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CPPQRTest.cpp
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CPPQRTest.cpp
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#include <stdio.h>
#include <stdlib.h>
#include <float.h>
#include <math.h>
#define USE_LOCAL_HEADERS
#ifndef USE_LOCAL_HEADERS
#include <cqrlib.h>
#else
#include "cqrlib.h"
#endif
int errorcount = 0;
int main ( )
{
CPPQR<double> q1, q4, qx, qy, qz;
double normsq;
double PI;
double vx[3] = {1.,0.,0.};
double vy[3] = {0.,1.,0.};
double vz[3] = {0.,0.,1.};
double EXX,EXY,EXZ;
double EYX,EYY,EYZ;
double EZX,EZY,EZZ;
PI = 4.*atan2(1.,1.);
errorcount=0;
if (q1.GetW() !=0. || q1.GetX( ) !=0. || q1.GetY( ) !=0. || q1.GetZ( ) !=0.) {
errorcount++;
fprintf(stdout," CPPQRCreateEmptyQuaternion for q1 non-zero [ %g, %g, %g, %g ]\n",q1.GetW(),q1.GetX(),q1.GetY( ),q1.GetZ());
}
CPPQR<double> q2(1.,2.,3.,4.);
if (q2.GetW() !=1. || q2.GetX() !=2. || q2.GetY() !=3. || q2.GetZ() !=4.) {
errorcount++;
fprintf(stdout," CPPQRCreateQuaternion for q2 wrong value [ %g, %g, %g, %g ] != [1.,2,3.,4.]\n",q2.GetW(),q2.GetX(),q2.GetY(),q2.GetZ());
}
CPPQR<double> q3;
q3 = q1 + q2;
if (q3.GetW() !=1. || q3.GetX() !=2. || q3.GetY() !=3. || q3.GetZ() !=4.) {
fprintf(stdout," CPPQRAdd(q3,q1,q2) q3 wrong value [ %g, %g, %g, %g ] != [1.,2.,3.,4.]\n",q3.GetW(),q3.GetX(),q3.GetY(),q3.GetZ());
}
q1.Set( -9999.,-9998.,-9997.,-9996.);
if (q1.GetW() !=-9999. || q1.GetX() !=-9998. || q1.GetY() !=-9997. || q1.GetZ() !=-9996.) {
errorcount++;
fprintf(stdout," CPPQRSetQuaternion q1 wrong value [ %g, %g, %g, %g ] != [-9999.,-9998.,-9997.,-9996.]\n",q1.GetW(),q1.GetX(),q1.GetY(),q1.GetZ());
}
q1 = q3 - q2;
if (q1.GetW() !=0. || q1.GetX() !=0. || q1.GetY() !=0. || q1.GetZ() !=0.) {
errorcount++;
fprintf(stdout," CPPQR Subtract(q1,q3,q2) for q1 non-zero [ %g, %g, %g, %g ]\n",q1.GetW(),q1.GetX(),q1.GetY(),q1.GetZ());
}
q4.Set(1.,-2.,-3.,-4.);
if (q4.GetW() != 1. || q4.GetX() !=-2. || q4.GetY() !=-3. || q4.GetZ() !=-4.) {
errorcount++;
fprintf(stdout," CPPQRSetQuaternion &q4 wrong value [ %g, %g, %g, %g ] != [1.,-2.,-3.,-4.]\n",q4.GetW(),q4.GetX(),q4.GetY(),q4.GetZ());
}
q1 = q4 * q2;
if (fabs(q1.GetW()-30.)>300.*DBL_EPSILON || fabs(q1.GetX())>300.*DBL_EPSILON || fabs(q1.GetY())>300.*DBL_EPSILON ||fabs(q1.GetZ())>300.*DBL_EPSILON ) {
errorcount++;
fprintf(stdout," CPPQRMultiply(q1,&q4,q2) q1 wrong value [ %g, %g, %g, %g ] != [30.,0.,0.,0.]\n",q1.GetW(),q1.GetX(),q1.GetY(),q1.GetZ());
}
q3 = q1 / q2;
