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/**
* @file testMatrix.cpp
* @brief Unit test for Matrix Library
* @author Christian Potthast
* @author Carlos Nieto
**/
#include <iostream>
#include <CppUnitLite/TestHarness.h>
#include <boost/tuple/tuple.hpp>
#include <boost/foreach.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include "Matrix.h"
#include "NoiseModel.h"
using namespace std;
using namespace gtsam;
static double inf = std::numeric_limits<double>::infinity();
/* ************************************************************************* */
TEST( matrix, constructor_data )
{
double data[] = {-5, 3,
0, -5 };
Matrix A = Matrix_(2,2,data);
Matrix B(2,2);
B(0,0) = -5 ; B(0,1) = 3;
B(1,0) = 0 ; B(1,1) = -5;
EQUALITY(A,B);
}
/* ************************************************************************* */
TEST( matrix, constructor_vector )
{
double data[] = {-5, 3,
0, -5 };
Matrix A = Matrix_(2,2,data);
Vector v(4); copy(data,data+4,v.begin());
Matrix B = Matrix_(2,2,v); // this one is column order !
EQUALITY(A,trans(B));
}
/* ************************************************************************* */
TEST( matrix, Matrix_ )
{
Matrix A = Matrix_(2,2,
-5.0 , 3.0,
00.0, -5.0 );
Matrix B(2,2);
B(0,0) = -5 ; B(0,1) = 3;
B(1,0) = 0 ; B(1,1) = -5;
EQUALITY(A,B);
}
/* ************************************************************************* */
TEST( matrix, row_major )
{
Matrix A = Matrix_(2,2,
1.0, 2.0,
3.0, 4.0 );
const double * const a = &A(0,0);
CHECK(a[0] == 1);
CHECK(a[1] == 2);
CHECK(a[2] == 3);
CHECK(a[3] == 4);
}
/* ************************************************************************* */
TEST( matrix, collect1 )
{
Matrix A = Matrix_(2,2,
-5.0 , 3.0,
00.0, -5.0 );
Matrix B = Matrix_(2,3,
-0.5 , 2.1, 1.1,
3.4 , 2.6 , 7.1);
Matrix AB = collect(2, &A, &B);
Matrix C(2,5);
for(int i = 0; i < 2; i++) for(int j = 0; j < 2; j++) C(i,j) = A(i,j);
for(int i = 0; i < 2; i++) for(int j = 0; j < 3; j++) C(i,j+2) = B(i,j);
EQUALITY(C,AB);
}
/* ************************************************************************* */
TEST( matrix, collect2 )
{
Matrix A = Matrix_(2,2,
-5.0 , 3.0,
00.0, -5.0 );
Matrix B = Matrix_(2,3,
-0.5 , 2.1, 1.1,
3.4 , 2.6 , 7.1);
vector<const Matrix*> matrices;
matrices.push_back(&A);
matrices.push_back(&B);
Matrix AB = collect(matrices);
Matrix C(2,5);
for(int i = 0; i < 2; i++) for(int j = 0; j < 2; j++) C(i,j) = A(i,j);
for(int i = 0; i < 2; i++) for(int j = 0; j < 3; j++) C(i,j+2) = B(i,j);
EQUALITY(C,AB);
}
/* ************************************************************************* */
TEST( matrix, collect3 )
{
Matrix A, B;
A = eye(2,3);
B = eye(2,3);
vector<const Matrix*> matrices;
matrices.push_back(&A);
matrices.push_back(&B);
Matrix AB = collect(matrices, 2, 3);
Matrix exp = Matrix_(2, 6,
1.0, 0.0, 0.0, 1.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0, 1.0, 0.0);
EQUALITY(exp,AB);
}
/* ************************************************************************* */
TEST( matrix, stack )
{
Matrix A = Matrix_(2,2,
-5.0 , 3.0,
00.0, -5.0 );
Matrix B = Matrix_(3,2,
-0.5 , 2.1,
1.1, 3.4 ,
2.6 , 7.1);
Matrix AB = stack(2, &A, &B);
Matrix C(5,2);
for(int i = 0; i < 2; i++) for(int j = 0; j < 2; j++) C(i,j) = A(i,j);
for(int i = 0; i < 3; i++) for(int j = 0; j < 2; j++) C(i+2,j) = B(i,j);
EQUALITY(C,AB);
}
/* ************************************************************************* */
TEST( matrix, column )
{
Matrix A = Matrix_(4, 7,
-1., 0., 1., 0., 0., 0., -0.2,
