608 lines
16 KiB
C++
608 lines
16 KiB
C++
/**
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* @file testMatrix.cpp
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* @brief Unit test for Matrix Library
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* @author Christian Potthast
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* @author Carlos Nieto
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**/
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#include <iostream>
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#include <CppUnitLite/TestHarness.h>
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#include <boost/tuple/tuple.hpp>
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#include <boost/foreach.hpp>
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#include "Matrix.h"
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using namespace std;
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using namespace gtsam;
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/* ************************************************************************* */
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TEST( matrix, constructor_data )
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{
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double data[] = {-5, 3,
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0, -5 };
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Matrix A = Matrix_(2,2,data);
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Matrix B(2,2);
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B(0,0) = -5 ; B(0,1) = 3;
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B(1,0) = 0 ; B(1,1) = -5;
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EQUALITY(A,B);
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}
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/* ************************************************************************* */
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TEST( matrix, constructor_vector )
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{
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double data[] = {-5, 3,
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0, -5 };
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Matrix A = Matrix_(2,2,data);
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Vector v(4); copy(data,data+4,v.begin());
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Matrix B = Matrix_(2,2,v); // this one is column order !
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EQUALITY(A,trans(B));
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}
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/* ************************************************************************* */
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TEST( matrix, Matrix_ )
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{
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Matrix A = Matrix_(2,2,
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-5.0 , 3.0,
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00.0, -5.0 );
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Matrix B(2,2);
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B(0,0) = -5 ; B(0,1) = 3;
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B(1,0) = 0 ; B(1,1) = -5;
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EQUALITY(A,B);
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}
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/* ************************************************************************* */
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TEST( matrix, row_major )
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{
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Matrix A = Matrix_(2,2,
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1.0, 2.0,
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3.0, 4.0 );
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const double * const a = &A(0,0);
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CHECK(a[0] == 1);
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CHECK(a[1] == 2);
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CHECK(a[2] == 3);
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CHECK(a[3] == 4);
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}
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/* ************************************************************************* */
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TEST( matrix, collect )
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{
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Matrix A = Matrix_(2,2,
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-5.0 , 3.0,
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00.0, -5.0 );
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Matrix B = Matrix_(2,3,
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-0.5 , 2.1, 1.1,
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3.4 , 2.6 , 7.1);
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Matrix AB = collect(2, &A, &B);
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Matrix C(2,5);
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for(int i = 0; i < 2; i++) for(int j = 0; j < 2; j++) C(i,j) = A(i,j);
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for(int i = 0; i < 2; i++) for(int j = 0; j < 3; j++) C(i,j+2) = B(i,j);
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EQUALITY(C,AB);
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}
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/* ************************************************************************* */
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TEST( matrix, stack )
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{
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Matrix A = Matrix_(2,2,
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-5.0 , 3.0,
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00.0, -5.0 );
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Matrix B = Matrix_(3,2,
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-0.5 , 2.1,
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1.1, 3.4 ,
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2.6 , 7.1);
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Matrix AB = stack(2, &A, &B);
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Matrix C(5,2);
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for(int i = 0; i < 2; i++) for(int j = 0; j < 2; j++) C(i,j) = A(i,j);
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for(int i = 0; i < 3; i++) for(int j = 0; j < 2; j++) C(i+2,j) = B(i,j);
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EQUALITY(C,AB);
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}
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/* ************************************************************************* */
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TEST( matrix, column )
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{
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Matrix A = Matrix_(4, 7,
