Cubic Spline Matrices (fiducia.cspline)¶

Created on Fri Mar 8 09:41:36 2019

Functions for working with cubic spline equation in matrix form.

@author: Pawel M. Kozlowski

Functions¶

`splineCoords`(energy, energyStart, energyEnd)	Convert photon energy value into normalized coordinates for a particular spline region.
`splineCoordsInv`(energyNorm, energyStart, …)	Given a normalized energy value and the bounds of a spline segment, return the un-normalized photon energy value.
`yCoeffArr`(energyNorm, chLen)	Returns the matrix M_y(t) for a given value of t in:
`dCoeffArr`(energyNorm, chLen)	Returns the matrix M_D(t) for a given value of t in:
`dToyArr`(chLen)	Construct matrix for converting from \(D_i\) to \(y_i\) vector.
`responseInterp`(energyNorm, energyMin, …)	Given a DANTE detector response as a function of energy, convert the response to normalized photon energy, t, over a given spline segment, and return interpolated response values for a given value of t.
`yChiCoeffArr`(energyNorm, chLen, dToY)	This is the matrix corresponding to:
`yChiCoeffArrEnergies`(energyNorms, chLen, dToY)	This is the matrix corresponding to:
`fancyTrapz2`(energyNorms, yChis, segments, …)	Trap rule integration of the folding between our \(M_{y \chi}\) matrix and response function matrix, with respect to normalized photon energy, for each channel.
`segmentsArr`(knots)	Returns the bounds of each spline segment, given the spline knot points.
`detectorArr`(channels, knots, responseFrame)	Matrix representing the spectrally integrated folding of the detector response with a cubic spline interpolation of the x-ray spectrum.
`knotSolve`(signals, detArr, …[, …])	Get knot points \(y_i\) from measured DANTE signals \(S_d\).
`reconstructSpectrum`(chLen, knots, knotsY[, …])	Reconstruct the inferred DANTE spectrum given the knot points \(y_i\) obtained from knotSolve().