3.5.12. horton/grid/cubic_spline.h
– One-dimensional cubic splines (on uniform grids)¶
Functions
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void
tridiagsym_solve
(double *diag_mid, double *diag_up, double *right, double *solution, int n)¶
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void
solve_cubic_spline_system
(double *y, double *d, int npoint)¶
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void
compute_cubic_spline_int_weights
(double *weights, int npoint)¶
- class
- #include <cubic_spline.h>
Construct and use cubic splines, with optional transformation of x-axis and extrapolation rules beyond spline range.
Public Functions
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CubicSpline::
CubicSpline
(double *y, double *dt, Extrapolation *extrapolation, RTransform *rtf, int n)¶ Create a CubicSpline object.
- Parameters
y
-An array with y-values on the grid.
dt
-An array with derivatives of y toward the uniform x-axis (thus t-axis).
extrapolation
-An instance of an Extrapolation subclass that describes the function outside the spline range.
rtf
-The transformation from the t-axis to the x-axis.
n
-The number of grid points.
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void
CubicSpline::
eval
(double *new_x, double *new_y, int new_n)¶ Evaluate the cubic spline in a set of new x values.
- Parameters
new_x
-An array with new x values.
new_y
-An output array with the corresponding y values.
new_n
-The number of values in new_x.
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void
CubicSpline::
eval_deriv
(double *new_x, double *new_dx, int new_n)¶ Evaluate the derivative of the cubic spline (dy/dx) in a set of new x values.
- Parameters
new_x
-An array with new x values.
new_dx
-An output array with the corresponding dy/dx values.
new_n
-The number of values in new_x.
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RTransform *
CubicSpline::
get_rtransform
()¶ Return the transformation of the x-axis.
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double
CubicSpline::
get_first_x
()¶ Return the first grid point on the x-axis (transformed coordinates).
-
double
CubicSpline::
get_last_x
()¶ Return the last grid point on the x-axis (transformed coordinates).
-
Extrapolation *
CubicSpline::
get_extrapolation
()¶ Return the extrapolation function used outside the spline range.
Public Members
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double *
CubicSpline::
y
¶ The y-values of the spline at each grid point.
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double *
CubicSpline::
dt
¶ The derivative towards the t-axis (uniform x-axis).
-
int
CubicSpline::
n
¶ The number of grid points.
Private Members
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Extrapolation *
CubicSpline::
extrapolation
¶ Describes how function goes outside spline range.
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RTransform *
CubicSpline::
rtf
¶ Transformation of the x-axis.
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double
CubicSpline::
first_x
¶ Transformed first grid point.
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double
CubicSpline::
last_x
¶ Transformed last grid point.
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- class
- #include <cubic_spline.h>
Base class for extrapolation of cubic splines outside their range.
Subclassed by CuspExtrapolation, PotentialExtrapolation, PowerExtrapolation, ZeroExtrapolation
Public Functions
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Extrapolation::
Extrapolation
()¶ Constructor.
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virtual
Extrapolation::
~Extrapolation
()¶ Destructor.
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virtual void
Extrapolation::
prepare
(CubicSpline *cs)¶
= 0 Derive parameters from spline.
-
virtual double
Extrapolation::
eval_left
(double x)¶
= 0 Compute extrapolation for low x.
-
virtual double
Extrapolation::
eval_right
(double x)¶
= 0 Derivative of extrapolation for low x.
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virtual double
Extrapolation::
deriv_left
(double x)¶
= 0 Compute extrapolation for high x.
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virtual double
Extrapolation::
deriv_right
(double x)¶
= 0 Derivative of extrapolation for high x.
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virtual bool
Extrapolation::
has_tail
()¶
= 0 Returns true if right extrapolation is nonzero.
-
- class
- #include <cubic_spline.h>
No extrapolation at all. Returns zero outside the spline range.
Inherits from Extrapolation
Public Functions
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void
ZeroExtrapolation::
prepare
(CubicSpline *cs)¶ Derive parameters from spline.
-
double
ZeroExtrapolation::
eval_left
(double x)¶ Compute extrapolation for low x.
