bspline

class pydl.pydlutils.bspline.bspline(x, nord=4, npoly=1, bkpt=None, bkspread=1.0, placed=None, bkspace=None, nbkpts=None, everyn=None)

Bases: object

B-spline class.

Functions in the idlutils bspline library are implemented as methods on this class.

Parameters:

xnumpy.ndarray

The data.

nordint, optional

The order of the B-spline. Default is 4, which is cubic.

npolyint, optional

Polynomial order to fit over 2nd variable, if supplied. If not supplied the order is 1.

bkptnumpy.ndarray, optional

An initial breakpoint vector. If omitted, breakpoints will be computed from other options.

bkspreadfloat, optional

Applies a scale factor to the difference between successive value of bkpt.

placednumpy.ndarray, optional

Precalculated breakpoint positions.

bkspacefloat, optional

Spacing of breakpoints in units of x.

nbkptsint, optional

Number of breakpoints to span x range; minimum is 2 (the endpoints).

everynint, optional

Spacing of breakpoints in good pixels.

Attributes:

breakpoints

The processed breakpoints for the fit, based on the initialization options.

nord

The order of the B-spline. Default is 4, which is cubic.

npoly

Polynomial order to fit over 2nd variable, if supplied. If not supplied the order is 1.

mask

A mask for breakpoints.

coeff

Internal attribute used by fit().

icoeff

Internal attribute used by fit().

xmin

Normalization minimum for the second variable in 2-dimensional fits.

xmax

Normalization maximum for the second variable in 2-dimensional fits.

funcname

For 2-dimensional fits, this is the function for the second variable. The default is ‘legendre’.

Notes

Although this code has been tested (in the sense that it reproduces the original idlutils code) and appears to work for a subset 1-dimensional cases, it should not be used for 2 dimensions or more exotic 1-dimensional cases.

Init creates an object whose attributes are similar to the structure returned by the create_bsplineset() function.

Methods Summary

action(x[, x2])	Construct banded B-spline matrix, with dimensions [ndata, bandwidth].
bsplvn(x, ileft)	Calculates the value of all possibly nonzero B-splines at x of a certain order.
fit(xdata, ydata, invvar[, x2])	Calculate a B-spline in the least-squares sense.
intrv(x)	Find the segment between breakpoints which contain each value in the array x.
maskpoints(err)	Perform simple logic of which breakpoints to mask.
value(x[, x2, action, lower, upper])	Evaluate a B-spline at specified values.

Methods Documentation

action(x, x2=None)

Construct banded B-spline matrix, with dimensions [ndata, bandwidth].

Parameters:

xnumpy.ndarray

Independent variable.

x2numpy.ndarray, optional

Orthogonal dependent variable for 2d fits.

Returns:

tuple

A tuple containing the B-spline action matrix; the ‘lower’ parameter, a list of pixel positions, each corresponding to the first occurence of position greater than breakpoint indx; and ‘upper’, Same as lower, but denotes the upper pixel positions.

bsplvn(x, ileft)

Calculates the value of all possibly nonzero B-splines at x of a certain order.

Parameters:

xnumpy.ndarray

Independent variable.

ileftint

Breakpoint segements that contain x.

Returns:

numpy.ndarray

B-spline values.

fit(xdata, ydata, invvar, x2=None)

Calculate a B-spline in the least-squares sense.

Fit is based on two variables: xdata which is sorted and spans a large range where breakpoints are required ydata which can be described with a low order polynomial.

Parameters:

xdatanumpy.ndarray

Independent variable.

ydatanumpy.ndarray

Dependent variable.

invvarnumpy.ndarray

Inverse variance of ydata.

x2numpy.ndarray, optional

Orthogonal dependent variable for 2d fits.

Returns:

tuple

A tuple containing an integer error code, and the evaluation of the b-spline at the input values. An error code of -2 is a failure, -1 indicates dropped breakpoints, 0 is success, and positive integers indicate ill-conditioned breakpoints.

intrv(x)

Find the segment between breakpoints which contain each value in the array x.

The minimum breakpoint is nbkptord - 1, and the maximum is nbkpt - nbkptord - 1.

Parameters:

xnumpy.ndarray

Data values, assumed to be monotonically increasing.

Returns:

numpy.ndarray

Position of array elements with respect to breakpoints.

maskpoints(err)

Perform simple logic of which breakpoints to mask.

Parameters:

errnumpy.ndarray

The list of indexes returned by the cholesky routines.

Returns:

int

An integer indicating the results of the masking. -1 indicates that the error points were successfully masked. -2 indicates failure; the calculation should be aborted.

Notes

The mask attribute is modified, assuming it is possible to create the mask.

value(x, x2=None, action=None, lower=None, upper=None)

Evaluate a B-spline at specified values.

Parameters:

xnumpy.ndarray

Independent variable.

x2numpy.ndarray, optional

Orthogonal dependent variable for 2d fits.

actionnumpy.ndarray, optional

Action matrix to use. If not supplied it is calculated.

lowernumpy.ndarray, optional

If the action parameter is supplied, this parameter must also be supplied.

uppernumpy.ndarray, optional

If the action parameter is supplied, this parameter must also be supplied.

Returns:

tuple

A tuple containing the results of the bspline evaluation and a mask indicating where the evaluation was good.