def solve_system(x0, params):
xtol = gtol = ftol = 1e-12
max_iter = 200
n = p = 2
T = multifit_nlinear.cvar.trust
w = multifit_nlinear.workspace(T, params, n, p)
# What a hack
w.set_pyobject(w)
w.init(x0, f=func_f, df=func_df, fvv=func_fvv, args=None)
#w.init(x0, f = func_f, args=None)
f = w.residual()
chisq0 = np.dot(f, f)
pygsl.set_debug_level(0)
w.driver(max_iter, xtol, gtol, ftol, callback=None, callback_params=None)
f = w.residual()
chisq = np.dot(f, f)
rcond = w.rcond()
print(" NITER = %d" % w.niter())
print(" NFEV = %d" % w.params.fdf.nevalf)
print(" NJEV = %d" % w.params.fdf.nevaldf)
print(" NAEV = %d" % w.params.fdf.nevalfvv)
print(" initial cost = %.12e" % chisq0)
print(" final cost = %.12e" % chisq)
print(" final x = (%.12e, %.12e)" % tuple(w.position()))
print(" final cond(J) = %.12e" % (1.0 / rcond, ))
def run_driver():
mu = 10
sys = odeiv2.system(func, jac, 2, mu)
#sys = odeiv2.system(func, None, 2, mu)
T = odeiv2.step_rk8pd
pygsl.set_debug_level(0)
d = driver_y_new(sys, T, 1e-6, 1e-6, 0.0);
d.reset()
d.reset_hstart(2)
d.set_hmin(0.0)
d.set_hmax(1.0)
d.set_nmax(2)
d.set_nmax(0)
d.set_hmax(1e-6)
d.set_hmin(2e-6)
y = numx.array([1.0, 0.0])
N = 100
t = 0.0
t1 = N * 1.
ti = (numx.arange(N) +1) / float(N)
pygsl.set_debug_level(0)
for tnext in ti:
#pygsl.set_debug_level(3)
t, y = d.apply(t, tnext, y)
print(t, y)
def testCos(self):
x = numx.arange(self.n) * (2 * numx.pi / self.n)
for i in range(1, self.n / 2):
if self.__class__.__name__ == "testrealforwardfloat":
pygsl.set_debug_level(0)
try:
self.CosOne(x, i)
finally:
pygsl.set_debug_level(0)
def run2():
pygsl.set_debug_level(10)
x = 2.0
step = odeiv.step_rk8pd(2, func, None, x)
control = odeiv.control_y_new(step, 1e-6, 1e-6)
evolve = odeiv.evolve(step, control)
pass
def run2():
pygsl.set_debug_level(10)
x = 2.0
step = odeiv.step_rk8pd(2, func, None, x)
control = odeiv.control_y_new(step, 1e-6, 1e-6)
evolve = odeiv.evolve(step, control)
pass
def testCos(self):
x = numx.arange(self.n) * (2 * numx.pi / self.n)
for i in range(1,self.n/2):
if self.__class__.__name__ == "testrealforwardfloat":
pygsl.set_debug_level(0)
try:
self.CosOne(x,i)
finally:
pygsl.set_debug_level(0)
def run():
N = 100
n = N - 2
A = matrix.sparse_matrix(n, n)
h = 1.0 / ( N - 1.0)
# first row
A.set(0, 0, -2.0)
A.set(0, 1, 1.0)
# rows [1:n-2]
for i in range(1, n - 1):
A.set(i, i + 1, 1.0)
A.set(i, i, -2.0)
A.set(i, i - 1, 1.0)
# last row
A.set(n - 1, n -1, -2.0)
A.set(n - 1, n -2, 1.0)
A.scale(1.0 / h**2)
cnt = (np.arange(n))
x = (cnt + 1) * h
f = - np.pi**2 * np.sin(np.pi * x)
C = A.ccs()
tol = 1.0e-6
max_iter = 10
work = linalg.GMRES(n, 0)
u = np.zeros(len(x), np.float_)
for t_iter in range(max_iter):
pygsl.set_debug_level(0)
#status, u = work.iterate(C, f, tol)
status, u = work.iterate(C, f, tol, u)
pygsl.set_debug_level(0)
residual = work.normr()
print("iter %d residual = %.12e" %(t_iter, residual))
if status == errno.GSL_SUCCESS:
break
else:
raise ValueError("Exceed maximum number of iterations")
return x, u
def run_driver_fixed_step():
