish!" << endl;
+            ++result;
+        }
+    }
+    
+    return result;
+}
+
+/* determinants of some symbolic matrices with multivariate rational function
+ * coefficients. */
+static unsigned rational_matrix_determinants(void)
+{
+    unsigned result = 0;
+    symbol a("a"), b("b"), c("c");
+    
+    for (unsigned size=3; size<8; ++size) {
+        matrix A(size,size);
+        for (unsigned r=0; r<size-1; ++r) {
+            // populate one or two elements in each row:
+            for (unsigned ec=0; ec<2; ++ec) {
+                ex numer = sparse_tree(a, b, c, 1+rand()%4, false, false, false);
+                ex denom;
+                do {
+                    denom = sparse_tree(a, b, c, rand()%2, false, false, false);
+                } while (denom.is_zero());
+                A.set(r,unsigned(rand()%size),numer/denom);
+            }
+        }
+        // set the last row to a linear combination of two other lines
+        // to guarantee that the determinant is zero:
+        for (unsigned co=0; co<size; ++co)
+            A.set(size-1,co,A(0,co)-A(size-2,co));
+        if (!A.determinant().is_zero()) {
+            clog << "Determinant of " << size << "x" << size << " matrix "
+                 << endl << A << endl
+                 << "was not found to vanish!" << endl;
+            ++result;
+        }
+    }
+    
+    return result;
+}
+
+/* Some quite funny determinants with functions and stuff like that inside. */
+static unsigned funny_matrix_determinants(void)
+{
+    unsigned result = 0;
+    symbol a("a"), b("b"), c("c");
+    
+    for (unsigned size=3; size<7; ++size) {
+        matrix A(size,size);
+        for (unsigned co=0; co<size-1; ++co) {
+            // populate one or two elements in each row:
+            for (unsigned ec=0; ec<2; ++ec) {
+                ex numer = sparse_tree(a, b, c, 1+rand()%3, true, true, false);
+                ex denom;
+                do {
+                    denom = sparse_tree(a, b, c, rand()%2, false, true, false);
+                } while (denom.is_zero());
+                A.set(unsigned(rand()%size),co,numer/denom);
+            }
         }
+        // set the last column to a linear combination of two other columns
+        // to guarantee that the determinant is zero:
+        for (unsigned ro=0; ro<size; ++ro)
+            A.set(ro,size-1,A(ro,0)-A(ro,size-2));
         if (!A.determinant().is_zero()) {
             clog << "Determinant of " << size << "x" << size << " matrix "
                  << endl << A << endl
@@ -50,6 +118,81 @@ static unsigned matrix_determinants(void)
     return result;
 }
 
+/* compare results from different determinant algorithms.*/
+static unsigned compare_matrix_determinants(void)
+{
+    unsigned result = 0;
+    symbol a("a");
+    
+    for (unsigned size=2; size<7; ++size) {
+        matrix A(size,size);
+        for (unsigned co=0; co<size; ++co) {
+            for (unsigned ro=0; ro<size; ++ro) {
+                // populate some elements
+                ex elem = 0;
+                if (rand()%(size/2) == 0)
+                    elem = sparse_tree(a, a, a, rand()%3, false, true, false);
+                A.set(ro,co,elem);
+            }
+        }
+        ex det_gauss = A.determinant(determinant_algo::gauss);
+        ex det_laplace = A.determinant(determinant_algo::laplace);
+        ex det_divfree = A.determinant(determinant_algo::divfree);
+        ex det_bareiss = A.determinant(determinant_algo::bareiss);
+        if ((det_gauss-det_laplace).normal() != 0 ||
+            (det_bareiss-det_laplace).normal() != 0 ||
+            (det_divfree-det_laplace).normal() != 0) {
+            clog << "Determinant of " << size << "x" << size << " matrix "
+                 << endl << A << endl
+                 << "is inconsistent between different algorithms:" << endl
+                 << "Gauss elimination:   " << det_gauss << endl
+                 << "Minor elimination:   " << det_laplace << endl
+                 << "Division-free elim.: " << det_divfree << endl
+                 << "Fraction-free elim.: " << det_bareiss << endl;
+            ++result;
+        }
+    }
+    
+    return result;
+}
+
+static unsigned symbolic_matrix_inverse(void)
+{
+    unsigned result = 0;
+    symbol a("a"), b("b"), c("c");
+    
+    for (unsigned size=2; size<5; ++size) {
+        matrix A(size,size);
+        do {
+            for (unsigned co=0; co<size; ++co) {
+                for (unsigned ro=0; ro<size; ++ro) {
+                    // populate some elements
+                    ex elem = 0;
+                    if (rand()%(size/2) == 0)
+                        elem = sparse_tree(a, b, c, rand()%2, false, true, false);
+                    A.set(ro,co,elem);
+                }
+            }
+        } while (A.determinant() == 0);
+        matrix B = A.inverse();
+        matrix C = A.mul(B);
+        bool ok = true;
+        for (unsigned ro=0; ro<size; ++ro)
+            for (unsigned co=0; co<size; ++co)
+                if (C(ro,co).normal() != (ro==co?1:0))
+                    ok = false;
+        if (!ok) {
+            clog << "Inverse of " << size << "x" << size << " matrix "
+                 << endl << A << endl
+                 << "erroneously returned: "
+                 << endl << B << endl;
+            ++result;
+        }
+    }
+    
+    return result;
+}
+
 unsigned check_matrices(void)
 {
     unsigned result = 0;
@@ -57,7 +200,11 @@ unsigned check_matrices(void)
     cout << "checking symbolic matrix manipulations" << flush;
     clog << "---------symbolic matrix manipulations:" << endl;
     
-    result += matrix_determinants();  cout << '.' << flush;
+    result += integdom_matrix_determinants();  cout << '.' << flush;
+    result += rational_matrix_determinants();  cout << '.' << flush;
+    result += funny_matrix_determinants();  cout << '.' << flush;
+    result += compare_matrix_determinants();  cout << '.' << flush;
+    result += symbolic_matrix_inverse();  cout << '.' << flush;
     
     if (!result) {
         cout << " passed " << endl;