static assert M>=N. floats to Type, arguments as const reference

matrix/LeastSquaresSolver.hpp

@@ -30,31 +30,30 @@ public:
      *
      * Initialize the class with a MxN matrix. The constructor starts the
      * QR decomposition. This class does not check the rank of the matrix.
-     * The user needs to make sure that rank(A) = N and N >= M.
+     * The user needs to make sure that rank(A) = N and M >= N.
      */
-    LeastSquaresSolver(Matrix<Type, M, N> A)
+    LeastSquaresSolver(const Matrix<Type, M, N> &A)
     {
-        if (M < N) {
-            return;
-        }
+        static_assert(M >= N, "Matrix dimension should be M >= N");
+
         // Copy contentents of matrix A
         _A = A;
 
         for (size_t j = 0; j < N; j++) {
-            float normx = 0.0f;
+            Type normx = 0.;
             for (size_t i = j; i < M; i++) {
                 normx += _A(i,j) * _A(i,j);
             }
             normx = sqrt(normx);
-            float s = _A(j,j) > 0 ? -1.0f : 1.0f;
-            float u1 = _A(j,j) - s*normx;
+            Type s = _A(j,j) > 0 ? -1. : 1.;
+            Type u1 = _A(j,j) - s*normx;
             // prevent divide by zero
             // also covers u1. normx is never negative
-            if (normx < 1e-8f) {
+            if (normx < 1e-8) {
                 break;
             }
-            float w[M] = {};
-            w[0] = 1.0f;
+            Type w[M] = {};
+            w[0] = 1.;
             for (size_t i = j+1; i < M; i++) {
                 w[i-j] = _A(i,j) / u1;
                 _A(i,j) = w[i-j];
@@ -63,7 +62,7 @@ public:
             _tau(j) = -s*u1/normx;
 
             for (size_t k = j+1; k < N; k++) {
-                float tmp = 0.0f;
+                Type tmp = 0.;
                 for (size_t i = j; i < M; i++) {
                     tmp += w[i-j] * _A(i,k);
                 }
@@ -83,17 +82,17 @@ public:
      * This function calculates Q^T * b. This is useful for the solver
      * because R*x = Q^T*b.
      */
-    Vector<Type, M> qtb(Vector<Type, M> b) {
+    Vector<Type, M> qtb(const Vector<Type, M> &b) {
         Vector<Type, M> qtbv = b;
 
         for (size_t j = 0; j < N; j++) {
-            float w[M];
-            w[0] = 1.0f;
+            Type w[M];
+            w[0] = 1.;
             // fill vector w
             for (size_t i = j+1; i < M; i++) {
                 w[i-j] = _A(i,j);
             }
-            float tmp = 0.0f;
+            Type tmp = 0.;
             for (size_t i = j; i < M; i++) {
                 tmp += w[i-j] * qtbv(i);
             }
@@ -113,7 +112,7 @@ public:
      * Find x in the equation Ax = b.
      * A is provided in the initializer of the class.
      */
-    Vector<Type, N> solve(Vector<Type, M> b) {
+    Vector<Type, N> solve(const Vector<Type, M> &b) {
         Vector<Type, M> qtbv = qtb(b);
         Vector<Type, N> x;
 
@@ -124,9 +123,9 @@ public:
                 x(i) -= _A(i,r) * x(r);
             }
             // divide by zero, return vector of zeros
-            if (fabs(_A(i,i)) < 1e-8f) {
+            if (fabs(_A(i,i)) < 1e-8) {
                 for (size_t z = 0; z < N; z++) {
-                    x(z) = 0.0f;
+                    x(z) = 0.;
                 }
                 break;
             }

test/least_squares.cpp

@@ -5,6 +5,7 @@ using namespace matrix;
 
 int test_4x3(void);
 int test_4x4(void);
+int test_4x4_type_double(void);
 int test_div_zero(void);
 
 int main()
@@ -17,6 +18,8 @@ int main()
     ret = test_4x3();
     if (ret != 0) return ret;
 
+    ret = test_4x4_type_double();
+
     ret = test_div_zero();
     if (ret != 0) return ret;
 
@@ -74,6 +77,32 @@ int test_4x4() {
     return 0;
 }
 
+int test_4x4_type_double() {
+    // Start with an (m x n) A matrix
+    double data[16] = { 20., -10., -13.,  21.,
+                        17.,  16., -18., -14.,
+                        0.7,  -0.8,   0.9,  -0.5,
+                        -1.,  -1.1,  -1.2,  -1.3
+                      };
+    Matrix<double, 4, 4> A(data);
+
+    double b_data[4] = {2.0, 3.0, 4.0, 5.0};
+    Vector<double, 4> b(b_data);
+
+    double x_check_data[4] = { 0.97893433,
+                               -2.80798701,
+                               -0.03175765,
+                               -2.19387649
+                             };
+    Vector<double, 4> x_check(x_check_data);
+
+    LeastSquaresSolver<double, 4, 4> qrd = LeastSquaresSolver<double, 4, 4>(A);
+
+    Vector<double, 4> x = qrd.solve(b);
+    TEST(isEqual(x, x_check));
+    return 0;
+}
+
 int test_div_zero() {
     float data[4] = {0.0f, 0.0f, 0.0f, 0.0f};
     Matrix<float, 2, 2> A(data);