0., -1., 0., 1., 0., 0., 0.3,
1., 0., 0., 0., -1., 0., 0.2,
0., 1., 0., 0., 0., -1., -0.1);
Vector a1 = column_(A, 0);
Vector exp1 = Vector_(4, -1., 0., 1., 0.);
CHECK(assert_equal(a1, exp1));
Vector a2 = column_(A, 3);
Vector exp2 = Vector_(4, 0., 1., 0., 0.);
CHECK(assert_equal(a2, exp2));
Vector a3 = column_(A, 6);
Vector exp3 = Vector_(4, -0.2, 0.3, 0.2, -0.1);
CHECK(assert_equal(a3, exp3));
}
/* ************************************************************************* */
TEST( matrix, row )
{
Matrix A = Matrix_(4, 7,
-1., 0., 1., 0., 0., 0., -0.2,
0., -1., 0., 1., 0., 0., 0.3,
1., 0., 0., 0., -1., 0., 0.2,
0., 1., 0., 0., 0., -1., -0.1);
Vector a1 = row_(A, 0);
Vector exp1 = Vector_(7, -1., 0., 1., 0., 0., 0., -0.2);
CHECK(assert_equal(a1, exp1));
Vector a2 = row_(A, 2);
Vector exp2 = Vector_(7, 1., 0., 0., 0., -1., 0., 0.2);
CHECK(assert_equal(a2, exp2));
Vector a3 = row_(A, 3);
Vector exp3 = Vector_(7, 0., 1., 0., 0., 0., -1., -0.1);
CHECK(assert_equal(a3, exp3));
}
/* ************************************************************************* */
TEST( matrix, zeros )
{
Matrix A(2,3);
A(0,0) = 0 ; A(0,1) = 0; A(0,2) = 0;
A(1,0) = 0 ; A(1,1) = 0; A(1,2) = 0;
Matrix zero = zeros(2,3);
EQUALITY(A , zero);
}
/* ************************************************************************* */
TEST( matrix, scale_columns )
{
Matrix A(3,4);
A(0,0) = 1.; A(0,1) = 1.; A(0,2)= 1.; A(0,3)= 1.;
A(1,0) = 1.; A(1,1) = 1.; A(1,2)= 1.; A(1,3)= 1.;
A(2,0) = 1.; A(2,1) = 1.; A(2,2)= 1.; A(2,3)= 1.;
Vector v = Vector_(4, 2., 3., 4., 5.);
Matrix actual = vector_scale(A,v);
Matrix expected(3,4);
expected(0,0) = 2.; expected(0,1) = 3.; expected(0,2)= 4.; expected(0,3)= 5.;
expected(1,0) = 2.; expected(1,1) = 3.; expected(1,2)= 4.; expected(1,3)= 5.;
expected(2,0) = 2.; expected(2,1) = 3.; expected(2,2)= 4.; expected(2,3)= 5.;
CHECK(assert_equal(actual, expected));
}
/* ************************************************************************* */
TEST( matrix, scale_rows )
{
Matrix A(3,4);
A(0,0) = 1.; A(0,1) = 1.; A(0,2)= 1.; A(0,3)= 1.;
A(1,0) = 1.; A(1,1) = 1.; A(1,2)= 1.; A(1,3)= 1.;
A(2,0) = 1.; A(2,1) = 1.; A(2,2)= 1.; A(2,3)= 1.;
Vector v = Vector_(3, 2., 3., 4.);
Matrix actual = vector_scale(v,A);
Matrix expected(3,4);
expected(0,0) = 2.; expected(0,1) = 2.; expected(0,2)= 2.; expected(0,3)= 2.;
expected(1,0) = 3.; expected(1,1) = 3.; expected(1,2)= 3.; expected(1,3)= 3.;
expected(2,0) = 4.; expected(2,1) = 4.; expected(2,2)= 4.; expected(2,3)= 4.;
CHECK(assert_equal(actual, expected));
}
/* ************************************************************************* */
TEST( matrix, equal )
{
Matrix A(4,4);
A(0,0) = -1; A(0,1) = 1; A(0,2)= 2; A(0,3)= 3;
A(1,0) = 1; A(1,1) =-3; A(1,2)= 1; A(1,3)= 3;
A(2,0) = 1; A(2,1) = 2; A(2,2)=-1; A(2,3)= 4;
A(3,0) = 2; A(3,1) = 1; A(3,2)= 2; A(3,3)=-2;
Matrix A2(A);
Matrix A3(A);
A3(3,3)=-2.1;
CHECK(A==A2);
CHECK(A!=A3);
}
/* ************************************************************************* */
TEST( matrix, equal_nan )
{
Matrix A(4,4);
A(0,0) = -1; A(0,1) = 1; A(0,2)= 2; A(0,3)= 3;
A(1,0) = 1; A(1,1) =-3; A(1,2)= 1; A(1,3)= 3;
A(2,0) = 1; A(2,1) = 2; A(2,2)=-1; A(2,3)= 4;
A(3,0) = 2; A(3,1) = 1; A(3,2)= 2; A(3,3)=-2;
Matrix A2(A);
Matrix A3(A);
A3(3,3)=inf;
CHECK(A!=A3);
}
/* ************************************************************************* */
TEST( matrix, addition )
{
Matrix A = Matrix_(2,2,
1.0, 2.0,
3.0, 4.0);
Matrix B = Matrix_(2,2,
4.0, 3.0,
2.0, 1.0);
Matrix C = Matrix_(2,2,
