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""" fitpack --- curve and surface fitting with splines
fitpack is based on a collection of Fortran routines DIERCKX by P. Dierckx (see http://www.netlib.org/dierckx/) transformed to double routines by Pearu Peterson. """ # Created by Pearu Peterson, June,August 2003
'UnivariateSpline', 'InterpolatedUnivariateSpline', 'LSQUnivariateSpline', 'BivariateSpline', 'LSQBivariateSpline', 'SmoothBivariateSpline', 'LSQSphereBivariateSpline', 'SmoothSphereBivariateSpline', 'RectBivariateSpline', 'RectSphereBivariateSpline']
################ Univariate spline ####################
The required storage space exceeds the available storage space, as specified by the parameter nest: nest too small. If nest is already large (say nest > m/2), it may also indicate that s is too small. The approximation returned is the weighted least-squares spline according to the knots t[0],t[1],...,t[n-1]. (n=nest) the parameter fp gives the corresponding weighted sum of squared residuals (fp>s). """, 2:""" A theoretically impossible result was found during the iteration process for finding a smoothing spline with fp = s: s too small. There is an approximation returned but the corresponding weighted sum of squared residuals does not satisfy the condition abs(fp-s)/s < tol.""", 3:""" The maximal number of iterations maxit (set to 20 by the program) allowed for finding a smoothing spline with fp=s has been reached: s too small. There is an approximation returned but the corresponding weighted sum of squared residuals does not satisfy the condition abs(fp-s)/s < tol.""", 10:""" Error on entry, no approximation returned. The following conditions must hold: xb<=x[0]<x[1]<...<x[m-1]<=xe, w[i]>0, i=0..m-1 if iopt=-1: xb<t[k+1]<t[k+2]<...<t[n-k-2]<xe""" }
# UnivariateSpline, ext parameter can be an int or a string _extrap_modes = {0: 0, 'extrapolate': 0, 1: 1, 'zeros': 1, 2: 2, 'raise': 2, 3: 3, 'const': 3}
""" One-dimensional smoothing spline fit to a given set of data points.
Fits a spline y = spl(x) of degree `k` to the provided `x`, `y` data. `s` specifies the number of knots by specifying a smoothing condition.
Parameters ---------- x : (N,) array_like 1-D array of independent input data. Must be increasing. y : (N,) array_like 1-D array of dependent input data, of the same length as `x`. w : (N,) array_like, optional Weights for spline fitting. Must be positive. If None (default), weights are all equal. bbox : (2,) array_like, optional 2-sequence specifying the boundary of the approximation interval. If None (default), ``bbox=[x[0], x[-1]]``. k : int, optional Degree of the smoothing spline. Must be <= 5. Default is k=3, a cubic spline. s : float or None, optional Positive smoothing factor used to choose the number of knots. Number of knots will be increased until the smoothing condition is satisfied::
sum((w[i] * (y[i]-spl(x[i])))**2, axis=0) <= s
If None (default), ``s = len(w)`` which should be a good value if ``1/w[i]`` is an estimate of the standard deviation of ``y[i]``. If 0, spline will interpolate through all data points. ext : int or str, optional Controls the extrapolation mode for elements not in the interval defined by the knot sequence.
* if ext=0 or 'extrapolate', return the extrapolated value. * if ext=1 or 'zeros', return 0 * if ext=2 or 'raise', raise a ValueError * if ext=3 of 'const', return the boundary value.
The default value is 0.
check_finite : bool, optional Whether to check that the input arrays contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination or non-sensical results) if the inputs do contain infinities or NaNs. Default is False.
See Also -------- InterpolatedUnivariateSpline : Subclass with smoothing forced to 0 LSQUnivariateSpline : Subclass in which knots are user-selected instead of being set by smoothing condition splrep : An older, non object-oriented wrapping of FITPACK splev, sproot, splint, spalde BivariateSpline : A similar class for two-dimensional spline interpolation
Notes ----- The number of data points must be larger than the spline degree `k`.
**NaN handling**: If the input arrays contain ``nan`` values, the result is not useful, since the underlying spline fitting routines cannot deal with ``nan`` . A workaround is to use zero weights for not-a-number data points:
>>> from scipy.interpolate import UnivariateSpline >>> x, y = np.array([1, 2, 3, 4]), np.array([1, np.nan, 3, 4]) >>> w = np.isnan(y) >>> y[w] = 0. >>> spl = UnivariateSpline(x, y, w=~w)
Notice the need to replace a ``nan`` by a numerical value (precise value does not matter as long as the corresponding weight is zero.)
Examples -------- >>> import matplotlib.pyplot as plt >>> from scipy.interpolate import UnivariateSpline >>> x = np.linspace(-3, 3, 50) >>> y = np.exp(-x**2) + 0.1 * np.random.randn(50) >>> plt.plot(x, y, 'ro', ms=5)
Use the default value for the smoothing parameter:
>>> spl = UnivariateSpline(x, y) >>> xs = np.linspace(-3, 3, 1000) >>> plt.plot(xs, spl(xs), 'g', lw=3)
Manually change the amount of smoothing:
>>> spl.set_smoothing_factor(0.5) >>> plt.plot(xs, spl(xs), 'b', lw=3) >>> plt.show()
""" ext=0, check_finite=False):
if check_finite: w_finite = np.isfinite(w).all() if w is not None else True if (not np.isfinite(x).all() or not np.isfinite(y).all() or not w_finite): raise ValueError("x and y array must not contain NaNs or infs.") if not all(diff(x) > 0.0): raise ValueError('x must be strictly increasing')
# _data == x,y,w,xb,xe,k,s,n,t,c,fp,fpint,nrdata,ier try: self.ext = _extrap_modes[ext] except KeyError: raise ValueError("Unknown extrapolation mode %s." % ext)
data = dfitpack.fpcurf0(x,y,k,w=w, xb=bbox[0],xe=bbox[1],s=s) if data[-1] == 1: # nest too small, setting to maximum bound data = self._reset_nest(data) self._data = data self._reset_class()
"""Construct a spline object from given tck""" self = cls.__new__(cls) t, c, k = tck self._eval_args = tck #_data == x,y,w,xb,xe,k,s,n,t,c,fp,fpint,nrdata,ier self._data = (None,None,None,None,None,k,None,len(t),t, c,None,None,None,None) self.ext = ext return self
data = self._data n,t,c,k,ier = data[7],data[8],data[9],data[5],data[-1] self._eval_args = t[:n],c[:n],k if ier == 0: # the spline returned has a residual sum of squares fp # such that abs(fp-s)/s <= tol with tol a relative # tolerance set to 0.001 by the program pass elif ier == -1: # the spline returned is an interpolating spline self._set_class(InterpolatedUnivariateSpline) elif ier == -2: # the spline returned is the weighted least-squares # polynomial of degree k. In this extreme case fp gives # the upper bound fp0 for the smoothing factor s. self._set_class(LSQUnivariateSpline) else: # error if ier == 1: self._set_class(LSQUnivariateSpline) message = _curfit_messages.get(ier,'ier=%s' % (ier)) warnings.warn(message)
self._spline_class = cls if self.__class__ in (UnivariateSpline, InterpolatedUnivariateSpline, LSQUnivariateSpline): self.__class__ = cls else: # It's an unknown subclass -- don't change class. cf. #731 pass
n = data[10] if nest is None: k,m = data[5],len(data[0]) nest = m+k+1 # this is the maximum bound for nest else: if not n <= nest: raise ValueError("`nest` can only be increased") t, c, fpint, nrdata = [np.resize(data[j], nest) for j in [8,9,11,12]]
args = data[:8] + (t,c,n,fpint,nrdata,data[13]) data = dfitpack.fpcurf1(*args) return data
""" Continue spline computation with the given smoothing factor s and with the knots found at the last call.