mu = 10
sys = odeiv2.system(func, jac, 2, mu)
T = odeiv2.step_rk8pd
d = driver_y_new(sys, T, 1e-6, 1e-6, 0.0);
d.reset()
y = numx.array([1.0, 0.0])
N = 100
pygsl.set_debug_level(0)
t = 0
for cnt in range(N):
t, y = d.apply_fixed_step(t, 1e-3, 1000, y)
print(t, y)
def run():
r = rng.rng()
# slope
a = 1.45
# intercept
b = 3.88
# Generate the data
n = 20
i = numx.arange(n - 3)
dx = 10.0 / (n - 1.0)
e = r.uniform(n)
x = -5.0 + i * dx
y = a * x + b
#outliers
xo = numx.array([4.1, 3.5, 4.7])
yo = numx.array([-6.0, -6.7, -8.3])
x = numx.concatenate((x, xo))
y = numx.concatenate((y, yo))
X = numx.array([x * 0 + 1, x]).transpose()
ws = fr.workspace(*((fr.ols, ) + X.shape))
c_ols, cov_ols = ws.fit(X, y)
ws = fr.workspace(*((fr.bisquare, ) + X.shape))
c, cov = ws.fit(X, y)
y_rob = numx.zeros(n, numx.float_)
y_ols = numx.zeros(n, numx.float_)
yerr_rob = numx.zeros(n, numx.float_)
yerr_ols = numx.zeros(n, numx.float_)
pygsl.set_debug_level(0)
fr.est(X[0, :], c, cov)
y_rob, yerr_rob = fr.est_vector(X, c, cov)
pygsl.set_debug_level(0)
y_ols, yerr_ols = fr.est_vector(X, c_ols, cov_ols)
return x, y, (y_rob, yerr_rob), (y_ols, yerr_ols)
def run_fail():
"""Demonstrates pygsl capabilites in finding problems with callbacks
"""
def f1(x, *args):
return None
import pygsl
sys = integrate.gsl_function(f1, None)
# Enables printing debug messages. The higher the level the more information
# will be displayed
#pygsl.set_debug_level(3)
# Quite a few functions add traceback frames when they propage the error
# through the different levels. If you can not understand the error messages
# directly, looking at the source where the error occured can help.
#pygsl.add_c_traceback_frames(True)
flag, result, error, method = integrate.qng(sys, 0, numx.pi, 1e-8, 1e-8)
pygsl.set_debug_level(0)
def run():
N = 1024
x = numx.arange(N) * (numx.pi * 2 / N)
y = numx.sin(x)
b = bspline(4, nbreak)
k = b.get_internal_knots()
pygsl.set_debug_level(10)
b.knots(k)
X = b.eval_vector(x)
c, cov, chisq = multifit.linear(X, y)
b.set_coefficients_and_covariance_matrix(c, cov)
res_x = x[:: N / 64]
res_y, res_y_err = b.eval_dep_yerr_vector(res_x)
# res_y = b.eval_dep_vector(res_x)
print res_y
pylab.plot(x, y, "-")
pylab.errorbar(res_x, res_y, fmt="g-", xerr=res_y_err)
def run():
N = 1024
x = numx.arange(N) * (numx.pi * 2 / N)
y = numx.sin(x)
b = bspline(4, nbreak)
k = b.get_internal_knots()
pygsl.set_debug_level(10)
b.knots(k)
X = b.eval_vector(x)
c, cov, chisq = multifit.linear(X, y)
b.set_coefficients_and_covariance_matrix(c, cov)
res_x = x[::N / 64]
res_y, res_y_err = b.eval_dep_yerr_vector(res_x)
#res_y = b.eval_dep_vector(res_x)
print(res_y)
pylab.plot(x, y, '-')
pylab.errorbar(res_x, res_y, fmt='g-', xerr=res_y_err)
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 real_example_simple():
n = 1024*1024
data = numx.zeros((n,), numx.Int)
data[n/3:2*n/3] = 1
result = fft.real_transform(data)
#print "Nyqusit ->", result[0]
result[11:] = 0
final = fft.halfcomplex_inverse(result, n)
#print final
