def getNormilizedSpline(self): """ Returns the spline normilized by the integral of the absolute value. """ n = self.splineFiled.getSize() f = Function() for i in range(n): f.add(self.splineFiled.x(i),math.fabs(self.splineFiled.y(i))) integral = GaussLegendreIntegrator(500) integral.setLimits(self.splineFiled.x(0),self.splineFiled.x(n-1)) spline = SplineCH() spline.compile(f) res = integral.integral(spline) f = Function() for i in range(n): f.add(self.splineFiled.x(i),self.splineFiled.y(i)/res) spline = SplineCH() spline.compile(f) return spline
def FF(x): return math.sin(x) def FFP(x): return math.cos(x) n = 40 step = 2*math.pi/n for i in range(n): x = step*i+0.1*((1.0*i)/n)**2; y = FF(x) f.add(x,y) f.dump() spline = SplineCH() spline.compile(f) spline.dump() print "================" n = 100 step = 0.8*(f.getMaxX() - f.getMinX())/(n-1) y_dev_max = 0. yp_dev_max = 0. for j in range(n): x = f.getMinX() + j*step y = FF(x) yp = FFP(x) ys = math.fabs(spline.getY(x) - y) yps = math.fabs(spline.getYP(x) - yp)
integrator = GaussLegendreIntegrator(4)
print "Number of integral points =", integrator.getnPoints()
print "The integral of sin(x) from 0. to pi/2 is 1."
#------------------------------------------
# integral of sin(x) from 0. to pi/2 is 1.
#------------------------------------------
x_min = 0.
x_max = math.pi / 2
integrator.setLimits(x_min, x_max)
f = Function()
n = 10
for i in range(n):
x = x_min + i * (x_max - x_min) / (n - 1)
f.add(x, math.sin(x))
res = integrator.integral(f)
print "For Function integral =", res, " error=", math.fabs(res - 1.0)
spline = SplineCH()
spline.compile(f)
res = integrator.integral(spline)
print "For SplineCH integral =", res, " error=", math.fabs(res - 1.0)
print "=============== Integration points and weights ================"
point_weight_arr = integrator.getPointsAndWeights()
for (x, w) in point_weight_arr:
print "x = %8.5f w = %12.5g " % (x, w)
print "Done."
def __init__(self,splineFiled, zeroIsCenter = False): self.splineFiled = splineFiled #---------------------------------------------------- self.eps_root = 1.0e-6 self.rf_freq = 0.0 #self.e0_normalized_arr - normilized amplitudes of the gaps self.e0_normalized_arr = [] self.e0l_normalized_arr = [] # self.beta_arr - relativistic beta, cappa = 2*math.pi*rf_freq/(c_light*beta) self.beta_arr = [] self.cappa_arr = [] # self.ttp_ssp_gap_arr array with [T,Tp,S,Sp] for all gaps (T,Tp,S,Sp - Functions of cappa) self.ttp_ssp_gap_arr = [] # self.gap_polynoms_coef_arr array with polynomial coefficients for [T,Tp,S,Sp] for each gap self.gap_polynoms_coef_arr = [] # self.gap_polynoms_arr array with Polynomial instances for [T,Tp,S,Sp] for each gap self.gap_polynoms_arr = [] # self.gap_polynoms_t_tp_s_sp_err_arr - maximal relative errors for polynomial fitting self.gap_polynoms_t_tp_s_sp_err_arr = [] #----------------------------------------------------- #calculate the roots self.roots_arr = self.rootAnalysis() #find the roots of derivative - yp = y' - RFgap center positions if(zeroIsCenter): self.yp_roots_arr = [0.] else: self.yp_roots_arr = self.gapCentersAnalysis() #print "debug yp roots=",self.yp_roots_arr if(len(self.roots_arr) - 1 != len(self.yp_roots_arr)): rank = orbit_mpi.MPI_Comm_rank(mpi_comm.MPI_COMM_WORLD) if(rank == 0): print "Class RF_AxisFieldAnalysis." print "The structure of the input rf field spline is wrong!" print "roots of the filed =",self.roots_arr print "extrema positions =",self.yp_roots_arr sys.exit(1) # caluclate the position of the center of the cavity rf_center = 0 for i in range(1,len(self.yp_roots_arr)-1): rf_center += self.yp_roots_arr[i] rf_center /= (len(self.yp_roots_arr)-2) self.rf_center = rf_center # make spline for each RF gap self.gap_slpline_arr = [] #print "debug roots_arr=",self.roots_arr #---make splineGap with x in the [m] instead of [cm] for i in range(len(self.roots_arr)-1): x_center = self.yp_roots_arr[i] x0 = self.roots_arr[i] x1 = self.roots_arr[i+1] f = Function() f.add((x0-x_center),math.fabs(splineFiled.getY(x0))) for ix in range(splineFiled.getSize()-1): x = splineFiled.x(ix) if(x > x0 and x < x1): f.add((x-x_center),math.fabs(splineFiled.y(ix))) f.add((x1-x_center),math.fabs(splineFiled.getY(x1))) splineGap = SplineCH() splineGap.compile(f) n = splineGap.getSize() x_min = splineGap.x(0) x_max = splineGap.x(n-1) gap_length = x_max - x_min self.gap_slpline_arr.append([gap_length,(x_center - self.rf_center),splineGap])
