# HARK.interpolation¶

Custom interpolation methods for representing approximations to functions. It also includes wrapper classes to enforce standard methods across classes. Each interpolation class must have a distance() method that compares itself to another instance; this is used in HARK.core’s solve() method to check for solution convergence. The interpolator classes currently in this module inherit their distance method from HARKobject.

Functions

 calcChoiceProbs(Vals, sigma) Returns the choice probabilities given the choice specific value functions Vals. calcLogSum(Vals, sigma) Returns the optimal value given the choice specific value functions Vals. calcLogSumChoiceProbs(Vals, sigma) Returns the final optimal value and choice probabilities given the choice specific value functions Vals. main()

Classes

 BilinearInterp(f_values, x_list, y_list[, …]) Bilinear full (or tensor) grid interpolation of a function f(x,y). BilinearInterpOnInterp1D(xInterpolators, …) A 3D interpolator that bilinearly interpolates among a list of lists of 1D interpolators. BilinearInterpOnInterp2D(wxInterpolators, …) A 4D interpolation method that bilinearly interpolates among “layers” of arbitrary 2D interpolations. ConstantFunction(value) A class for representing trivial functions that return the same real output for any input. CubicInterp(x_list, y_list, dydx_list[, …]) An interpolating function using piecewise cubic splines. Curvilinear2DInterp(f_values, x_values, y_values) A 2D interpolation method for curvilinear or “warped grid” interpolation, as in White (2015). HARKinterpolator1D A wrapper class for 1D interpolation methods in HARK. HARKinterpolator2D A wrapper class for 2D interpolation methods in HARK. HARKinterpolator3D A wrapper class for 3D interpolation methods in HARK. HARKinterpolator4D A wrapper class for 4D interpolation methods in HARK. IdentityFunction([i_dim, n_dims]) A fairly trivial interpolator that simply returns one of its arguments. LinearInterp(x_list, y_list[, …]) A “from scratch” 1D linear interpolation class. LinearInterpOnInterp1D(xInterpolators, y_values) A 2D interpolator that linearly interpolates among a list of 1D interpolators. LinearInterpOnInterp2D(xyInterpolators, z_values) A 3D interpolation method that linearly interpolates between “layers” of arbitrary 2D interpolations. LowerEnvelope(*functions) The lower envelope of a finite set of 1D functions, each of which can be of any class that has the methods __call__, derivative, and eval_with_derivative. LowerEnvelope2D(*functions) The lower envelope of a finite set of 2D functions, each of which can be of any class that has the methods __call__, derivativeX, and derivativeY. LowerEnvelope3D(*functions) The lower envelope of a finite set of 3D functions, each of which can be of any class that has the methods __call__, derivativeX, derivativeY, and derivativeZ. QuadlinearInterp(f_values, w_list, x_list, …) Quadlinear full (or tensor) grid interpolation of a function f(w,x,y,z). TrilinearInterp(f_values, x_list, y_list, z_list) Trilinear full (or tensor) grid interpolation of a function f(x,y,z). TrilinearInterpOnInterp1D(wInterpolators, …) A 4D interpolator that trilinearly interpolates among a list of lists of 1D interpolators. UpperEnvelope(*functions) The upper envelope of a finite set of 1D functions, each of which can be of any class that has the methods __call__, derivative, and eval_with_derivative. VariableLowerBoundFunc2D(func, lowerBound) A class for representing a function with two real inputs whose lower bound in the first input depends on the second input. VariableLowerBoundFunc3D(func, lowerBound) A class for representing a function with three real inputs whose lower bound in the first input depends on the second input.
class HARK.interpolation.BilinearInterp(f_values, x_list, y_list, xSearchFunc=None, ySearchFunc=None)

Bilinear full (or tensor) grid interpolation of a function f(x,y).

Methods

 __call__(self, x, y) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y) Evaluates the partial derivative of interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y) Evaluates the partial derivative of interpolated function with respect to y (the second argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.BilinearInterpOnInterp1D(xInterpolators, y_values, z_values)

A 3D interpolator that bilinearly interpolates among a list of lists of 1D interpolators.

