TEST(FunctionalExpansionsTest, zernikeSeriesEvaluationYZ)
{
const unsigned int order = 4;
const Point location(-0.90922108754014, 0.262698547343, 0.156796889218);
expansion_type = "standard";
generation_type = "orthonormal";
Zernike zernike({FunctionalBasisInterface::_domain_options = "y",
FunctionalBasisInterface::_domain_options = "z"},
{order},
expansion_type,
generation_type);
zernike.setLocation(location);
const std::array<Real, 15> truth = {{0.318309886183791,
0.052230505695590,
0.330374978445085,
0.040657672622662,
-0.823129261009826,
0.125372638358686,
0.020923587239414,
-0.187295294511344,
-1.184703806003468,
0.041151106306071,
0.008896570968308,
-0.184582980412102,
0.978025517529447,
-0.569182979683797,
0.012274247968574}};
auto & answer = zernike.getAllGeneration();
for (std::size_t i = 0; i < zernike.getNumberOfTerms(); ++i)
EXPECT_NEAR(answer[i], truth[i], tol);
}
TEST(FunctionalExpansionsTest, zernikeSeriesEvaluationXZ)
{
const unsigned int order = 4;
const Point location(-0.90922108754014, 0.262698547343, 0.156796889218);
expansion_type = "standard";
generation_type = "orthonormal";
Zernike zernike({FunctionalBasisInterface::_domain_options = "x",
FunctionalBasisInterface::_domain_options = "z"},
{order},
expansion_type,
generation_type);
zernike.setLocation(location);
const std::array<Real, 15> truth = {{0.318309886183791,
-0.180774038043348,
-1.143454732567233,
0.487041727962393,
0.623918544603900,
1.501849527692451,
-0.867504286868072,
-0.173560777222340,
-1.097828505968007,
-1.706149176114187,
1.276644449771070,
0.248985426801565,
0.223343150486739,
0.767775375651402,
1.761335979897610}};
auto & answer = zernike.getAllGeneration();
for (std::size_t i = 0; i < zernike.getNumberOfTerms(); ++i)
EXPECT_NEAR(answer[i], truth[i], tol);
}
TEST(FunctionalExpansionsTest, zernikeSeriesEvaluationXY)
{
const unsigned int order = 4;
const Point location(-0.90922108754014, 0.262698547343, 0.156796889218);
expansion_type = "standard";
generation_type = "orthonormal";
Zernike zernike({FunctionalBasisInterface::_domain_options = "x",
FunctionalBasisInterface::_domain_options = "y"},
{order},
expansion_type,
generation_type);
zernike.setLocation(location);
const std::array<Real, 15> truth = {{0.318309886183791,
-0.300628811510287,
-1.117940202314423,
0.791881706198328,
0.623918544603900,
1.365900806059890,
-1.357069098439213,
-0.288633095470502,
-1.073332058640328,
-1.349767446988918,
1.887803726543957,
0.404825692079851,
0.223343150486739,
0.698275682841869,
1.080889714660983}};
auto & answer = zernike.getAllGeneration();
for (std::size_t i = 0; i < zernike.getNumberOfTerms(); ++i)
EXPECT_NEAR(answer[i], truth[i], tol);
}
void setup_zernike(void)
{
int i, j;
float rho, theta;
/* Make the mutex so this will be thread safe */
if (pthread_mutex_init(&zernike_mutex, NULL) != 0)
error(FATAL, "Unable to create Zernike mutex.");
/* Normalize the x and y */
for (i=1; i<= NUM_ACTUATORS; i++)
{
actuator_x[i] /= 3.0;
actuator_y[i] *= (sqrt(0.75)/3.0);
}
/* Setup the zernike stuff */
set_up_zernike_calcs(maxJ);
/* Allocate memory iand fill things in */
actuator_zernike_values[0] = NULL;