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-1., 0., 1., 0., 0., 0., -0.2,
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0., -1., 0., 1., 0., 0., 0.3,
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1., 0., 0., 0., -1., 0., 0.2,
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0., 1., 0., 0., 0., -1., -0.1);
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Vector a1 = column(A, 0);
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Vector exp1 = Vector_(4, -1., 0., 1., 0.);
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CHECK(assert_equal(a1, exp1));
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Vector a2 = column(A, 3);
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Vector exp2 = Vector_(4, 0., 1., 0., 0.);
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CHECK(assert_equal(a2, exp2));
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Vector a3 = column(A, 6);
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Vector exp3 = Vector_(4, -0.2, 0.3, 0.2, -0.1);
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CHECK(assert_equal(a3, exp3));
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}
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/* ************************************************************************* */
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TEST( matrix, row )
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{
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Matrix A = Matrix_(4, 7,
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-1., 0., 1., 0., 0., 0., -0.2,
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0., -1., 0., 1., 0., 0., 0.3,
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1., 0., 0., 0., -1., 0., 0.2,
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0., 1., 0., 0., 0., -1., -0.1);
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Vector a1 = row(A, 0);
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Vector exp1 = Vector_(7, -1., 0., 1., 0., 0., 0., -0.2);
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CHECK(assert_equal(a1, exp1));
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Vector a2 = row(A, 2);
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Vector exp2 = Vector_(7, 1., 0., 0., 0., -1., 0., 0.2);
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CHECK(assert_equal(a2, exp2));
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Vector a3 = row(A, 3);
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Vector exp3 = Vector_(7, 0., 1., 0., 0., 0., -1., -0.1);
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CHECK(assert_equal(a3, exp3));
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}
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/* ************************************************************************* */
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TEST( matrix, zeros )
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{
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Matrix A(2,3);
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A(0,0) = 0 ; A(0,1) = 0; A(0,2) = 0;
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A(1,0) = 0 ; A(1,1) = 0; A(1,2) = 0;
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Matrix zero = zeros(2,3);
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EQUALITY(A , zero);
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}
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/* ************************************************************************* */
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TEST( matrix, scale_columns )
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{
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Matrix A(3,4);
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A(0,0) = 1.; A(0,1) = 1.; A(0,2)= 1.; A(0,3)= 1.;
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A(1,0) = 1.; A(1,1) = 1.; A(1,2)= 1.; A(1,3)= 1.;
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A(2,0) = 1.; A(2,1) = 1.; A(2,2)= 1.; A(2,3)= 1.;
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Vector v = Vector_(4, 2., 3., 4., 5.);
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Matrix actual = vector_scale(A,v);
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Matrix expected(3,4);
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expected(0,0) = 2.; expected(0,1) = 3.; expected(0,2)= 4.; expected(0,3)= 5.;
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expected(1,0) = 2.; expected(1,1) = 3.; expected(1,2)= 4.; expected(1,3)= 5.;
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expected(2,0) = 2.; expected(2,1) = 3.; expected(2,2)= 4.; expected(2,3)= 5.;
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CHECK(assert_equal(actual, expected));
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}
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/* ************************************************************************* */
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TEST( matrix, scale_rows )
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{
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Matrix A(3,4);
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A(0,0) = 1.; A(0,1) = 1.; A(0,2)= 1.; A(0,3)= 1.;
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A(1,0) = 1.; A(1,1) = 1.; A(1,2)= 1.; A(1,3)= 1.;
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A(2,0) = 1.; A(2,1) = 1.; A(2,2)= 1.; A(2,3)= 1.;
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Vector v = Vector_(3, 2., 3., 4.);
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Matrix actual = vector_scale(v,A);
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Matrix expected(3,4);
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expected(0,0) = 2.; expected(0,1) = 2.; expected(0,2)= 2.; expected(0,3)= 2.;
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expected(1,0) = 3.; expected(1,1) = 3.; expected(1,2)= 3.; expected(1,3)= 3.;
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expected(2,0) = 4.; expected(2,1) = 4.; expected(2,2)= 4.; expected(2,3)= 4.;
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CHECK(assert_equal(actual, expected));
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}
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/* ************************************************************************* */
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TEST( matrix, equal )
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{
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Matrix A(4,4);
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A(0,0) = -1; A(0,1) = 1; A(0,2)= 2; A(0,3)= 3;
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A(1,0) = 1; A(1,1) =-3; A(1,2)= 1; A(1,3)= 3;
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A(2,0) = 1; A(2,1) = 2; A(2,2)=-1; A(2,3)= 4;
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A(3,0) = 2; A(3,1) = 1; A(3,2)= 2; A(3,3)=-2;
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Matrix A2(A);
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Matrix A3(A);
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A3(3,3)=-2.1;
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CHECK(A==A2);
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CHECK(A!=A3);
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}
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/* ************************************************************************* */
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TEST( matrix, equal_nan )
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{
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Matrix A(4,4);
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A(0,0) = -1; A(0,1) = 1; A(0,2)= 2; A(0,3)= 3;
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A(1,0) = 1; A(1,1) =-3; A(1,2)= 1; A(1,3)= 3;
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A(2,0) = 1; A(2,1) = 2; A(2,2)=-1; A(2,3)= 4;
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A(3,0) = 2; A(3,1) = 1; A(3,2)= 2; A(3,3)=-2;
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Matrix A2(A);
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Matrix A3(A);
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A3(3,3)=0.0/0.0;
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CHECK(A!=A3);
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}
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/* ************************************************************************* */
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TEST( matrix, addition )
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{
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Matrix A = Matrix_(2,2,
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1.0, 2.0,
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3.0, 4.0);
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Matrix B = Matrix_(2,2,
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4.0, 3.0,
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2.0, 1.0);
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Matrix C = Matrix_(2,2,
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5.0, 5.0,
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5.0, 5.0);
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EQUALITY(A+B,C);
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}
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/* ************************************************************************* */
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TEST( matrix, addition_in_place )
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{
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Matrix A = Matrix_(2,2,
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1.0, 2.0,
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3.0, 4.0);
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Matrix B = Matrix_(2,2,
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4.0, 3.0,
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2.0, 1.0);
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Matrix C = Matrix_(2,2,
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5.0, 5.0,
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5.0, 5.0);
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A += B;
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EQUALITY(A,C);
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}
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/* ************************************************************************* */
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TEST( matrix, subtraction )
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{
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Matrix A = Matrix_(2,2,
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1.0, 2.0,
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3.0, 4.0);
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Matrix B = Matrix_(2,2,
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4.0, 3.0,
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2.0, 1.0);
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Matrix C = Matrix_(2,2,
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-3.0, -1.0,
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1.0, 3.0);
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EQUALITY(A-B,C);
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}
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/* ************************************************************************* */
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TEST( matrix, subtraction_in_place )
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{
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Matrix A = Matrix_(2,2,
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1.0, 2.0,
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3.0, 4.0);
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Matrix B = Matrix_(2,2,
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4.0, 3.0,
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2.0, 1.0);
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Matrix C = Matrix_(2,2,
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-3.0, -1.0,
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1.0, 3.0);
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A -= B;
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EQUALITY(A,C);
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}
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/* ************************************************************************* */
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TEST( matrix, multiplication )
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{
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Matrix A(2,2);
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A(0,0) = -1; A(1,0) = 1;
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A(0,1) = 1; A(1,1) =-3;
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Matrix B(2,1);
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B(0,0) = 1.2;
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B(1,0) = 3.4;
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Matrix AB(2,1);
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AB(0,0) = 2.2;
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AB(1,0) = -9.;
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EQUALITY(A*B,AB);
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}
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/* ************************************************************************* */
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TEST( matrix, scalar_matrix_multiplication )
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{
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Vector result(2);
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Matrix A(2,2);
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A(0,0) = -1; A(1,0) = 1;
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A(0,1) = 1; A(1,1) =-3;
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Matrix B(2,2);
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B(0,0) = -10; B(1,0) = 10;