if (fabs(q3.GetW()-1.)>60.*DBL_EPSILON || fabs(q3.GetX()+2.)>60.*DBL_EPSILON || fabs(q3.GetY()+3.)>60.*DBL_EPSILON ||fabs(q3.GetZ()+4.)>60.*DBL_EPSILON ) {
errorcount++;
fprintf(stdout," CPPQRDivide(q3,q1,q2) q3 wrong value [ %g, %g, %g, %g ] != [1.,-2.,-3.,-4.]\n",q3.GetW(),q3.GetX(),q3.GetY(),q3.GetZ());
}
q3 = q2 * 3.0;
if (fabs(q3.GetW()-3.)>180.*DBL_EPSILON || fabs(q3.GetX()-6.)>180.*DBL_EPSILON || fabs(q3.GetY()-9.)>180.*DBL_EPSILON ||fabs(q3.GetZ()-12.)>180.*DBL_EPSILON ) {
errorcount++;
fprintf(stdout," CPPQRScalarMultiply(q3,q2,3.) q3 wrong value [ %g, %g, %g, %g ] != [3.,6.,9.,12.]\n",q3.GetW(),q3.GetX(),q3.GetY(),q3.GetZ());
}
q3 = q2.Conjugate( );
if (q3.GetW() != 1. || q3.GetX() !=-2. || q3.GetY() !=-3. || q3.GetZ() !=-4.) {
errorcount++;
fprintf(stdout," CPPQRConjugate(q3,q2) q3 wrong value [ %g, %g, %g, %g ] != [1.,-2.,-3.,-4.]\n",q3.GetW(),q3.GetX(),q3.GetY(),q3.GetZ());
}
if ( q4 != q3) {
errorcount++;
fprintf(stdout," CPPQREqual(&q4,q2) failed\n");
}
normsq = q4.Normsq();
if ( fabs(normsq-30.) > 300.*DBL_EPSILON) {
errorcount++;
fprintf(stdout," CPPQRNormsq(&normsq,&q4) failed normsq=%g != 30\n", normsq);
}
q3 = q4.Inverse( );
if (fabs(q3.GetW() - 1./30.) > 2.*DBL_EPSILON || fabs(q3.GetX() - 2./30.) > 2.*DBL_EPSILON || fabs(q3.GetY() - 3./30.) > 2.*DBL_EPSILON || fabs(q3.GetZ() - 4./30.) > 2.*DBL_EPSILON) {
errorcount++;
fprintf(stdout," CPPQRInverse(q3,&q4) q3 wrong value [ %g, %g, %g, %g ] != [1./30.,2./30.,3./30,4./30.]\n",q3.GetW(),q3.GetX(),q3.GetY(),q3.GetZ());
}
/* Create quaternions to rotate about the x,y and z-axes by 90 degrees */
qx = CPPQR<double>::Axis2Quaternion( vx, PI/2.0 );
qy = CPPQR<double>::Axis2Quaternion( vy, PI/2.0 );
qz = CPPQR<double>::Axis2Quaternion( vz, PI/2.0 );
if (qx.GetW()<0.||fabs(qx.GetW()*qx.GetW()-.5)>10.*DBL_EPSILON||fabs(qx.GetX()*qx.GetX()-.5)>10.*DBL_EPSILON||fabs(qx.GetY())>10.*DBL_EPSILON||fabs(qx.GetZ())>10.*DBL_EPSILON) {
errorcount++;
fprintf(stdout,"Axis2Quaternion qx wrong value [ %g, %g, %g, %g ] != [sqrt(1./2.),sqrt(1./2.),0,0]\n",qx.GetW(),qx.GetX(),qx.GetY(),qx.GetZ());
}
if (qy.GetW()<0.||fabs(qy.GetW()*qy.GetW()-.5)>10.*DBL_EPSILON||fabs(qy.GetY()*qy.GetY()-.5)>10.*DBL_EPSILON||fabs(qy.GetX())>10.*DBL_EPSILON||fabs(qy.GetZ())>10.*DBL_EPSILON) {
errorcount++;
fprintf(stdout,"Axis2Quaternion qy wrong value [ %g, %g, %g, %g ] != [sqrt(1./2.),sqrt(1./2.),0,0]\n",qy.GetW(),qy.GetX(),qy.GetY(),qy.GetZ());
}
