def fsolve(func,
x0,
args=(),
fprime=None,
full_output=0,
col_deriv=0,
xtol=1.49012e-8,
maxfev=0,
band=None,
epsfcn=0.0,
factor=100,
diag=None,
warning=True):
"""Find the roots of a function.
Description:
Return the roots of the (non-linear) equations defined by
func(x)=0 given a starting estimate.
Inputs:
func -- A Python function or method which takes at least one
(possibly vector) argument.
x0 -- The starting estimate for the roots of func(x)=0.
args -- Any extra arguments to func are placed in this tuple.
fprime -- A function or method to compute the Jacobian of func with
derivatives across the rows. If this is None, the
Jacobian will be estimated.
full_output -- non-zero to return the optional outputs.
col_deriv -- non-zero to specify that the Jacobian function
computes derivatives down the columns (faster, because
there is no transpose operation).
warning -- True to print a warning message when the call is
unsuccessful; False to suppress the warning message.
Outputs: (x, {infodict, ier, mesg})
x -- the solution (or the result of the last iteration for an
unsuccessful call.
infodict -- a dictionary of optional outputs with the keys:
'nfev' : the number of function calls
'njev' : the number of jacobian calls
'fvec' : the function evaluated at the output
'fjac' : the orthogonal matrix, q, produced by the
QR factorization of the final approximate
Jacobian matrix, stored column wise.
'r' : upper triangular matrix produced by QR
factorization of same matrix.
'qtf' : the vector (transpose(q) * fvec).
ier -- an integer flag. If it is equal to 1 the solution was
found. If it is not equal to 1, the solution was not
found and the following message gives more information.
mesg -- a string message giving information about the cause of
failure.
Extended Inputs:
xtol -- The calculation will terminate if the relative error
between two consecutive iterates is at most xtol.
maxfev -- The maximum number of calls to the function. If zero,
then 100*(N+1) is the maximum where N is the number
of elements in x0.
band -- If set to a two-sequence containing the number of sub-
and superdiagonals within the band of the Jacobi matrix,
the Jacobi matrix is considered banded (only for fprime=None).
epsfcn -- A suitable step length for the forward-difference
approximation of the Jacobian (for fprime=None). If
epsfcn is less than the machine precision, it is assumed
that the relative errors in the functions are of
the order of the machine precision.
factor -- A parameter determining the initial step bound
(factor * || diag * x||). Should be in interval (0.1,100).
diag -- A sequency of N positive entries that serve as a
scale factors for the variables.
Remarks:
"fsolve" is a wrapper around MINPACK's hybrd and hybrj algorithms.
See also:
scikits.openopt, which offers a unified syntax to call this and other solvers
fmin, fmin_powell, fmin_cg,
fmin_bfgs, fmin_ncg -- multivariate local optimizers
leastsq -- nonlinear least squares minimizer
fmin_l_bfgs_b, fmin_tnc,
fmin_cobyla -- constrained multivariate optimizers
anneal, brute -- global optimizers
fminbound, brent, golden, bracket -- local scalar minimizers
brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
fixed_point -- scalar and vector fixed-point finder
"""
x0 = array(x0, ndmin=1)
n = len(x0)
if type(args) != type(()): args = (args, )
check_func(func, x0, args, n, (n, ))
Dfun = fprime
if Dfun is None:
if band is None:
ml, mu = -10, -10
else:
ml, mu = band[:2]
if (maxfev == 0):
maxfev = 200 * (n + 1)
retval = _minpack._hybrd(func, x0, args, full_output, xtol, maxfev, ml,
mu, epsfcn, factor, diag)
else:
check_func(Dfun, x0, args, n, (n, n))
if (maxfev == 0):
maxfev = 100 * (n + 1)
retval = _minpack._hybrj(func, Dfun, x0, args, full_output, col_deriv,
xtol, maxfev, factor, diag)
errors = {
0: ["Improper input parameters were entered.", TypeError],
1: ["The solution converged.", None],
2: [
"The number of calls to function has reached maxfev = %d." %
maxfev, ValueError
],
3: [
"xtol=%f is too small, no further improvement in the approximate\n solution is possible."
