def run_fdfsolver():
a = 1.0
b = 0.0
c = -5.0
solver = roots.newton()
#solver = roots.secant()
#solver = roots.steffenson()
x = 5.0
solver.set(quadratic, quadratic_deriv, quadratic_fdf, x, (a,b,c))
r_expected = Numeric.sqrt(5.0)
print "# Using solver ", solver.name()
print "# %5s %9s %10s %9s" % ("iter", "root", "err", "err(est)")
ok = 1
for iter in range(10):
status = solver.iterate()
x0 = x
x = solver.root()
status = roots.test_delta(x, x0, 0.0, 1e-3)
r = solver.root()
if status == 0:
print "# Convereged :"
print "%5d %.7f % .6f % .6f" %(iter, r, r -r_expected, x - x0)
if status == 0:
break
else:
raise ValueError, "Exeeded maximum number of iterations!"
def run_fdfsolver():
a = 1.0
b = 0.0
c = -5.0
mysys = roots.gsl_function_fdf(quadratic, quadratic_deriv, quadratic_fdf,
numx.array((a, b, c)))
solver = roots.newton(mysys)
#solver = roots.secant(mysys)
#solver = roots.steffenson(mysys)
x = 5.0
solver.set(x)
r_expected = numx.sqrt(5.0)
print "# Using solver ", solver.name()
print "# %5s %9s %10s %9s" % ("iter", "root", "err", "err(est)")
ok = 1
for iter in range(10):
status = solver.iterate()
x0 = x
x = solver.root()
status = roots.test_delta(x, x0, 0.0, 1e-3)
r = solver.root()
if status == errno.GSL_SUCCESS:
print "# Convereged :"
print "%5d %.7f % .6f % .6f" % (iter, r, r - r_expected, x - x0)
if status == errno.GSL_SUCCESS:
break
else:
raise ValueError, "Exeeded maximum number of iterations!"
def run_fsolver():
a = 1.0
b = 0.0
c = -5.0
solver = roots.brent()
#solver = roots.bisection()
#solver = roots.falsepos()
solver.set(quadratic, 0.0, 5, -5.0, (a,b,c))
iter = 0
r_expected = Numeric.sqrt(5.0)
print "# Using solver ", solver.name()
print "# %5s [%9s %9s] %9s %10s %9s" % ("iter", "upper", "lower", "root",
"err", "err(est)")
for iter in range(100):
status = solver.iterate()
x_lo = solver.x_lower()
x_up = solver.x_upper()
status = solver.test_interval(0, 0.001)
r = solver.root()
if status == 0:
print "# Convereged :"
print " %5d [%.7f %.7f] %.7f % .6f % .6f" %(iter, x_lo, x_up, r,
r -r_expected,
x_up - x_lo)
if status == 0:
break
else:
raise ValueError, "Exeeded maximum number of iterations!"
def run_fsolver():
a = 1.0
b = 0.0
c = -5.0
mysys = roots.gsl_function(quadratic, (a, b, c))
solver = roots.brent(mysys)
#solver = roots.bisection(mysys)
#solver = roots.falsepos(mysys)
solver.set(0.0, 5.0)
iter = 0
r_expected = numx.sqrt(5.0)
print "# Using solver ", solver.name()
print "# %5s [%9s %9s] %9s %10s %9s" % ("iter", "upper", "lower", "root",
"err", "err(est)")
for iter in range(100):
status = solver.iterate()
x_lo = solver.x_lower()
x_up = solver.x_upper()
status = roots.test_interval(x_lo, x_up, 0, 0.001)
r = solver.root()
if status == errno.GSL_SUCCESS:
print "# Convereged :"
print " %5d [%.7f %.7f] %.7f % .6f % .6f" % (
iter, x_lo, x_up, r, r - r_expected, x_up - x_lo)
if status == errno.GSL_SUCCESS:
break
else:
raise ValueError, "Exeeded maximum number of iterations!"
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 _run(self, solver):
solver.set(0.0, 5.0)
iter = 0
r_expected = Numeric.sqrt(5.0)
#print "Testing solver ", solver.name()
#print "%5s [%9s %9s] %9s %10s %9s" % ("iter", "upper", "lower", "root", "err", "err(est)")
for iter in range(100):
status = solver.iterate()
x_lo = solver.x_lower()
x_up = solver.x_upper()
status = roots.test_interval(x_lo, x_up, 0, 0.001)
r = solver.root()
if status == 0:
break
else:
raise ValueError("Exeeded maximum number of iterations!")
assert (Numeric.absolute(r - r_expected) < _eps)
def _run(self, solver):
solver.set(0.0, 5.0)
iter = 0
r_expected = Numeric.sqrt(5.0)
#print "Testing solver ", solver.name()
#print "%5s [%9s %9s] %9s %10s %9s" % ("iter", "upper", "lower", "root", "err", "err(est)")
for iter in range(100):
status = solver.iterate()
x_lo = solver.x_lower()
x_up = solver.x_upper()
status = roots.test_interval(x_lo, x_up, 0, 0.001)
r = solver.root()
if status == 0:
break
else:
raise ValueError, "Exeeded maximum number of iterations!"
