A quadratic approximation to a 2D Mapping.
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#include <QuadApprox.h>
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std::vector< double > | fit |
| A vector of coefficients of the quadratic approximation to the specified transformation.
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double | rms |
| The RMS residual between the fit and the Mapping, summed over all Mapping outputs.
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A quadratic approximation to a 2D Mapping.
Construct the class to compute the contained fields:
Definition at line 36 of file QuadApprox.h.
◆ QuadApprox() [1/3]
ast::QuadApprox::QuadApprox |
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Mapping const & | map, |
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std::vector< double > const & | lbnd, |
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std::vector< double > const & | ubnd, |
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int | nx = 3, |
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int | ny = 3 ) |
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explicit |
Obtain a quadratic approximation to a 2D Mapping.
Compute the coefficients of a quadratic fit to the supplied Mapping over the input area specified by lbnd
and ubnd
. The Mapping must have 2 inputs, but may have any number of outputs. The i'th Mapping output is modeled as a quadratic function of the 2 inputs (x,y):
output_i = a_i_0 + a_i_1*x + a_i_2*y + a_i_3*x*y + a_i_4*x*x + a_i_5*y*y
The fit
vector is set tothe values of the co-efficients a_0_0, a_0_1, etc.
- Parameters
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[in] | map | Mapping to fit. |
[in] | lbnd | The lower bounds of a box defined within the input coordinate system of the Mapping. The number of elements in this vector should equal map.getNIn(). This box should specify the region over which the fit is to be performed. |
[in] | ubnd | The upper bounds of the box specifying the region over which the fit is to be performed. |
[in] | nx | The number of points to place along the first Mapping input. The first point is at lbnd[0] and the last is at ubnd[0]" . If a value less than three is supplied a value of three will be used. |
[in] | ny | The number of points to place along the second Mapping input. The first point is at lbnd[1] and the last is at ubnd[1] . If a value less than three is supplied a value of three will be used. |
- Exceptions
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Definition at line 31 of file QuadApprox.cc.
◆ QuadApprox() [2/3]
ast::QuadApprox::QuadApprox |
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QuadApprox const & | | ) |
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default |
◆ QuadApprox() [3/3]
◆ operator=() [1/2]
◆ operator=() [2/2]
◆ fit
A vector of coefficients of the quadratic approximation to the specified transformation.
This vector will contain "6*NOut", elements: the first 6 elements hold the fit to the first Mapping output, the next 6 elements hold the fit to the second Mapping output, etc. So if the Mapping has 2 inputs and 2 outputs the quadratic approximation to the forward transformation is:
X_out = fit[0] + fit[1]*X_in + fit[2]*Y_in + fit[3]*X_in*Y_in +
fit[4]*X_in*X_in + fit[5]*Y_in*Y_in
Y_out = fit[6] + fit[7]*X_in + fit[8]*Y_in + fit[9]*X_in*Y_in +
fit[10]*X_in*X_in + fit[11]*Y_in*Y_in
X_out = fit(1) + fit(2)*X_in + fit(3)*Y_in + fit(4)*X_in*Y_in +
fit(5)*X_in*X_in + fit(6)*Y_in*Y_in
Y_out = fit(7) + fit(8)*X_in + fit(9)*Y_in + fit(10)*X_in*Y_in +
fit(11)*X_in*X_in + fit(12)*Y_in*Y_in
Definition at line 98 of file QuadApprox.h.
◆ rms
double ast::QuadApprox::rms |
The documentation for this class was generated from the following files: