#!/usr/bin/env python
import numpy, math, sys, csv
from scipy.optimize import curve_fit

##############################################
# DECIMAL RANGE                              #
# A float version of Python's range function #
##############################################
# start - the start value for the range      #
# stop  - the stop value for the range       #
# step  - the step value for the range       #
##############################################
def drange(start, stop, step):
	r = start
	while r < stop:
		yield r
		r += step

##############################################
# TRIG SERIES                                #
# A function for curve_fit.  This function   #
# is a trig series with elements:            #
#           sin2x, cos2x, sinx, cosx         #
##############################################
def trig_series(x, a, b, c, d, e):
	return a*numpy.cos(x) + b*numpy.sin(x) + c*numpy.cos(2*x) + d*numpy.sin(2*x) + e
	
def linsum(time, z_cellb):
	sum = 0.
	ndegs = len(z_cellb)
	for deg in range(ndegs):
		sum += z_cellb[deg] * math.pow(time, ndegs - deg - 1)
	return sum
	
def trigsum(time, z_cellb):
	sum = 0.
	pairs = zip(z_cellb[::4], z_cellb[1::4], z_cellb[2::4], z_cellb[3::4])
	for a, b, c, d in pairs:
		sum += a * numpy.cos(time * b) + c * numpy.sin(d)
	return sum

# prepare the initial parameters
header = None
time_in = list()
cellb_raw = dict()
y_cellb = dict()
z_cellb = dict()
resolution = 10
reader = csv.reader(sys.stdin, dialect='excel-tab')

# read in the data
for row in reader:
	if not header:
		header = row
		for col in header[1:]:
			cellb_raw[col] = list()
	else:
		if len(row) > 1 and row[0] != '':
			time_in.append(float(row[0]))
			for col in range(1, len(row)):
				cellb_raw[header[col]].append(float(row[col]))

# obtain the program parameters
x_time = numpy.array(time_in)
max_x = max(time_in)
if len(sys.argv) > 1:
	resolution = sys.argv[1]
if len(sys.argv) > 2:
	max_x = float(sys.argv[2])

# calculate the linear regression
print >> sys.stderr, x_time
for key in cellb_raw:
	y_cellb = numpy.array(cellb_raw[key])
	print >> sys.stderr, key + ": " + str(y_cellb)
	z_cellb[key] = numpy.polyfit(x_time, y_cellb, resolution)
	#z_cellb, z_pcov = curve_fit(func1, x_time, y_cellb, p0=(1.0,0.2))
	#z_cellb, z_pcov = curve_fit(func1a, x_time, y_cellb, p0=(1.0,1.2,1.0,0.2))

csv_out = csv.writer(sys.stdout, dialect='excel-tab')
csv_out.writerow(header)
for time in drange(0, max_x + 0.01, 0.01):
	#sum = trigsum(time, z_cellb)
	row = ['%.2f' % (time)]
	for key in header[1:]:
		sum = linsum(time, z_cellb[key])
		row.append('%.4f' % (sum))
	csv_out.writerow(row)