Methods

 __call__(self, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to y (the second argument) at the given input. derivativeZ(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to z (the third argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.BilinearInterpOnInterp2D(wxInterpolators, y_values, z_values)

A 4D interpolation method that bilinearly interpolates among “layers” of arbitrary 2D interpolations. Useful for models with two endogenous state variables and two exogenous state variables when solving with the endogenous grid method. NOTE: should not be used if an exogenous 4D grid is used, will be significantly slower than QuadlinearInterp.

Methods

 __call__(self, w, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeW(self, w, x, y, z) Evaluates the partial derivative with respect to w (the first argument) of the interpolated function at the given input. derivativeX(self, w, x, y, z) Evaluates the partial derivative with respect to x (the second argument) of the interpolated function at the given input. derivativeY(self, w, x, y, z) Evaluates the partial derivative with respect to y (the third argument) of the interpolated function at the given input. derivativeZ(self, w, x, y, z) Evaluates the partial derivative with respect to z (the fourth argument) of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.ConstantFunction(value)

A class for representing trivial functions that return the same real output for any input. This is convenient for models where an object might be a (non-trivial) function, but in some variations that object is just a constant number. Rather than needing to make a (Bi/Tri/Quad)- LinearInterpolation with trivial state grids and the same f_value in every entry, ConstantFunction allows the user to quickly make a constant/trivial function. This comes up, e.g., in models with endogenous pricing of insurance contracts; a contract’s premium might depend on some state variables of the individual, but in some variations the premium of a contract is just a number.

Methods

 __call__(self, \*args) Evaluate the constant function. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivative(self, \*args) Evaluate the derivative of the function. derivativeW(self, \*args) Evaluate the derivative of the function. derivativeX(self, \*args) Evaluate the derivative of the function. derivativeXX(self, \*args) Evaluate the derivative of the function. derivativeY(self, \*args) Evaluate the derivative of the function. derivativeZ(self, \*args) Evaluate the derivative of the function. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
derivative(self, *args)

Evaluate the derivative of the function. The first input must exist and should be an array. Returns an array of identical shape to args[0] (if it exists). This is an array of zeros.

derivativeW(self, *args)

Evaluate the derivative of the function. The first input must exist and should be an array. Returns an array of identical shape to args[0] (if it exists). This is an array of zeros.

derivativeX(self, *args)

Evaluate the derivative of the function. The first input must exist and should be an array. Returns an array of identical shape to args[0] (if it exists). This is an array of zeros.

derivativeXX(self, *args)

Evaluate the derivative of the function. The first input must exist and should be an array. Returns an array of identical shape to args[0] (if it exists). This is an array of zeros.

derivativeY(self, *args)

Evaluate the derivative of the function. The first input must exist and should be an array. Returns an array of identical shape to args[0] (if it exists). This is an array of zeros.

derivativeZ(self, *args)

Evaluate the derivative of the function. The first input must exist and should be an array. Returns an array of identical shape to args[0] (if it exists). This is an array of zeros.

class HARK.interpolation.CubicInterp(x_list, y_list, dydx_list, intercept_limit=None, slope_limit=None, lower_extrap=False)

An interpolating function using piecewise cubic splines. Matches level and slope of 1D function at gridpoints, smoothly interpolating in between. Extrapolation above highest gridpoint approaches a limiting linear function if desired (linear extrapolation also enabled.)

Methods

 __call__(self, x) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivative(self, x) Evaluates the derivative of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. eval_with_derivative(self, x) Evaluates the interpolated function and its derivative at the given input. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.Curvilinear2DInterp(f_values, x_values, y_values)

A 2D interpolation method for curvilinear or “warped grid” interpolation, as in White (2015). Used for models with two endogenous states that are solved with the endogenous grid method.

Methods

 __call__(self, x, y) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y) Evaluates the partial derivative of interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y) Evaluates the partial derivative of interpolated function with respect to y (the second argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. findCoords(self, x, y, x_pos, y_pos) Calculates the relative coordinates (alpha,beta) for each point (x,y), given the sectors (x_pos,y_pos) in which they reside. findSector(self, x, y) Finds the quadrilateral “sector” for each (x,y) point in the input. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance. updatePolarity(self) Fills in the polarity attribute of the interpolation, determining whether the “plus” (True) or “minus” (False) solution of the system of equations should be used for each sector.
findCoords(self, x, y, x_pos, y_pos)

Calculates the relative coordinates (alpha,beta) for each point (x,y), given the sectors (x_pos,y_pos) in which they reside. Only called as a subroutine of __call__().

