def bisplrep(x,
y,
z,
w=None,
xb=None,
xe=None,
yb=None,
ye=None,
kx=3,
ky=3,
task=0,
s=None,
eps=1e-16,
tx=None,
ty=None,
full_output=0,
nxest=None,
nyest=None,
quiet=1):
"""Find a bivariate B-spline representation of a surface.
Description:
Given a set of data points (x[i], y[i], z[i]) representing a surface
z=f(x,y), compute a B-spline representation of the surface. Based on
the routine SURFIT from FITPACK.
Inputs:
x, y, z -- Rank-1 arrays of data points.
w -- Rank-1 array of weights. By default w=ones(len(x)).
xb, xe -- End points of approximation interval in x.
yb, ye -- End points of approximation interval in y.
By default xb, xe, yb, ye = x.min(), x.max(), y.min(), y.max()
kx, ky -- The degrees of the spline (1 <= kx, ky <= 5). Third order
(kx=ky=3) is recommended.
task -- If task=0, find knots in x and y and coefficients for a given
smoothing factor, s.
If task=1, find knots and coefficients for another value of the
smoothing factor, s. bisplrep must have been previously called
with task=0 or task=1.
If task=-1, find coefficients for a given set of knots tx, ty.
s -- A non-negative smoothing factor. If weights correspond
to the inverse of the standard-deviation of the errors in z,
then a good s-value should be found in the range
(m-sqrt(2*m),m+sqrt(2*m)) where m=len(x)
eps -- A threshold for determining the effective rank of an
over-determined linear system of equations (0 < eps < 1)
--- not likely to need changing.
tx, ty -- Rank-1 arrays of the knots of the spline for task=-1
full_output -- Non-zero to return optional outputs.
nxest, nyest -- Over-estimates of the total number of knots.
If None then nxest = max(kx+sqrt(m/2),2*kx+3),
nyest = max(ky+sqrt(m/2),2*ky+3)
quiet -- Non-zero to suppress printing of messages.
Outputs: (tck, {fp, ier, msg})
tck -- A list [tx, ty, c, kx, ky] containing the knots (tx, ty) and
coefficients (c) of the bivariate B-spline representation of the
surface along with the degree of the spline.
fp -- The weighted sum of squared residuals of the spline approximation.
ier -- An integer flag about splrep success. Success is indicated if
ier<=0. If ier in [1,2,3] an error occurred but was not raised.
Otherwise an error is raised.
msg -- A message corresponding to the integer flag, ier.
Remarks:
SEE bisplev to evaluate the value of the B-spline given its tck
representation.
See also:
splprep, splrep, splint, sproot, splev - evaluation, roots, integral
UnivariateSpline, BivariateSpline - an alternative wrapping
of the FITPACK functions
Notes:
Based on algorithms from:
Dierckx P. : An algorithm for surface fitting with spline functions
Ima J. Numer. Anal. 1 (1981) 267-283.
Dierckx P. : An algorithm for surface fitting with spline functions
report tw50, Dept. Computer Science,K.U.Leuven, 1980.
Dierckx P. : Curve and surface fitting with splines, Monographs on
Numerical Analysis, Oxford University Press, 1993.
"""
x, y, z = map(myasarray, [x, y, z])
x, y, z = map(ravel, [x, y, z]) # ensure 1-d arrays.
m = len(x)
if not (m == len(y) == len(z)):
raise TypeError, 'len(x)==len(y)==len(z) must hold.'