This routine modifies the spline in place.
""" data = self._data if data[6] == -1: warnings.warn('smoothing factor unchanged for' 'LSQ spline with fixed knots') return args = data[:6] + (s,) + data[7:] data = dfitpack.fpcurf1(*args) if data[-1] == 1: # nest too small, setting to maximum bound data = self._reset_nest(data) self._data = data self._reset_class()
""" Evaluate spline (or its nu-th derivative) at positions x.
Parameters ---------- x : array_like A 1-D array of points at which to return the value of the smoothed spline or its derivatives. Note: x can be unordered but the evaluation is more efficient if x is (partially) ordered. nu : int The order of derivative of the spline to compute. ext : int Controls the value returned for elements of ``x`` not in the interval defined by the knot sequence.
* if ext=0 or 'extrapolate', return the extrapolated value. * if ext=1 or 'zeros', return 0 * if ext=2 or 'raise', raise a ValueError * if ext=3 or 'const', return the boundary value.
The default value is 0, passed from the initialization of UnivariateSpline.
""" x = np.asarray(x) # empty input yields empty output if x.size == 0: return array([]) # if nu is None: # return dfitpack.splev(*(self._eval_args+(x,))) # return dfitpack.splder(nu=nu,*(self._eval_args+(x,))) if ext is None: ext = self.ext else: try: ext = _extrap_modes[ext] except KeyError: raise ValueError("Unknown extrapolation mode %s." % ext) return fitpack.splev(x, self._eval_args, der=nu, ext=ext)
""" Return positions of interior knots of the spline.
Internally, the knot vector contains ``2*k`` additional boundary knots. """ data = self._data k,n = data[5],data[7] return data[8][k:n-k]
"""Return spline coefficients.""" data = self._data k,n = data[5],data[7] return data[9][:n-k-1]
"""Return weighted sum of squared residuals of the spline approximation.
This is equivalent to::
sum((w[i] * (y[i]-spl(x[i])))**2, axis=0)
""" return self._data[10]
""" Return definite integral of the spline between two given points.
Parameters ---------- a : float Lower limit of integration. b : float Upper limit of integration.
Returns ------- integral : float The value of the definite integral of the spline between limits.
Examples -------- >>> from scipy.interpolate import UnivariateSpline >>> x = np.linspace(0, 3, 11) >>> y = x**2 >>> spl = UnivariateSpline(x, y) >>> spl.integral(0, 3) 9.0
which agrees with :math:`\\int x^2 dx = x^3 / 3` between the limits of 0 and 3.
A caveat is that this routine assumes the spline to be zero outside of the data limits:
>>> spl.integral(-1, 4) 9.0 >>> spl.integral(-1, 0) 0.0
""" return dfitpack.splint(*(self._eval_args+(a,b)))
""" Return all derivatives of the spline at the point x.
Parameters ---------- x : float The point to evaluate the derivatives at.
Returns ------- der : ndarray, shape(k+1,) Derivatives of the orders 0 to k.
Examples -------- >>> from scipy.interpolate import UnivariateSpline >>> x = np.linspace(0, 3, 11) >>> y = x**2 >>> spl = UnivariateSpline(x, y) >>> spl.derivatives(1.5) array([2.25, 3.0, 2.0, 0])
""" d,ier = dfitpack.spalde(*(self._eval_args+(x,))) if not ier == 0: raise ValueError("Error code returned by spalde: %s" % ier) return d
""" Return the zeros of the spline.
Restriction: only cubic splines are supported by fitpack. """ k = self._data[5] if k == 3: z,m,ier = dfitpack.sproot(*self._eval_args[:2]) if not ier == 0: raise ValueError("Error code returned by spalde: %s" % ier) return z[:m] raise NotImplementedError('finding roots unsupported for ' 'non-cubic splines')
""" Construct a new spline representing the derivative of this spline.
Parameters ---------- n : int, optional Order of derivative to evaluate. Default: 1
Returns ------- spline : UnivariateSpline Spline of order k2=k-n representing the derivative of this spline.
See Also -------- splder, antiderivative
Notes -----
.. versionadded:: 0.13.0
Examples -------- This can be used for finding maxima of a curve:
>>> from scipy.interpolate import UnivariateSpline >>> x = np.linspace(0, 10, 70) >>> y = np.sin(x) >>> spl = UnivariateSpline(x, y, k=4, s=0)
Now, differentiate the spline and find the zeros of the derivative. (NB: `sproot` only works for order 3 splines, so we fit an order 4 spline):
>>> spl.derivative().roots() / np.pi array([ 0.50000001, 1.5 , 2.49999998])
This agrees well with roots :math:`\\pi/2 + n\\pi` of :math:`\\cos(x) = \\sin'(x)`.
""" tck = fitpack.splder(self._eval_args, n) return UnivariateSpline._from_tck(tck, self.ext)
""" Construct a new spline representing the antiderivative of this spline.
Parameters ---------- n : int, optional Order of antiderivative to evaluate. Default: 1
Returns ------- spline : UnivariateSpline Spline of order k2=k+n representing the antiderivative of this spline.