5.0, 5.0,
5.0, 5.0);
EQUALITY(A+B,C);
}
/* ************************************************************************* */
TEST( matrix, addition_in_place )
{
Matrix A = Matrix_(2,2,
1.0, 2.0,
3.0, 4.0);
Matrix B = Matrix_(2,2,
4.0, 3.0,
2.0, 1.0);
Matrix C = Matrix_(2,2,
5.0, 5.0,
5.0, 5.0);
A += B;
EQUALITY(A,C);
}
/* ************************************************************************* */
TEST( matrix, subtraction )
{
Matrix A = Matrix_(2,2,
1.0, 2.0,
3.0, 4.0);
Matrix B = Matrix_(2,2,
4.0, 3.0,
2.0, 1.0);
Matrix C = Matrix_(2,2,
-3.0, -1.0,
1.0, 3.0);
EQUALITY(A-B,C);
}
/* ************************************************************************* */
TEST( matrix, subtraction_in_place )
{
Matrix A = Matrix_(2,2,
1.0, 2.0,
3.0, 4.0);
Matrix B = Matrix_(2,2,
4.0, 3.0,
2.0, 1.0);
Matrix C = Matrix_(2,2,
-3.0, -1.0,
1.0, 3.0);
A -= B;
EQUALITY(A,C);
}
/* ************************************************************************* */
TEST( matrix, multiplication )
{
Matrix A(2,2);
A(0,0) = -1; A(1,0) = 1;
A(0,1) = 1; A(1,1) =-3;
Matrix B(2,1);
B(0,0) = 1.2;
B(1,0) = 3.4;
Matrix AB(2,1);
AB(0,0) = 2.2;
AB(1,0) = -9.;
EQUALITY(A*B,AB);
}
/* ************************************************************************* */
TEST( matrix, scalar_matrix_multiplication )
{
Vector result(2);
Matrix A(2,2);
A(0,0) = -1; A(1,0) = 1;
A(0,1) = 1; A(1,1) =-3;
Matrix B(2,2);
B(0,0) = -10; B(1,0) = 10;
B(0,1) = 10; B(1,1) =-30;
EQUALITY((10*A),B);
}
/* ************************************************************************* */
TEST( matrix, matrix_vector_multiplication )
{
Vector result(2);
Matrix A = Matrix_(2,3,
1.0,2.0,3.0,
4.0,5.0,6.0
);
Vector v = Vector_(3,1.,2.,3.);
Vector Av = Vector_(2,14.,32.);
Vector AtAv = Vector_(3,142.,188.,234.);
EQUALITY(A*v,Av);
EQUALITY(A^Av,AtAv);
}
/* ************************************************************************* */
TEST( matrix, nrRowsAndnrCols )
{
Matrix A(3,6);
LONGS_EQUAL( A.size1() , 3 );
LONGS_EQUAL( A.size2() , 6 );
}
/* ************************************************************************* */
TEST( matrix, scalar_divide )
{
Matrix A(2,2);
A(0,0) = 10; A(1,0) = 30;
A(0,1) = 20; A(1,1) = 40;
Matrix B(2,2);
B(0,0) = 1; B(1,0) = 3;
B(0,1) = 2; B(1,1) = 4;
EQUALITY(B,A/10);
}
/* ************************************************************************* */
TEST( matrix, inverse )
{
Matrix A(3,3);
A(0,0)= 1; A(0,1)=2; A(0,2)=3;
A(1,0)= 0; A(1,1)=4; A(1,2)=5;
A(2,0)= 1; A(2,1)=0; A(2,2)=6;
Matrix Ainv = inverse(A);
Matrix expected(3,3);
expected(0,0)= 1.0909; expected(0,1)=-0.5454; expected(0,2)=-0.0909;
expected(1,0)= 0.2272; expected(1,1)= 0.1363; expected(1,2)=-0.2272;
expected(2,0)= -0.1818; expected(2,1)= 0.0909; expected(2,2)=0.1818;
CHECK(assert_equal(expected, Ainv, 1e-4));
}
/* ************************************************************************* */
TEST( matrix, backsubtitution )
{
// TEST ONE 2x2 matrix U1*x=b1
Vector expected1 = Vector_(2, 3.6250, -0.75);
Matrix U22 = Matrix_(2, 2,
2., 3.,
0., 4.);
Vector b1 = U22*expected1;
CHECK( assert_equal(expected1 , backSubstituteUpper(U22, b1), 0.000001));
// TEST TWO 3x3 matrix U2*x=b2
Vector expected2 = Vector_(3, 5.5, -8.5, 5.);
Matrix U33 = Matrix_(3, 3,
3., 5., 6.,
0., 2., 3.,
0., 0., 1.);
Vector b2 = U33*expected2;
CHECK( assert_equal(expected2 , backSubstituteUpper(U33, b2), 0.000001));
// TEST THREE Lower triangular 3x3 matrix L3*x=b3
Vector expected3 = Vector_(3, 1., 1., 1.);
Matrix L3 = trans(U33);
Vector b3 = L3*expected3;