Parameters: x : np.array Values whose sector should be found. y : np.array Values whose sector should be found. Should be same size as x. x_pos : np.array Sector x-coordinates for each point in (x,y), of the same size. y_pos : np.array Sector y-coordinates for each point in (x,y), of the same size. alpha : np.array Relative “horizontal” position of the input in their respective sectors. beta : np.array Relative “vertical” position of the input in their respective sectors.
findSector(self, x, y)

Finds the quadrilateral “sector” for each (x,y) point in the input. Only called as a subroutine of _evaluate().

Parameters: x : np.array Values whose sector should be found. y : np.array Values whose sector should be found. Should be same size as x. x_pos : np.array Sector x-coordinates for each point of the input, of the same size. y_pos : np.array Sector y-coordinates for each point of the input, of the same size.
updatePolarity(self)

Fills in the polarity attribute of the interpolation, determining whether the “plus” (True) or “minus” (False) solution of the system of equations should be used for each sector. Needs to be called in __init__.

Parameters: none none
class HARK.interpolation.HARKinterpolator1D

A wrapper class for 1D interpolation methods in HARK.

Methods

 __call__(self, x) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivative(self, x) Evaluates the derivative of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. eval_with_derivative(self, x) Evaluates the interpolated function and its derivative at the given input. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
derivative(self, x)

Evaluates the derivative of the interpolated function at the given input.

Parameters: x : np.array or float Real values to be evaluated in the interpolated function. dydx : np.array or float The interpolated function’s first derivative evaluated at x: dydx = f’(x), with the same shape as x.
eval_with_derivative(self, x)

Evaluates the interpolated function and its derivative at the given input.

Parameters: x : np.array or float Real values to be evaluated in the interpolated function. y : np.array or float The interpolated function evaluated at x: y = f(x), with the same shape as x. dydx : np.array or float The interpolated function’s first derivative evaluated at x: dydx = f’(x), with the same shape as x.
class HARK.interpolation.HARKinterpolator2D

A wrapper class for 2D interpolation methods in HARK.

Methods

 __call__(self, x, y) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y) Evaluates the partial derivative of interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y) Evaluates the partial derivative of interpolated function with respect to y (the second argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
derivativeX(self, x, y)

Evaluates the partial derivative of interpolated function with respect to x (the first argument) at the given input.

Parameters: x : np.array or float Real values to be evaluated in the interpolated function. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as x. dfdx : np.array or float The derivative of the interpolated function with respect to x, eval- uated at x,y: dfdx = f_x(x,y), with the same shape as x and y.
derivativeY(self, x, y)

Evaluates the partial derivative of interpolated function with respect to y (the second argument) at the given input.

Parameters: x : np.array or float Real values to be evaluated in the interpolated function. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as x. dfdy : np.array or float The derivative of the interpolated function with respect to y, eval- uated at x,y: dfdx = f_y(x,y), with the same shape as x and y.
class HARK.interpolation.HARKinterpolator3D

A wrapper class for 3D interpolation methods in HARK.

Methods

 __call__(self, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to y (the second argument) at the given input. derivativeZ(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to z (the third argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
derivativeX(self, x, y, z)

Evaluates the partial derivative of the interpolated function with respect to x (the first argument) at the given input.

Parameters: x : np.array or float Real values to be evaluated in the interpolated function. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as x. z : np.array or float Real values to be evaluated in the interpolated function; must be the same size as x. dfdx : np.array or float The derivative with respect to x of the interpolated function evaluated at x,y,z: dfdx = f_x(x,y,z), with the same shape as x, y, and z.
derivativeY(self, x, y, z)

Evaluates the partial derivative of the interpolated function with respect to y (the second argument) at the given input.

Parameters: x : np.array or float Real values to be evaluated in the interpolated function. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as x. z : np.array or float Real values to be evaluated in the interpolated function; must be the same size as x. dfdy : np.array or float The derivative with respect to y of the interpolated function evaluated at x,y,z: dfdy = f_y(x,y,z), with the same shape as x, y, and z.
derivativeZ(self, x, y, z)

Evaluates the partial derivative of the interpolated function with respect to z (the third argument) at the given input.