Notes -----
.. versionadded:: 0.13.0
See Also -------- splantider, derivative
Examples -------- >>> from scipy.interpolate import UnivariateSpline >>> x = np.linspace(0, np.pi/2, 70) >>> y = 1 / np.sqrt(1 - 0.8*np.sin(x)**2) >>> spl = UnivariateSpline(x, y, s=0)
The derivative is the inverse operation of the antiderivative, although some floating point error accumulates:
>>> spl(1.7), spl.antiderivative().derivative()(1.7) (array(2.1565429877197317), array(2.1565429877201865))
Antiderivative can be used to evaluate definite integrals:
>>> ispl = spl.antiderivative() >>> ispl(np.pi/2) - ispl(0) 2.2572053588768486
This is indeed an approximation to the complete elliptic integral :math:`K(m) = \\int_0^{\\pi/2} [1 - m\\sin^2 x]^{-1/2} dx`:
>>> from scipy.special import ellipk >>> ellipk(0.8) 2.2572053268208538
""" tck = fitpack.splantider(self._eval_args, n) return UnivariateSpline._from_tck(tck, self.ext)
""" One-dimensional interpolating spline for a given set of data points.
Fits a spline y = spl(x) of degree `k` to the provided `x`, `y` data. Spline function passes through all provided points. Equivalent to `UnivariateSpline` with s=0.
Parameters ---------- x : (N,) array_like Input dimension of data points -- must be increasing y : (N,) array_like input dimension of data points w : (N,) array_like, optional Weights for spline fitting. Must be positive. If None (default), weights are all equal. bbox : (2,) array_like, optional 2-sequence specifying the boundary of the approximation interval. If None (default), ``bbox=[x[0], x[-1]]``. k : int, optional Degree of the smoothing spline. Must be 1 <= `k` <= 5. ext : int or str, optional Controls the extrapolation mode for elements not in the interval defined by the knot sequence.
* if ext=0 or 'extrapolate', return the extrapolated value. * if ext=1 or 'zeros', return 0 * if ext=2 or 'raise', raise a ValueError * if ext=3 of 'const', return the boundary value.
The default value is 0.
check_finite : bool, optional Whether to check that the input arrays contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination or non-sensical results) if the inputs do contain infinities or NaNs. Default is False.
See Also -------- UnivariateSpline : Superclass -- allows knots to be selected by a smoothing condition LSQUnivariateSpline : spline for which knots are user-selected splrep : An older, non object-oriented wrapping of FITPACK splev, sproot, splint, spalde BivariateSpline : A similar class for two-dimensional spline interpolation
Notes ----- The number of data points must be larger than the spline degree `k`.
Examples -------- >>> import matplotlib.pyplot as plt >>> from scipy.interpolate import InterpolatedUnivariateSpline >>> x = np.linspace(-3, 3, 50) >>> y = np.exp(-x**2) + 0.1 * np.random.randn(50) >>> spl = InterpolatedUnivariateSpline(x, y) >>> plt.plot(x, y, 'ro', ms=5) >>> xs = np.linspace(-3, 3, 1000) >>> plt.plot(xs, spl(xs), 'g', lw=3, alpha=0.7) >>> plt.show()
Notice that the ``spl(x)`` interpolates `y`:
>>> spl.get_residual() 0.0
""" ext=0, check_finite=False):
if check_finite: w_finite = np.isfinite(w).all() if w is not None else True if (not np.isfinite(x).all() or not np.isfinite(y).all() or not w_finite): raise ValueError("Input must not contain NaNs or infs.") if not all(diff(x) > 0.0): raise ValueError('x must be strictly increasing')
# _data == x,y,w,xb,xe,k,s,n,t,c,fp,fpint,nrdata,ier self._data = dfitpack.fpcurf0(x,y,k,w=w, xb=bbox[0],xe=bbox[1],s=0) self._reset_class()
try: self.ext = _extrap_modes[ext] except KeyError: raise ValueError("Unknown extrapolation mode %s." % ext)
This means that at least one of the following conditions is violated:
1) k+1 <= n-k-1 <= m 2) t(1) <= t(2) <= ... <= t(k+1) t(n-k) <= t(n-k+1) <= ... <= t(n) 3) t(k+1) < t(k+2) < ... < t(n-k) 4) t(k+1) <= x(i) <= t(n-k) 5) The conditions specified by Schoenberg and Whitney must hold for at least one subset of data points, i.e., there must be a subset of data points y(j) such that t(j) < y(j) < t(j+k+1), j=1,2,...,n-k-1 """
""" One-dimensional spline with explicit internal knots.
Fits a spline y = spl(x) of degree `k` to the provided `x`, `y` data. `t` specifies the internal knots of the spline
Parameters ---------- x : (N,) array_like Input dimension of data points -- must be increasing y : (N,) array_like Input dimension of data points t : (M,) array_like interior knots of the spline. Must be in ascending order and::
bbox[0] < t[0] < ... < t[-1] < bbox[-1]
w : (N,) array_like, optional weights for spline fitting. Must be positive. If None (default), weights are all equal. bbox : (2,) array_like, optional 2-sequence specifying the boundary of the approximation interval. If None (default), ``bbox = [x[0], x[-1]]``. k : int, optional Degree of the smoothing spline. Must be 1 <= `k` <= 5. Default is k=3, a cubic spline. ext : int or str, optional Controls the extrapolation mode for elements not in the interval defined by the knot sequence.
* if ext=0 or 'extrapolate', return the extrapolated value. * if ext=1 or 'zeros', return 0 * if ext=2 or 'raise', raise a ValueError * if ext=3 of 'const', return the boundary value.
The default value is 0.
check_finite : bool, optional Whether to check that the input arrays contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination or non-sensical results) if the inputs do contain infinities or NaNs. Default is False.
Raises ------ ValueError If the interior knots do not satisfy the Schoenberg-Whitney conditions
See Also -------- UnivariateSpline : Superclass -- knots are specified by setting a smoothing condition InterpolatedUnivariateSpline : spline passing through all points splrep : An older, non object-oriented wrapping of FITPACK splev, sproot, splint, spalde BivariateSpline : A similar class for two-dimensional spline interpolation
Notes ----- The number of data points must be larger than the spline degree `k`.
Knots `t` must satisfy the Schoenberg-Whitney conditions, i.e., there must be a subset of data points ``x[j]`` such that ``t[j] < x[j] < t[j+k+1]``, for ``j=0, 1,...,n-k-2``.
