quad

Defining various quadrature routines.

Based on the quadrature routines found in the CompEcon toolbox by Miranda and Fackler.

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwbeta(n, a=1.0, b=1.0)

Computes nodes and weights for beta distribution

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

ascalar or array_like(float), optional(default=1.0)

A length-d

barray_like(float), optional(default=1.0)

A d x d array representing the variance-covariance matrix of the multivariate normal distribution.

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwbeta in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwcheb(n, a=1, b=1)

Computes multivariate Guass-Checbychev quadrature nodes and weights.

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

ascalar or array_like(float)

A length-d iterable of lower endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

bscalar or array_like(float)

A length-d iterable of upper endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwcheb in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwequi(n, a, b, kind='N', equidist_pp=None, random_state=None)

Generates equidistributed sequences with property that averages value of integrable function evaluated over the sequence converges to the integral as n goes to infinity.

Parameters:

nint

Number of sequence points

ascalar or array_like(float)

A length-d iterable of lower endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

bscalar or array_like(float)

A length-d iterable of upper endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

kindstring, optional(default=”N”)

One of the following:

• N - Neiderreiter (default)

• W - Weyl

• H - Haber

• R - pseudo Random

equidist_pparray_like, optional(default=None)

TODO: I don’t know what this does

random_stateint or np.random.RandomState/Generator, optional

Random seed (integer) or np.random.RandomState or Generator instance to set the initial state of the random number generator for reproducibility. If None, a randomly initialized RandomState is used. Relevant only when setting kind=’R’.

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwequi in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwgamma(n, a=1.0, b=1.0, tol=3e-14)

Computes nodes and weights for gamma distribution

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

ascalar or array_like(float)optional(default=ones(d))

Shape parameter of the gamma distribution parameter. Must be positive

bscalar or array_like(float)optional(default=ones(d))

Scale parameter of the gamma distribution parameter. Must be positive

tolscalar or array_like(float)optional(default=ones(d) * 3e-14)

Tolerance parameter for newton iterations for each node

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwgamma in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwlege(n, a, b)

Computes multivariate Guass-Legendre quadrature nodes and weights.

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

ascalar or array_like(float)

A length-d iterable of lower endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

bscalar or array_like(float)

A length-d iterable of upper endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwlege in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwlogn(n, mu=None, sig2=None)

Computes nodes and weights for multivariate lognormal distribution

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

muscalar or array_like(float), optional(default=zeros(d))

The means of each dimension of the random variable. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

sig2array_like(float), optional(default=eye(d))

A d x d array representing the variance-covariance matrix of the multivariate normal distribution.

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwlogn in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwnorm(n, mu=None, sig2=None, usesqrtm=False)

Computes nodes and weights for multivariate normal distribution

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

muscalar or array_like(float), optional(default=zeros(d))

The means of each dimension of the random variable. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

sig2array_like(float), optional(default=eye(d))

A d x d array representing the variance-covariance matrix of the multivariate normal distribution.

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwnorm in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwsimp(n, a, b)

Computes multivariate Simpson quadrature nodes and weights.

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

ascalar or array_like(float)

A length-d iterable of lower endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

bscalar or array_like(float)

A length-d iterable of upper endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwsimp in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwtrap(n, a, b)

Computes multivariate trapezoid rule quadrature nodes and weights.

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

ascalar or array_like(float)

A length-d iterable of lower endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

bscalar or array_like(float)

A length-d iterable of upper endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwtrap in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.qnwunif(n, a, b)

Computes quadrature nodes and weights for multivariate uniform distribution

Parameters:

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

ascalar or array_like(float)

A length-d iterable of lower endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

bscalar or array_like(float)

A length-d iterable of upper endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

Returns:

nodesnp.ndarray(dtype=float)

Quadrature nodes

weightsnp.ndarray(dtype=float)

Weights for quadrature nodes

Notes

Based of original function qnwunif in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.

quantecon.quad.quadrect(f, n, a, b, kind='lege', random_state=None, *args, **kwargs)

Integrate the d-dimensional function f on a rectangle with lower and upper bound for dimension i defined by a[i] and b[i], respectively; using n[i] points.

Parameters:

ffunction

The function to integrate over. This should be a function that accepts as its first argument a matrix representing points along each dimension (each dimension is a column). Other arguments that need to be passed to the function are caught by *args and **kwargs

nint or array_like(float)

A length-d iterable of the number of nodes in each dimension

ascalar or array_like(float)

A length-d iterable of lower endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

bscalar or array_like(float)

A length-d iterable of upper endpoints. If a scalar is given, that constant is repeated d times, where d is the number of dimensions

kindstring, optional(default=’lege’)

Specifies which type of integration to perform. Valid values are:

lege - Gauss-Legendre cheb - Gauss-Chebyshev trap - trapezoid rule simp - Simpson rule N - Neiderreiter equidistributed sequence W - Weyl equidistributed sequence H - Haber equidistributed sequence R - Monte Carlo

random_stateint or np.random.RandomState/Generator, optional

Random seed (integer) or np.random.RandomState or Generator instance to set the initial state of the random number generator for reproducibility. If None, a randomly initialized RandomState is used. Relevant only when setting kind=’R’.

*args, **kwargs

Other arguments passed to the function f

Returns:

outscalar (float)

The value of the integral on the region [a, b]

Notes

Based of original function quadrect in CompEcon toolbox by Miranda and Fackler

References

Miranda, Mario J, and Paul L Fackler. Applied Computational Economics and Finance, MIT Press, 2002.