least squares solver for MxN matrices using QR householder algorithm

test/CMakeLists.txt

@@ -17,6 +17,7 @@ set(tests
     helper
     hatvee
     copyto
+    least_squares
     )
 
 add_custom_target(test_build)

test/least_squares.cpp

@@ -0,0 +1,69 @@
+#include "test_macros.hpp"
+#include <matrix/math.hpp>
+
+using namespace matrix;
+
+int test_4x3(void);
+int test_4x4(void);
+
+int main()
+{
+    int ret;
+
+    ret = test_4x4();
+    if (ret != 0) return ret;
+
+    ret = test_4x3();
+    if (ret != 0) return ret;
+
+    return 0;
+}
+
+int test_4x3() {
+    // Start with an (m x n) A matrix
+    float data[12] = {20.f , -10.f , -13.f ,
+                      17.f ,  16.f , -18.f ,
+                       0.7f,  -0.8f,   0.9f,
+                      -1.f ,  -1.1f,  -1.2f};
+    Matrix<float, 4, 3> A(data);
+
+    float b_data[4] = {2.0, 3.0, 4.0, 5.0};
+    Vector<float, 4> b(b_data);
+
+    float x_check_data[3] = {-0.69168233f,
+                             -0.26227593f,
+                             -1.03767522f};
+    Vector<float, 3> x_check(x_check_data);
+
+    LeastSquaresSolver<float, 4, 3> qrd = LeastSquaresSolver<float, 4, 3>(A);
+
+    Vector<float, 3> x = qrd.solve(b);
+    TEST(isEqual(x, x_check));
+    return 0;
+}
+
+int test_4x4() {
+    // Start with an (m x n) A matrix
+    float data[16] = { 20.f , -10.f , -13.f ,  21.f ,
+                       17.f ,  16.f , -18.f , -14.f ,
+                        0.7f,  -0.8f,   0.9f,  -0.5f,
+                       -1.f ,  -1.1f,  -1.2f,  -1.3f};
+    Matrix<float, 4, 4> A(data);
+
+    float b_data[4] = {2.0, 3.0, 4.0, 5.0};
+    Vector<float, 4> b(b_data);
+
+    float x_check_data[4] = { 0.97893433f,
+                             -2.80798701f,
+                             -0.03175765f,
+                             -2.19387649f};
+    Vector<float, 4> x_check(x_check_data);
+
+    LeastSquaresSolver<float, 4, 4> qrd = LeastSquaresSolver<float, 4, 4>(A);
+
+    Vector<float, 4> x = qrd.solve(b);
+    TEST(isEqual(x, x_check));
+    return 0;
+}
+
+/* vim: set et fenc=utf-8 ff=unix sts=0 sw=4 ts=4 : */

test/test_data.py

@@ -124,4 +124,26 @@ for i in range(1,3):
     A_pow = A_pow.dot(A)
 print(eA_approx)
 
+print('\nqr decomposition 4x4')
+A = array([[20.0, -10.0, -13.0, 21.0], [ 17.0, 16.0, -18.0, -14], [0.7, -0.8, 0.9, -0.5], [-1.0, -1.1, -1.2, -1.3]])
+b = array([[2.], [3.], [4.], [5.]])
+x = scipy.linalg.lstsq(A,b)[0]
+print('A:')
+pprint(A)
+print('b:')
+pprint(b)
+print('x:')
+pprint(scipy.linalg.lstsq(A,b)[0])
+
+print('\nqr decomposition 4x3')
+A = array([[20.0, -10.0, -13.0], [ 17.0, 16.0, -18.0], [0.7, -0.8, 0.9], [-1.0, -1.1, -1.2]])
+b = array([[2.], [3.], [4.], [5.]])
+x = scipy.linalg.lstsq(A,b)[0]
+print('A:')
+pprint(A)
+print('b:')
+pprint(b)
+print('x:')
+pprint(x)
+
 # vim: set et ft=python fenc=utf-8 ff=unix sts=4 sw=4 ts=8 :