Examples -------- >>> from scipy.interpolate import LSQUnivariateSpline, UnivariateSpline >>> import matplotlib.pyplot as plt >>> x = np.linspace(-3, 3, 50) >>> y = np.exp(-x**2) + 0.1 * np.random.randn(50)
Fit a smoothing spline with a pre-defined internal knots:
>>> t = [-1, 0, 1] >>> spl = LSQUnivariateSpline(x, y, t)
>>> xs = np.linspace(-3, 3, 1000) >>> plt.plot(x, y, 'ro', ms=5) >>> plt.plot(xs, spl(xs), 'g-', lw=3) >>> plt.show()
Check the knot vector:
>>> spl.get_knots() array([-3., -1., 0., 1., 3.])
Constructing lsq spline using the knots from another spline:
>>> x = np.arange(10) >>> s = UnivariateSpline(x, x, s=0) >>> s.get_knots() array([ 0., 2., 3., 4., 5., 6., 7., 9.]) >>> knt = s.get_knots() >>> s1 = LSQUnivariateSpline(x, x, knt[1:-1]) # Chop 1st and last knot >>> s1.get_knots() array([ 0., 2., 3., 4., 5., 6., 7., 9.])
"""
ext=0, check_finite=False):
if check_finite: w_finite = np.isfinite(w).all() if w is not None else True if (not np.isfinite(x).all() or not np.isfinite(y).all() or not w_finite or not np.isfinite(t).all()): raise ValueError("Input(s) must not contain NaNs or infs.") if not all(diff(x) > 0.0): raise ValueError('x must be strictly increasing')
# _data == x,y,w,xb,xe,k,s,n,t,c,fp,fpint,nrdata,ier xb = bbox[0] xe = bbox[1] if xb is None: xb = x[0] if xe is None: xe = x[-1] t = concatenate(([xb]*(k+1), t, [xe]*(k+1))) n = len(t) if not alltrue(t[k+1:n-k]-t[k:n-k-1] > 0, axis=0): raise ValueError('Interior knots t must satisfy ' 'Schoenberg-Whitney conditions') if not dfitpack.fpchec(x, t, k) == 0: raise ValueError(_fpchec_error_string) data = dfitpack.fpcurfm1(x, y, k, t, w=w, xb=xb, xe=xe) self._data = data[:-3] + (None, None, data[-1]) self._reset_class()
try: self.ext = _extrap_modes[ext] except KeyError: raise ValueError("Unknown extrapolation mode %s." % ext)
################ Bivariate spline ####################
""" Base class for Bivariate spline s(x,y) interpolation on the rectangle [xb,xe] x [yb, ye] calculated from a given set of data points (x,y,z).
See Also -------- bisplrep, bisplev : an older wrapping of FITPACK BivariateSpline : implementation of bivariate spline interpolation on a plane grid SphereBivariateSpline : implementation of bivariate spline interpolation on a spherical grid """
""" Return weighted sum of squared residuals of the spline approximation: sum ((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0) """ return self.fp
""" Return a tuple (tx,ty) where tx,ty contain knots positions of the spline with respect to x-, y-variable, respectively. The position of interior and additional knots are given as t[k+1:-k-1] and t[:k+1]=b, t[-k-1:]=e, respectively. """ return self.tck[:2]
""" Return spline coefficients.""" return self.tck[2]
""" Evaluate the spline or its derivatives at given positions.
Parameters ---------- x, y : array_like Input coordinates.
If `grid` is False, evaluate the spline at points ``(x[i], y[i]), i=0, ..., len(x)-1``. Standard Numpy broadcasting is obeyed.
If `grid` is True: evaluate spline at the grid points defined by the coordinate arrays x, y. The arrays must be sorted to increasing order.
Note that the axis ordering is inverted relative to the output of meshgrid. dx : int Order of x-derivative
.. versionadded:: 0.14.0 dy : int Order of y-derivative
.. versionadded:: 0.14.0 grid : bool Whether to evaluate the results on a grid spanned by the input arrays, or at points specified by the input arrays.
.. versionadded:: 0.14.0
"""
if x.size == 0 or y.size == 0: return np.zeros((x.size, y.size), dtype=self.tck[2].dtype)
if dx or dy: z,ier = dfitpack.parder(tx,ty,c,kx,ky,dx,dy,x,y) if not ier == 0: raise ValueError("Error code returned by parder: %s" % ier) else: z,ier = dfitpack.bispev(tx,ty,c,kx,ky,x,y) if not ier == 0: raise ValueError("Error code returned by bispev: %s" % ier) else: # standard Numpy broadcasting x, y = np.broadcast_arrays(x, y)
return np.zeros(shape, dtype=self.tck[2].dtype)
z,ier = dfitpack.pardeu(tx,ty,c,kx,ky,dx,dy,x,y) if not ier == 0: raise ValueError("Error code returned by pardeu: %s" % ier) else: raise ValueError("Error code returned by bispeu: %s" % ier)
The required storage space exceeds the available storage space: nxest or nyest too small, or s too small. The weighted least-squares spline corresponds to the current set of knots.""", 2:""" A theoretically impossible result was found during the iteration process for finding a smoothing spline with fp = s: s too small or badly chosen eps. Weighted sum of squared residuals does not satisfy abs(fp-s)/s < tol.""", 3:""" the maximal number of iterations maxit (set to 20 by the program) allowed for finding a smoothing spline with fp=s has been reached: s too small. Weighted sum of squared residuals does not satisfy abs(fp-s)/s < tol.""", 4:""" No more knots can be added because the number of b-spline coefficients (nx-kx-1)*(ny-ky-1) already exceeds the number of data points m: either s or m too small. The weighted least-squares spline corresponds to the current set of knots.""", 5:""" No more knots can be added because the additional knot would (quasi) coincide with an old one: s too small or too large a weight to an inaccurate data point. The weighted least-squares spline corresponds to the current set of knots.""", 10:""" Error on entry, no approximation returned. The following conditions must hold: xb<=x[i]<=xe, yb<=y[i]<=ye, w[i]>0, i=0..m-1 If iopt==-1, then xb<tx[kx+1]<tx[kx+2]<...<tx[nx-kx-2]<xe yb<ty[ky+1]<ty[ky+2]<...<ty[ny-ky-2]<ye""", -3:""" The coefficients of the spline returned have been computed as the minimal norm least-squares solution of a (numerically) rank deficient system (deficiency=%i). If deficiency is large, the results may be inaccurate. Deficiency may strongly depend on the value of eps.""" }
""" Base class for bivariate splines.
This describes a spline ``s(x, y)`` of degrees ``kx`` and ``ky`` on the rectangle ``[xb, xe] * [yb, ye]`` calculated from a given set of data points ``(x, y, z)``.
This class is meant to be subclassed, not instantiated directly. To construct these splines, call either `SmoothBivariateSpline` or `LSQBivariateSpline`.