% xtol, ValueError
],
4: [
"The iteration is not making good progress, as measured by the \n improvement from the last five Jacobian evaluations.",
ValueError
],
5: [
"The iteration is not making good progress, as measured by the \n improvement from the last ten iterations.",
ValueError
],
'unknown': ["An error occurred.", TypeError]
}
info = retval[-1] # The FORTRAN return value
if (info != 1 and not full_output):
if info in [2, 3, 4, 5]:
if warning: print "Warning: " + errors[info][0]
else:
try:
raise errors[info][1], errors[info][0]
except KeyError:
raise errors['unknown'][1], errors['unknown'][0]
if n == 1:
retval = (retval[0][0], ) + retval[1:]
if full_output:
try:
return retval + (errors[info][0], ) # Return all + the message
except KeyError:
return retval + (errors['unknown'][0], )
else:
return retval[0]
def fsolve(func, x0, args=(), fprime=None, full_output=0,
col_deriv=0, xtol=1.49012e-8, maxfev=0, band=None,
epsfcn=0.0, factor=100, diag=None):
"""
Find the roots of a function.
Return the roots of the (non-linear) equations defined by
``func(x) = 0`` given a starting estimate.
Parameters
----------
func : callable f(x, *args)
A function that takes at least one (possibly vector) argument.
x0 : ndarray
The starting estimate for the roots of ``func(x) = 0``.
args : tuple
Any extra arguments to `func`.
fprime : callable(x)
A function to compute the Jacobian of `func` with derivatives
across the rows. By default, the Jacobian will be estimated.
full_output : bool
If True, return optional outputs.
col_deriv : bool
Specify whether the Jacobian function computes derivatives down
the columns (faster, because there is no transpose operation).
Returns
-------
x : ndarray
The solution (or the result of the last iteration for
an unsuccessful call).
infodict : dict
A dictionary of optional outputs with the keys::
* 'nfev': number of function calls
* 'njev': number of Jacobian calls
* 'fvec': function evaluated at the output
* 'fjac': the orthogonal matrix, q, produced by the QR
factorization of the final approximate Jacobian
matrix, stored column wise
* 'r': upper triangular matrix produced by QR factorization of same
matrix
* 'qtf': the vector (transpose(q) * fvec)
ier : int
An integer flag. Set to 1 if a solution was found, otherwise refer
to `mesg` for more information.
mesg : str
If no solution is found, `mesg` details the cause of failure.
Other Parameters
----------------
xtol : float
The calculation will terminate if the relative error between two
consecutive iterates is at most `xtol`.
maxfev : int
The maximum number of calls to the function. If zero, then
``100*(N+1)`` is the maximum where N is the number of elements
in `x0`.
band : tuple
If set to a two-sequence containing the number of sub- and
super-diagonals within the band of the Jacobi matrix, the
Jacobi matrix is considered banded (only for ``fprime=None``).
epsfcn : float
A suitable step length for the forward-difference
approximation of the Jacobian (for ``fprime=None``). If
`epsfcn` is less than the machine precision, it is assumed
that the relative errors in the functions are of the order of
the machine precision.
factor : float
A parameter determining the initial step bound
(``factor * || diag * x||``). Should be in the interval
``(0.1, 100)``.
diag : sequence
N positive entries that serve as a scale factors for the
variables.
Notes
-----
``fsolve`` is a wrapper around MINPACK's hybrd and hybrj algorithms.
"""
x0 = array(x0, ndmin=1)
n = len(x0)
if type(args) != type(()): args = (args,)
_check_func('fsolve', 'func', func, x0, args, n, (n,))
Dfun = fprime
if Dfun is None:
if band is None:
ml, mu = -10,-10
else:
ml, mu = band[:2]
if (maxfev == 0):
maxfev = 200*(n + 1)
retval = _minpack._hybrd(func, x0, args, full_output, xtol,
maxfev, ml, mu, epsfcn, factor, diag)
else:
_check_func('fsolve', 'fprime', Dfun, x0, args, n, (n,n))
if (maxfev == 0):
maxfev = 100*(n + 1)
retval = _minpack._hybrj(func, Dfun, x0, args, full_output,
col_deriv, xtol, maxfev, factor,diag)
errors = {0:["Improper input parameters were entered.",TypeError],
1:["The solution converged.", None],
2:["The number of calls to function has "
"reached maxfev = %d." % maxfev, ValueError],
3:["xtol=%f is too small, no further improvement "
"in the approximate\n solution "
"is possible." % xtol, ValueError],
4:["The iteration is not making good progress, as measured "
"by the \n improvement from the last five "
"Jacobian evaluations.", ValueError],
5:["The iteration is not making good progress, "
"as measured by the \n improvement from the last "
"ten iterations.", ValueError],
'unknown': ["An error occurred.", TypeError]}
info = retval[-1] # The FORTRAN return value
if (info != 1 and not full_output):
if info in [2,3,4,5]:
msg = errors[info][0]
warnings.warn(msg, RuntimeWarning)
else:
try:
raise errors[info][1](errors[info][0])
except KeyError:
raise errors['unknown'][1](errors['unknown'][0])
if full_output:
try:
return retval + (errors[info][0],) # Return all + the message
except KeyError:
return retval + (errors['unknown'][0],)
else:
return retval[0]
def fsolve(func,
x0,
args=(),
fprime=None,
full_output=0,
col_deriv=0,
xtol=1.49012e-8,
maxfev=0,
band=None,
epsfcn=0.0,
factor=100,
diag=None,
warning=True):
"""
Find the roots of a function.