if w is None: w = ones(m, float)
else: w = myasarray(w)
if not len(w) == m:
raise TypeError, ' len(w)=%d is not equal to m=%d' % (len(w), m)
if xb is None: xb = x.min()
if xe is None: xe = x.max()
if yb is None: yb = y.min()
if ye is None: ye = y.max()
if not (-1 <= task <= 1): raise TypeError, 'task must be either -1,0, or 1'
if s is None: s = m - sqrt(2 * m)
if tx is None and task == -1:
raise TypeError, 'Knots_x must be given for task=-1'
if tx is not None: _surfit_cache['tx'] = myasarray(tx)
nx = len(_surfit_cache['tx'])
if ty is None and task == -1:
raise TypeError, 'Knots_y must be given for task=-1'
if ty is not None: _surfit_cache['ty'] = myasarray(ty)
ny = len(_surfit_cache['ty'])
if task == -1 and nx < 2 * kx + 2:
raise TypeError, 'There must be at least 2*kx+2 knots_x for task=-1'
if task == -1 and ny < 2 * ky + 2:
raise TypeError, 'There must be at least 2*ky+2 knots_x for task=-1'
if not ((1 <= kx <= 5) and (1 <= ky <= 5)):
raise TypeError, 'Given degree of the spline (kx,ky=%d,%d) is not supported. (1<=k<=5)' % (
kx, ky)
if m < (kx + 1) * (ky + 1): raise TypeError, 'm>=(kx+1)(ky+1) must hold'
if nxest is None: nxest = kx + sqrt(m / 2)
if nyest is None: nyest = ky + sqrt(m / 2)
nxest, nyest = max(nxest, 2 * kx + 3), max(nyest, 2 * ky + 3)
if task >= 0 and s == 0:
nxest = int(kx + sqrt(3 * m))
nyest = int(ky + sqrt(3 * m))
if task == -1:
_surfit_cache['tx'] = myasarray(tx)
_surfit_cache['ty'] = myasarray(ty)
tx, ty = _surfit_cache['tx'], _surfit_cache['ty']
wrk = _surfit_cache['wrk']
iwrk = _surfit_cache['iwrk']
u, v, km, ne = nxest - kx - 1, nyest - ky - 1, max(kx, ky) + 1, max(
nxest, nyest)
bx, by = kx * v + ky + 1, ky * u + kx + 1
b1, b2 = bx, bx + v - ky
if bx > by: b1, b2 = by, by + u - kx
try:
lwrk1 = int32(u * v * (2 + b1 + b2) + 2 *
(u + v + km * (m + ne) + ne - kx - ky) + b2 + 1)
lwrk2 = int32(u * v * (b2 + 1) + b2)
except OverflowError:
raise OverflowError("Too many data points to interpolate")
tx, ty, c, o = _fitpack._surfit(x, y, z, w, xb, xe, yb, ye, kx, ky, task,
s, eps, tx, ty, nxest, nyest, wrk, lwrk1,
lwrk2)
_curfit_cache['tx'] = tx
_curfit_cache['ty'] = ty
_curfit_cache['wrk'] = o['wrk']
ier, fp = o['ier'], o['fp']
tck = [tx, ty, c, kx, ky]
if ier <= 0 and not quiet:
print _iermess2[ier][0]
print "\tkx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f" % (kx, ky, len(tx),
len(ty), m, fp, s)
ierm = min(11, max(-3, ier))
if ierm > 0 and not full_output:
if ier in [1, 2, 3, 4, 5]:
print "Warning: " + _iermess2[ierm][0]
print "\tkx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f" % (
kx, ky, len(tx), len(ty), m, fp, s)
else:
try:
raise _iermess2[ierm][1], _iermess2[ierm][0]
except KeyError:
raise _iermess2['unknown'][1], _iermess2['unknown'][0]
if full_output:
try:
return tck, fp, ier, _iermess2[ierm][0]
except KeyError:
return tck, fp, ier, _iermess2['unknown'][0]
else:
return tck
def bisplrep(x,y,z,w=None,xb=None,xe=None,yb=None,ye=None,kx=3,ky=3,task=0,
s=None,eps=1e-16,tx=None,ty=None,full_output=0,
nxest=None,nyest=None,quiet=1):
"""Find a bivariate B-spline representation of a surface.
Description:
Given a set of data points (x[i], y[i], z[i]) representing a surface
z=f(x,y), compute a B-spline representation of the surface.
Inputs:
x, y, z -- Rank-1 arrays of data points.
w -- Rank-1 array of weights. By default w=ones(len(x)).
xb, xe -- End points of approximation interval in x.
yb, ye -- End points of approximation interval in y.
By default xb, xe, yb, ye = x.min(), x.max(), y.min(), y.max()
kx, ky -- The degrees of the spline (1 <= kx, ky <= 5). Third order
(kx=ky=3) is recommended.
task -- If task=0, find knots in x and y and coefficients for a given
smoothing factor, s.
If task=1, find knots and coefficients for another value of the
smoothing factor, s. bisplrep must have been previously called
with task=0 or task=1.
