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|
/* -------------------------------------------------------------------------- *
* Simbody(tm): SimTKcommon *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2008-12 Stanford University and the Authors. *
* Authors: Peter Eastman *
* Contributors: Michael Sherman *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may *
* not use this file except in compliance with the License. You may obtain a *
* copy of the License at http://www.apache.org/licenses/LICENSE-2.0. *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* -------------------------------------------------------------------------- */
#include "SimTKcommon.h"
#include "SimTKcommon/Testing.h"
#include <iostream>
using std::cout;
using std::endl;
using namespace SimTK;
using namespace std;
// A matrix operation of size N can be expected to achieve an
// accuracy of about N*tol where tol is the expected accuracy
// of a scalar operation.
template <int N>
void testInverse() {
Mat<N,N> identity(1);
Mat<N,N> mat = Test::randMat<N,N>();
SimTK_TEST_EQ_SIZE(mat*mat.invert(), identity, N);
mat = ~mat;
SimTK_TEST_EQ_SIZE(mat*mat.invert(), identity, N);
SimTK_TEST_EQ_SIZE((-mat)*(-mat).invert(), identity, N);
}
void testDotProducts() {
Vec3 v1(1, 2, 3);
Vec3 v2(-1, -2, -3);
Row3 r1(0.1, 0.2, 0.3);
Row3 r2(-0.1, -0.2, -0.3);
SimTK_TEST_EQ(dot(v1, v2), -14.0);
SimTK_TEST_EQ(dot(r1, r2), -0.14);
SimTK_TEST_EQ(dot(v1, r2), -1.4);
SimTK_TEST_EQ(dot(r1, v2), -1.4);
SimTK_TEST_EQ(r1*v2, -1.4);
SpatialVec sv(Vec3(1, 2, 3), Vec3(4, 5, 6));
SpatialRow sr(Row3(1, 2, 3), Row3(4, 5, 6));
SimTK_TEST_EQ(sr*sv, 91.0);
}
void testCrossProducts() {
const Vec3 w = Test::randVec3();
const Vec3 v = Test::randVec3();
const Vec3 wp = UnitVec3(w).perp() * Test::randReal();
const Vec3 vp = UnitVec3(v).perp() * Test::randReal();
const Mat33 vx = crossMat(v);
const Mat33 wx = crossMat(w);
const Mat33 vpx = crossMat(vp);
const Mat33 wpx = crossMat(wp);
const Mat33 m33 = Test::randMat33();
const Mat34 m = Test::randMat<3,4>();
const Mat43 mt = ~m;
const Mat<3,1> m1 = Test::randMat<3,1>();
SimTK_TEST_EQ( w%v, Vec3(w[1]*v[2]-w[2]*v[1],
w[2]*v[0]-w[0]*v[2],
w[0]*v[1]-w[1]*v[0]) );
SimTK_TEST_EQ( w % v, cross( w, v));
SimTK_TEST_EQ( ~w % ~v, -cross( ~v, ~w));
SimTK_TEST_EQ( wx*v, w % v );
SimTK_TEST_EQ( crossMat(~w), wx );
SimTK_TEST_EQ( crossMat(-w), ~wx );
SimTK_TEST_EQ( crossMatSq(w)*v, -w % (w%v) );
// cross(vector, matrix) (columnwise)
Mat34 c = v % m;
SimTK_TEST_EQ(c(0), v%m(0));
SimTK_TEST_EQ(c(1), v%m(1));
SimTK_TEST_EQ(c(2), v%m(2));
SimTK_TEST_EQ(c(3), v%m(3));
SimTK_TEST_EQ(c, vx*m);
SimTK_TEST_EQ(c, (~v)%m); // row same as col here
Mat<3,1> c1 = v % m1;
SimTK_TEST_EQ(c1(0), v%m1(0));
// cross(matrix, vector) (rowwise)
Mat43 cr = mt % w;
SimTK_TEST_EQ(cr[0], mt[0]%w);
SimTK_TEST_EQ(cr[1], mt[1]%w);
SimTK_TEST_EQ(cr[2], mt[2]%w);
SimTK_TEST_EQ(cr[3], mt[3]%w);
SimTK_TEST_EQ(cr, mt*wx);
SimTK_TEST_EQ(cr, mt % (~w)); // row same as col here
SimTK_TEST_EQ( vx * m33 * vx, v % m33 % v );
}
// Individually test 2x2, 3x3, and 4x4 because the
// smaller sizes may have specialized inline operators.