if (qz.GetW()<0.||fabs(qz.GetW()*qz.GetW()-.5)>10.*DBL_EPSILON||fabs(qz.GetZ()*qz.GetZ()-.5)>10.*DBL_EPSILON||fabs(qz.GetX())>10.*DBL_EPSILON||fabs(qz.GetY())>10.*DBL_EPSILON) {
errorcount++;
fprintf(stdout,"CPPAxis2Quaternion qz wrong value [ %g, %g, %g, %g ] != [sqrt(1./2.),sqrt(1./2.),0,0]\n",qz.GetW(),qz.GetX(),qz.GetY(),qz.GetZ());
}
double Matx[9];
double Maty[9];
double Matz[9];
CPPQR<double>::Quaternion2Matrix(Matx,qx);
CPPQR<double>::Quaternion2Matrix(Maty,qy);
CPPQR<double>::Quaternion2Matrix(Matz,qz);
if ( fabs(Matx[0]-1.)>10.*DBL_EPSILON ||fabs(Matx[5]+1.)>10.*DBL_EPSILON ||fabs(Matx[7]-1.)>10.*DBL_EPSILON
||fabs(Matx[1])>10.*DBL_EPSILON ||fabs(Matx[2])>10.*DBL_EPSILON
||fabs(Matx[3])>10.*DBL_EPSILON ||fabs(Matx[4])>10.*DBL_EPSILON
||fabs(Matx[6])>10.*DBL_EPSILON ||fabs(Matx[8])>10.*DBL_EPSILON) {
errorcount++;
fprintf(stdout," Quaternion2Matrix Matx wrong value \n [ %g, %g, %g ]\n [ %g, %g, %g ]\n [ %g, %g, %g ]\n"
"!= [1, 0, 0]\n [0, 0, -1]\n [0, 1, 0]\n",
Matx[0]-1.0,Matx[1],Matx[2],
Matx[3],Matx[4],Matx[5]+1.0,
Matx[6],Matx[7]-1.0,Matx[8]);
}
if (fabs(Maty[2]-1.)>10.*DBL_EPSILON ||fabs(Maty[4]-1.)>10.*DBL_EPSILON||fabs(Maty[6]+1.)>10.*DBL_EPSILON
||fabs(Maty[0])>10.*DBL_EPSILON ||fabs(Maty[1])>10.*DBL_EPSILON
||fabs(Maty[3])>10.*DBL_EPSILON ||fabs(Maty[5])>10.*DBL_EPSILON
||fabs(Maty[7])>10.*DBL_EPSILON ||fabs(Maty[8])>10.*DBL_EPSILON) {
errorcount++;
fprintf(stdout," Quaternion2Matrix Maty wrong value \n [ %g, %g, %g]\n [ %g, %g, %g]\n [ %g, %g, %g ]\n"
"!= [0, 0, 1]\n [0, 1, 0]\n [-1, 0, 0]\n",
Maty[0],Maty[1],Maty[2]-1.0,
Maty[3],Maty[4],Maty[5]-1.0,
Maty[6]+1.0,Maty[7],Maty[8]);
}
if (fabs(Matz[1]+1.)>10.*DBL_EPSILON ||fabs(Matz[3]-1.)>10.*DBL_EPSILON||fabs(Matz[8]-1.)>10.*DBL_EPSILON
||fabs(Matz[0])>10.*DBL_EPSILON ||fabs(Matz[2])>10.*DBL_EPSILON
||fabs(Matz[4])>10.*DBL_EPSILON ||fabs(Matz[5])>10.*DBL_EPSILON
||fabs(Matz[6])>10.*DBL_EPSILON ||fabs(Matz[7])>10.*DBL_EPSILON) {
errorcount++;
fprintf(stdout," Quaternion2Matrix Matz wrong value \n [ %g, %g, %g]\n [ %g, %g, %g]\n [ %g, %g, %g ]\n"
"!= [0, -1, 0]\n [1, 0, 0]\n [0, 0, 1]\n",
Matz[0],Matz[1],Matz[2],
Matz[3],Matz[4],Matz[5],
Matz[6],Matz[7],Matz[8]);
}
EXX = EXY = EXZ = 0.;
EYX = EYY = EYZ = 0.;
EZX = EZY = EZZ = 0.;
qx.Quaternion2Angles(EXX,EXY,EXZ);
qy.Quaternion2Angles(EYX,EYY,EYZ);
qz.Quaternion2Angles(EZX,EZY,EZZ);
q1 = CPPQR<double>::Angles2Quaternion(EXX,EXY,EXZ);
q2 = CPPQR<double>::Angles2Quaternion(EYX,EYY,EYZ);
q3 = CPPQR<double>::Angles2Quaternion(EZX,EZY,EZZ);
q4 = qx / q1;
normsq = q4.Normsq( );