Return the roots of the (non-linear) equations defined by
``func(x) = 0`` given a starting estimate.
Parameters
----------
func : callable f(x, *args)
A function that takes at least one (possibly vector) argument.
x0 : ndarray
The starting estimate for the roots of ``func(x) = 0``.
args : tuple
Any extra arguments to `func`.
fprime : callable(x)
A function to compute the Jacobian of `func` with derivatives
across the rows. By default, the Jacobian will be estimated.
full_output : bool
If True, return optional outputs.
col_deriv : bool
Specify whether the Jacobian function computes derivatives down
the columns (faster, because there is no transpose operation).
warning : bool
Whether to print a warning message when the call is unsuccessful.
This option is deprecated, use the warnings module instead.
Returns
-------
x : ndarray
The solution (or the result of the last iteration for
an unsuccessful call).
infodict : dict
A dictionary of optional outputs with the keys::
* 'nfev': number of function calls
* 'njev': number of Jacobian calls
* 'fvec': function evaluated at the output
* 'fjac': the orthogonal matrix, q, produced by the QR
factorization of the final approximate Jacobian
matrix, stored column wise
* 'r': upper triangular matrix produced by QR factorization of same
matrix
* 'qtf': the vector (transpose(q) * fvec)
ier : int
An integer flag. Set to 1 if a solution was found, otherwise refer
to `mesg` for more information.
mesg : str
If no solution is found, `mesg` details the cause of failure.
Other Parameters
----------------
xtol : float
The calculation will terminate if the relative error between two
consecutive iterates is at most `xtol`.
maxfev : int
The maximum number of calls to the function. If zero, then
``100*(N+1)`` is the maximum where N is the number of elements
in `x0`.
band : tuple
If set to a two-sequence containing the number of sub- and
super-diagonals within the band of the Jacobi matrix, the
Jacobi matrix is considered banded (only for ``fprime=None``).
epsfcn : float
A suitable step length for the forward-difference
approximation of the Jacobian (for ``fprime=None``). If
`epsfcn` is less than the machine precision, it is assumed
that the relative errors in the functions are of the order of
the machine precision.
factor : float
A parameter determining the initial step bound
(``factor * || diag * x||``). Should be in the interval
``(0.1, 100)``.
diag : sequence
N positive entries that serve as a scale factors for the
variables.
Notes
-----
``fsolve`` is a wrapper around MINPACK's hybrd and hybrj algorithms.
From scipy 0.8.0 `fsolve` returns an array of size one instead of a scalar
when solving for a single parameter.
"""
if not warning:
msg = "The warning keyword is deprecated. Use the warnings module."
