def splint(a, b, tck, full_output=0): """ Evaluate the definite integral of a B-spline. Given the knots and coefficients of a B-spline, evaluate the definite integral of the smoothing polynomial between two given points. Parameters ---------- a, b : float The end-points of the integration interval. tck : tuple A tuple (t,c,k) containing the vector of knots, the B-spline coefficients, and the degree of the spline (see `splev`). full_output : int, optional Non-zero to return optional output. Returns ------- integral : float The resulting integral. wrk : ndarray An array containing the integrals of the normalized B-splines defined on the set of knots. See Also -------- splprep, splrep, sproot, spalde, splev bisplrep, bisplev UnivariateSpline, BivariateSpline References ---------- .. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines", J. Inst. Maths Applics, 17, p.37-41, 1976. .. [2] P. Dierckx, "Curve and surface fitting with splines", Monographs on Numerical Analysis, Oxford University Press, 1993. """ t, c, k = tck try: c[0][0] parametric = True except: parametric = False if parametric: return _ntlist( map(lambda c, a=a, b=b, t=t, k=k: splint(a, b, [t, c, k]), c)) else: aint, wrk = _fitpack._splint(t, c, k, a, b) if full_output: return aint, wrk else: return aint
def splint(a,b,tck,full_output=0): """ Evaluate the definite integral of a B-spline. Given the knots and coefficients of a B-spline, evaluate the definite integral of the smoothing polynomial between two given points. Parameters ---------- a, b : float The end-points of the integration interval. tck : tuple A tuple (t,c,k) containing the vector of knots, the B-spline coefficients, and the degree of the spline (see `splev`). full_output : int, optional Non-zero to return optional output. Returns ------- integral : float The resulting integral. wrk : ndarray An array containing the integrals of the normalized B-splines defined on the set of knots. See Also -------- splprep, splrep, sproot, spalde, splev bisplrep, bisplev UnivariateSpline, BivariateSpline References ---------- .. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines", J. Inst. Maths Applics, 17, p.37-41, 1976. .. [2] P. Dierckx, "Curve and surface fitting with splines", Monographs on Numerical Analysis, Oxford University Press, 1993. """ t,c,k=tck try: c[0][0] parametric = True except: parametric = False if parametric: return _ntlist(map(lambda c,a=a,b=b,t=t,k=k:splint(a,b,[t,c,k]),c)) else: aint,wrk=_fitpack._splint(t,c,k,a,b) if full_output: return aint,wrk else: return aint
def splint(a,b,tck,full_output=0): """ Evaluate the definite integral of a B-spline. Given the knots and coefficients of a B-spline, evaluate the definite integral of the smoothing polynomial between two given points. Parameters ---------- a, b -- The end-points of the integration interval. tck -- A length 3 sequence describing the given spline (See splev). full_output -- Non-zero to return optional output. Returns ------- integral -- The resulting integral. wrk -- An array containing the integrals of the normalized B-splines defined on the set of knots. See Also -------- splprep, splrep, sproot, spalde, splev : evaluation, roots, integral bisplrep, bisplev : bivariate splines UnivariateSpline, BivariateSpline : An alternative wrapping of the FITPACK functions. References ---------- .. [1] P.W. Gaffney, The calculation of indefinite integrals of b-splines", J. Inst. Maths Applics, 17, p.37-41, 1976. .. [2] P. Dierckx, "Curve and surface fitting with splines", Monographs on Numerical Analysis, Oxford University Press, 1993. """ t,c,k=tck try: c[0][0] parametric = True except: parametric = False if parametric: return _ntlist(map(lambda c,a=a,b=b,t=t,k=k:splint(a,b,[t,c,k]),c)) else: aint,wrk=_fitpack._splint(t,c,k,a,b) if full_output: return aint,wrk else: return aint
def splint(a,b,tck,full_output=0): """Evaluate the definite integral of a B-spline. Description: Given the knots and coefficients of a B-spline, evaluate the definite integral of the smoothing polynomial between two given points. Inputs: a, b -- The end-points of the integration interval. tck -- A length 3 sequence describing the given spline (See splev). full_output -- Non-zero to return optional output. Outputs: (integral, {wrk}) integral -- The resulting integral. wrk -- An array containing the integrals of the normalized B-splines defined on the set of knots. See also: splprep, splrep, sproot, spalde, splev - evaluation, roots, integral bisplrep, bisplev - bivariate splines UnivariateSpline, BivariateSpline - an alternative wrapping of the FITPACK functions """ t,c,k=tck try: c[0][0] parametric = True except: parametric = False if parametric: return _ntlist(map(lambda c,a=a,b=b,t=t,k=k:splint(a,b,[t,c,k]),c)) else: aint,wrk=_fitpack._splint(t,c,k,a,b) if full_output: return aint,wrk else: return aint