-
double
ZeroExtrapolation::
eval_right
(double x)¶ Derivative of extrapolation for low x.
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double
ZeroExtrapolation::
deriv_left
(double x)¶ Compute extrapolation for high x.
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double
ZeroExtrapolation::
deriv_right
(double x)¶ Derivative of extrapolation for high x.
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virtual bool
ZeroExtrapolation::
has_tail
()¶ Returns false because tail is zero.
-
void
- class
- #include <cubic_spline.h>
An extrapolation suitable for electronic densities. It uses a 1s Slater-type density function close to the nucleus.
Inherits from Extrapolation
Public Functions
-
CuspExtrapolation::
CuspExtrapolation
()¶ Constructor.
-
void
CuspExtrapolation::
prepare
(CubicSpline *cs)¶ Derive parameters from spline.
-
double
CuspExtrapolation::
eval_left
(double x)¶ Compute extrapolation for low x.
-
double
CuspExtrapolation::
eval_right
(double x)¶ Derivative of extrapolation for low x.
-
double
CuspExtrapolation::
deriv_left
(double x)¶ Compute extrapolation for high x.
-
double
CuspExtrapolation::
deriv_right
(double x)¶ Derivative of extrapolation for high x.
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virtual bool
CuspExtrapolation::
has_tail
()¶ Returns false because tail is zero.
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- class
- #include <cubic_spline.h>
An extrapolation with a polynomial of arbitrary order for high x values.
The prefactor of the polynomial is such that the function remains continuous at the last grid point of the spline.
Inherits from Extrapolation
Public Functions
-
PowerExtrapolation::
PowerExtrapolation
(double power)¶ Construct a PowerExtrapolation.
- Parameters
power
-The power of the polynomial tail, i.e. extrapolation on the right.
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void
PowerExtrapolation::
prepare
(CubicSpline *cs)¶ Derive parameters from spline.
-
double
PowerExtrapolation::
eval_left
(double x)¶ Compute extrapolation for low x.
-
double
PowerExtrapolation::
eval_right
(double x)¶ Derivative of extrapolation for low x.
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double
PowerExtrapolation::
deriv_left
(double x)¶ Compute extrapolation for high x.
-
double
PowerExtrapolation::
deriv_right
(double x)¶ Derivative of extrapolation for high x.
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virtual bool
PowerExtrapolation::
has_tail
()¶ Returns true because if R**power tail.
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double
PowerExtrapolation::
get_power
()¶ The power of the polynomial tail.
-
- class
- #include <cubic_spline.h>
An extrapolation suitable for solutions of the Poisson equation.
The prefactor of the left and right polynomial are such that the function remains continuous at the last grid point of the spline. The power of R on the left and right side is consistent with the boundary conditions of the solutions of the Poisson equation.
Inherits from Extrapolation
Public Functions
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PotentialExtrapolation::
PotentialExtrapolation
(int64_t l)¶ Construct a PotentialExtrapolation.
- Parameters
l
-The angular momentum for which the Coulomb potential is generated.
-
void
PotentialExtrapolation::
prepare
(CubicSpline *cs)¶ Derive parameters from spline.
-
double
PotentialExtrapolation::
eval_left
(double x)¶ Compute extrapolation for low x.
-
double
PotentialExtrapolation::
eval_right
(double x)¶ Derivative of extrapolation for low x.
-
double
PotentialExtrapolation::
deriv_left
(double x)¶ Compute extrapolation for high x.
-
double
PotentialExtrapolation::
deriv_right
(double x)¶ Derivative of extrapolation for high x.
-
virtual bool
PotentialExtrapolation::
has_tail
()¶ Returns true because if 1/R**(l+1) tail.
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int64_t
PotentialExtrapolation::
get_l
()¶ The angular momentum of the Coulomb potential spline.
-
double
PotentialExtrapolation::
get_amp_left
()¶ The prefactor for the polynomial for low x.
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double
PotentialExtrapolation::
get_amp_right
()¶ The prefactor for the polynomial for high x.
-