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B(0,1) = 10; B(1,1) =-30;
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EQUALITY((10*A),B);
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}
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/* ************************************************************************* */
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TEST( matrix, matrix_vector_multiplication )
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{
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Vector result(2);
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Matrix A = Matrix_(2,3,
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1.0,2.0,3.0,
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4.0,5.0,6.0
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);
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Vector v = Vector_(3,1.,2.,3.);
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Vector Av = Vector_(2,14.,32.);
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Vector AtAv = Vector_(3,142.,188.,234.);
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EQUALITY(A*v,Av);
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EQUALITY(A^Av,AtAv);
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}
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/* ************************************************************************* */
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TEST( matrix, nrRowsAndnrCols )
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{
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Matrix A(3,6);
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LONGS_EQUAL( A.size1() , 3 );
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LONGS_EQUAL( A.size2() , 6 );
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}
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/* ************************************************************************* */
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TEST( matrix, scalar_divide )
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{
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Matrix A(2,2);
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A(0,0) = 10; A(1,0) = 30;
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A(0,1) = 20; A(1,1) = 40;
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Matrix B(2,2);
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B(0,0) = 1; B(1,0) = 3;
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B(0,1) = 2; B(1,1) = 4;
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EQUALITY(B,A/10);
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}
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/* ************************************************************************* */
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TEST( matrix, inverse )
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{
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Matrix A(3,3);
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A(0,0)= 1; A(0,1)=2; A(0,2)=3;
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A(1,0)= 0; A(1,1)=4; A(1,2)=5;
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A(2,0)= 1; A(2,1)=0; A(2,2)=6;
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Matrix Ainv = inverse(A);
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Matrix expected(3,3);
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expected(0,0)= 1.0909; expected(0,1)=-0.5454; expected(0,2)=-0.0909;
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expected(1,0)= 0.2272; expected(1,1)= 0.1363; expected(1,2)=-0.2272;
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expected(2,0)= -0.1818; expected(2,1)= 0.0909; expected(2,2)=0.1818;
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CHECK(assert_equal(expected, Ainv, 1e-4));
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}
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/* ************************************************************************* */
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TEST( matrix, backsubtitution )
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{
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// TEST ONE 2x2 matrix U1*x=b1
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Vector expected1 = Vector_(2, 3.6250, -0.75);
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Matrix U1 = Matrix_(2, 2,
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2., 3.,
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0., 4.);
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Vector b1 = U1*expected1;
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CHECK( assert_equal(expected1 , backSubstituteUpper(U1, b1), 0.000001));
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// TEST TWO 3x3 matrix U2*x=b2
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Vector expected2 = Vector_(3, 5.5, -8.5, 5.);
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Matrix U2 = Matrix_(3, 3,
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3., 5., 6.,
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0., 2., 3.,
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0., 0., 1.);
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Vector b2 = U2*expected2;
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CHECK( assert_equal(expected2 , backSubstituteUpper(U2, b2), 0.000001));
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// TEST THREE Lower triangular 3x3 matrix L3*x=b3
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Vector expected3 = Vector_(3, 1., 1., 1.);
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Matrix L3 = Matrix_(3, 3,
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3., 0., 0.,
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5., 2., 0.,
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6., 3., 1.);
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Vector b3 = L3*expected3;
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CHECK( assert_equal(expected3 , backSubstituteLower(L3, b3), 0.000001));
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}
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/* ************************************************************************* */
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// unit tests for housholder transformation
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/* ************************************************************************* */
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TEST( matrix, houseHolder )
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{
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double data[] = {-5, 0, 5, 0, 0, 0, -1,
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00, -5, 0, 5, 0, 0, 1.5,
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10, 0, 0, 0,-10, 0, 2,
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00, 10, 0, 0, 0,-10, -1};
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// check in-place householder, with v vectors below diagonal
