def setUp(self):
self.dim = 100
self.param = 2
self.a = 1000.1
self.b = 100
self.x = Numeric.arange(self.dim)
x = self.x
self.y = self.a + self.b * self.x
self.w = Numeric.ones((self.dim,))
self.ws = multifit.linear_workspace(self.dim, self.param)
self.X = Numeric.transpose(Numeric.array((Numeric.ones(self.dim,), x)))
def setUp(self):
self.dim = 100
self.param = 2
self.a = 1000.1
self.b = 100
self.x = Numeric.arange(self.dim)
x = self.x
self.y = self.a + self.b * self.x
self.w = Numeric.ones((self.dim, ))
self.ws = multifit.linear_workspace(self.dim, self.param)
self.X = Numeric.transpose(Numeric.array(
(Numeric.ones(self.dim, ), x)))
def setUp(self):
t = Numeric.arange(self._getn())
y = testfunc(t, self.A, self.lambda_, self.b)
sigma = Numeric.ones(self._getn()) * 0.1
self.data = Numeric.array((t, y, sigma), Float)
self.sys = multifit_nlin.gsl_multifit_function_fdf(
exp_f, exp_df, exp_fdf, self.data, self._getn(), self._getp())
def jac(t, y, mu):
dfdy = numx.ones((2, 2), ) * 1.
dfdy[0, 0] = 0.0
dfdy[0, 1] = 1.0
dfdy[1, 0] = -2.0 * mu * y[0] * y[1] - 1.0
dfdy[1, 1] = -mu * (y[0]**2 - 1.0)
dfdt = numx.zeros((2, ))
return dfdy, dfdt
def jac(t, y, mu):
dfdy = numx.ones((2,2),) * 1.
dfdy[0, 0] = 0.0
dfdy[0, 1] = 1.0
dfdy[1, 0] = -2.0 * mu * y[0] * y[1] - 1.0
dfdy[1, 1] = -mu * (y[0]**2 - 1.0)
dfdt = numx.zeros((2,))
return dfdy, dfdt
def jac(t, y, mu):
dfdy = Numeric.ones((2,2), Numeric.Float)
dfdy[0, 0] = 0.0
dfdy[0, 1] = 1.0
dfdy[1, 0] = -2.0 * mu * y[0] * y[1] - 1.0
dfdy[1, 1] = -mu * (y[0]**2 - 1.0)
dfdt = Numeric.zeros((2,))
return dfdy, dfdt
def jac(t, y, mu):
dfdy = Numeric.ones((2, 2), Numeric.Float)
dfdy[0, 0] = 0.0
dfdy[0, 1] = 1.0
dfdy[1, 0] = -2.0 * mu * y[0] * y[1] - 1.0
dfdy[1, 1] = -mu * (y[0]**2 - 1.0)
dfdt = Numeric.zeros((2, ))
return dfdy, dfdt
def setUp(self):
t = Numeric.arange(self._getn());
y = testfunc(t, self.A, self.lambda_, self.b)
sigma = Numeric.ones(self._getn()) * 0.1
self.data = Numeric.array((t,y,sigma), Float)
self.sys = multifit_nlin.gsl_multifit_function_fdf(exp_f, exp_df,
exp_fdf, self.data,
self._getn(),
self._getp())
def jac(t, y, mu):
dfdy = Numeric.ones((2,2), Numeric.Float)
dfdy[0, 0] = 0.0
dfdy[0, 1] = 0.0
dfdy[1, 0] = 0.0
dfdy[1, 1] = 0.0
dfdt = Numeric.zeros((2,))
dfdt[0] = 2
dfdt[1] = 3 * 2 * t
return dfdy, dfdt
def jac(t, y, mu):
dfdy = Numeric.ones((2, 2), Numeric.Float)
dfdy[0, 0] = 0.0
dfdy[0, 1] = 0.0
dfdy[1, 0] = 0.0
dfdy[1, 1] = 0.0
dfdt = Numeric.zeros((2, ))
dfdt[0] = 2
dfdt[1] = 3 * 2 * t
return dfdy, dfdt
def test_wmean(self):
self.failIf(wmean(numx.array([1,1,1]), numx.array([-1.,-3.,1.])) != -1.0)
self.failIf(wmean(numx.array([1,1,1]),[1,2,3]) != 2)
data = numx.array([1.,2.,3.,4.,5.,6.,7.,8.,9.,10.])