See Also -------- UnivariateSpline : a similar class for univariate spline interpolation SmoothBivariateSpline : to create a BivariateSpline through the given points LSQBivariateSpline : to create a BivariateSpline using weighted least-squares fitting SphereBivariateSpline : bivariate spline interpolation in spherical cooridinates bisplrep : older wrapping of FITPACK bisplev : older wrapping of FITPACK
"""
def _from_tck(cls, tck): """Construct a spline object from given tck and degree""" self = cls.__new__(cls) if len(tck) != 5: raise ValueError("tck should be a 5 element tuple of tx, ty, c, kx, ky") self.tck = tck[:3] self.degrees = tck[3:] return self
""" Evaluate the spline at points
Returns the interpolated value at ``(xi[i], yi[i]), i=0,...,len(xi)-1``.
Parameters ---------- xi, yi : array_like Input coordinates. Standard Numpy broadcasting is obeyed. dx : int, optional Order of x-derivative
.. versionadded:: 0.14.0 dy : int, optional Order of y-derivative
.. versionadded:: 0.14.0 """
""" Evaluate the integral of the spline over area [xa,xb] x [ya,yb].
Parameters ---------- xa, xb : float The end-points of the x integration interval. ya, yb : float The end-points of the y integration interval.
Returns ------- integ : float The value of the resulting integral.
""" tx,ty,c = self.tck[:3] kx,ky = self.degrees return dfitpack.dblint(tx,ty,c,kx,ky,xa,xb,ya,yb)
""" Smooth bivariate spline approximation.
Parameters ---------- x, y, z : array_like 1-D sequences of data points (order is not important). w : array_like, optional Positive 1-D sequence of weights, of same length as `x`, `y` and `z`. bbox : array_like, optional Sequence of length 4 specifying the boundary of the rectangular approximation domain. By default, ``bbox=[min(x,tx),max(x,tx), min(y,ty),max(y,ty)]``. kx, ky : ints, optional Degrees of the bivariate spline. Default is 3. s : float, optional Positive smoothing factor defined for estimation condition: ``sum((w[i]*(z[i]-s(x[i], y[i])))**2, axis=0) <= s`` Default ``s=len(w)`` which should be a good value if ``1/w[i]`` is an estimate of the standard deviation of ``z[i]``. eps : float, optional A threshold for determining the effective rank of an over-determined linear system of equations. `eps` should have a value between 0 and 1, the default is 1e-16.
See Also -------- bisplrep : an older wrapping of FITPACK bisplev : an older wrapping of FITPACK UnivariateSpline : a similar class for univariate spline interpolation LSQUnivariateSpline : to create a BivariateSpline using weighted
Notes ----- The length of `x`, `y` and `z` should be at least ``(kx+1) * (ky+1)``.
"""
eps=None): xb,xe,yb,ye = bbox nx,tx,ny,ty,c,fp,wrk1,ier = dfitpack.surfit_smth(x,y,z,w, xb,xe,yb,ye, kx,ky,s=s, eps=eps,lwrk2=1) if ier > 10: # lwrk2 was to small, re-run nx,tx,ny,ty,c,fp,wrk1,ier = dfitpack.surfit_smth(x,y,z,w, xb,xe,yb,ye, kx,ky,s=s, eps=eps,lwrk2=ier) if ier in [0,-1,-2]: # normal return pass else: message = _surfit_messages.get(ier,'ier=%s' % (ier)) warnings.warn(message)
self.fp = fp self.tck = tx[:nx],ty[:ny],c[:(nx-kx-1)*(ny-ky-1)] self.degrees = kx,ky
""" Weighted least-squares bivariate spline approximation.
Parameters ---------- x, y, z : array_like 1-D sequences of data points (order is not important). tx, ty : array_like Strictly ordered 1-D sequences of knots coordinates. w : array_like, optional Positive 1-D array of weights, of the same length as `x`, `y` and `z`. bbox : (4,) array_like, optional Sequence of length 4 specifying the boundary of the rectangular approximation domain. By default, ``bbox=[min(x,tx),max(x,tx), min(y,ty),max(y,ty)]``. kx, ky : ints, optional Degrees of the bivariate spline. Default is 3. eps : float, optional A threshold for determining the effective rank of an over-determined linear system of equations. `eps` should have a value between 0 and 1, the default is 1e-16.
See Also -------- bisplrep : an older wrapping of FITPACK bisplev : an older wrapping of FITPACK UnivariateSpline : a similar class for univariate spline interpolation SmoothBivariateSpline : create a smoothing BivariateSpline
Notes ----- The length of `x`, `y` and `z` should be at least ``(kx+1) * (ky+1)``.
"""
eps=None): nx = 2*kx+2+len(tx) ny = 2*ky+2+len(ty) tx1 = zeros((nx,),float) ty1 = zeros((ny,),float) tx1[kx+1:nx-kx-1] = tx ty1[ky+1:ny-ky-1] = ty
xb,xe,yb,ye = bbox tx1,ty1,c,fp,ier = dfitpack.surfit_lsq(x,y,z,tx1,ty1,w, xb,xe,yb,ye, kx,ky,eps,lwrk2=1) if ier > 10: tx1,ty1,c,fp,ier = dfitpack.surfit_lsq(x,y,z,tx1,ty1,w, xb,xe,yb,ye, kx,ky,eps,lwrk2=ier) if ier in [0,-1,-2]: # normal return pass else: if ier < -2: deficiency = (nx-kx-1)*(ny-ky-1)+ier message = _surfit_messages.get(-3) % (deficiency) else: message = _surfit_messages.get(ier, 'ier=%s' % (ier)) warnings.warn(message) self.fp = fp self.tck = tx1, ty1, c self.degrees = kx, ky
""" Bivariate spline approximation over a rectangular mesh.
Can be used for both smoothing and interpolating data.
Parameters ---------- x,y : array_like 1-D arrays of coordinates in strictly ascending order. z : array_like 2-D array of data with shape (x.size,y.size). bbox : array_like, optional Sequence of length 4 specifying the boundary of the rectangular approximation domain. By default, ``bbox=[min(x,tx),max(x,tx), min(y,ty),max(y,ty)]``. kx, ky : ints, optional Degrees of the bivariate spline. Default is 3. s : float, optional Positive smoothing factor defined for estimation condition: ``sum((w[i]*(z[i]-s(x[i], y[i])))**2, axis=0) <= s`` Default is ``s=0``, which is for interpolation.
