我们从Python开源项目中，提取了以下13个代码示例，用于说明如何使用numpy.polyder()。
def calc_approx(time, altitude, div = 5, dt = 1.0, deg = 100, lim = 1): time_list, altitude_list, velocity_y = [],[],[] for i in range(div): f = trendline.approx_func( time[max(int((i - lim) * len(time) / div), 0):min(len(time), int((i + lim) * len(time) / div))], altitude[max(int((i - lim) * len(time) / div), 0):min(len(time), int((i + lim) * len(time) / div))], deg) der = np.polyder(f) #print(time[int(i * len(time) / div)], min(time[-1], time[int((i + 1) * len(time) / div) - 1])) for t in np.arange(time[int(i * len(time) / div)], min(time[-1], time[int((i + 1) * len(time) / div) - 1]), dt): #for t in time: # if t >= time[int(i * len(time) / div)] and t < min(time[-1], time[int((i + 1) * len(time) / div) - 1]): time_list.append(t) altitude_list.append(f(t)) velocity_y.append(der(t)) return time_list, velocity_y, altitude_list
def calc_adot(cp,order=1): a=[] for i in range(len(cp)): ptmp = [] tmp = 0 for j in range(len(cp)): if j != i: row = [] row.insert(0,1/(cp[i]-cp[j])) row.insert(1,-cp[j]/(cp[i]-cp[j])) ptmp.insert(tmp,row) tmp += 1 p=[1] for j in range(len(cp)-1): p = conv(p,ptmp[j]) pder = numpy.polyder(p,order) arow = [] for j in range(len(cp)): arow.append(numpy.polyval(pder,cp[j])) a.append(arow) return a
def test_polyder_return_type(self): # Ticket #1249 assert_(isinstance(np.polyder(np.poly1d([1]), 0), np.poly1d)) assert_(isinstance(np.polyder([1], 0), np.ndarray)) assert_(isinstance(np.polyder(np.poly1d([1]), 1), np.poly1d)) assert_(isinstance(np.polyder([1], 1), np.ndarray))
def compute_grun_along_one_direction(nq,modes,ngeo,cgeo,celldmsx,freqgeo,rangegeo,xindex=0): """ Compute the Gruneisen parameters along one direction. This function uses a 1-dimensional polynomial of fourth degree to fit the frequencies along a certain direction (along a and c axis in hexagonal systems for example). """ # set a numpy array of volumes for the fit (n=5) xtemp=[] for igeo in rangegeo: xtemp.append(celldmsx[igeo,xindex]) x=np.array(xtemp) grun=[] for iq in range(0,nq): grunq=[] for ifreq in range(0,modes): ytemp=[] for igeo in rangegeo: ytemp.append(freqgeo[igeo,iq,ifreq]) y=np.array(ytemp) z=np.polyfit(x, y, 4) p=np.poly1d(z) pderiv=np.polyder(p) if freqgeo[cgeo[xindex],iq,ifreq]<1E-3: grunq.append(0.0) else: grunq.append(pderiv(celldmsx[cgeo[xindex],xindex])/freqgeo[cgeo[xindex],iq,ifreq]) #*celldmsx[cgeo[xindex],xindex]) grun.append(grunq) return np.array(grun) ################################################################################
def basis_polys(): """ Returns the basis polynomials and their derivatives and antiderivatives """ nodes, _, _ = quad() ? = [lagrange(nodes,eye(N+1)[i]) for i in range(N+1)] ?Der = [[polyder(?_p, m=a) for ?_p in ?] for a in range(N+1)] ?Int = [polyint(?_p) for ?_p in ?] return ?, ?Der, ?Int
def polyval(fit, points, der=0, avg=False): """Evaluate polynomial generated by ``polyfit()`` on `points`. Parameters ---------- fit, points : see polyfit() der : int, optional Derivative order. Only for 1D, uses np.polyder(). avg : bool, optional Internal hack, only used by ``avgpolyval()``. Notes ----- For 1D we provide "analytic" derivatives using np.polyder(). For ND, we didn't implement an equivalent machinery. For 2D, you might get away with fitting a bispline (see Interpol2D) and use it's derivs. For ND, try rbf.py's RBF interpolator which has at least 1st derivatives for arbitrary dimensions. See Also -------- :class:`PolyFit`, :class:`PolyFit1D`, :func:`polyfit` """ pscale, pmin = fit['pscale'], fit['pmin'] vscale, vmin = fit['vscale'], fit['vmin'] if der > 0: assert points.shape[1] == 1, "deriv only for 1d poly (ndim=1)" # ::-1 b/c numpy stores poly coeffs in reversed order dcoeffs = np.polyder(fit['coeffs'][::-1], m=der) return np.polyval(dcoeffs, (points[:,0] - pmin[0,0]) / pscale[0,0]) / \ pscale[0,0]**der * vscale else: vand = vander((points - pmin) / pscale, fit['deg']) if avg: return np.dot(vand, fit['coeffs']) * vscale else: return np.dot(vand, fit['coeffs']) * vscale + vmin
def calc_approx_func(time, altitude, div = 5, der = 0 ,deg = 100, lim = 1): dict = {} for i in range(div): f = trendline.approx_func( time[max(int((i - lim) * len(time) / div), 0):min(len(time), int((i + lim) * len(time) / div))], altitude[max(int((i - lim) * len(time) / div), 0):min(len(time), int((i + lim) * len(time) / div))], deg) for j in range(der): f = np.polyder(f) dict[min(time[-1], time[int((i + 1) * len(time) / div) - 1])] = f return dict
def birch_murnaghan_fit(energies, volumes): """ least squares fit of a Birch-Murnaghan equation of state curve. From delta project containing in its columns the volumes in A^3/atom and energies in eV/atom # The following code is based on the source code of eos.py from the Atomic # Simulation Environment (ASE) <https://wiki.fysik.dtu.dk/ase/>. :params energies: list (numpy arrays!) of total energies eV/atom :params volumes: list (numpy arrays!) of volumes in A^3/atom #volume, bulk_modulus, bulk_deriv, residuals = Birch_Murnaghan_fit(data) """ fitdata = np.polyfit(volumes[:]**(-2./3.), energies[:], 3, full=True) ssr = fitdata[1] sst = np.sum((energies[:] - np.average(energies[:]))**2.) #print(fitdata) #print(ssr) #print(sst) residuals0 = ssr/sst deriv0 = np.poly1d(fitdata[0]) deriv1 = np.polyder(deriv0, 1) deriv2 = np.polyder(deriv1, 1) deriv3 = np.polyder(deriv2, 1) volume0 = 0 x = 0 for x in np.roots(deriv1): if x > 0 and deriv2(x) > 0: volume0 = x**(-3./2.) break if volume0 == 0: print('Error: No minimum could be found') exit() derivV2 = 4./9. * x**5. * deriv2(x) derivV3 = (-20./9. * x**(13./2.) * deriv2(x) - 8./27. * x**(15./2.) * deriv3(x)) bulk_modulus0 = derivV2 / x**(3./2.) #print('bulk modulus 0: {} '.format(bulk_modulus0)) bulk_deriv0 = -1 - x**(-3./2.) * derivV3 / derivV2 return volume0, bulk_modulus0, bulk_deriv0, residuals0