void testSymMat() {
// 2x2
const Vec3 a = Test::randVec3();
const Vec<2> v = Test::randVec<2>();
SymMat<2> sm( a[0],
a[1], a[2] );
Mat<2,2> m( a[0], a[1],
a[1], a[2] );
SimTK_TEST_EQ( (Mat<2,2>(sm)), m );
SimTK_TEST_EQ( sm, SymMat<2>().setFromSymmetric(m) );
SimTK_TEST_EQ( sm*v, m*v );
SimTK_TEST_EQ( ~v*sm, ~v*m );
// 3x3
const Vec<6> a3 = Test::randVec<6>();
const Vec<3> v3 = Test::randVec<3>();
SymMat<3> sm3( a3[0],
a3[1], a3[2],
a3[3], a3[4], a3[5]);
Mat<3,3> m3( a3[0], a3[1], a3[3],
a3[1], a3[2], a3[4],
a3[3], a3[4], a3[5]);
SimTK_TEST_EQ( (Mat<3,3>(sm3)), m3 );
SimTK_TEST_EQ( sm3, SymMat<3>().setFromSymmetric(m3) );
SimTK_TEST_EQ( sm3*v3, m3*v3 );
SimTK_TEST_EQ( ~v3*sm3, ~v3*m3 );
// 4x4 (hopefully the general case)
const Vec<10> a4 = Test::randVec<10>();
const Vec<4> v4 = Test::randVec<4>();
SymMat<4> sm4( a4[0],
a4[1], a4[2],
a4[3], a4[4], a4[5],
a4[6], a4[7], a4[8], a4[9]);
Mat<4,4> m4( a4[0], a4[1], a4[3], a4[6],
a4[1], a4[2], a4[4], a4[7],
a4[3], a4[4], a4[5], a4[8],
a4[6], a4[7], a4[8], a4[9]);
SimTK_TEST_EQ( (Mat<4,4>(sm4)), m4 );
SimTK_TEST_EQ( sm4, SymMat<4>().setFromSymmetric(m4) );
SimTK_TEST_EQ( sm4*v4, m4*v4 );
SimTK_TEST_EQ( ~v4*sm4, ~v4*m4 );
// Complex is tricky for symmetric (really Hermitian) matrices because
// the diagonals must be real and the corresponding off-diagonals are
// complex conjugate pairs, NOT the same value even though the off
// diagonal data is only stored once.
const Vec<3,Complex> ac( Test::randComplex(), Test::randComplex(), Test::randComplex() );
const Vec<2,Complex> vc( Test::randComplex(), Test::randComplex() );
SymMat<2,Complex> smc( ac[0],
ac[1], ac[2] );
Mat<2,2,Complex> mc( ac[0].real(), std::conj(ac[1]),
ac[1], ac[2].real() );
// This constructor has to figure out how to generate a conjugate
// element for the upper right in the full Mat.