warnings.warn(msg, DeprecationWarning)
x0 = array(x0, ndmin=1)
n = len(x0)
if type(args) != type(()): args = (args, )
check_func(func, x0, args, n, (n, ))
Dfun = fprime
if Dfun is None:
if band is None:
ml, mu = -10, -10
else:
ml, mu = band[:2]
if (maxfev == 0):
maxfev = 200 * (n + 1)
retval = _minpack._hybrd(func, x0, args, full_output, xtol, maxfev, ml,
mu, epsfcn, factor, diag)
else:
check_func(Dfun, x0, args, n, (n, n))
if (maxfev == 0):
maxfev = 100 * (n + 1)
retval = _minpack._hybrj(func, Dfun, x0, args, full_output, col_deriv,
xtol, maxfev, factor, diag)
errors = {
0: ["Improper input parameters were entered.", TypeError],
1: ["The solution converged.", None],
2: [
"The number of calls to function has "
"reached maxfev = %d." % maxfev, ValueError
],
3: [
"xtol=%f is too small, no further improvement "
"in the approximate\n solution "
"is possible." % xtol, ValueError
],
4: [
"The iteration is not making good progress, as measured "
"by the \n improvement from the last five "
"Jacobian evaluations.", ValueError
],
5: [
"The iteration is not making good progress, "
"as measured by the \n improvement from the last "
"ten iterations.", ValueError
],
'unknown': ["An error occurred.", TypeError]
}
info = retval[-1] # The FORTRAN return value
if (info != 1 and not full_output):
if info in [2, 3, 4, 5]:
msg = errors[info][0]
warnings.warn(msg, RuntimeWarning)
else:
try:
raise errors[info][1](errors[info][0])
except KeyError:
raise errors['unknown'][1](errors['unknown'][0])
if full_output:
try:
return retval + (errors[info][0], ) # Return all + the message
except KeyError:
return retval + (errors['unknown'][0], )
else:
return retval[0]
def _root_hybr(func, x0, args=(), jac=None,
col_deriv=0, xtol=1.49012e-08, maxfev=0, band=None, eps=0.0,
factor=100, diag=None, full_output=0, **unknown_options):
"""
Find the roots of a multivariate function using MINPACK's hybrd and
hybrj routines (modified Powell method).
Options for the hybrd algorithm are:
col_deriv : bool
Specify whether the Jacobian function computes derivatives down
the columns (faster, because there is no transpose operation).
xtol : float
The calculation will terminate if the relative error between two
consecutive iterates is at most `xtol`.
maxfev : int
The maximum number of calls to the function. If zero, then
``100*(N+1)`` is the maximum where N is the number of elements
in `x0`.
band : tuple
If set to a two-sequence containing the number of sub- and
super-diagonals within the band of the Jacobi matrix, the
Jacobi matrix is considered banded (only for ``fprime=None``).
eps : float
A suitable step length for the forward-difference
approximation of the Jacobian (for ``fprime=None``). If
`eps` is less than the machine precision, it is assumed
that the relative errors in the functions are of the order of
the machine precision.
factor : float
A parameter determining the initial step bound
(``factor * || diag * x||``). Should be in the interval
``(0.1, 100)``.
diag : sequence
N positive entries that serve as a scale factors for the
variables.
This function is called by the `root` function with `method=hybr`. It
is not supposed to be called directly.
"""
_check_unknown_options(unknown_options)
epsfcn = eps
x0 = array(x0, ndmin=1)
n = len(x0)
if type(args) != type(()):
args = (args,)
_check_func('fsolve', 'func', func, x0, args, n, (n,))
Dfun = jac
if Dfun is None:
if band is None:
ml, mu = -10,-10
else:
ml, mu = band[:2]
if (maxfev == 0):
maxfev = 200*(n + 1)
retval = _minpack._hybrd(func, x0, args, 1, xtol, maxfev,
ml, mu, epsfcn, factor, diag)
else:
_check_func('fsolve', 'fprime', Dfun, x0, args, n, (n,n))
if (maxfev == 0):
maxfev = 100*(n + 1)
retval = _minpack._hybrj(func, Dfun, x0, args, 1,
col_deriv, xtol, maxfev, factor,diag)
x, status = retval[0], retval[-1]
errors = {0:["Improper input parameters were entered.",TypeError],
1:["The solution converged.", None],
2:["The number of calls to function has "
"reached maxfev = %d." % maxfev, ValueError],
3:["xtol=%f is too small, no further improvement "
"in the approximate\n solution "
"is possible." % xtol, ValueError],
4:["The iteration is not making good progress, as measured "
"by the \n improvement from the last five "
"Jacobian evaluations.", ValueError],
5:["The iteration is not making good progress, "
"as measured by the \n improvement from the last "
"ten iterations.", ValueError],
'unknown': ["An error occurred.", TypeError]}
if status != 1 and not full_output:
if status in [2,3,4,5]:
msg = errors[status][0]
warnings.warn(msg, RuntimeWarning)
else:
try:
raise errors[status][1](errors[status][0])
except KeyError:
raise errors['unknown'][1](errors['unknown'][0])
info = retval[1]
info['fun'] = info.pop('fvec')
sol = Result(x=x, success=(status==1), status=status)
sol.update(info)
try:
sol['message'] = errors[status][0]
except KeyError:
info['message'] = errors['unknown'][0]
return sol
def fsolve(func,x0,args=(),fprime=None,full_output=0,col_deriv=0,xtol=1.49012e-8,maxfev=0,band=None,epsfcn=0.0,factor=100,diag=None, warning=True):
"""
Find the roots of a function.