return
import Gnuplot
g = Gnuplot.Gnuplot()
g.plot(Gnuplot.Data(data, with='line'),
Gnuplot.Data(final, with='linespoints'),)
raw_input()
def halfcomplex_radix2_unpack():
n = 32
a = numx.arange(n)
c = numx.zeros((n,))
c[1:n/2+1]=a[1::2]
c[n/2+1:]=a[-2:1:-2]
print c
print fft.halfcomplex_radix2_unpack(c)
def doc():
help(fft)
if __name__ == '__main__':
import pygsl
pygsl.set_debug_level(0)
complex_example_simple()
complex_example()
real_example_simple()
real_example_simple1()
halfcomplex_radix2_unpack()
#import Gnuplot
# g = Gnuplot.Gnuplot()
# g.plot(Gnuplot.Data(data, with='line'),
# Gnuplot.Data(final, with='linespoints'),)
# raw_input()
def halfcomplex_radix2_unpack():
n = 32
a = numx.arange(n)
c = numx.zeros((n, ))
c[1:n / 2 + 1] = a[1::2]
c[n / 2 + 1:] = a[-2:1:-2]
print(c)
print(fft.halfcomplex_radix2_unpack(c))
def doc():
help(fft)
if __name__ == '__main__':
import pygsl
pygsl.set_debug_level(0)
complex_example_simple()
complex_example()
real_example_simple()
real_example_simple1()
halfcomplex_radix2_unpack()
doc()
def run():
x_init = np.array([1.0, 1.0, 0.0])
xtol = 1e-8
gtol = 1e-8
ftol = 0
fdf = (expb_f, expb_df)
p = 3
n = 40
r = rng.rng()
t = np.arange(n)
y = 1.0 + 5 * np.exp(-0.1 * t)
dy = r.gaussian(n)
y += dy
weights = 1. / ((0.1 * y)**2)
T = multifit_nlinear.cvar.trust
pygsl.add_c_traceback_frames(True)
pygsl.set_debug_level(0)
params = multifit_nlinear.default_parameters()
w = multifit_nlinear.workspace(T, params, n, p)
w.set_pyobject(w)
# w.params.fdf.p = p
# w.params.fdf.n = n
args = y
#print(w.init.__doc__)
print("params factor: up %s down %s" % (
params.factor_up,
params.factor_down,
))
errors.error_safe_state.reset()
pygsl.set_debug_level(0)
# w.init(x_init, df= expb_df, f=expb_f, fvv=None, args=args)
w.init(x_init, df=None, f=expb_f, fvv=None, args=args)
pygsl.set_debug_level(0)
f = w.residual()
chisq0 = np.dot(f, f)
pygsl.set_debug_level(0)
status, info = w.driver(200, xtol, gtol, ftol, callback)
pygsl.set_debug_level(0)
J = w.jac()
covar = multifit_nlinear.covar(J, 0.0, p)
J = w.jac()
covar = w.covar(0.0)
f = w.residual()
chisq = np.dot(f, f)
dof = n - p
c = max(1, np.sqrt(chisq / dof))
reasons = ("small step size", "small gradient")
print("Summary from method %s/%s" % (w.name(), w.trs_name()))
print(" number of iterations %d" % (w.niter(), ))
print(" function evaluations %d" % (w.params.fdf.nevalf, ))
print(" jacobian evaluations %d" % (w.params.fdf.nevaldf, ))
print(" reason for stopping %s" % (reasons[info]))
print(" chisq / dof %g" % (chisq / dof))
x = w.position()
x = w.x()
print(" A = %.5f +/- %.5f" % (x[0], c * covar[0, 0]))
print(" lamba = %.5f +/- %.5f" % (x[1], c * covar[1, 1]))
print(" b = %.5f +/- %.5f" % (x[2], c * covar[2, 2]))
A.set(4, 0, 4.1)
print("printing all matrix elements:\n")
for i in range(5):
for j in range(4):
val = A.get(i, j)
val2 = A.get_val_or_none(i, j)
print("A[%d, %d] = %g %s" % (i, j, val, val2))
print(dir(matrix))
print(dir(matrix.sparse_matrix))
print(dir(A))
print(A.get_shape())
print(A.shape)