Mat<2,2,Complex> sm2mc(smc);
SimTK_TEST_EQ( sm2mc, mc );
SimTK_TEST_EQ( smc, (SymMat<2,Complex>().setFromSymmetric(mc)) );
SimTK_TEST_EQ( smc*vc, mc*vc );
SimTK_TEST_EQ( ~vc*smc, ~vc*mc );
SimTK_TEST_EQ( ~smc*vc, ~mc*vc );
SimTK_TEST_EQ( ~smc*vc, smc*vc );
}
void testNumericallyEqual() {
Mat<3,4,float> fm1(1), fm1e(1), fm1n(1), fm1nz(1);
fm1e(1,1) += (float)(0.5*fm1.getDefaultTolerance()); // should test equal
fm1n(2,2) += (float)(2 *fm1.getDefaultTolerance()); // should test not equal
fm1nz(1,3) = (float)(2 *fm1.getDefaultTolerance()); // should test not equal
const Mat<3,4,float> fmident34( 1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0 );
SimTK_TEST(fm1==fmident34); // exact
SimTK_TEST(fm1.isNumericallyEqual(fm1));
SimTK_TEST(fm1.isNumericallyEqual(fm1e));
SimTK_TEST(!fm1.isNumericallyEqual(fm1n));
SimTK_TEST(!fm1.isNumericallyEqual(fm1nz));
SimTK_TEST((fm1.getSubMat<3,3>(0,0).isNumericallyEqual(fm1nz.getSubMat<3,3>(0,0))));
SimTK_TEST((fm1e.getSubMat<3,3>(0,0).isNumericallyEqual(fm1nz.getSubMat<3,3>(0,0))));
SimTK_TEST(!(fm1n.getSubMat<3,3>(0,0).isNumericallyEqual(fm1nz.getSubMat<3,3>(0,0))));
// Tightening tolerance should make fm1e not equal.
SimTK_TEST(!fm1.isNumericallyEqual(fm1e, .3*fm1.getDefaultTolerance()));
SimTK_TEST(fm1.isNumericallyEqual(1.f));
SimTK_TEST(fm1e.isNumericallyEqual(1.f));
SimTK_TEST(!fm1n.isNumericallyEqual(1.f));
Mat<3,4,double> dm1(1), dfm1e(fm1e);
// Try mixed-precision.
SimTK_TEST(dm1.isNumericallyEqual(fm1));
SimTK_TEST(dm1.isNumericallyEqual(fm1e)); // because should use float tolerance
SimTK_TEST(!dm1.isNumericallyEqual(dfm1e)); // because should use double tolerance
SimTK_TEST(dm1.isNumericallyEqual(dfm1e, fm1e.getDefaultTolerance())); // force float tolerance
// Repeat for symmetric matrix.
SymMat<3,float> fs1(1), fs1e(1), fs1n(1), fs1nz(1);
fs1e(1,1) += (float)(0.5*fs1.getDefaultTolerance()); // should test equal
fs1n(2,2) += (float)(2 *fs1.getDefaultTolerance()); // should test not equal
fs1nz(2,1) = (float)(2 *fs1.getDefaultTolerance()); // should test not equal
const SymMat<3,float> fsident3( 1,
0, 1,
0, 0, 1 );
SimTK_TEST(fs1==fsident3); // exact
SimTK_TEST(fs1.isNumericallyEqual(fs1));
SimTK_TEST(fs1.isNumericallyEqual(fs1e));
SimTK_TEST(!fs1.isNumericallyEqual(fs1n));
SimTK_TEST(!fs1.isNumericallyEqual(fs1nz));
// Tightening tolerance should make fs1e not equal.
SimTK_TEST(!fs1.isNumericallyEqual(fs1e, .3*fs1.getDefaultTolerance()));
SimTK_TEST(fs1.isNumericallyEqual(1.f));
SimTK_TEST(fs1e.isNumericallyEqual(1.f));
SimTK_TEST(!fs1n.isNumericallyEqual(1.f));
SymMat<3,double> ds1(1), dfs1e(fs1e);
// Try mixed-precision.
SimTK_TEST(ds1.isNumericallyEqual(fs1));
SimTK_TEST(ds1.isNumericallyEqual(fs1e)); // because should use float tolerance
SimTK_TEST(!ds1.isNumericallyEqual(dfs1e)); // because should use double tolerance
SimTK_TEST(ds1.isNumericallyEqual(dfs1e, fs1e.getDefaultTolerance())); // force float tolerance
// Check Vec and Row.