CHECK( assert_equal(expected3 , backSubstituteLower(L3, b3), 0.000001));
// TEST FOUR Try the above with transpose backSubstituteUpper
CHECK( assert_equal(expected3 , backSubstituteUpper(b3,U33), 0.000001));
}
/* ************************************************************************* */
// unit tests for housholder transformation
/* ************************************************************************* */
TEST( matrix, houseHolder )
{
double data[] = {-5, 0, 5, 0, 0, 0, -1,
00, -5, 0, 5, 0, 0, 1.5,
10, 0, 0, 0,-10, 0, 2,
00, 10, 0, 0, 0,-10, -1};
// check in-place householder, with v vectors below diagonal
double data1[] = {
11.1803, 0, -2.2361, 0, -8.9443, 0, 2.236,
0, 11.1803, 0, -2.2361, 0, -8.9443, -1.565,
-0.618034, 0, 4.4721, 0, -4.4721, 0, 0,
0, -0.618034, 0, 4.4721, 0, -4.4721, 0.894 };
Matrix expected1 = Matrix_(4,7, data1);
Matrix A1 = Matrix_(4, 7, data);
householder_(A1,3);
CHECK(assert_equal(expected1, A1, 1e-3));
// in-place, with zeros below diagonal
double data2[] = {
11.1803, 0, -2.2361, 0, -8.9443, 0, 2.236,
0, 11.1803, 0, -2.2361, 0, -8.9443, -1.565,
0, 0, 4.4721, 0, -4.4721, 0, 0,
0, 0, 0, 4.4721, 0, -4.4721, 0.894 };
Matrix expected = Matrix_(4,7, data2);
Matrix A2 = Matrix_(4, 7, data);
householder(A2,3);
CHECK(assert_equal(expected, A2, 1e-3));
}
/* ************************************************************************* */
// unit test for qr factorization (and hence householder)
// This behaves the same as QR in matlab: [Q,R] = qr(A), except for signs
/* ************************************************************************* */
TEST( matrix, qr )
{
double data[] = {-5, 0, 5, 0,
00, -5, 0, 5,
10, 0, 0, 0,
00, 10, 0, 0,
00, 0, 0,-10,
10, 0,-10, 0};
Matrix A = Matrix_(6, 4, data);
double dataQ[] = {
-0.3333, 0, 0.2981, 0, 0, -0.8944,
0000000, -0.4472, 0, 0.3651, -0.8165, 0,
00.6667, 0, 0.7454, 0, 0, 0,
0000000, 0.8944, 0, 0.1826, -0.4082, 0,
0000000, 0, 0, -0.9129, -0.4082, 0,
00.6667, 0, -0.5963, 0, 0, -0.4472,
};
Matrix expectedQ = Matrix_(6,6, dataQ);
double dataR[] = {
15, 0, -8.3333, 0,
00, 11.1803, 0, -2.2361,
00, 0, 7.4536, 0,
00, 0, 0, 10.9545,
00, 0, 0, 0,
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);
}
/* ************************************************************************* */
// update A, b
// A' \define A_{S}-ar and b'\define b-ad
// __attribute__ ((noinline)) // uncomment to prevent inlining when profiling
static void updateAb(Matrix& A, Vector& b, int j, const Vector& a,
const Vector& r, double d) {
const size_t m = A.size1(), n = A.size2();
for (int i = 0; i < m; i++) { // update all rows
double ai = a(i);
b(i) -= ai * d;
double *Aij = A.data().begin() + i * n + j + 1;
const double *rptr = r.data().begin() + j + 1;
// A(i,j+1:end) -= ai*r(j+1:end)
for (int j2 = j + 1; j2 < n; j2++, Aij++, rptr++)
*Aij -= ai * (*rptr);
}
}
/* ************************************************************************* */
list<boost::tuple<Vector, double, double> >
weighted_eliminate2(Matrix& A, Vector& b, const sharedGaussian& model) {
size_t m = A.size1(), n = A.size2(); // get size(A)
size_t maxRank = min(m,n);
// pre-whiten everything
model->WhitenInPlace(A);
b = model->whiten(b);
// create list
list<boost::tuple<Vector, double, double> > results;
// We loop over all columns, because the columns that can be eliminated
// are not necessarily contiguous. For each one, estimate the corresponding
// scalar variable x as d-rS, with S the separator (remaining columns).