See Also -------- SmoothBivariateSpline : a smoothing bivariate spline for scattered data bisplrep : an older wrapping of FITPACK bisplev : an older wrapping of FITPACK UnivariateSpline : a similar class for univariate spline interpolation
"""
raise ValueError('x must be strictly increasing') raise ValueError('y must be strictly increasing') raise ValueError('x must be strictly ascending') raise ValueError('y must be strictly ascending') raise ValueError('x dimension of z must have same number of ' 'elements as x') raise ValueError('y dimension of z must have same number of ' 'elements as y') ye, kx, ky, s)
msg = _surfit_messages.get(ier, 'ier=%s' % (ier)) raise ValueError(msg)
ERROR. On entry, the input data are controlled on validity. The following restrictions must be satisfied: -1<=iopt<=1, m>=2, ntest>=8 ,npest >=8, 0<eps<1, 0<=teta(i)<=pi, 0<=phi(i)<=2*pi, w(i)>0, i=1,...,m lwrk1 >= 185+52*v+10*u+14*u*v+8*(u-1)*v**2+8*m kwrk >= m+(ntest-7)*(npest-7) if iopt=-1: 8<=nt<=ntest , 9<=np<=npest 0<tt(5)<tt(6)<...<tt(nt-4)<pi 0<tp(5)<tp(6)<...<tp(np-4)<2*pi if iopt>=0: s>=0 if one of these conditions is found to be violated,control is immediately repassed to the calling program. in that case there is no approximation returned.""" WARNING. The coefficients of the spline returned have been computed as the minimal norm least-squares solution of a (numerically) rank deficient system (deficiency=%i, rank=%i). Especially if the rank deficiency, which is computed by 6+(nt-8)*(np-7)+ier, is large, the results may be inaccurate. They could also seriously depend on the value of eps."""
""" Bivariate spline s(x,y) of degrees 3 on a sphere, calculated from a given set of data points (theta,phi,r).
.. versionadded:: 0.11.0
See Also -------- bisplrep, bisplev : an older wrapping of FITPACK UnivariateSpline : a similar class for univariate spline interpolation SmoothUnivariateSpline : to create a BivariateSpline through the given points LSQUnivariateSpline : to create a BivariateSpline using weighted least-squares fitting """
""" Evaluate the spline or its derivatives at given positions.
Parameters ---------- theta, phi : array_like Input coordinates.
If `grid` is False, evaluate the spline at points ``(theta[i], phi[i]), i=0, ..., len(x)-1``. Standard Numpy broadcasting is obeyed.
If `grid` is True: evaluate spline at the grid points defined by the coordinate arrays theta, phi. The arrays must be sorted to increasing order. dtheta : int, optional Order of theta-derivative
.. versionadded:: 0.14.0 dphi : int Order of phi-derivative
.. versionadded:: 0.14.0 grid : bool Whether to evaluate the results on a grid spanned by the input arrays, or at points specified by the input arrays.
.. versionadded:: 0.14.0
""" theta = np.asarray(theta) phi = np.asarray(phi)
if theta.size > 0 and (theta.min() < 0. or theta.max() > np.pi): raise ValueError("requested theta out of bounds.") if phi.size > 0 and (phi.min() < 0. or phi.max() > 2. * np.pi): raise ValueError("requested phi out of bounds.")
return _BivariateSplineBase.__call__(self, theta, phi, dx=dtheta, dy=dphi, grid=grid)
""" Evaluate the spline at points
Returns the interpolated value at ``(theta[i], phi[i]), i=0,...,len(theta)-1``.
Parameters ---------- theta, phi : array_like Input coordinates. Standard Numpy broadcasting is obeyed. dtheta : int, optional Order of theta-derivative
.. versionadded:: 0.14.0 dphi : int, optional Order of phi-derivative
.. versionadded:: 0.14.0 """ return self.__call__(theta, phi, dtheta=dtheta, dphi=dphi, grid=False)
""" Smooth bivariate spline approximation in spherical coordinates.
.. versionadded:: 0.11.0
Parameters ---------- theta, phi, r : array_like 1-D sequences of data points (order is not important). Coordinates must be given in radians. Theta must lie within the interval (0, pi), and phi must lie within the interval (0, 2pi). w : array_like, optional Positive 1-D sequence of weights. s : float, optional Positive smoothing factor defined for estimation condition: ``sum((w(i)*(r(i) - s(theta(i), phi(i))))**2, axis=0) <= s`` Default ``s=len(w)`` which should be a good value if 1/w[i] is an estimate of the standard deviation of r[i]. eps : float, optional A threshold for determining the effective rank of an over-determined linear system of equations. `eps` should have a value between 0 and 1, the default is 1e-16.
Notes ----- For more information, see the FITPACK_ site about this function.
.. _FITPACK: http://www.netlib.org/dierckx/sphere.f
Examples -------- Suppose we have global data on a coarse grid (the input data does not have to be on a grid):
>>> theta = np.linspace(0., np.pi, 7) >>> phi = np.linspace(0., 2*np.pi, 9) >>> data = np.empty((theta.shape[0], phi.shape[0])) >>> data[:,0], data[0,:], data[-1,:] = 0., 0., 0. >>> data[1:-1,1], data[1:-1,-1] = 1., 1. >>> data[1,1:-1], data[-2,1:-1] = 1., 1. >>> data[2:-2,2], data[2:-2,-2] = 2., 2. >>> data[2,2:-2], data[-3,2:-2] = 2., 2. >>> data[3,3:-2] = 3. >>> data = np.roll(data, 4, 1)
We need to set up the interpolator object
>>> lats, lons = np.meshgrid(theta, phi) >>> from scipy.interpolate import SmoothSphereBivariateSpline >>> lut = SmoothSphereBivariateSpline(lats.ravel(), lons.ravel(), ... data.T.ravel(), s=3.5)
As a first test, we'll see what the algorithm returns when run on the input coordinates
>>> data_orig = lut(theta, phi)
Finally we interpolate the data to a finer grid
>>> fine_lats = np.linspace(0., np.pi, 70) >>> fine_lons = np.linspace(0., 2 * np.pi, 90)
>>> data_smth = lut(fine_lats, fine_lons)
>>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax1 = fig.add_subplot(131) >>> ax1.imshow(data, interpolation='nearest') >>> ax2 = fig.add_subplot(132) >>> ax2.imshow(data_orig, interpolation='nearest') >>> ax3 = fig.add_subplot(133) >>> ax3.imshow(data_smth, interpolation='nearest') >>> plt.show()
"""
if np.issubclass_(w, float): w = ones(len(theta)) * w nt_, tt_, np_, tp_, c, fp, ier = dfitpack.spherfit_smth(theta, phi, r, w=w, s=s, eps=eps) if ier not in [0, -1, -2]: message = _spherefit_messages.get(ier, 'ier=%s' % (ier)) raise ValueError(message)
self.fp = fp self.tck = tt_[:nt_], tp_[:np_], c[:(nt_ - 4) * (np_ - 4)] self.degrees = (3, 3)
""" Weighted least-squares bivariate spline approximation in spherical coordinates.
