plotting module

plotting.SG(m)

This function evaluates the coordinates of all points on the gasket up to a certain level V_m.

Parameters

- number of levels V_m we would like to find coordinates for (m) –

Returns

y - ((3^m+3)/2)*2 matrix holding coordinate values

from http://www.math.cornell.edu/~mhall/SGprograms/SG.m

plotting.eval_op(deg, k, level=7, T=None, frac=True, coefs=None, symm=False)

Function that evaluates the Sobolev Orthogonal Polynomials

Parameters

• - Degree of SOP s_{j} we would like to evaluate (deg) –

• - Coefficient Matrix of the Orthogonal Polynomials (T) –

• - Type of SOP (k) –

• - Number of levels we want to evaluate the SOP (level) –

• - array of monomial values at the required level and degree or (T) – tuple of (filename of .npz/.npy file containing this array , array name key string)

• - array of coefficient values at the required degree and symmetry or (coefs) – tuple of (filename of .npz/.npy file containing this array , array name key string)

• - Boolean representing whether or not the fully symmetric orthogonal polynomials are needed (symm) –

Returns

q - Values of the SOP of type k at some level

plotting.fi(x, qi)

This function is a contractive similarity of the plane centered at the point qi of dilation factor 1/2.

Parameters

• - point in the plane (x) –

• - point toward which to contract distances by 1/2 (qi) –

Returns

evaluates the similarity

from http://www.math.cornell.edu/~mhall/SGprograms/fi.m

plotting.gaskplot(f, m, ax, color='b')

This function plots a function defined on the level m vertices of SG.

Parameters

• - vector of size 3^ (f) –

• - level of the function (m) –

Returns

plots figure of the graph

from http://www.math.cornell.edu/~mhall/SGprograms/gaskplot.m

plotting.getOmegas(deg, k, frac=True, coefs=None, symm=False)

Function that generates the Sobolev Orthogonal Polynomials

Parameters

• - highest degree of the Sobolev Orthogonal Polynomial (deg) – we would like to find

• - Type of Sobolev Orthogonal Polynomial (k) –

• - array of coefficient values at the required degree and symmetry or (coefs) – tuple of (filename of .npz/.npy file containing this array , array name key string)

• - Boolean representing whether or not the fully symmetric orthogonal polynomials are needed (symm) –

Returns

W - (deg+2)*(deg+2) matrix, representing the coefficients of

the Sobolev Orthogonal Polynomial of order 0 - deg+1

plotting.plot_easy_basis(num, k, level=7, W=None)

Plot the Easy Basis

Parameters

• - Number of monomials we would like to plot (num) –

• - Type of Monomial (k) –

• - The level we would like to plot each monomial (level) –

• - array of easy basis values at the required level and degree or (W) – tuple of (filename of .npz/.npy file containing this array , array name key string)

Returns

figures of the SOP of type k, from P_{num-1, k} down to P_{0, k}.

plotting.plot_general(T, level=7)

Plot a general function given input

Parameters

• - Number of monomials we would like to plot (num) –

• - Type of Monomial (k) –

• - The level we would like to plot each monomial (level) –

Returns

figures of the SOP of type k, from P_{num-1, k} down to P_{0, k}.

plotting.plot_monomial(num, k, level=7, T=None, symm=False)

Plot the Monomials

Parameters

• - Number of monomials we would like to plot (num) –

• - Type of Monomial (k) –

• - The level we would like to plot each monomial (level) –

• - array of monomial values at the required level and degree or (T) – tuple of (filename of .npz/.npy file containing this array , array name key string)

• - Boolean representing whether or not the fully symmetric orthogonal polynomials are needed (symm) –

Returns

figures of the SOP of type k, from P_{num-1, k} down to P_{0, k}.

plotting.plot_op(num, k, level=7, T=None, coefs=None, symm=False)

Plot the Sobolev Orthogonal Polynomials

Parameters

• - Number of Antisymmetric SOPs we would like to plot (num) –

• - Type of SOP (k) –

• - The level we would like to plot each SOP (level) –

• - array of monomial values at the required level and degree or (T) – tuple of (filename of .npz/.npy file containing this array , array name key string)

• - array of coefficient values at the required degree and symmetry or (coefs) – tuple of (filename of .npz/.npy file containing this array , array name key string)

• - Boolean representing whether or not the fully symmetric orthogonal polynomials are needed (symm) –

Returns

figures of the SOP of type k, from s_{num-1} down to s_{0}.

plotting.qcontract(x, q)

This function takes in a column of coordinate pairs and computes their image under the similarity which contracts distance to the point q by a factor of 1/2.

Parameters

• - (x) –

• - the number of points (n) –

Returns

y - coordinates of the n images

from http://www.math.cornell.edu/~mhall/SGprograms/qcontract.m