Integrate a Chebyshev series. Returns the Chebyshev series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear cha
(c, m=1, k=[], lbnd=0, scl=1, axis=0)
| 965 | |
| 966 | |
| 967 | def chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0): |
| 968 | """ |
| 969 | Integrate a Chebyshev series. |
| 970 | |
| 971 | Returns the Chebyshev series coefficients `c` integrated `m` times from |
| 972 | `lbnd` along `axis`. At each iteration the resulting series is |
| 973 | **multiplied** by `scl` and an integration constant, `k`, is added. |
| 974 | The scaling factor is for use in a linear change of variable. ("Buyer |
| 975 | beware": note that, depending on what one is doing, one may want `scl` |
| 976 | to be the reciprocal of what one might expect; for more information, |
| 977 | see the Notes section below.) The argument `c` is an array of |
| 978 | coefficients from low to high degree along each axis, e.g., [1,2,3] |
| 979 | represents the series ``T_0 + 2*T_1 + 3*T_2`` while [[1,2],[1,2]] |
| 980 | represents ``1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + 2*T_0(x)*T_1(y) + |
| 981 | 2*T_1(x)*T_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. |
| 982 | |
| 983 | Parameters |
| 984 | ---------- |
| 985 | c : array_like |
| 986 | Array of Chebyshev series coefficients. If c is multidimensional |
| 987 | the different axis correspond to different variables with the |
| 988 | degree in each axis given by the corresponding index. |
| 989 | m : int, optional |
| 990 | Order of integration, must be positive. (Default: 1) |
| 991 | k : {[], list, scalar}, optional |
| 992 | Integration constant(s). The value of the first integral at zero |
| 993 | is the first value in the list, the value of the second integral |
| 994 | at zero is the second value, etc. If ``k == []`` (the default), |
| 995 | all constants are set to zero. If ``m == 1``, a single scalar can |
| 996 | be given instead of a list. |
| 997 | lbnd : scalar, optional |
| 998 | The lower bound of the integral. (Default: 0) |
| 999 | scl : scalar, optional |
| 1000 | Following each integration the result is *multiplied* by `scl` |
| 1001 | before the integration constant is added. (Default: 1) |
| 1002 | axis : int, optional |
| 1003 | Axis over which the integral is taken. (Default: 0). |
| 1004 | |
| 1005 | .. versionadded:: 1.7.0 |
| 1006 | |
| 1007 | Returns |
| 1008 | ------- |
| 1009 | S : ndarray |
| 1010 | C-series coefficients of the integral. |
| 1011 | |
| 1012 | Raises |
| 1013 | ------ |
| 1014 | ValueError |
| 1015 | If ``m < 1``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or |
| 1016 | ``np.ndim(scl) != 0``. |
| 1017 | |
| 1018 | See Also |
| 1019 | -------- |
| 1020 | chebder |
| 1021 | |
| 1022 | Notes |
| 1023 | ----- |
| 1024 | Note that the result of each integration is *multiplied* by `scl`. |
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