Return the roots of the (non-linear) equations defined by func(x)=0 given a
starting estimate.
Parameters
----------
func
A Python function or method which takes at least one (possibly vector)
argument.
x0
The starting estimate for the roots of func(x)=0.
args
Any extra arguments to func are placed in this tuple.
fprime
A function or method to compute the Jacobian of func with derivatives
across the rows. If this is None, the Jacobian will be estimated.
full_output
Non-zero to return the optional outputs.
col_deriv
Non-zero to specify that the Jacobian function computes derivatives down
the columns (faster, because there is no transpose operation).
warning
True to print a warning message when the call is unsuccessful; False to
suppress the warning message.
Returns
-------
x
The solution (or the result of the last iteration for an unsuccessful call.
infodict
A dictionary of optional outputs with the keys:
* 'nfev': number of function calls
* 'njev': number of Jacobian calls
* 'fvec': function evaluated at the output
* 'fjac': the orthogonal matrix, q, produced by the QR factorization of
the final approximate Jacobian matrix, stored column wise
* 'r': upper triangular matrix produced by QR factorization of same
matrix
* 'qtf': the vector (transpose(q) * fvec)
ier
An integer flag. If it is 1, the solution was found. If it is 1, the solution was
not found and the following message gives more information.
mesg
A string message giving information about the cause of failure.
Other Parameters
----------------
xtol
The calculation will terminate if the relative error between two
consecutive iterates is at most `xtol`.
maxfev
The maximum number of calls to the function. If zero, then 100*(N+1) is
the maximum where N is the number of elements in x0.
band
If set to a two-sequence containing the number of sub- and super-diagonals
within the band of the Jacobi matrix, the Jacobi matrix is considered
banded (only for fprime=None).
epsfcn
A suitable step length for the forward-difference approximation of the
Jacobian (for fprime=None). If `epsfcn` is less than the machine
precision, it is assumed that the relative errors in the functions are of
the order of the machine precision.
factor
A parameter determining the initial step bound (`factor` * || `diag` * x||).
Should be in the interval (0.1,100).
diag
A sequency of N positive entries that serve as a scale factors for the
variables.
Notes
-----
"fsolve" is a wrapper around MINPACK's hybrd and hybrj algorithms.
See Also
--------
scikits.openopt : offers a unified syntax to call this and other solvers
fmin, fmin_powell, fmin_cg, fmin_bfgs, fmin_ncg : multivariate local optimizers
leastsq : nonlinear least squares minimizer
fmin_l_bfgs_b, fmin_tnc, fmin_cobyla : constrained multivariate optimizers
anneal, brute : global optimizers
fminbound, brent, golden, bracket : local scalar minimizers
brentq, brenth, ridder, bisect, newton : one-dimensional root-finding
fixed_point : scalar and vector fixed-point finder
"""
x0 = array(x0,ndmin=1)
n = len(x0)
if type(args) != type(()): args = (args,)
check_func(func,x0,args,n,(n,))
Dfun = fprime
if Dfun is None:
if band is None:
ml,mu = -10,-10
else:
ml,mu = band[:2]
if (maxfev == 0):
maxfev = 200*(n+1)
retval = _minpack._hybrd(func,x0,args,full_output,xtol,maxfev,ml,mu,epsfcn,factor,diag)
else:
check_func(Dfun,x0,args,n,(n,n))
if (maxfev == 0):
maxfev = 100*(n+1)
retval = _minpack._hybrj(func,Dfun,x0,args,full_output,col_deriv,xtol,maxfev,factor,diag)
errors = {0:["Improper input parameters were entered.",TypeError],
1:["The solution converged.",None],
2:["The number of calls to function has reached maxfev = %d." % maxfev, ValueError],
3:["xtol=%f is too small, no further improvement in the approximate\n solution is possible." % xtol, ValueError],
4:["The iteration is not making good progress, as measured by the \n improvement from the last five Jacobian evaluations.", ValueError],
5:["The iteration is not making good progress, as measured by the \n improvement from the last ten iterations.", ValueError],
'unknown': ["An error occurred.", TypeError]}
info = retval[-1] # The FORTRAN return value
if (info != 1 and not full_output):
if info in [2,3,4,5]:
if warning: print "Warning: " + errors[info][0]
else:
try:
raise errors[info][1], errors[info][0]
except KeyError:
raise errors['unknown'][1], errors['unknown'][0]
if n == 1:
retval = (retval[0][0],) + retval[1:]
if full_output:
try:
return retval + (errors[info][0],) # Return all + the message
except KeyError:
return retval + (errors['unknown'][0],)
else:
return retval[0]
def _root_hybr(func,
x0,
args=(),
jac=None,
col_deriv=0,
xtol=1.49012e-08,
maxfev=0,
band=None,
eps=0.0,
factor=100,
diag=None,
full_output=0,
**unknown_options):
"""
Find the roots of a multivariate function using MINPACK's hybrd and
hybrj routines (modified Powell method).