if ( fabs(normsq-1.) > 10.*DBL_EPSILON || fabs(q4.GetW()*q4.GetW()-1.) > 10.*DBL_EPSILON) {
errorcount++;
fprintf(stdout," Angles2Quaternion q1 wrong value [%g, %g, %g, %g] != +/-[%g, %g, %g, %g]\n",
qx.GetW(), qx.GetX(), qx.GetY(), qx.GetZ(), q1.GetW(), q1.GetX(), q1.GetY(), q1.GetZ() );
}
q4 = qy / q2;
normsq = q4.Normsq( );
if (fabs(normsq-1.) > 10.*DBL_EPSILON || fabs(q4.GetW()*q4.GetW()-1.) > 10.*DBL_EPSILON) {
fprintf(stdout," Angles2Quaternion q2 wrong value [%g, %g, %g, %g] != +/-[%g, %g, %g, %g]\n",
qy.GetW(), qy.GetX(), qy.GetY(), qy.GetZ(), q2.GetW(), q2.GetX(), q2.GetY(), q2.GetZ() );
}
q4 = qz / q3;
normsq = q4.Normsq( );
if (fabs(normsq-1.) > 10.*DBL_EPSILON || fabs(q4.GetW()*q4.GetW()-1.) > 10.*DBL_EPSILON) {
fprintf(stdout," Angles2Quaternion q3 wrong value [%g, %g, %g, %g] != +/-[%g, %g, %g, %g]\n",
qz.GetW(), qz.GetX(), qz.GetY(), qz.GetZ(), q3.GetW(), q3.GetX(), q3.GetY(), q3.GetZ() );
}
{ /* lca */
double m[9] = { 0.0,0.0,1.0, 1.0,0.0,0.0, 0.0,1.0,0.0 };
double mx[9];
double sum;
CPPQR<double> qq1, qq2, qq3;
CPPQR<double> qq4, qqx, qqy, qqz;
CPPQR<double>::Matrix2Quaternion(qq4, m );
CPPQR<double>::Quaternion2Matrix(mx,qq4 );
sum = 0.0;
for ( int i=0; i<9; ++i )
sum += fabs(m[i]-mx[i]);
if ( sum > 1.0E-8 )
{
errorcount++;
fprintf( stdout, " Matrix2Quaternion difference\n" );
fprintf( stdout, " qq4 = {%g,%g,%g,%g}\n",qq4.GetW(),qq4.GetX(),qq4.GetY(),qq4.GetZ());
fprintf( stdout, " m = {{%g,%g,%g},{%g,%g,%g},{%g,%g,%g))\n",
m[0],m[1],m[2],m[3],m[4],m[5],m[6],m[7],m[8]);
fprintf( stdout, " mx = {{%g,%g,%g},{%g,%g,%g},{%g,%g,%g))\n",
mx[0],mx[1],mx[2],mx[3],mx[4],mx[5],mx[6],mx[7],mx[8]);
}
}
{
CPPQR<double> q1( 3,5,7,11 );
CPPQR<double> q2( q1.GetW(), q1.GetX(), q1.GetY(), q1.GetZ() );
if ( q1 != q2 || !(q1==q2) )
{
errorcount++;
fprintf( stdout, " CPPQR test constructors, gets, ==, != failed\n" );
}
}
{
CPPQR<double> q;
if( ::fabs( q.GetW()) + ::fabs( q.GetX()) + ::fabs( q.GetY()) + ::fabs( q.GetZ()) != 0.0 )
{
errorcount++;
fprintf( stdout, " CPPQR default constructor not zero\n" );
}
}
{
CPPQR<double> q1( 3,5,7,11 );
CPPQR<double> q2( q1 );
CPPQR<double> q3 = q2;
if ( q1 != q2 || q1 != q3 )
{
errorcount++;
fprintf( stdout, " CPPQR copy constructor or assignment operator failed\n" );
}
}
{
CPPQR<double> q1( 3,5,7,11 );
CPPQR<double> q2;
q2.Set( q1.GetW(), q1.GetX(), q1.GetY(), q1.GetZ() );
if( q1 != q2 )
{
errorcount++;
fprintf( stdout, " CPPQR Set failed\n" );
}
}
{
if( CPPQR<double>(1,3,5,7)+CPPQR<double>(-1,-3,-5,-7) !=CPPQR<double>(0,0,0,0) )