Vec<3,float> fv1(1), fv1e(1), fv1n(1); // should be 1 1 1
Row<3,float> fr1(1);
fv1e[1] += (float)(0.5*fv1.getDefaultTolerance()); // should test equal
fv1n[0] += (float)(2 *fv1.getDefaultTolerance()); // should test not equal
const Vec<3,float> fone(1,1,1);
SimTK_TEST(fv1==fone); // exact
SimTK_TEST(fv1.isNumericallyEqual(fv1));
SimTK_TEST(fv1.isNumericallyEqual(fv1e));
SimTK_TEST(!fv1.isNumericallyEqual(fv1n));
SimTK_TEST(fr1==~fone); // exact
SimTK_TEST(fr1.isNumericallyEqual(~fv1));
SimTK_TEST(fr1.isNumericallyEqual(~fv1e));
SimTK_TEST(!fr1.isNumericallyEqual(~fv1n));
// Check symmetry tests in Mat.
Mat<2,7,double> notSquare(0); // can't be symmetric
SimTK_TEST(!notSquare.isExactlySymmetric());
SimTK_TEST(!notSquare.isNumericallySymmetric());
Mat<3,3,float> f33(1), // exactly symmetric
f33e(1), // numerically symmetric
f33n(1); // too sloppy
f33e(1,2) += (float)(0.5*f33.getDefaultTolerance()); // should test equal
f33n(2,0) += (float)(2 *f33.getDefaultTolerance()); // should test not equal
SimTK_TEST(f33.isExactlySymmetric());
SimTK_TEST(!f33e.isExactlySymmetric());
SimTK_TEST(!f33n.isExactlySymmetric());
SimTK_TEST(f33.isNumericallySymmetric());
SimTK_TEST(f33e.isNumericallySymmetric());
SimTK_TEST(!f33n.isNumericallySymmetric());
// Things are trickier for complex matrices where symmetry means
// Hermitian (conjugate) symmetry.
// This one has *positional* symmetry, not Hermitian.
Mat<2,2, std::complex<double> > mcp( std::complex<double>(1,2), std::complex<double>(3,4),
std::complex<double>(3,4), std::complex<double>(5,6) );
// This one is Hermitian.
Mat<2,2, std::complex<double> > mch( std::complex<double>(1,0), std::complex<double>(3,-4),
std::complex<double>(3,4), std::complex<double>(5,0) );
SimTK_TEST(!mcp.isExactlySymmetric());
SimTK_TEST(!mcp.isNumericallySymmetric());
SimTK_TEST(mch.isExactlySymmetric());
SimTK_TEST(mch.isNumericallySymmetric());
// This should be OK because mch is symmetric.
SymMat<2, std::complex<double> > symTest;
symTest.setFromSymmetric(mch);
mch(0,1) += 0.5*mch.getDefaultTolerance();
SimTK_TEST(!mch.isExactlySymmetric());
SimTK_TEST(mch.isNumericallySymmetric());
// This should be OK because mch is almost symmetric.
symTest.setFromSymmetric(mch);
mch(0,1) += 5*mch.getDefaultTolerance();
SimTK_TEST(!mch.isExactlySymmetric());
SimTK_TEST(!mch.isNumericallySymmetric());
// This should throw in Debug mode because mch is too far off.