.. versionadded:: 0.11.0
Parameters ---------- theta, phi, r : array_like 1-D sequences of data points (order is not important). Coordinates must be given in radians. Theta must lie within the interval (0, pi), and phi must lie within the interval (0, 2pi). tt, tp : array_like Strictly ordered 1-D sequences of knots coordinates. Coordinates must satisfy ``0 < tt[i] < pi``, ``0 < tp[i] < 2*pi``. w : array_like, optional Positive 1-D sequence of weights, of the same length as `theta`, `phi` and `r`. eps : float, optional A threshold for determining the effective rank of an over-determined linear system of equations. `eps` should have a value between 0 and 1, the default is 1e-16.
Notes ----- For more information, see the FITPACK_ site about this function.
.. _FITPACK: http://www.netlib.org/dierckx/sphere.f
Examples -------- Suppose we have global data on a coarse grid (the input data does not have to be on a grid):
>>> theta = np.linspace(0., np.pi, 7) >>> phi = np.linspace(0., 2*np.pi, 9) >>> data = np.empty((theta.shape[0], phi.shape[0])) >>> data[:,0], data[0,:], data[-1,:] = 0., 0., 0. >>> data[1:-1,1], data[1:-1,-1] = 1., 1. >>> data[1,1:-1], data[-2,1:-1] = 1., 1. >>> data[2:-2,2], data[2:-2,-2] = 2., 2. >>> data[2,2:-2], data[-3,2:-2] = 2., 2. >>> data[3,3:-2] = 3. >>> data = np.roll(data, 4, 1)
We need to set up the interpolator object. Here, we must also specify the coordinates of the knots to use.
>>> lats, lons = np.meshgrid(theta, phi) >>> knotst, knotsp = theta.copy(), phi.copy() >>> knotst[0] += .0001 >>> knotst[-1] -= .0001 >>> knotsp[0] += .0001 >>> knotsp[-1] -= .0001 >>> from scipy.interpolate import LSQSphereBivariateSpline >>> lut = LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), ... data.T.ravel(), knotst, knotsp)
As a first test, we'll see what the algorithm returns when run on the input coordinates
>>> data_orig = lut(theta, phi)
Finally we interpolate the data to a finer grid
>>> fine_lats = np.linspace(0., np.pi, 70) >>> fine_lons = np.linspace(0., 2*np.pi, 90)
>>> data_lsq = lut(fine_lats, fine_lons)
>>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax1 = fig.add_subplot(131) >>> ax1.imshow(data, interpolation='nearest') >>> ax2 = fig.add_subplot(132) >>> ax2.imshow(data_orig, interpolation='nearest') >>> ax3 = fig.add_subplot(133) >>> ax3.imshow(data_lsq, interpolation='nearest') >>> plt.show()
"""
if np.issubclass_(w, float): w = ones(len(theta)) * w nt_, np_ = 8 + len(tt), 8 + len(tp) tt_, tp_ = zeros((nt_,), float), zeros((np_,), float) tt_[4:-4], tp_[4:-4] = tt, tp tt_[-4:], tp_[-4:] = np.pi, 2. * np.pi tt_, tp_, c, fp, ier = dfitpack.spherfit_lsq(theta, phi, r, tt_, tp_, w=w, eps=eps) if ier < -2: deficiency = 6 + (nt_ - 8) * (np_ - 7) + ier message = _spherefit_messages.get(-3) % (deficiency, -ier) warnings.warn(message) elif ier not in [0, -1, -2]: message = _spherefit_messages.get(ier, 'ier=%s' % (ier)) raise ValueError(message)
self.fp = fp self.tck = tt_, tp_, c self.degrees = (3, 3)
ERROR: on entry, the input data are controlled on validity the following restrictions must be satisfied. -1<=iopt(1)<=1, 0<=iopt(2)<=1, 0<=iopt(3)<=1, -1<=ider(1)<=1, 0<=ider(2)<=1, ider(2)=0 if iopt(2)=0. -1<=ider(3)<=1, 0<=ider(4)<=1, ider(4)=0 if iopt(3)=0. mu >= mumin (see above), mv >= 4, nuest >=8, nvest >= 8, kwrk>=5+mu+mv+nuest+nvest, lwrk >= 12+nuest*(mv+nvest+3)+nvest*24+4*mu+8*mv+max(nuest,mv+nvest) 0< u(i-1)<u(i)< pi,i=2,..,mu, -pi<=v(1)< pi, v(1)<v(i-1)<v(i)<v(1)+2*pi, i=3,...,mv if iopt(1)=-1: 8<=nu<=min(nuest,mu+6+iopt(2)+iopt(3)) 0<tu(5)<tu(6)<...<tu(nu-4)< pi 8<=nv<=min(nvest,mv+7) v(1)<tv(5)<tv(6)<...<tv(nv-4)<v(1)+2*pi the schoenberg-whitney conditions, i.e. there must be subset of grid co-ordinates uu(p) and vv(q) such that tu(p) < uu(p) < tu(p+4) ,p=1,...,nu-4 (iopt(2)=1 and iopt(3)=1 also count for a uu-value tv(q) < vv(q) < tv(q+4) ,q=1,...,nv-4 (vv(q) is either a value v(j) or v(j)+2*pi) if iopt(1)>=0: s>=0 if s=0: nuest>=mu+6+iopt(2)+iopt(3), nvest>=mv+7 if one of these conditions is found to be violated,control is immediately repassed to the calling program. in that case there is no approximation returned."""
""" Bivariate spline approximation over a rectangular mesh on a sphere.
Can be used for smoothing data.