{
errorcount++;
fprintf( stdout, " CPPQR add failed\n" );
}
if( CPPQR<double>(1,3,5,7)-CPPQR<double>(1,3,5,7) !=CPPQR<double>(0,0,0,0) )
{
errorcount++;
fprintf( stdout, " CPPQR subtract failed\n" );
}
}
{
if ( CPPQR<double>(1,3,5,7)*2.0 != CPPQR<double>(4,12,20,28)/2.0 )
{
errorcount++;
fprintf( stdout, " CPPQR multiply or divide by scalar failed\n" );
}
}
{
const CPPQR<double> q1( CPPQR<double>( 3,5,7,9 ) );
const double normsq = q1.Normsq( );
if ( normsq != 164.0 )
{
errorcount++;
fprintf ( stdout, " CPPQR Normsq failed \n" );
}
const CPPQR<double> q2 = q1.UnitQ( );
if( q1/sqrt(normsq) != q2 )
{
errorcount++;
fprintf( stdout, "UnitQ failed\n" );
}
}
{
const CPPQR<double> q1( CPPQR<double>( 3,5,7,9 ) );
if ( q1.GetW() != q1[0] || q1.GetX() != q1[1] || q1.GetY() != q1[2] || q1.GetZ() != q1[3] )
{
errorcount++;
fprintf( stdout, "component fetches failed\n" );
}
}
/* Tests on [-sqrt(7),2,3,4] = 6*[-sqrt(7)/6,1/3,1/2,2/3]
= 6*[-cos(1.11412994158827),sin(1.11412994158827)*[.3713906763541037, .5570860145311556, .7427813527082074]]
= 6*[cos(2.027462712001523),sin(2.027462712001523)*[.3713906763541037, .5570860145311556, .7427813527082074]]
= 6*exp([0,.3713906763541037, .5570860145311556, .7427813527082074]*2.027462712001523)
so the log should be
[log(6),0,0,0] +[0,.3713906763541037, .5570860145311556, .7427813527082074]*2.027462712001523]
=[1.791759469228055, 0.752980747892971, 1.129471121839456, 1.505961495785942]
Note that the log is multivalued
*/
{
const CPPQR<double> q1( CPPQR<double>( -sqrt(7.),2,3,4 ));
if ( q1.GetIm() != CPPQR<double>( 0,2,3,4 ) )
{
errorcount++;
fprintf( stdout, "GetIm failed\n" );
}
if ( q1.GetAxis().Dist(CPPQR<double>( 0,2./sqrt(4.+9.+16.),3./sqrt(4.+9.+16.),4./sqrt(4.+9.+16.) ))>100.*DBL_EPSILON )
{
errorcount++;
fprintf( stdout, "GetAxis failed\n" );
}
if (fabs(q1.GetAngle()-2.027462712001523)>40.*DBL_EPSILON*2.027462712001523)
{
errorcount++;
fprintf( stdout, "GetAngle failed, got %g, expected %g\n",q1.GetAngle(),2.027462712001523 );
}
if ((q1.log() - CPPQR<double>(log(6.), 0.752980747892971, 1.129471121839457, 1.505961495785942)).Norm() >
40.*DBL_EPSILON*q1.log().Norm())
{
errorcount++;
fprintf( stdout, "quaternion log failed log([%g,%g,%g,%g]) = [%g,%g,%g,%g] instead of [%g,%g,%g,%g], normdiff = %g\n",
q1.GetW(), q1.GetX(), q1.GetY(), q1.GetZ(),
q1.log().GetW(), q1.log().GetX(), q1.log().GetY(), q1.log().GetZ(),
log(6.), 0.752980747892971, 1.129471121839457, 1.505961495785942,