// Then update A and b by substituting x with d-rS, zero-ing out x's column.
for (int j=0; j<n; ++j) {
// extract the first column of A
Vector a(column(A, j)); // ublas::matrix_column is slower !
// Calculate weighted pseudo-inverse and corresponding precision
double precision = dot(a,a);
Vector pseudo = a/precision;
// if precision is zero, no information on this column
if (precision < 1e-8) continue;
// create solution and copy into r
Vector r(basis(n, j));
for (int j2=j+1; j2<n; ++j2) // expensive !!
r(j2) = inner_prod(pseudo, boost::numeric::ublas::matrix_column<Matrix>(A, j2));
// create the rhs
double d = inner_prod(pseudo, b);
// construct solution (r, d, sigma)
// TODO: avoid sqrt, store precision or at least variance
results.push_back(boost::make_tuple(r, d, 1./sqrt(precision)));
// exit after rank exhausted
if (results.size()>=maxRank) break;
// update A, b, expensive, suing outer product
// A' \define A_{S}-a*r and b'\define b-d*a
updateAb(A, b, j, a, r, d);
}
return results;
}
/* ************************************************************************* */
void weighted_eliminate3(Matrix& A, Vector& b, const sharedGaussian& model) {
size_t m = A.size1(), n = A.size2(); // get size(A)
size_t maxRank = min(m,n);
// pre-whiten everything
model->WhitenInPlace(A);
b = model->whiten(b);
householder_(A, maxRank);
}
/* ************************************************************************* */
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);
// 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);
Vector r; double di, sigma;
size_t i;
// perform elimination
Matrix A1 = A; Vector b1 = b;
std::list<boost::tuple<Vector, double, double> > solution =
weighted_eliminate(A1, b1, sigmas);
// unpack and verify
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;
}
// perform elimination with NoiseModel
Matrix A2 = A; Vector b2 = b;
sharedGaussian model = noiseModel::Diagonal::Sigmas(sigmas);
std::list<boost::tuple<Vector, double, double> > solution2 =
weighted_eliminate2(A2, b2, model);
// unpack and verify
i=0;
BOOST_FOREACH(boost::tie(r, di, sigma), solution2) {
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;
}
// perform elimination with NoiseModel
weighted_eliminate3(A, b, model);
sharedGaussian newModel = noiseModel::Diagonal::Sigmas(newSigmas);
// print(A);
// print(newModel->Whiten(expectedR));
}
/* ************************************************************************* */
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 expected = Matrix_(3,3,
2.0, 0.0, 0.0,
0.0, 2.0, 0.0,
0.0, 0.0, 10.0
);
EQUALITY(expected,actual);
EQUALITY(measurement_covariance,inverse(actual*actual));
}
/* ************************************************************************* */
TEST( matrix, square_root_positive )
{
Matrix cov = Matrix_(3,3,
4.0, 0.0, 0.0,
0.0, 4.0, 0.0,
0.0, 0.0, 100.0
);
Matrix expected = Matrix_(3,3,
2.0, 0.0, 0.0,
0.0, 2.0, 0.0,
0.0, 0.0, 10.0
);
Matrix actual = square_root_positive(cov);
CHECK(assert_equal(expected, actual));
CHECK(assert_equal(cov, prod(trans(actual),actual)));
}
/* ************************************************************************* */
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
/* ************************************************************************* */
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