Parameters: x : np.array or float Real values to be evaluated in the interpolated function. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as x. z : np.array or float Real values to be evaluated in the interpolated function; must be the same size as x. dfdz : np.array or float The derivative with respect to z of the interpolated function evaluated at x,y,z: dfdz = f_z(x,y,z), with the same shape as x, y, and z.
class HARK.interpolation.HARKinterpolator4D

A wrapper class for 4D interpolation methods in HARK.

Methods

 __call__(self, w, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeW(self, w, x, y, z) Evaluates the partial derivative with respect to w (the first argument) of the interpolated function at the given input. derivativeX(self, w, x, y, z) Evaluates the partial derivative with respect to x (the second argument) of the interpolated function at the given input. derivativeY(self, w, x, y, z) Evaluates the partial derivative with respect to y (the third argument) of the interpolated function at the given input. derivativeZ(self, w, x, y, z) Evaluates the partial derivative with respect to z (the fourth argument) of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
derivativeW(self, w, x, y, z)

Evaluates the partial derivative with respect to w (the first argument) of the interpolated function at the given input.

Parameters: w : np.array or float Real values to be evaluated in the interpolated function. x : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. z : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. dfdw : np.array or float The derivative with respect to w of the interpolated function eval- uated at w,x,y,z: dfdw = f_w(w,x,y,z), with the same shape as inputs.
derivativeX(self, w, x, y, z)

Evaluates the partial derivative with respect to x (the second argument) of the interpolated function at the given input.

Parameters: w : np.array or float Real values to be evaluated in the interpolated function. x : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. z : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. dfdx : np.array or float The derivative with respect to x of the interpolated function eval- uated at w,x,y,z: dfdx = f_x(w,x,y,z), with the same shape as inputs.
derivativeY(self, w, x, y, z)

Evaluates the partial derivative with respect to y (the third argument) of the interpolated function at the given input.

Parameters: w : np.array or float Real values to be evaluated in the interpolated function. x : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. z : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. dfdy : np.array or float The derivative with respect to y of the interpolated function eval- uated at w,x,y,z: dfdy = f_y(w,x,y,z), with the same shape as inputs.
derivativeZ(self, w, x, y, z)

Evaluates the partial derivative with respect to z (the fourth argument) of the interpolated function at the given input.

Parameters: w : np.array or float Real values to be evaluated in the interpolated function. x : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. y : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. z : np.array or float Real values to be evaluated in the interpolated function; must be the same size as w. dfdz : np.array or float The derivative with respect to z of the interpolated function eval- uated at w,x,y,z: dfdz = f_z(w,x,y,z), with the same shape as inputs.
class HARK.interpolation.IdentityFunction(i_dim=0, n_dims=1)

A fairly trivial interpolator that simply returns one of its arguments. Useful for avoiding numeric error in extreme cases.

Methods

 __call__(self, \*args) Evaluate the identity function. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivative(self, \*args) Returns the derivative of the function with respect to the first dimension. derivativeW(self, \*args) Returns the derivative of the function with respect to the W dimension. derivativeX(self, \*args) Returns the derivative of the function with respect to the X dimension. derivativeY(self, \*args) Returns the derivative of the function with respect to the Y dimension. derivativeZ(self, \*args) Returns the derivative of the function with respect to the Z dimension. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
derivative(self, *args)

Returns the derivative of the function with respect to the first dimension.

derivativeW(self, *args)

Returns the derivative of the function with respect to the W dimension. This should only exist when n_dims >= 4.

derivativeX(self, *args)

Returns the derivative of the function with respect to the X dimension. This is the first input whenever n_dims < 4 and the second input otherwise.

derivativeY(self, *args)

Returns the derivative of the function with respect to the Y dimension. This is the second input whenever n_dims < 4 and the third input otherwise.

derivativeZ(self, *args)

Returns the derivative of the function with respect to the Z dimension. This is the third input whenever n_dims < 4 and the fourth input otherwise.

class HARK.interpolation.LinearInterp(x_list, y_list, intercept_limit=None, slope_limit=None, lower_extrap=False)

A “from scratch” 1D linear interpolation class. Allows for linear or decay extrapolation (approaching a limiting linear function from below).