(q1.log() - CPPQR<double>(log(6.), 0.752980747892971, 1.129471121839457, 1.505961495785942)).Norm()
);
}
if (((q1.log()).exp()-q1).Norm()>10.*DBL_EPSILON*q1.Norm() ||
((q1.exp()).log().exp()-q1.exp()).Norm()>10.*DBL_EPSILON*q1.exp().Norm())
{
errorcount++;
fprintf( stdout, "log(exp) or exp(log) failed\n,"
" q = [%g,%g,%g,%g],"
" log = [%g,%g,%g,%g], exp(log) = [%g,%g,%g,%g],"
" exp = [%g,%g,%g,%g], log(exp) = [%g,%g,%g,%g]\n",
q1.GetW(),q1.GetX(),q1.GetY(),q1.GetZ(),
q1.log().GetW(),q1.log().GetX(),q1.log().GetY(),q1.log().GetZ(),
q1.log().exp().GetW(),q1.log().exp().GetX(),q1.log().exp().GetY(),q1.log().exp().GetZ(),
q1.exp().GetW(),q1.exp().GetX(),q1.exp().GetY(),q1.exp().GetZ(),
q1.exp().log().exp().GetW(),q1.exp().log().exp().GetX(),q1.exp().log().exp().GetY(),q1.exp().log().exp().GetZ()
);
}
for (int i = -5; i < 6; i++) {
if ((q1.pow(i) - q1.pow(double(i))).Norm() > 10.*DBL_EPSILON*(q1.pow(i)).Norm())
{
errorcount++;
fprintf( stdout, "integer power double power comparison failed\n,");
}
}
}
{
const CPPQR<double> q1( CPPQR<double>( -4.,0.,0.,0. ));
const CPPQR<double> q2( CPPQR<double>( -4.,1.,1.,1. ));
const CPPQR<double> q3( CPPQR<double>( 4.,0.,0.,0. ));
CPPQR <double> qout1, qout2, qout3, qtest1, qtest2, qtest3;
for (int i = 1; i < 9; i++) {
for (int j = 0; j < i; j++ ) {
qout1 = q1.root(i,j);
qout2 = q2.root(i,j);
qout3 = q3.root(i,j);
qtest1 = qout1.pow(i);
qtest2 = qout2.pow(i);
qtest3 = qout3.pow(i);
if (q1.Dist(qtest1) > 100.*DBL_EPSILON*q1.Norm()
|| q2.Dist(qtest2) > 100.*DBL_EPSILON*q2.Norm()
|| q3.Dist(qtest3) > 100.*DBL_EPSILON*q3.Norm()) {
errorcount++;
fprintf(stdout," %d'th root of [%g,%g,%g,%g] = [%g,%g,%g,%g], power = [%g,%g,%g,%g], delta %g\n",
i, q1.GetW(), q1.GetX(), q1.GetY(), q1.GetZ(),
qout1.GetW(), qout1.GetX(), qout1.GetY(), qout1.GetZ(),
qtest1.GetW(), qtest1.GetX(), qtest1.GetY(), qtest1.GetZ(),
(q1-qtest1).Norm());
fprintf(stdout," %d'th root of [%g,%g,%g,%g] = [%g,%g,%g,%g], power = [%g,%g,%g,%g], delta %g\n",
i, q2.GetW(), q2.GetX(), q2.GetY(), q2.GetZ(),
qout2.GetW(), qout2.GetX(), qout2.GetY(), qout2.GetZ(),
qtest2.GetW(), qtest2.GetX(), qtest2.GetY(), qtest2.GetZ(),
(q2-qtest2).Norm());
fprintf(stdout," %d'th root of [%g,%g,%g,%g] = [%g,%g,%g,%g], power = [%g,%g,%g,%g], delta %g\n",
i, q3.GetW(), q3.GetX(), q3.GetY(), q3.GetZ(),
qout3.GetW(), qout3.GetX(), qout3.GetY(), qout3.GetZ(),
qtest3.GetW(), qtest3.GetX(), qtest3.GetY(), qtest3.GetZ(),
(q3-qtest3).Norm());
}
}
}
}
return errorcount;
}