.. versionadded:: 0.11.0
Parameters ---------- u : array_like 1-D array of latitude coordinates in strictly ascending order. Coordinates must be given in radians and lie within the interval (0, pi). v : array_like 1-D array of longitude coordinates in strictly ascending order. Coordinates must be given in radians. First element (v[0]) must lie within the interval [-pi, pi). Last element (v[-1]) must satisfy v[-1] <= v[0] + 2*pi. r : array_like 2-D array of data with shape ``(u.size, v.size)``. s : float, optional Positive smoothing factor defined for estimation condition (``s=0`` is for interpolation). pole_continuity : bool or (bool, bool), optional Order of continuity at the poles ``u=0`` (``pole_continuity[0]``) and ``u=pi`` (``pole_continuity[1]``). The order of continuity at the pole will be 1 or 0 when this is True or False, respectively. Defaults to False. pole_values : float or (float, float), optional Data values at the poles ``u=0`` and ``u=pi``. Either the whole parameter or each individual element can be None. Defaults to None. pole_exact : bool or (bool, bool), optional Data value exactness at the poles ``u=0`` and ``u=pi``. If True, the value is considered to be the right function value, and it will be fitted exactly. If False, the value will be considered to be a data value just like the other data values. Defaults to False. pole_flat : bool or (bool, bool), optional For the poles at ``u=0`` and ``u=pi``, specify whether or not the approximation has vanishing derivatives. Defaults to False.
See Also -------- RectBivariateSpline : bivariate spline approximation over a rectangular mesh
Notes ----- Currently, only the smoothing spline approximation (``iopt[0] = 0`` and ``iopt[0] = 1`` in the FITPACK routine) is supported. The exact least-squares spline approximation is not implemented yet.
When actually performing the interpolation, the requested `v` values must lie within the same length 2pi interval that the original `v` values were chosen from.
For more information, see the FITPACK_ site about this function.
.. _FITPACK: http://www.netlib.org/dierckx/spgrid.f
Examples -------- Suppose we have global data on a coarse grid
>>> lats = np.linspace(10, 170, 9) * np.pi / 180. >>> lons = np.linspace(0, 350, 18) * np.pi / 180. >>> data = np.dot(np.atleast_2d(90. - np.linspace(-80., 80., 18)).T, ... np.atleast_2d(180. - np.abs(np.linspace(0., 350., 9)))).T
We want to interpolate it to a global one-degree grid
>>> new_lats = np.linspace(1, 180, 180) * np.pi / 180 >>> new_lons = np.linspace(1, 360, 360) * np.pi / 180 >>> new_lats, new_lons = np.meshgrid(new_lats, new_lons)
We need to set up the interpolator object
>>> from scipy.interpolate import RectSphereBivariateSpline >>> lut = RectSphereBivariateSpline(lats, lons, data)
Finally we interpolate the data. The `RectSphereBivariateSpline` object only takes 1-D arrays as input, therefore we need to do some reshaping.
>>> data_interp = lut.ev(new_lats.ravel(), ... new_lons.ravel()).reshape((360, 180)).T
Looking at the original and the interpolated data, one can see that the interpolant reproduces the original data very well:
>>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax1 = fig.add_subplot(211) >>> ax1.imshow(data, interpolation='nearest') >>> ax2 = fig.add_subplot(212) >>> ax2.imshow(data_interp, interpolation='nearest') >>> plt.show()
Choosing the optimal value of ``s`` can be a delicate task. Recommended values for ``s`` depend on the accuracy of the data values. If the user has an idea of the statistical errors on the data, she can also find a proper estimate for ``s``. By assuming that, if she specifies the right ``s``, the interpolator will use a spline ``f(u,v)`` which exactly reproduces the function underlying the data, she can evaluate ``sum((r(i,j)-s(u(i),v(j)))**2)`` to find a good estimate for this ``s``. For example, if she knows that the statistical errors on her ``r(i,j)``-values are not greater than 0.1, she may expect that a good ``s`` should have a value not larger than ``u.size * v.size * (0.1)**2``.
If nothing is known about the statistical error in ``r(i,j)``, ``s`` must be determined by trial and error. The best is then to start with a very large value of ``s`` (to determine the least-squares polynomial and the corresponding upper bound ``fp0`` for ``s``) and then to progressively decrease the value of ``s`` (say by a factor 10 in the beginning, i.e. ``s = fp0 / 10, fp0 / 100, ...`` and more carefully as the approximation shows more detail) to obtain closer fits.
The interpolation results for different values of ``s`` give some insight into this process:
>>> fig2 = plt.figure() >>> s = [3e9, 2e9, 1e9, 1e8] >>> for ii in range(len(s)): ... lut = RectSphereBivariateSpline(lats, lons, data, s=s[ii]) ... data_interp = lut.ev(new_lats.ravel(), ... new_lons.ravel()).reshape((360, 180)).T ... ax = fig2.add_subplot(2, 2, ii+1) ... ax.imshow(data_interp, interpolation='nearest') ... ax.set_title("s = %g" % s[ii]) >>> plt.show()
"""
pole_exact=False, pole_flat=False): iopt = np.array([0, 0, 0], dtype=int) ider = np.array([-1, 0, -1, 0], dtype=int) if pole_values is None: pole_values = (None, None) elif isinstance(pole_values, (float, np.float32, np.float64)): pole_values = (pole_values, pole_values) if isinstance(pole_continuity, bool): pole_continuity = (pole_continuity, pole_continuity) if isinstance(pole_exact, bool): pole_exact = (pole_exact, pole_exact) if isinstance(pole_flat, bool): pole_flat = (pole_flat, pole_flat)
r0, r1 = pole_values iopt[1:] = pole_continuity if r0 is None: ider[0] = -1 else: ider[0] = pole_exact[0]
if r1 is None: ider[2] = -1 else: ider[2] = pole_exact[1]
ider[1], ider[3] = pole_flat
u, v = np.ravel(u), np.ravel(v) if not np.all(np.diff(u) > 0.0): raise ValueError('u must be strictly increasing') if not np.all(np.diff(v) > 0.0): raise ValueError('v must be strictly increasing')
if not u.size == r.shape[0]: raise ValueError('u dimension of r must have same number of ' 'elements as u') if not v.size == r.shape[1]: raise ValueError('v dimension of r must have same number of ' 'elements as v')
if pole_continuity[1] is False and pole_flat[1] is True: raise ValueError('if pole_continuity is False, so must be ' 'pole_flat') if pole_continuity[0] is False and pole_flat[0] is True: raise ValueError('if pole_continuity is False, so must be ' 'pole_flat')
r = np.ravel(r) nu, tu, nv, tv, c, fp, ier = dfitpack.regrid_smth_spher(iopt, ider, u.copy(), v.copy(), r.copy(), r0, r1, s)
if ier not in [0, -1, -2]: msg = _spfit_messages.get(ier, 'ier=%s' % (ier)) raise ValueError(msg)
self.fp = fp self.tck = tu[:nu], tv[:nv], c[:(nu - 4) * (nv-4)] self.degrees = (3, 3) |