zernike_max = -1e32;
zernike_min = 1e32;
for (i=1; i<= NUM_ACTUATORS; i++)
{
actuator_zernike_values[i]=malloc(sizeof(float)*(maxJ+1));
if (actuator_zernike_values[i] == NULL)
error(FATAL, "Not enough memory.");
rho = sqrt(actuator_x[i]*actuator_x[i] +
actuator_y[i]*actuator_y[i]);
if (rho > 1.0) rho = 1.0;
theta = atan2(actuator_y[i], actuator_x[i]);
if (theta < 0.0) theta += (2.0*M_PI);
for(j=1; j<= maxJ; j++)
{
actuator_zernike_values[i][j] = zernike(j,rho,theta);
if (actuator_zernike_values[i][j] > zernike_max)
zernike_max = actuator_zernike_values[i][j];
else if (actuator_zernike_values[i][j] < zernike_min)
zernike_min = actuator_zernike_values[i][j];
}
}
/* Now we allocate the first version of the zernike values */
zernike_values = malloc(sizeof(float)*(maxJ+1));
if (zernike_values == NULL) error(FATAL, "Not enough memory.");
zernike_values[0] = 1.0;
zernike_values[1] = 0.0;
for(j = 2; j <= maxJ; j++) zernike_values[j] = 0.0;
} /* setup_zernike() */
TEST(FunctionalExpansionsTest, zernikeConstructor)
{
const unsigned int order = 5;
expansion_type = "orthonormal";
generation_type = "standard";
Zernike zernike({FunctionalBasisInterface::_domain_options = "x",
FunctionalBasisInterface::_domain_options = "y"},
{order},
expansion_type,
generation_type);
EXPECT_EQ(zernike.getOrder(0), order);
}
TEST(FunctionalExpansionsTest, zernikeSeriesStandardEvaluation)
{
const unsigned int order = 4;
const Point location(-0.90922108754014, 0.262698547343, 0.156796889218);
expansion_type = "standard";
generation_type = "standard";
Zernike zernike({FunctionalBasisInterface::_domain_options = "y",
FunctionalBasisInterface::_domain_options = "z"},
{order},
expansion_type,
generation_type);
zernike.setLocation(location);
const std::array<Real, 15> truth = {{0.318309886183791,
0.052230505695590,
0.330374978445085,
0.040657672622662,
-0.823129261009826,
0.125372638358686,
0.020923587239414,
-0.187295294511344,
-1.184703806003468,
0.041151106306071,
0.008896570968308,
-0.184582980412102,
0.978025517529447,
-0.569182979683797,
0.012274247968574}};
auto & answer = zernike.getAllGeneration();
EXPECT_NEAR(answer[0], truth[0] * M_PI, tol);
size_t i = 1;
for (size_t n = 1; n < order + 1; ++n)
{
for (size_t m = 0; m < n + 1; ++m)
{
if (m != 0 && n / m == 2 && n % m == 0)
EXPECT_NEAR(answer[i], truth[i] * M_PI / (n + 1), tol);
else
EXPECT_NEAR(answer[i], truth[i] * M_PI / (2 * n + 2), tol);
++i;
}
}
}
/*
* zernike_grid()
*
* Add zernike polynomial values to pre-defined grid.
*
* grid - pre-allocated & initialized double storage (square).
* gsize - size of the grid in x / y.
* gcenter - center point of the grid.
* radius - radius on which to calculate the polynomial.
* scale - scaling factor.
* m - zernike m value.
* n - zernike n value.
*/
void zernike_grid(double *grid, int gsize, double gcenter, double radius, double scale, int m, int n)
{
int i, j;
double dd, dx, dy, phi, rr;
rr = radius * radius;
for(i=0;i<gsize;i++){
dx = i - gcenter;
for(j=0;j<gsize;j++){
dy = j - gcenter;
dd = dx * dx + dy * dy;
if(dd <= rr){
dd = sqrt(dd)/radius;
phi = atan2(dy, dx);
grid[i*gsize+j] += scale * zernike(m, n, dd, phi);
}
}
}
}