Methods

 __call__(self, x) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivative(self, x) Evaluates the derivative of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. eval_with_derivative(self, x) Evaluates the interpolated function and its derivative at the given input. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.LinearInterpOnInterp1D(xInterpolators, y_values)

A 2D interpolator that linearly interpolates among a list of 1D interpolators.

Methods

 __call__(self, x, y) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y) Evaluates the partial derivative of interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y) Evaluates the partial derivative of interpolated function with respect to y (the second argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.LinearInterpOnInterp2D(xyInterpolators, z_values)

A 3D interpolation method that linearly interpolates between “layers” of arbitrary 2D interpolations. Useful for models with two endogenous state variables and one exogenous state variable when solving with the endogenous grid method. NOTE: should not be used if an exogenous 3D grid is used, will be significantly slower than TrilinearInterp.

Methods

 __call__(self, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to y (the second argument) at the given input. derivativeZ(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to z (the third argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.LowerEnvelope(*functions)

The lower envelope of a finite set of 1D functions, each of which can be of any class that has the methods __call__, derivative, and eval_with_derivative. Generally: it combines HARKinterpolator1Ds.

Methods

 __call__(self, x) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivative(self, x) Evaluates the derivative of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. eval_with_derivative(self, x) Evaluates the interpolated function and its derivative at the given input. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.LowerEnvelope2D(*functions)

The lower envelope of a finite set of 2D functions, each of which can be of any class that has the methods __call__, derivativeX, and derivativeY. Generally: it combines HARKinterpolator2Ds.

Methods

 __call__(self, x, y) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y) Evaluates the partial derivative of interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y) Evaluates the partial derivative of interpolated function with respect to y (the second argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.LowerEnvelope3D(*functions)

The lower envelope of a finite set of 3D functions, each of which can be of any class that has the methods __call__, derivativeX, derivativeY, and derivativeZ. Generally: it combines HARKinterpolator2Ds.

Methods

 __call__(self, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to y (the second argument) at the given input. derivativeZ(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to z (the third argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.QuadlinearInterp(f_values, w_list, x_list, y_list, z_list, wSearchFunc=None, xSearchFunc=None, ySearchFunc=None, zSearchFunc=None)

Quadlinear full (or tensor) grid interpolation of a function f(w,x,y,z).

Methods

 __call__(self, w, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeW(self, w, x, y, z) Evaluates the partial derivative with respect to w (the first argument) of the interpolated function at the given input. derivativeX(self, w, x, y, z) Evaluates the partial derivative with respect to x (the second argument) of the interpolated function at the given input. derivativeY(self, w, x, y, z) Evaluates the partial derivative with respect to y (the third argument) of the interpolated function at the given input. derivativeZ(self, w, x, y, z) Evaluates the partial derivative with respect to z (the fourth argument) of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.TrilinearInterp(f_values, x_list, y_list, z_list, xSearchFunc=None, ySearchFunc=None, zSearchFunc=None)

Trilinear full (or tensor) grid interpolation of a function f(x,y,z).

Methods

 __call__(self, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to x (the first argument) at the given input. derivativeY(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to y (the second argument) at the given input. derivativeZ(self, x, y, z) Evaluates the partial derivative of the interpolated function with respect to z (the third argument) at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.TrilinearInterpOnInterp1D(wInterpolators, x_values, y_values, z_values)

A 4D interpolator that trilinearly interpolates among a list of lists of 1D interpolators.

Methods

 __call__(self, w, x, y, z) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeW(self, w, x, y, z) Evaluates the partial derivative with respect to w (the first argument) of the interpolated function at the given input. derivativeX(self, w, x, y, z) Evaluates the partial derivative with respect to x (the second argument) of the interpolated function at the given input. derivativeY(self, w, x, y, z) Evaluates the partial derivative with respect to y (the third argument) of the interpolated function at the given input. derivativeZ(self, w, x, y, z) Evaluates the partial derivative with respect to z (the fourth argument) of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.UpperEnvelope(*functions)

The upper envelope of a finite set of 1D functions, each of which can be of any class that has the methods __call__, derivative, and eval_with_derivative. Generally: it combines HARKinterpolator1Ds.