If task=-1, find coefficients for a given set of knots tx, ty.
s -- A non-negative smoothing factor. If weights correspond
to the inverse of the standard-deviation of the errors in z,
then a good s-value should be found in the range
(m-sqrt(2*m),m+sqrt(2*m)) where m=len(x)
eps -- A threshold for determining the effective rank of an
over-determined linear system of equations (0 < eps < 1)
--- not likely to need changing.
tx, ty -- Rank-1 arrays of the knots of the spline for task=-1
full_output -- Non-zero to return optional outputs.
nxest, nyest -- Over-estimates of the total number of knots.
If None then nxest = max(kx+sqrt(m/2),2*kx+3),
nyest = max(ky+sqrt(m/2),2*ky+3)
quiet -- Non-zero to suppress printing of messages.
Outputs: (tck, {fp, ier, msg})
tck -- A list [tx, ty, c, kx, ky] containing the knots (tx, ty) and
coefficients (c) of the bivariate B-spline representation of the
surface along with the degree of the spline.
fp -- The weighted sum of squared residuals of the spline approximation.
ier -- An integer flag about splrep success. Success is indicated if
ier<=0. If ier in [1,2,3] an error occurred but was not raised.
Otherwise an error is raised.
msg -- A message corresponding to the integer flag, ier.
Remarks:
SEE bisplev to evaluate the value of the B-spline given its tck
representation.
See also:
splprep, splrep, splint, sproot, splev - evaluation, roots, integral
UnivariateSpline, BivariateSpline - an alternative wrapping
of the FITPACK functions
"""
x,y,z=map(myasarray,[x,y,z])
x,y,z=map(ravel,[x,y,z]) # ensure 1-d arrays.
m=len(x)
if not (m==len(y)==len(z)): raise TypeError, 'len(x)==len(y)==len(z) must hold.'
if w is None: w=ones(m,float)
else: w=myasarray(w)
if not len(w) == m: raise TypeError,' len(w)=%d is not equal to m=%d'%(len(w),m)
if xb is None: xb=x.min()
if xe is None: xe=x.max()
if yb is None: yb=y.min()
if ye is None: ye=y.max()
if not (-1<=task<=1): raise TypeError, 'task must be either -1,0, or 1'
if s is None: s=m-sqrt(2*m)
if tx is None and task==-1: raise TypeError, 'Knots_x must be given for task=-1'
if tx is not None: _surfit_cache['tx']=myasarray(tx)
nx=len(_surfit_cache['tx'])
if ty is None and task==-1: raise TypeError, 'Knots_y must be given for task=-1'
if ty is not None: _surfit_cache['ty']=myasarray(ty)
ny=len(_surfit_cache['ty'])
if task==-1 and nx<2*kx+2:
raise TypeError, 'There must be at least 2*kx+2 knots_x for task=-1'
if task==-1 and ny<2*ky+2:
raise TypeError, 'There must be at least 2*ky+2 knots_x for task=-1'
if not ((1<=kx<=5) and (1<=ky<=5)):
raise TypeError, 'Given degree of the spline (kx,ky=%d,%d) is not supported. (1<=k<=5)'%(kx,ky)
if m<(kx+1)*(ky+1): raise TypeError, 'm>=(kx+1)(ky+1) must hold'
if nxest is None: nxest=kx+sqrt(m/2)
if nyest is None: nyest=ky+sqrt(m/2)
nxest,nyest=max(nxest,2*kx+3),max(nyest,2*ky+3)
if task>=0 and s==0:
nxest=int(kx+sqrt(3*m))
nyest=int(ky+sqrt(3*m))
if task==-1:
_surfit_cache['tx']=myasarray(tx)
_surfit_cache['ty']=myasarray(ty)
tx,ty=_surfit_cache['tx'],_surfit_cache['ty']
wrk=_surfit_cache['wrk']
iwrk=_surfit_cache['iwrk']
u,v,km,ne=nxest-kx-1,nyest-ky-1,max(kx,ky)+1,max(nxest,nyest)
bx,by=kx*v+ky+1,ky*u+kx+1
b1,b2=bx,bx+v-ky
if bx>by: b1,b2=by,by+u-kx
lwrk1=u*v*(2+b1+b2)+2*(u+v+km*(m+ne)+ne-kx-ky)+b2+1
lwrk2=u*v*(b2+1)+b2
tx,ty,c,o = _fitpack._surfit(x,y,z,w,xb,xe,yb,ye,kx,ky,task,s,eps,
tx,ty,nxest,nyest,wrk,lwrk1,lwrk2)
_curfit_cache['tx']=tx
_curfit_cache['ty']=ty
_curfit_cache['wrk']=o['wrk']
ier,fp=o['ier'],o['fp']
tck=[tx,ty,c,kx,ky]
if ier<=0 and not quiet:
print _iermess2[ier][0]
print "\tkx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f"%(kx,ky,len(tx),
len(ty),m,fp,s)
ierm=min(11,max(-3,ier))
if ierm>0 and not full_output:
if ier in [1,2,3,4,5]:
print "Warning: "+_iermess2[ierm][0]
print "\tkx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f"%(kx,ky,len(tx),
len(ty),m,fp,s)
else:
try:
raise _iermess2[ierm][1],_iermess2[ierm][0]
except KeyError:
raise _iermess2['unknown'][1],_iermess2['unknown'][0]
if full_output:
try:
return tck,fp,ier,_iermess2[ierm][0]
except KeyError:
return tck,fp,ier,_iermess2['unknown'][0]
else:
return tck
def bisplrep(x,y,z,w=None,xb=None,xe=None,yb=None,ye=None,kx=3,ky=3,task=0,
s=None,eps=1e-16,tx=None,ty=None,full_output=0,
nxest=None,nyest=None,quiet=1):
"""
Find a bivariate B-spline representation of a surface.
Given a set of data points (x[i], y[i], z[i]) representing a surface
z=f(x,y), compute a B-spline representation of the surface. Based on
the routine SURFIT from FITPACK.
Parameters
----------
x, y, z : ndarray
Rank-1 arrays of data points.
w : ndarray, optional
Rank-1 array of weights. By default ``w=np.ones(len(x))``.
xb, xe : float, optional
End points of approximation interval in `x`.
By default ``xb = x.min(), xe=x.max()``.
yb, ye : float, optional
End points of approximation interval in `y`.
By default ``yb=y.min(), ye = y.max()``.
kx, ky : int, optional
The degrees of the spline (1 <= kx, ky <= 5).
Third order (kx=ky=3) is recommended.
task : int, optional
If task=0, find knots in x and y and coefficients for a given
smoothing factor, s.
If task=1, find knots and coefficients for another value of the
smoothing factor, s. bisplrep must have been previously called
with task=0 or task=1.
If task=-1, find coefficients for a given set of knots tx, ty.
s : float, optional
A non-negative smoothing factor. If weights correspond
to the inverse of the standard-deviation of the errors in z,
then a good s-value should be found in the range
``(m-sqrt(2*m),m+sqrt(2*m))`` where m=len(x).
eps : float, optional
A threshold for determining the effective rank of an
over-determined linear system of equations (0 < eps < 1).
`eps` is not likely to need changing.
tx, ty : ndarray, optional
Rank-1 arrays of the knots of the spline for task=-1
full_output : int, optional
Non-zero to return optional outputs.
nxest, nyest : int, optional
Over-estimates of the total number of knots. If None then
``nxest = max(kx+sqrt(m/2),2*kx+3)``,
``nyest = max(ky+sqrt(m/2),2*ky+3)``.
quiet : int, optional
Non-zero to suppress printing of messages.
Returns
-------
tck : array_like
A list [tx, ty, c, kx, ky] containing the knots (tx, ty) and
coefficients (c) of the bivariate B-spline representation of the
surface along with the degree of the spline.
fp : ndarray
The weighted sum of squared residuals of the spline approximation.
ier : int
An integer flag about splrep success. Success is indicated if
ier<=0. If ier in [1,2,3] an error occurred but was not raised.
Otherwise an error is raised.
msg : str
A message corresponding to the integer flag, ier.
See Also
--------
splprep, splrep, splint, sproot, splev
UnivariateSpline, BivariateSpline
Notes
-----
See `bisplev` to evaluate the value of the B-spline given its tck
representation.
References
----------
.. [1] Dierckx P.:An algorithm for surface fitting with spline functions
Ima J. Numer. Anal. 1 (1981) 267-283.
.. [2] Dierckx P.:An algorithm for surface fitting with spline functions
report tw50, Dept. Computer Science,K.U.Leuven, 1980.