assert(Numeric.absolute(r-r_expected) < _eps)
def _run(self, solver):
#x = Numeric.array((1.0, .4, .1))
x = Numeric.array((1.0, 0.0, 0.0))
solver.set(x)
#g.title('Start')
#g.plot(Gnuplot.Data(self.data[0], self.data[1]),
# Gnuplot.Data(self.data[0], testfunc(self.data[0]),
# with = 'line'),
# )
#raw_input()
#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()
assert (status == 0 or status == -2)
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)
#status = multifit_nlin.test_gradient(dx, 1e-4)
fn = Numeric.sqrt(Numeric.sum(f * f))
#g.title('Iteration')
if status == 0:
break
#print "%5d % .7f % .7f % .7f % .7f" %(iter, x[0], x[1], x[2], fn)
#g.plot(Gnuplot.Data(self.data[0], self.data[1]),
# Gnuplot.Data(self.data[0],
# testfunc(self.data[0], x[0], x[1], x[2]),
# with = 'line', title='iteration ' + str(iter)),
# )
#raw_input()
else:
raise ValueError, "Number of Iterations exceeded!"
#print "Convereged :"
#print "%5d % .7f % .7f %.7f % .7f" %(iter, x[0], x[1], x[2], fn)
assert (Numeric.absolute(x[0] - self.A) < _eps)
assert (Numeric.absolute(x[1] - self.lambda_) < _eps)
assert (Numeric.absolute(x[2] - self.b) < _eps)
#J = solver.getJ()
#print "shape = ", J.shape
covar = multifit_nlin.covar(solver.getJ(), 0.0)
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(self, solver):
#x = Numeric.array((1.0, .4, .1))
x = Numeric.array((1.0, 0.0, 0.0))
solver.set(x)
#g.title('Start')
#g.plot(Gnuplot.Data(self.data[0], self.data[1]),
# Gnuplot.Data(self.data[0], testfunc(self.data[0]),
# with = 'line'),
# )
#raw_input()
#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()
assert(status == 0 or status == -2)
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)
#status = multifit_nlin.test_gradient(dx, 1e-4)
fn = Numeric.sqrt(Numeric.sum(f*f))
#g.title('Iteration')
if status == 0:
break
#print "%5d % .7f % .7f % .7f % .7f" %(iter, x[0], x[1], x[2], fn)
#g.plot(Gnuplot.Data(self.data[0], self.data[1]),
# Gnuplot.Data(self.data[0],
# testfunc(self.data[0], x[0], x[1], x[2]),
# with = 'line', title='iteration ' + str(iter)),
# )
#raw_input()
else:
raise ValueError, "Number of Iterations exceeded!"
#print "Convereged :"
#print "%5d % .7f % .7f %.7f % .7f" %(iter, x[0], x[1], x[2], fn)
assert(Numeric.absolute(x[0] - self.A) < _eps)
assert(Numeric.absolute(x[1] - self.lambda_) < _eps)
assert(Numeric.absolute(x[2] - self.b) < _eps)
#J = solver.getJ()
#print "shape = ", J.shape
covar = multifit_nlin.covar(solver.getJ(), 0.0)
def _run(self, solver):
x = Numeric.array((1.0, 0.0, 0.0))
solver.set(x)
for iter in range(20):
status = solver.iterate()
assert (status == 0 or status == -2)
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 = Numeric.sqrt(Numeric.sum(f * f))
if status == 0:
break
else:
raise ValueError("Number of Iterations exceeded!")
assert (Numeric.absolute(x[0] - self.A) < _eps)
assert (Numeric.absolute(x[1] - self.lambda_) < _eps)
assert (Numeric.absolute(x[2] - self.b) < _eps)
covar = multifit_nlin.covar(solver.getJ(), 0.0)
def _run(self, solver):
x = 5.0
solver.set(x)
r_expected = Numeric.sqrt(5.0)
#print "Testing solver ", solver.name()
#print "%5s %9s %10s %9s" % ("iter", "root", "err", "err(est)")
ok = 1
for iter in range(10):
status = solver.iterate()
x0 = x
x = solver.root()
status = roots.test_delta(x, x0, 0.0, 1e-3)
r = solver.root()
if status == 0:
#print "Convereged :"
ok = 0
#print "%5d %.7f % .6f % .6f" %(iter, r, r -r_expected, x - x0)
if ok == 0:
break
else:
raise ValueError("Exeeded maximum number of iterations!")
assert (Numeric.absolute(r - r_expected) < _eps)
def _run(self, solver):
x = 5.0
solver.set(x)
r_expected = Numeric.sqrt(5.0)
#print "Testing solver ", solver.name()
#print "%5s %9s %10s %9s" % ("iter", "root", "err", "err(est)")
ok = 1
for iter in range(10):
status = solver.iterate()
x0 = x
x = solver.root()
status = roots.test_delta(x, x0, 0.0, 1e-3)
r = solver.root()
if status == 0:
#print "Convereged :"
ok = 0
#print "%5d %.7f % .6f % .6f" %(iter, r, r -r_expected, x - x0)
if ok == 0:
break
else:
raise ValueError, "Exeeded maximum number of iterations!"
assert(Numeric.absolute(r-r_expected) < _eps)
def f(x, params):
alpha = params
return Numeric.log(alpha * x) / Numeric.sqrt(x)
def f(x, params):
alpha = params
return Numeric.log(alpha *x) / Numeric.sqrt(x)