#ifndef NDEBUG
SimTK_TEST_MUST_THROW(symTest.setFromSymmetric(mch));
#endif
}
static bool isXAxis(const UnitVec3& test) {return test==UnitVec3(1,0,0);}
static bool isNegZAxis(const UnitVec3& test) {return test==UnitVec3(0,0,-1);}
void testUnitVec() {
SimTK_TEST_EQ(Vec3(UnitVec3(1,1,0)), Vec3(Sqrt2/2,Sqrt2/2,0));
SimTK_TEST(UnitVec3(XAxis) == UnitVec3(1,0,0));
SimTK_TEST(UnitVec3(YAxis) == UnitVec3(0,1,0));
SimTK_TEST(UnitVec3(ZAxis) == UnitVec3(0,0,1));
SimTK_TEST(UnitVec3(NegXAxis) == UnitVec3(-1,0,0));
SimTK_TEST(UnitVec3(NegYAxis) == UnitVec3(0,-1,0));
SimTK_TEST(UnitVec3(NegZAxis) == UnitVec3(0,0,-1));
SimTK_TEST(isXAxis(XAxis)); // implicit conversion
SimTK_TEST(!isXAxis(YAxis)); // implicit conversion
SimTK_TEST(isNegZAxis(NegZAxis)); // implicit conversion
SimTK_TEST(!isNegZAxis(NegYAxis)); // implicit conversion
SimTK_TEST(!isNegZAxis(ZAxis)); // implicit conversion
SimTK_TEST(XAxis.dotProduct(XAxis) == 1);
SimTK_TEST(XAxis.dotProduct(YAxis) == 0);
SimTK_TEST(XAxis.dotProduct(ZAxis) == 0);
SimTK_TEST(ZAxis.dotProduct(YAxis) == 0);
SimTK_TEST(XAxis.crossProductSign(XAxis) == 0);
SimTK_TEST(XAxis.crossProductAxis(YAxis) == ZAxis);
SimTK_TEST(XAxis.crossProductSign(YAxis) == 1);
SimTK_TEST(XAxis.crossProductAxis(ZAxis) == YAxis);
SimTK_TEST(XAxis.crossProductSign(ZAxis) == -1);
SimTK_TEST(ZAxis.crossProductAxis(XAxis) == YAxis);
SimTK_TEST(ZAxis.crossProductSign(XAxis) == 1);
int sign;
CoordinateAxis axis = ZAxis.crossProduct(YAxis, sign);
SimTK_TEST(CoordinateDirection(axis,sign) == NegXAxis);
SimTK_TEST(CoordinateDirection(YAxis,CoordinateDirection::Negative())
== NegYAxis);
SimTK_TEST(-XAxis == NegXAxis);
SimTK_TEST(-YAxis == NegYAxis);
SimTK_TEST(-ZAxis == NegZAxis);
SimTK_TEST(-ZAxis != NegYAxis);
SimTK_TEST(ZAxis == -NegZAxis);
SimTK_TEST(-(-NegXAxis) == -XAxis);
SimTK_TEST(-(-NegYAxis) == -(-(-YAxis)));
SimTK_TEST(NegXAxis.crossProductAxis(NegYAxis) == ZAxis);
SimTK_TEST(NegYAxis.crossProductAxis(ZAxis) == XAxis);
SimTK_TEST(NegYAxis.crossProductSign(ZAxis) == -1);
SimTK_TEST(NegYAxis.crossProductSign(NegZAxis) == 1);
}
// Test append/drop/insert rows and columns.
