Lesser Functions

• bigRoots(x,r) - Find roots with extremely large magnitude.
• bitreverse(n) - An extremely efficient way to compute the bit reversal of 0:(-1 + 2^n).
• csort(z,method) - Sort a complex array by abs(z), angle(z), real(z) or imag(z)
• deflate(x,z) - Deflate 1 root (and its complex conjugate if it is not real).
• expfitJWF(x,y) - Compute an L2 fit of the form y(x) = a*b^x. Note, Matlab has added a routine called expfit().
• expGain(x) - Exponential gain control.
• extremeRoots(x,ID_NUMBER) - Find roots with magnitude >1e8 or <1e-8.
• flip(x) - Combines flipud and fliplr for 1D arrays.
• hornerWithError(x,z) - Horner's method of polynomial evaluation with error estimates.
• hp2fp(z) - "Half plane to full plane." Given roots only in the upper half-plane, add their complex conjugates.
• hp2fp_2d(z,err,mul) - Given upper half-plane roots and error estimates and multiplicites, find the full plane set of roots with errors as a 2d array.
• hpdegree(z) - Find the polynomial degree given onlyl the upper half-plane roots.
• innerpart(x,z) - Find the inner part of a polynomial evaluation. It can not overflow, and it can be used for the purposes of polishing.
• ismembr(x, xErr, y, yErr) - A fuzzy test of which elements of x are members of y.
• iterativeDeflation(x, z, zErr, ID_NUM) - Deflate to find missing roots.
• ixFirstNz(x, threshold) - Index of the first non-zero value.
• ixLastNz(x, threshold) - Index of the last non-zero value.
• laguerre2(x,z) - The first version of Laguerre's polishing method.
• laguerre3(x,z) - The second version of Laguerre's polishing method.
• lejaJWF(z) - James Fox's version of leja sorting a set of complex numbers.
• lejaLang(z) - Marcus Lang's version of leja sorting a set of complex numbers - with a bug fix. Matlab uses the uncorrected version.
• linfit(x,y,LpNorm) - Linear fitting in the LP norm. CUrrently LP must be 2.
• normalizeJWF(x) - Normalize an array to have maximum absolute value of 1. Note, Matlab has added a routine called normalize() that works only on atoms.
• normalizePow2(x) - Normalize a polynomial to equalize the chances of underflow/overflow.
• nroots(x,r) - The approximate number of roots of polynomial x with magnitude < r.
• permuteVDC(x) - Permute the values of x by bit reversing its indicies.
• polishMultipleRoot(x,z,mul) - Polish a root with a known multiplicity.
• plotroots(z1, [z2, [z3]]) - plot 1, 2, or 3 sets of roots in polar coordinates.
• polycmp(x,y) - Normalize to unity and compare 2 polynomials for approximate equality.
• quadraticRoots(x) - Find the roots of a quadratic equation.
• rdft(x,direction) - The forward (direction=1) or inverse (direction=-1) split radix real FFT.
• rootsIni - Establish global variables.
• rootSpectrum(z, rootsOfUnity) - Find and multiply together the spectra of a set of roots.
• uhp(z) - Extract the roots which are in the upper half-plane.
• unfactor(z,polyType,Flag,Nspectrum) - Unfactor the roots of a polynomial.
• uniq(z,zerr) - Find the unique values of a fuzzy complex array.
• winding(s,flag) - Find the winding number of the curve s about 0. Flag tells whether to repeat the first value at the end.