def splmake(xk,yk,order=3,kind='smoothest',conds=None):
"""Return a (xk, cvals, k) representation of a spline given
data-points where the (internal) knots are at the data-points.
yk can be an N-d array to represent more than one curve, through
the same xk points. The first dimension is assumed to be the
interpolating dimension.
kind can be 'smoothest', 'not_a_knot', 'fixed',
'clamped', 'natural', 'periodic', 'symmetric',
'user', 'mixed'
it is ignored if order < 2
"""
yk = np.asanyarray(yk)
N = yk.shape[0]-1
order = int(order)
if order < 0:
raise ValueError("order must not be negative")
if order == 0:
return xk, yk[:-1], order
elif order == 1:
return xk, yk, order
try:
func = eval('_find_%s' % kind)
except:
raise NotImplementedError
# the constraint matrix
B = _fitpack._bsplmat(order, xk)
coefs = func(xk, yk, order, conds, B)
return xk, coefs, order
def splmake(xk, yk, order=3, kind='smoothest', conds=None):
"""Return a (xk, cvals, k) representation of a spline given
data-points where the (internal) knots are at the data-points.
yk can be an N-d array to represent more than one curve, through
the same xk points. The first dimension is assumed to be the
interpolating dimension.
kind can be 'smoothest', 'not_a_knot', 'fixed',
'clamped', 'natural', 'periodic', 'symmetric',
'user', 'mixed'
it is ignored if order < 2
"""
yk = np.asanyarray(yk)
N = yk.shape[0] - 1
order = int(order)
if order < 0:
raise ValueError("order must not be negative")
if order == 0:
return xk, yk[:-1], order
elif order == 1:
return xk, yk, order
try:
func = eval('_find_%s' % kind)
except:
raise NotImplementedError
# the constraint matrix
B = _fitpack._bsplmat(order, xk)
coefs = func(xk, yk, order, conds, B)
return xk, coefs, order
def _find_smoothest(xk, yk, order, conds=None, B=None):
# construct Bmatrix, and Jmatrix
# e = J*c
# minimize norm(e,2) given B*c=yk
# if desired B can be given
# conds is ignored
N = len(xk)-1
K = order
if B is None:
B = _fitpack._bsplmat(order, xk)
J = _fitpack._bspldismat(order, xk)
u,s,vh = np.dual.svd(B)
ind = K-1
V2 = vh[-ind:,:].T
V1 = vh[:-ind,:].T
A = dot(J.T,J)
tmp = dot(V2.T,A)
Q = dot(tmp,V2)
p = np.dual.solve(Q,tmp)
tmp = dot(V2,p)
tmp = np.eye(N+K) - tmp
tmp = dot(tmp,V1)
tmp = dot(tmp,np.diag(1.0/s))
tmp = dot(tmp,u.T)
return dot(tmp, yk)
def _find_smoothest(xk, yk, order, conds=None, B=None):
# construct Bmatrix, and Jmatrix
# e = J*c
# minimize norm(e,2) given B*c=yk
# if desired B can be given
# conds is ignored
N = len(xk) - 1
K = order
if B is None:
B = _fitpack._bsplmat(order, xk)
J = _fitpack._bspldismat(order, xk)
u, s, vh = np.dual.svd(B)
ind = K - 1
V2 = vh[-ind:, :].T
V1 = vh[:-ind, :].T
A = dot(J.T, J)
tmp = dot(V2.T, A)
Q = dot(tmp, V2)
p = np.dual.solve(Q, tmp)
tmp = dot(V2, p)
tmp = np.eye(N + K) - tmp
tmp = dot(tmp, V1)
tmp = dot(tmp, np.diag(1.0 / s))
tmp = dot(tmp, u.T)
return _dot0(tmp, yk)