pygsl.set_debug_level(5)
A.sp2d()
#print(A == A)
B = A.memcpy()
print("A == B", A == B)
B.scale(2)
print("A == 2*B", A == B)
#: Minimum maximum of the matrix
A.minmax()
#: compact row type
A.crs()
#: compact column type
A.ccs()
def run():
x_init = np.array([1.0, 1.0, 0.0])
xtol = 1e-8
gtol = 1e-8
ftol = 0
p = 3
n = 40
rng.env_setup()
r = rng.rng()
t = np.arange(n)
x_final = 5., .1 , 1
y = func(x_final, t)
s = 0.1 * y
dy = np.array(list(map(r.gaussian, s)))
y = y + dy
weights = 1./((0.1 * y)**2)
T = multifit_nlinear.cvar.trust
pygsl.add_c_traceback_frames(True)
pygsl.set_debug_level(0)
params = multifit_nlinear.default_parameters()
w = multifit_nlinear.workspace(T, params, n, p)
# What a hack
w.set_pyobject(w)
w.winit(x_init, weights, df= expb_df, f=expb_f, fvv = None, args=y)
f = w.residual()
chisq0 = np.dot(f, f)
#plt.ion()
fig = plt.figure()
ax = fig.add_subplot(111)
ax.clear()
ax.errorbar(t, y, yerr=dy)
Y = func(x_init, t)
line, = ax.plot(t, Y, '-')
plt.show(False)
plt.draw()
max_iter = 200
#status, info = w.driver(200, xtol, gtol, ftol, callback)
for step in range(max_iter):
x = w.position()
print("x = %s" %(x,))
#x = w.x()
Y = func(x, t)
line.set_data(t, Y)
w.iterate()
status, info = w.test(xtol, gtol, ftol)
fig.canvas.draw()
plt.pause(0.5)
#ax.figure.clf()
if status == errno.GSL_SUCCESS:
break
elif status == errno.GSL_CONTINUE:
continue
else:
raise ValueError("Unexpected status %d" %(status,))
else:
raise ValueError("Did not finish within %d steps" %(max_iter,))
covar = w.covar(0.0)
f = w.residual()
chisq = np.dot(f, f)
dof = n - p
c = max(1, np.sqrt(chisq / dof))
reasons = ("small gradient", "small step size")
status, info = w.test(xtol, gtol, ftol)
print("Summary from method %s/%s" %(w.name(), w.trs_name()) )
print(" number of iterations %d" %(w.niter(),) )
print(" function evaluations %d" %(w.params.fdf.nevalf,))
print(" jacobian evaluations %d" %(w.params.fdf.nevaldf,))
print(" reason for stopping %s" %(reasons[info],))
print(" initial |f(x)| = %f" %(np.sqrt(chisq0),) )
print(" final |f(x)| = %f" %(np.sqrt(chisq),) )
print(" chisq / dof %g" %(chisq / dof) )
x = w.position()
x = w.x()
print(" A = %.5f +/- %.5f" % ( x[0], c * covar[0,0]) )
print(" lamba = %.5f +/- %.5f" % ( x[1], c * covar[1,1]) )
print(" b = %.5f +/- %.5f" % ( x[2], c * covar[2,2]) )
plt.show()
# Author : Pierre Schnizer
"""
The python equivalent of the C example found in the GSL Reference document.
It prints the calculational ouput to stdout. The first column is t, the
second y[0] and the thrid y[1]. Plot it with your favourite programm to see
the output.
"""
import sys
sys.stdout = sys.stderr
import pygsl._numobj as Numeric
import pygsl
pygsl.set_debug_level(0)
import time
from pygsl.testing import odeiv
def func(t, y, mu):
f = Numeric.zeros((2,), Numeric.Float) * 1.0
f[0] = y[1]
f[1] = -y[0] - mu * y[1] * (y[0] ** 2 -1);
#f[0] = y[1]
#f[1] = y[0] * mu
#print "y", y, "f", f
return f
def jac(t, y, mu):
dfdy = Numeric.ones((2,2), Numeric.Float)
dfdy[0, 0] = 0.0
dfdy[0, 1] = 1.0