def interval_design(a, b, N):
"""
Equally spaced points on an interval.
:param float a: The left endpoint of the interval.
:param flaot b: The right endpoint of the interval.
:param int N: int The number of points in the design.
:return: design, N-by-1 matrix that contains the design points in the
interval. It does not contain the endpoints.
:rtype: ndarray
"""
logging.getLogger(__name__).debug('Interval design with {:d} points.'.format(N))
y = np.linspace(a, b, N+2)
design = mi.atleast_2d_col(y[1:-1])
return design
def gauss_hermite(N):
"""
Tensor product Gauss-Hermite quadrature rule.
:param int[] N: Number of nodes in each dimension of the quadrature rule
:return: x, N-by-1 array of quadrature nodes
:rtype: ndarray
:return: w, N-by-1 array of quadrature weights
:rtype: ndarray
**Notes**
This computation is inspired by Walter Gautschi's code at
https://www.cs.purdue.edu/archives/2002/wxg/codes/OPQ.html.
"""
if isinstance(N, int):
N = [N]
if type(N) is not list:
raise TypeError("N must be a list.")
Npts = int(np.prod(np.array(N)))
logging.getLogger(__name__).debug(
"Making a tensor product Gauss-Hermite rule with {:d} points in {:d} dimensions.".format(Npts, len(N))
)
if len(N) == 1:
x, w = gh1d(N[0])
else:
x = np.array([[1.0]])
w = np.array([[1.0]])
for n in N:
xi, wi = gh1d(n)
xL = np.kron(x.copy(), np.ones(xi.shape))
xU = np.kron(np.ones((x.shape[0], 1)), xi)
x = np.hstack((xL, xU))
w = np.kron(w.copy(), wi)
x, w = np.atleast_2d(x[:, 1:]), mi.atleast_2d_col(w)
return x, w
def gauss_legendre(N):
"""Tensor product Gauss-Legendre quadrature rule.
Parameters
----------
N : int[]
number of nodes in each dimension of the quadrature rule
Returns
-------
x : ndarray
N-by-1 array of quadrature nodes
w : ndarray
N-by-1 array of quadrature weights
Notes
-----
This computation is inspired by Walter Gautschi's code at
https://www.cs.purdue.edu/archives/2002/wxg/codes/OPQ.html.
"""
if isinstance(N, Integral):
N = [N]
if type(N) is not list:
raise TypeError('N must be a list.')
if len(N) == 1:
x, w = gl1d(N[0])
else:
x = np.array([[1.0]])
w = np.array([[1.0]])
for n in N:
xi, wi = gl1d(n)
xL = np.kron(x.copy(), np.ones(xi.shape))
xU = np.kron(np.ones((x.shape[0],1)), xi)
x = np.hstack((xL, xU))
w = np.kron(w.copy(), wi)
x, w = np.atleast_2d(x[:,1:]), mi.atleast_2d_col(w)
return x, w
def gauss_legendre(N):
"""Tensor product Gauss-Legendre quadrature rule.
Parameters
----------
N : int[]
number of nodes in each dimension of the quadrature rule
Returns
-------
x : ndarray
N-by-1 array of quadrature nodes
w : ndarray
N-by-1 array of quadrature weights
Notes
-----
This computation is inspired by Walter Gautschi's code at
https://www.cs.purdue.edu/archives/2002/wxg/codes/OPQ.html.
"""
if isinstance(N, int):
N = [N]
if type(N) is not list:
raise TypeError('N must be a list.')
if len(N) == 1:
x, w = gl1d(N[0])
else:
x = np.array([[1.0]])
w = np.array([[1.0]])
for n in N:
xi, wi = gl1d(n)
xL = np.kron(x.copy(), np.ones(xi.shape))
xU = np.kron(np.ones((x.shape[0],1)), xi)
x = np.hstack((xL, xU))
w = np.kron(w.copy(), wi)
x, w = np.atleast_2d(x[:,1:]), mi.atleast_2d_col(w)
return x, w
def interval_design(a, b, N):
"""Equally spaced points on an interval.
Parameters
----------
a : float
the left endpoint of the interval
b : float
the right endpoint of the interval
N : int
the number of points in the design
Returns
-------
design, ndarray
N-by-1 matrix that contains the design points in the interval. It does
not contain the endpoints.
"""
y = np.linspace(a, b, N+2)
design = mi.atleast_2d_col(y[1:-1])
return design