weight = numx.ones(data.shape)
self.failIf(wmean(weight,data) != 5.5)
self.failIf(wmean(weight[::2],data[::2]) != 5.0)
self.failIf(wmean(weight[::-1],data[::-1]) != 5.5)
self.failIf(wmean(weight[::-2],data[::-2]) != 6.0)
def jac(t, y, mu):
#print "--> jac", t, y
dfdy = numx.ones((2, 2), Float)
dfdy[0, 0] = 0.0
dfdy[0, 1] = 1.0
dfdy[1, 0] = -2.0 * mu * y[0] * y[1] - 1.0
dfdy[1, 1] = -mu * (y[0]**2 - 1.0)
#print "dfdy[0, 0]", dfdy[0, 0]
#print "dfdy[0, 1]", dfdy[0, 1]
#print "dfdy[1, 0]", dfdy[1, 0]
#print "dfdy[1, 1]", dfdy[1, 1]
dfdt = numx.zeros((2, ))
return dfdy, dfdt
def jac(t, y, mu):
#print "--> jac", t, y
dfdy = numx.ones((2,2), Float)
dfdy[0, 0] = 0.0
dfdy[0, 1] = 1.0
dfdy[1, 0] = -2.0 * mu * y[0] * y[1] - 1.0
dfdy[1, 1] = -mu * (y[0]**2 - 1.0)
#print "dfdy[0, 0]", dfdy[0, 0]
#print "dfdy[0, 1]", dfdy[0, 1]
#print "dfdy[1, 0]", dfdy[1, 0]
#print "dfdy[1, 1]", dfdy[1, 1]
dfdt = numx.zeros((2,))
return dfdy, dfdt
def run_fdfsolver():
A = 1.
lambda_ = .1
b = .5
n = 40
p = 3
t = numx.arange(n);
y = testfunc(t, A, lambda_, b)
sigma = numx.ones(n) * 0.1
data = numx.array((t,y,sigma), numx.Float)
#mysys = multifit_nlin.gsl_multifit_function_fdf(exp_f, exp_df, exp_fdf,
# data, n,p)
pygsl.set_debug_level(0)
solver = multifit_nlin.lmsder(n, p)
pygsl.set_debug_level(0)
#solver = multifit_nlin.lmder(mysys, n, p)
x = numx.array((1.0, 0.0, 0.0))
pygsl.set_debug_level(0)
solver.set(exp_f, exp_df, exp_fdf, x, data)
pygsl.set_debug_level(0)
print "# Testing solver ", solver.name()
print "# %5s %9s %9s %9s %10s" % ("iter", "A", "lambda", "b", "|f(x)|")
for iter in range(20):
status = solver.iterate()
x = solver.x()
dx = solver.dx()
f = solver.f()
J = solver.J()
#tdx = multifit_nlin.gradient(J, f)
#status = multifit_nlin.test_delta(dx, x, 1e-8, 1e-8)
status = solver.test_delta(1e-8, 1e-8)
fn = numx.sqrt(numx.sum(f*f))
if status == 0:
print "# Convereged :"
if status == 0:
break
print " %5d % .7f % .7f % .7f % .7f" %(iter, x[0], x[1], x[2], fn)
else:
raise ValueError, "Number of Iterations exceeded!"
J = solver.J()
covar = multifit_nlin.covar(solver.J(), 0.0)
print "# A = % .5f +/- % .5f" % (x[0], covar[0,0])
print "# lambda = % .5f +/- % .5f" % (x[1], covar[1,1])
print "# b = % .5f +/- % .5f" % (x[2], covar[2,2])
def calculate(x, y, sigma):
n = len(x)
X = numx.ones((n,3),)*1.
X[:,0] = 1.0
X[:,1] = x
X[:,2] = x ** 2
w = 1.0 / sigma ** 2
work = pygsl.multifit.linear_workspace(n,3)
c, cov, chisq = pygsl.multifit.wlinear(X, w, y, work)
c, cov, chisq = pygsl.multifit.linear(X, y, work)
print "# best fit: Y = %g + %g * X + %g * X ** 2" % tuple(c)
print "# covariance matrix #"
print "[[ %+.5e, %+.5e, %+.5e ] " % tuple(cov[0,:])
print " [ %+.5e, %+.5e, %+.5e ] " % tuple(cov[1,:])
print " [ %+.5e, %+.5e, %+.5e ]]" % tuple(cov[2,:])
print "# chisq = %g " % chisq
return c, cov, chisq
def run_fdfsolver():
A = 1.
lambda_ = .1
b = .5
n = 40
p = 3
t = numx.arange(n)
y = testfunc(t, A, lambda_, b)
sigma = numx.ones(n) * 0.1
data = numx.array((t, y, sigma), )
mysys = multifit_nlin.gsl_multifit_function_fdf(exp_f, exp_df, exp_fdf,
data, n, p)
solver = multifit_nlin.lmsder(mysys, n, p)
#solver = multifit_nlin.lmder(mysys, n, p)
x = numx.array((1.0, 0.0, 0.0))
solver.set(x)
print("# Testing solver ", solver.name())
print("# %5s %9s %9s %9s %10s" % ("iter", "A", "lambda", "b", "|f(x)|"))
for iter in range(20):
status = solver.iterate()
x = solver.getx()
dx = solver.getdx()
f = solver.getf()
J = solver.getJ()
tdx = multifit_nlin.gradient(J, f)
status = multifit_nlin.test_delta(dx, x, 1e-8, 1e-8)
fn = numx.sqrt(numx.sum(f * f))
if status == errno.GSL_SUCCESS:
print("# Convereged :")
if status == errno.GSL_SUCCESS:
break
print(" %5d % .7f % .7f % .7f % .7f" % (iter, x[0], x[1], x[2], fn))
else:
raise ValueError("Number of Iterations exceeded!")
