Test inversion by verifying identity product

src/testing/test_zinvert.cpp

@@ -37,6 +37,36 @@
 
 #include "../include/algebraic.h"
 
+dcomplex* matrix_mult(
+		 dcomplex *a1, const magma_int_t r1, const magma_int_t c1,
+		 dcomplex *a2, const magma_int_t r2, const magma_int_t c2
+) {
+  dcomplex *result = NULL;
+  dcomplex value;
+  if (c1 == r2) {
+    result = new dcomplex[r1 * c2]();
+    for (magma_int_t i = 0; i < r1; i++) {
+      for (magma_int_t j = 0; j < c2; j++) {
+	value = 0.0 + I * 0.0;
+	for (magma_int_t k = 0; k < c1; k++) {
+	  value += a1[i * c1 + k] * a2[k * c2 + j];
+	}
+	result[i * c2 + j] = value;
+      }
+    }
+  }
+  return result;
+}
+
+void print_matrix(dcomplex *a, const magma_int_t rows, const magma_int_t columns) {
+  for (magma_int_t i = 0; i < rows; i++) {
+    for (magma_int_t j = 0; j < columns; j++) {
+      printf("\t(%.5le,%.5le)", real(a[i * columns + j]), imag(a[i * columns + j]));
+    }
+    printf("\n");
+  }
+}
+
 int main() {
   int result = (int)SUCCESS;
 #ifdef USE_MAGMA
@@ -47,13 +77,13 @@ int main() {
   const double tolerance = 1.0e-6;
   dcomplex **test_matrix;
   dcomplex *vec_matrix = new dcomplex[nn];
-  dcomplex *vec_inv_matrix = new dcomplex[nn];
-  for (int ivi = 0; ivi < nn; ivi++) vec_matrix[ivi] = 1.0 + ivi + I * (1.0 + ivi);
+  dcomplex *old_matrix = new dcomplex[nn];
+  dcomplex *prod_matrix;
+  for (int ivi = 0; ivi < nn; ivi++) {
+    vec_matrix[ivi] = 2.0 + ivi - I * (2 + ivi) / 2.0;
+    old_matrix[ivi] = vec_matrix[ivi];
+  }
   test_matrix = &vec_matrix;
-  vec_inv_matrix[0] = -1.0 + I * 1.0;
-  vec_inv_matrix[1] = 0.5 - I * 0.5;
-  vec_inv_matrix[2] = 0.75 - I * 0.75;
-  vec_inv_matrix[3] = -0.25 + I * 0.25;
 #ifdef USE_MAGMA
   if (sizeof(np_int) != sizeof(magma_int_t)) {
     printf("ERROR: sizeof(np_int) = %ld; sizeof(magma_int_t) = %ld\n",
@@ -62,16 +92,29 @@ int main() {
   }
 #endif
   if (result == 0) {
+    dcomplex difference;
     invert_matrix(test_matrix, n, result, n);
-    for (int tvi = 0; tvi < 4; tvi++) {
-      dcomplex difference = vec_matrix[tvi] - vec_inv_matrix[tvi];
+    prod_matrix = matrix_mult(vec_matrix, n, n, old_matrix, n, n);
+    for (int tvi = 0; tvi < n; tvi++) {
+      for (int tvj = 0; tvj < n; tvj++) {
+	difference = (tvi == tvj) ? prod_matrix[n * tvi + tvj] - 1.0 : prod_matrix[n * tvi + tvj];
 	if (real(difference) < -tolerance || real(difference) > tolerance) result = 1;
 	if (imag(difference) < -tolerance || imag(difference) > tolerance) result = 1;
       }
-    if (result != 0) printf("ERROR: failed matrix inversion test!\n");
     }
-  delete[] vec_inv_matrix;
+    if (result != 0) {
+      printf("ERROR: failed matrix inversion test!\n");
+    }
+    printf("INFO: original matrix:\n");
+    print_matrix(old_matrix, n, n);
+    printf("INFO: inverted matrix:\n");
+    print_matrix(vec_matrix, n, n);
+    printf("INFO: product matrix:\n");
+    print_matrix(prod_matrix, n, n);
+    delete[] prod_matrix;
+  }
   delete[] vec_matrix;
+  delete[] old_matrix;
 #ifdef USE_MAGMA
   magma_finalize();
 #endif