Methods

 __call__(self, x) Evaluates the interpolated function at the given input. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivative(self, x) Evaluates the derivative of the interpolated function at the given input. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. eval_with_derivative(self, x) Evaluates the interpolated function and its derivative at the given input. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
class HARK.interpolation.VariableLowerBoundFunc2D(func, lowerBound)

A class for representing a function with two real inputs whose lower bound in the first input depends on the second input. Useful for managing curved natural borrowing constraints, as occurs in the persistent shocks model.

Methods

 __call__(self, x, y) Evaluate the function at given state space points. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y) Evaluate the first derivative with respect to x of the function at given state space points. derivativeY(self, x, y) Evaluate the first derivative with respect to y of the function at given state space points. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
derivativeX(self, x, y)

Evaluate the first derivative with respect to x of the function at given state space points.

Parameters: x : np.array First input values. y : np.array Second input values; should be of same shape as x. dfdx_out : np.array First derivative of function with respect to the first input, evaluated at (x,y), of same shape as inputs.
derivativeY(self, x, y)

Evaluate the first derivative with respect to y of the function at given state space points.

Parameters: x : np.array First input values. y : np.array Second input values; should be of same shape as x. dfdy_out : np.array First derivative of function with respect to the second input, evaluated at (x,y), of same shape as inputs.
class HARK.interpolation.VariableLowerBoundFunc3D(func, lowerBound)

A class for representing a function with three real inputs whose lower bound in the first input depends on the second input. Useful for managing curved natural borrowing constraints.

Methods

 __call__(self, x, y, z) Evaluate the function at given state space points. assignParameters(self, \*\*kwds) Assign an arbitrary number of attributes to this agent. derivativeX(self, x, y, z) Evaluate the first derivative with respect to x of the function at given state space points. derivativeY(self, x, y, z) Evaluate the first derivative with respect to y of the function at given state space points. derivativeZ(self, x, y, z) Evaluate the first derivative with respect to z of the function at given state space points. distance(self, other) A generic distance method, which requires the existence of an attribute called distance_criteria, giving a list of strings naming the attributes to be considered by the distance metric. getAvg(self, varname, \*\*kwds) Calculates the average of an attribute of this instance.
derivativeX(self, x, y, z)

Evaluate the first derivative with respect to x of the function at given state space points.

Parameters: x : np.array First input values. y : np.array Second input values; should be of same shape as x. z : np.array Third input values; should be of same shape as x. dfdx_out : np.array First derivative of function with respect to the first input, evaluated at (x,y,z), of same shape as inputs.
derivativeY(self, x, y, z)

Evaluate the first derivative with respect to y of the function at given state space points.

Parameters: x : np.array First input values. y : np.array Second input values; should be of same shape as x. z : np.array Third input values; should be of same shape as x. dfdy_out : np.array First derivative of function with respect to the second input, evaluated at (x,y,z), of same shape as inputs.
derivativeZ(self, x, y, z)

Evaluate the first derivative with respect to z of the function at given state space points.

Parameters: x : np.array First input values. y : np.array Second input values; should be of same shape as x. z : np.array Third input values; should be of same shape as x. dfdz_out : np.array First derivative of function with respect to the third input, evaluated at (x,y,z), of same shape as inputs.
HARK.interpolation.calcChoiceProbs(Vals, sigma)

Returns the choice probabilities given the choice specific value functions Vals. Probabilities are degenerate if sigma == 0.0. Parameters ———- Vals : [numpy.array]

A numpy.array that holds choice specific values at common grid points.
sigma : float
A number that controls the variance of the taste shocks
Probs : [numpy.array]
A numpy.array that holds the discrete choice probabilities
HARK.interpolation.calcLogSum(Vals, sigma)

Returns the optimal value given the choice specific value functions Vals. Parameters ———- Vals : [numpy.array]

A numpy.array that holds choice specific values at common grid points.
sigma : float
A number that controls the variance of the taste shocks
V : [numpy.array]
A numpy.array that holds the integrated value function.
HARK.interpolation.calcLogSumChoiceProbs(Vals, sigma)

Returns the final optimal value and choice probabilities given the choice specific value functions Vals. Probabilities are degenerate if sigma == 0.0. Parameters ———- Vals : [numpy.array]

A numpy.array that holds choice specific values at common grid points.
sigma : float
A number that controls the variance of the taste shocks
V : [numpy.array]
A numpy.array that holds the integrated value function.
P : [numpy.array]
A numpy.array that holds the discrete choice probabilities