Options for the hybrd algorithm are:
col_deriv : bool
Specify whether the Jacobian function computes derivatives down
the columns (faster, because there is no transpose operation).
xtol : float
The calculation will terminate if the relative error between two
consecutive iterates is at most `xtol`.
maxfev : int
The maximum number of calls to the function. If zero, then
``100*(N+1)`` is the maximum where N is the number of elements
in `x0`.
band : tuple
If set to a two-sequence containing the number of sub- and
super-diagonals within the band of the Jacobi matrix, the
Jacobi matrix is considered banded (only for ``fprime=None``).
eps : float
A suitable step length for the forward-difference
approximation of the Jacobian (for ``fprime=None``). If
`eps` is less than the machine precision, it is assumed
that the relative errors in the functions are of the order of
the machine precision.
factor : float
A parameter determining the initial step bound
(``factor * || diag * x||``). Should be in the interval
``(0.1, 100)``.
diag : sequence
N positive entries that serve as a scale factors for the
variables.
This function is called by the `root` function with `method=hybr`. It
is not supposed to be called directly.
"""
_check_unknown_options(unknown_options)
epsfcn = eps
x0 = array(x0, ndmin=1)
n = len(x0)
if type(args) != type(()):
args = (args, )
_check_func('fsolve', 'func', func, x0, args, n, (n, ))
Dfun = jac
if Dfun is None:
if band is None:
ml, mu = -10, -10
else:
ml, mu = band[:2]
if (maxfev == 0):
maxfev = 200 * (n + 1)
retval = _minpack._hybrd(func, x0, args, 1, xtol, maxfev, ml, mu,
epsfcn, factor, diag)
else:
_check_func('fsolve', 'fprime', Dfun, x0, args, n, (n, n))
if (maxfev == 0):
maxfev = 100 * (n + 1)
retval = _minpack._hybrj(func, Dfun, x0, args, 1, col_deriv, xtol,
maxfev, factor, diag)
x, status = retval[0], retval[-1]
errors = {
0: ["Improper input parameters were entered.", TypeError],
1: ["The solution converged.", None],
2: [
"The number of calls to function has "
"reached maxfev = %d." % maxfev, ValueError
],
3: [
"xtol=%f is too small, no further improvement "
"in the approximate\n solution "
"is possible." % xtol, ValueError
],
4: [
"The iteration is not making good progress, as measured "
"by the \n improvement from the last five "
"Jacobian evaluations.", ValueError
],
5: [
"The iteration is not making good progress, "
"as measured by the \n improvement from the last "
"ten iterations.", ValueError
],
'unknown': ["An error occurred.", TypeError]
}
if status != 1 and not full_output:
if status in [2, 3, 4, 5]:
msg = errors[status][0]
warnings.warn(msg, RuntimeWarning)
else:
try:
raise errors[status][1](errors[status][0])
except KeyError:
raise errors['unknown'][1](errors['unknown'][0])
info = retval[1]
info['fun'] = info.pop('fvec')
sol = Result(x=x, success=(status == 1), status=status)
sol.update(info)
try:
sol['message'] = errors[status][0]
except KeyError:
info['message'] = errors['unknown'][0]
return sol