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double data1[] = {0011.1803, 0, -2.2361, 0, -8.9443, 0, 2.236,
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000000000, 11.1803, 0, -2.2361, 0, -8.9443, -1.565,
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-0.618034, 0, 4.4721, 0, -4.4721, 0, 0,
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000000000,-0.618034, 0, 4.4721, 0, -4.4721, 0.894};
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Matrix expected1 = Matrix_(4,7, data1);
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Matrix A1 = Matrix_(4, 7, data);
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householder_(A1,3);
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CHECK(assert_equal(expected1, A1, 1e-3));
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// in-place, with zeros below diagonal
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double data2[] = {0011.1803, 0, -2.2361, 0, -8.9443, 0, 2.236,
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000000000, 11.1803, 0, -2.2361, 0, -8.9443, -1.565,
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000000000, 0, 4.4721, 0, -4.4721, 0, 0,
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000000000, 0, 0, 4.4721, 0, -4.4721, 0.894};
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Matrix expected = Matrix_(4,7, data2);
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Matrix A2 = Matrix_(4, 7, data);
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householder(A2,3);
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CHECK(assert_equal(expected, A2, 1e-3));
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}
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/* ************************************************************************* */
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// unit test for qr factorization (and hence householder)
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// This behaves the same as QR in matlab: [Q,R] = qr(A), except for signs
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/* ************************************************************************* */
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TEST( matrix, qr )
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{
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double data[] = {-5, 0, 5, 0,
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00, -5, 0, 5,
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10, 0, 0, 0,
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00, 10, 0, 0,
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00, 0, 0,-10,
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10, 0,-10, 0};
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Matrix A = Matrix_(6, 4, data);
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double dataQ[] = {
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-0.3333, 0, 0.2981, 0, 0, -0.8944,
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0000000, -0.4472, 0, 0.3651, -0.8165, 0,
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00.6667, 0, 0.7454, 0, 0, 0,
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0000000, 0.8944, 0, 0.1826, -0.4082, 0,
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0000000, 0, 0, -0.9129, -0.4082, 0,
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00.6667, 0, -0.5963, 0, 0, -0.4472,
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};
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Matrix expectedQ = Matrix_(6,6, dataQ);
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double dataR[] = {
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15, 0, -8.3333, 0,
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00, 11.1803, 0, -2.2361,
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00, 0, 7.4536, 0,
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00, 0, 0, 10.9545,
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00, 0, 0, 0,
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00, 0, 0, 0,
|
|
};
|
|
Matrix expectedR = Matrix_(6,4, dataR);
|
|
|
|
Matrix Q,R;
|
|
boost::tie(Q,R) = qr(A);
|
|
CHECK(assert_equal(expectedQ, Q, 1e-4));
|
|
CHECK(assert_equal(expectedR, R, 1e-4));
|
|
CHECK(assert_equal(A, Q*R, 1e-14));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, sub )
|
|
{
|
|
double data1[] = {
|
|
-5, 0, 5, 0, 0, 0,
|
|
00, -5, 0, 5, 0, 0,
|
|
10, 0, 0, 0,-10, 0,
|
|
00, 10, 0, 0, 0,-10
|
|
};
|
|
Matrix A = Matrix_(4,6, data1);
|
|
Matrix actual = sub(A,1,3,1,5);
|
|
|
|
double data2[] = {
|
|
-5, 0, 5, 0,
|
|
00, 0, 0,-10,
|
|
};
|
|
Matrix expected = Matrix_(2,4, data2);
|
|
|
|
EQUALITY(actual,expected);
|
|
}
|
|
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, trans )
|
|
{
|
|
Matrix A = Matrix_(2,2,
|
|
1.0 ,3.0,
|
|
2.0, 4.0 );
|
|
Matrix B = Matrix_(2,2,
|
|
1.0 ,2.0,
|
|
3.0, 4.0 );
|
|
EQUALITY(trans(A),B);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, row_major_access )
|
|
{
|
|
Matrix A = Matrix_(2,2,1.0,2.0,3.0,4.0);
|
|
const double* a = &A(0,0);
|
|
DOUBLES_EQUAL(3,a[2],1e-9);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, svd )
|
|
{
|
|
double data[] = {2,1,0};
|
|
Vector v(3); copy(data,data+3,v.begin());
|
|
Matrix U1=eye(4,3), S1=diag(v), V1=eye(3,3), A=(U1*S1)*Matrix(trans(V1));
|
|
Matrix U,V;
|
|
Vector s;
|
|
svd(A,U,s,V);
|
|
Matrix S=diag(s);
|
|
EQUALITY(U*S*Matrix(trans(V)),A);
|
|
EQUALITY(S,S1);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, weighted_elimination )
|
|
{
|
|
// create a matrix to eliminate
|
|
Matrix A = Matrix_(4, 6,
|
|
-1., 0., 1., 0., 0., 0.,
|
|
0., -1., 0., 1., 0., 0.,
|
|
1., 0., 0., 0., -1., 0.,
|
|
0., 1., 0., 0., 0., -1.);
|
|
Vector b = Vector_(4, -0.2, 0.3, 0.2, -0.1);
|
|
Vector sigmas = Vector_(4, 0.2, 0.2, 0.1, 0.1);
|
|
|
|
// perform elimination
|
|
std::list<boost::tuple<Vector, double, double> > solution =
|
|
weighted_eliminate(A, b, sigmas);
|
|
|
|
// expected values
|
|
Matrix expectedR = Matrix_(4, 6,
|
|
1., 0.,-0.2, 0.,-0.8, 0.,
|
|
0., 1., 0.,-0.2, 0.,-0.8,
|
|
0., 0., 1., 0., -1., 0.,
|
|
0., 0., 0., 1., 0., -1.);
|
|
Vector d = Vector_(4, 0.2, -0.14, 0.0, 0.2);
|
|
Vector newSigmas = Vector_(4,
|
|
0.0894427,
|
|
0.0894427,
|
|
0.223607,
|
|
0.223607);
|
|
|
|
// unpack and verify
|
|
Vector r; double di, sigma;
|
|
size_t i = 0;
|
|
BOOST_FOREACH(boost::tie(r, di, sigma), solution) {
|
|
CHECK(assert_equal(r, row(expectedR, i))); // verify r
|
|
DOUBLES_EQUAL(d(i), di, 1e-8); // verify d
|
|
DOUBLES_EQUAL(newSigmas(i), sigma, 1e-5); // verify sigma
|
|
i += 1;
|
|
}
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
TEST( matrix, inverse_square_root )
|
|
{
|
|
Matrix measurement_covariance = Matrix_(3,3,
|
|
0.25, 0.0, 0.0,
|
|
0.0, 0.25, 0.0,
|
|
0.0, 0.0, 0.01
|
|
);
|
|
Matrix actual = inverse_square_root(measurement_covariance);
|
|
|
|
Matrix square_root_inverse_covariance = Matrix_(3,3,
|
|
-2.0, 0.0, 0.0,
|
|
0.0, -2.0, 0.0,
|
|
0.0, 0.0, -10.0
|
|
);
|
|
|
|
EQUALITY(square_root_inverse_covariance,actual);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
|
|
/* ************************************************************************* */
|