.. [3] Dierckx P.:Curve and surface fitting with splines, Monographs on
Numerical Analysis, Oxford University Press, 1993.
"""
x,y,z=map(myasarray,[x,y,z])
x,y,z=map(ravel,[x,y,z]) # ensure 1-d arrays.
m=len(x)
if not (m==len(y)==len(z)): raise TypeError, 'len(x)==len(y)==len(z) must hold.'
if w is None: w=ones(m,float)
else: w=myasarray(w)
if not len(w) == m: raise TypeError,' len(w)=%d is not equal to m=%d'%(len(w),m)
if xb is None: xb=x.min()
if xe is None: xe=x.max()
if yb is None: yb=y.min()
if ye is None: ye=y.max()
if not (-1<=task<=1): raise TypeError, 'task must be either -1,0, or 1'
if s is None: s=m-sqrt(2*m)
if tx is None and task==-1: raise TypeError, 'Knots_x must be given for task=-1'
if tx is not None: _surfit_cache['tx']=myasarray(tx)
nx=len(_surfit_cache['tx'])
if ty is None and task==-1: raise TypeError, 'Knots_y must be given for task=-1'
if ty is not None: _surfit_cache['ty']=myasarray(ty)
ny=len(_surfit_cache['ty'])
if task==-1 and nx<2*kx+2:
raise TypeError, 'There must be at least 2*kx+2 knots_x for task=-1'
if task==-1 and ny<2*ky+2:
raise TypeError, 'There must be at least 2*ky+2 knots_x for task=-1'
if not ((1<=kx<=5) and (1<=ky<=5)):
raise TypeError, 'Given degree of the spline (kx,ky=%d,%d) is not supported. (1<=k<=5)'%(kx,ky)
if m<(kx+1)*(ky+1): raise TypeError, 'm>=(kx+1)(ky+1) must hold'
if nxest is None: nxest=kx+sqrt(m/2)
if nyest is None: nyest=ky+sqrt(m/2)
nxest,nyest=max(nxest,2*kx+3),max(nyest,2*ky+3)
if task>=0 and s==0:
nxest=int(kx+sqrt(3*m))
nyest=int(ky+sqrt(3*m))
if task==-1:
_surfit_cache['tx']=myasarray(tx)
_surfit_cache['ty']=myasarray(ty)
tx,ty=_surfit_cache['tx'],_surfit_cache['ty']
wrk=_surfit_cache['wrk']
iwrk=_surfit_cache['iwrk']
u,v,km,ne=nxest-kx-1,nyest-ky-1,max(kx,ky)+1,max(nxest,nyest)
bx,by=kx*v+ky+1,ky*u+kx+1
b1,b2=bx,bx+v-ky
if bx>by: b1,b2=by,by+u-kx
try:
lwrk1=int32(u*v*(2+b1+b2)+2*(u+v+km*(m+ne)+ne-kx-ky)+b2+1)
lwrk2=int32(u*v*(b2+1)+b2)
except OverflowError:
raise OverflowError("Too many data points to interpolate")
tx,ty,c,o = _fitpack._surfit(x,y,z,w,xb,xe,yb,ye,kx,ky,task,s,eps,
tx,ty,nxest,nyest,wrk,lwrk1,lwrk2)
_curfit_cache['tx']=tx
_curfit_cache['ty']=ty
_curfit_cache['wrk']=o['wrk']
ier,fp=o['ier'],o['fp']
tck=[tx,ty,c,kx,ky]
ierm=min(11,max(-3,ier))
if ierm<=0 and not quiet:
print _iermess2[ierm][0]
print "\tkx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f"%(kx,ky,len(tx),
len(ty),m,fp,s)
if ierm>0 and not full_output:
if ier in [1,2,3,4,5]:
print "Warning: "+_iermess2[ierm][0]
print "\tkx,ky=%d,%d nx,ny=%d,%d m=%d fp=%f s=%f"%(kx,ky,len(tx),
len(ty),m,fp,s)
else:
try:
raise _iermess2[ierm][1],_iermess2[ierm][0]
except KeyError:
raise _iermess2['unknown'][1],_iermess2['unknown'][0]
if full_output:
try:
return tck,fp,ier,_iermess2[ierm][0]
except KeyError:
return tck,fp,ier,_iermess2['unknown'][0]
else:
return tck