J = solver.getJ()
covar = multifit_nlin.covar(solver.getJ(), 0.0)
print("# A = % .5f +/- % .5f" % (x[0], covar[0, 0]))
print("# lambda = % .5f +/- % .5f" % (x[1], covar[1, 1]))
print("# b = % .5f +/- % .5f" % (x[2], covar[2, 2]))
def run():
r = rng.rng()
bw = bspline(4, nbreak)
# Data to be fitted
x = 15. / (N - 1) * numx.arange(N)
y = numx.cos(x) * numx.exp(0.1 * x)
sigma = .1
w = 1.0 / sigma**2 * numx.ones(N)
dy = r.gaussian(sigma, N)
y = y + dy
# use uniform breakpoints on [0, 15]
bw.knots_uniform(0.0, 15.0)
X = numx.zeros((N, ncoeffs))
for i in range(N):
B = bw.eval(x[i])
X[i, :] = B
# do the fit
c, cov, chisq = multifit.wlinear(X, w, y,
multifit.linear_workspace(N, ncoeffs))
# output the smoothed curve
res_y = []
res_y_err = []
for i in range(N):
B = bw.eval(x[i])
yi, yi_err = multifit.linear_est(B, c, cov)
res_y.append(yi)
res_y_err.append(yi_err)
#print yi, yerr
res_y = numx.array(res_y)
res_y_err = numx.array(res_y_err)
return (
x,
y,
), (x, res_y), res_y_err
def calculate(x, y, sigma):
n = len(x)
X = numx.ones((n, 3), ) * 1.
X[:, 0] = 1.0
X[:, 1] = x
X[:, 2] = x**2
w = 1.0 / sigma**2
work = pygsl.multifit.linear_workspace(n, 3)
# pygsl.init.set_debug_level(3)
print(X.shape, w.shape)
#c, cov, chisq = pygsl.multifit.linear(X, y, work)
#c, cov, chisq = pygsl.multifit.linear(X, y)
pygsl.init.set_debug_level(3)
c, cov, chisq = pygsl.multifit.wlinear(X, w, y, work)
print("# best fit: Y = %g + %g * X + %g * X ** 2" % tuple(c))
print("# covariance matrix #")
print("[[ %+.5e, %+.5e, %+.5e ] " % tuple(cov[0, :]))
print(" [ %+.5e, %+.5e, %+.5e ] " % tuple(cov[1, :]))
print(" [ %+.5e, %+.5e, %+.5e ]]" % tuple(cov[2, :]))
print("# chisq = %g " % chisq)
return c, cov, chisq
def run():
r = rng.rng()
bw = bspline(4, nbreak)
# Data to be fitted
x = 15. / (N-1) * numx.arange(N)
y = numx.cos(x) * numx.exp(0.1 * x)
sigma = .1
w = 1.0 / sigma**2 * numx.ones(N)
dy = r.gaussian(sigma, N)
y = y + dy
# use uniform breakpoints on [0, 15]
bw.knots_uniform(0.0, 15.0)
X = numx.zeros((N, ncoeffs))
for i in range(N):
B = bw.eval(x[i])
X[i,:] = B
# do the fit
c, cov, chisq = multifit.wlinear(X, w, y, multifit.linear_workspace(N, ncoeffs))
# output the smoothed curve
res_y = []
res_y_err = []
for i in range(N):
B = bw.eval(x[i])
yi, yi_err = multifit.linear_est(B, c, cov)
res_y.append(yi)
res_y_err.append(yi_err)
#print yi, yerr
res_y = numx.array(res_y)
res_y_err = numx.array(res_y_err)
return (x, y,), (x, res_y), res_y_err
def test_poly_eval(self):
c = Numeric.ones((3,))
x = 2
assert(poly.poly_eval(c,x) == 7.0)
def setUp(self):
self.a = 0.0
self.b = 100
self.x = Numeric.arange(100)
self.y = self.a + self.b * self.x
self.w = Numeric.ones(100) * 1000000
def test_poly_eval():
c = numx.ones((3,))
x = 2
poly.poly_eval(c,x)
def test_poly_eval(self):
c = Numeric.ones((3,))
x = 2
assert(poly.poly_eval(c,x) == 7.0)
def test_poly_eval():
c = numx.ones((3, ))
x = 2
poly.poly_eval(c, x)
def setUp(self):
self.a = 0.0
self.b = 100
self.x = Numeric.arange(100)
self.y = self.a + self.b * self.x
self.w = Numeric.ones(100) * 1000000