void testAppendRowCol() {
Mat34 m34( 1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12);
Mat44 m44 = m34.appendRow(Row4(-1, -2, -3, -4));
SimTK_TEST(m44==Mat44( 1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
-1, -2, -3, -4));
m44 = m34.insertRow(0, Row4(-1, -2, -3, -4));
SimTK_TEST(m44==Mat44( -1, -2, -3, -4,
1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12));
m44 = m34.insertRow(1, Row4(-1, -2, -3, -4));
SimTK_TEST(m44==Mat44( 1, 2, 3, 4,
-1, -2, -3, -4,
5, 6, 7, 8,
9, 10, 11, 12));
m44 = m34.insertRow(3, Row4(-1, -2, -3, -4));
SimTK_TEST(m44==m34.appendRow(Row4(-1, -2, -3, -4)));
Mat35 m35 = m34.appendCol(Vec3(-6, -7, -8));
SimTK_TEST(m35==Mat35( 1, 2, 3, 4, -6,
5, 6, 7, 8, -7,
9, 10, 11, 12, -8));
m35 = m34.insertCol(0, Vec3(-6, -7, -8));
SimTK_TEST(m35==Mat35( -6, 1, 2, 3, 4,
-7, 5, 6, 7, 8,
-8, 9, 10, 11, 12));
m35 = m34.insertCol(2, Vec3(-6, -7, -8));
SimTK_TEST(m35==Mat35( 1, 2, -6, 3, 4,
5, 6, -7, 7, 8,
9, 10, -8, 11, 12));
m35 = m34.insertCol(4, Vec3(-6, -7, -8));
SimTK_TEST(m35==m34.appendCol(Vec3(-6, -7, -8)));
Mat45 m45 = m34.appendRowCol(Row5(-1, -2, -3, -4, -5),
Vec4(-6, -7, -8, -9));
SimTK_TEST(m45==Mat45( Row5(1, 2, 3, 4, -6),
Row5(5, 6, 7, 8, -7),
Row5(9, 10, 11, 12, -8),
Row5(-1, -2, -3, -4, -9)));
m45 = m34.insertRowCol(0,0, Row5(-1, -2, -3, -4, -5),
Vec4(-6, -7, -8, -9));
SimTK_TEST(m45==Mat45( Row5(-6, -2, -3, -4, -5),
Row5(-7, 1, 2, 3, 4),
Row5(-8, 5, 6, 7, 8),
Row5(-9, 9, 10, 11, 12)));
m45 = m34.insertRowCol(1,2, Row5(-1, -2, -3, -4, -5),
Vec4(-6, -7, -8, -9));
SimTK_TEST(m45==Mat45( Row5( 1, 2, -6, 3, 4),
Row5(-1, -2, -7, -4, -5),
Row5( 5, 6, -8, 7, 8),
Row5( 9, 10, -9, 11, 12)));
m45 = m34.insertRowCol(3,4, Row5(-1, -2, -3, -4, -5),
Vec4(-6, -7, -8, -9));
SimTK_TEST(m45== m34.appendRowCol(Row5(-1, -2, -3, -4, -5),
Vec4(-6, -7, -8, -9)));
Mat24 m24_0 = m34.dropRow(0);
Mat24 m24_1 = m34.dropRow(1);
Mat24 m24_2 = m34.dropRow(2);
SimTK_TEST(m24_0==Mat24(5, 6, 7, 8,
9, 10, 11, 12));
SimTK_TEST(m24_1==Mat24(1, 2, 3, 4,
9, 10, 11, 12));
SimTK_TEST(m24_2==Mat24(1, 2, 3, 4,
5, 6, 7, 8));
Mat33 m33_0 = m34.dropCol(0);
Mat33 m33_1 = m34.dropCol(1);
Mat33 m33_2 = m34.dropCol(2);
Mat33 m33_3 = m34.dropCol(3);
SimTK_TEST(m33_0==Mat33( 2, 3, 4,
6, 7, 8,
10, 11, 12));
SimTK_TEST(m33_1==Mat33( 1, 3, 4,
5, 7, 8,
9, 11, 12));
SimTK_TEST(m33_2==Mat33( 1, 2, 4,
5, 6, 8,
9, 10, 12));
SimTK_TEST(m33_3==Mat33( 1, 2, 3,
5, 6, 7,
9, 10, 11));
}
int main() {
SimTK_START_TEST("TestSmallMatrix");
SimTK_SUBTEST(testSymMat);
SimTK_SUBTEST(testInverse<1>);
SimTK_SUBTEST(testInverse<2>);
SimTK_SUBTEST(testInverse<3>);
SimTK_SUBTEST(testInverse<5>);
SimTK_SUBTEST(testInverse<10>);
SimTK_SUBTEST(testDotProducts);
SimTK_SUBTEST(testCrossProducts);
SimTK_SUBTEST(testNumericallyEqual);
SimTK_SUBTEST(testUnitVec);
SimTK_SUBTEST(testAppendRowCol);
SimTK_END_TEST();
}
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