def makeTransitTimeTables(self,beta_min,beta_max,n_table_points,rf_freq): """ It will calculate transit time factor tables for all RF gaps TTFs (T,S,Tp,Sp) are funcftions of the cappa variable = 2*pi*f/(c*beta) """ self.rf_freq = rf_freq c_light = 2.99792458e+8 self.beta_arr = [] self.cappa_arr = [] for i_beta in range(n_table_points): beta = beta_min + i_beta*(beta_max-beta_min)/(n_table_points-1) cappa = 2*math.pi*rf_freq/(c_light*beta) self.beta_arr.append(beta) self.cappa_arr.append(cappa) self.beta_arr.reverse() self.cappa_arr.reverse() #--calculate realtive gap amplitudes integral = GaussLegendreIntegrator(500) e0l_arr = [] e0l_sum = 0. for i in range(len(self.gap_slpline_arr)): [gap_length,x_center,splineGap] = self.gap_slpline_arr[i] n = splineGap.getSize() x_min = splineGap.x(0) x_max = splineGap.x(n-1) integral.setLimits(x_min,x_max) e0l = integral.integral(splineGap) e0l_sum += e0l e0l_arr.append(e0l) self.e0_normalized_arr = [] self.e0l_normalized_arr = [] e0_norm = e0l_arr[0]/self.gap_slpline_arr[0][0] e0l_norm = e0l_arr[0] for i in range(len(e0l_arr)): self.e0_normalized_arr.append((e0l_arr[i]/self.gap_slpline_arr[i][0])/e0_norm) self.e0l_normalized_arr.append((e0l_arr[i]/e0l_norm)) #--- calculate transit time factors self.ttp_ssp_gap_arr = [] for i in range(len(self.gap_slpline_arr)): func_T = Function() func_TP = Function() func_S = Function() func_SP = Function() self.ttp_ssp_gap_arr.append([func_T,func_TP,func_S,func_SP]) for i_gap in range(len(self.gap_slpline_arr)): [func_T,func_TP,func_S,func_SP] = self.ttp_ssp_gap_arr[i_gap] [gap_length,x0,spline] = self.gap_slpline_arr[i_gap] x_min = spline.x(0) x_max = spline.x(spline.getSize()-1) integral.setLimits(x_min,x_max) for i_beta in range(n_table_points): beta = self.beta_arr[i_beta] cappa = self.cappa_arr[i_beta] f_cos = Function() f_sin = Function() for isp in range(spline.getSize()): x = spline.x(isp) y = spline.y(isp) phase = cappa*x s = math.sin(phase) c = math.cos(phase) f_cos.add(x,c*y) f_sin.add(x,s*y) f_sp_cos = SplineCH() f_sp_sin = SplineCH() f_sp_cos.compile(f_cos) f_sp_sin.compile(f_sin) T = integral.integral(f_sp_cos) S = integral.integral(f_sp_sin) func_T.add(cappa,T/e0l_arr[i_gap]) func_S.add(cappa,S/e0l_arr[i_gap]) spline_T = SplineCH() spline_S = SplineCH() spline_T.compile(func_T) spline_S.compile(func_S) for i_beta in range(spline_T.getSize()): cappa = spline_T.x(i_beta) TP = spline_T.getYP(cappa) SP = spline_S.getYP(cappa) func_TP.add(cappa,TP) func_SP.add(cappa,SP) return self.ttp_ssp_gap_arr
data_in_arr.append(
["SDTL", sdtl_cav, sdtl_cav_rf_gap_names, rf_freq, 0.27, 0.65])
n_poly_order = 4
n_table_points = 100
dir_name = "ttf_results_data"
for [
cav_directory_name, cav_name, rf_gap_names_arr, rf_freq, beta_min,
beta_max
] in data_in_arr:
file_cav_name = cav_name + ".dat"
for rf_gap_name in rf_gap_names_arr:
file_gap_name = data_root_dir + cav_directory_name + "/" + rf_gap_name + ".SFO"
func = getAxisFieldFunction(file_gap_name)
splineGap = SplineCH()
splineGap.compile(func)
rf_gap_analysis = RF_AxisFieldAnalysis(splineGap, zeroIsCenter=True)
rf_gap_analysis.makeTransitTimeTables(beta_min, beta_max,
n_table_points, rf_freq)
gap_polynoms_coef_arr = rf_gap_analysis.makePlynomialFittings(
n_poly_order)
gap_polynoms_t_tp_s_sp_err_arr = rf_gap_analysis.gap_polynoms_t_tp_s_sp_err_arr
(err_t, err_tp, err_s, err_sp) = gap_polynoms_t_tp_s_sp_err_arr[0]
print "gap=", rf_gap_name, " spline size = ", splineGap.getSize(
), " err = %5.6f %5.6f %5.6f %5.6f " % (err_t, err_tp, err_s, err_sp)
rf_gap_analysis.dumpTransitTimeTables("./" + dir_name + "/" +
rf_gap_name + "_t_tp_s_sp.dat")
rf_gap_analysis.dumpTTFandFitting("./" + dir_name + "/" + rf_gap_name +
"_ttf_fiitings.dat")
#--------------------------------------------
import sys import math from orbit_utils import Function from orbit_utils import SplineCH from orbit.utils.fitting import PolynomialFit f = Function() for i in range(15): x = 0.1*i y = -1+1.0*x**2+2.0*x**3 + 0.01*x**4 f.add(x,y) print "polynomial for fitting = y = -1+1.0*x**2+2.0*x**3 + 0.01*x**4" print "================Function====================================" poly = PolynomialFit(4) poly.fitFunction(f) [coef_arr,err_arr] = poly.getCoefficientsAndErr() for i in range(len(coef_arr)): print "i=",i," coef = %8.5f +- %8.5f"%(coef_arr[i],err_arr[i]) print "================SplineCH====================================" spline = SplineCH() spline.compile(f) poly.fitSpline(f) [coef_arr,err_arr] = poly.getCoefficientsAndErr() for i in range(len(coef_arr)): print "i=",i," coef = %8.5f +- %8.5f"%(coef_arr[i],err_arr[i])