diff options
Diffstat (limited to 'numpy/polynomial/chebyshev.py')
| -rw-r--r-- | numpy/polynomial/chebyshev.py | 217 |
1 files changed, 33 insertions, 184 deletions
diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py index e0734e1b8..c37b2c6d6 100644 --- a/numpy/polynomial/chebyshev.py +++ b/numpy/polynomial/chebyshev.py @@ -225,15 +225,15 @@ def _zseries_div(z1, z2): """ z1 = z1.copy() z2 = z2.copy() - len1 = len(z1) - len2 = len(z2) - if len2 == 1: + lc1 = len(z1) + lc2 = len(z2) + if lc2 == 1: z1 /= z2 return z1, z1[:1]*0 - elif len1 < len2: + elif lc1 < lc2: return z1[:1]*0, z1 else: - dlen = len1 - len2 + dlen = lc1 - lc2 scl = z2[0] z2 /= scl quo = np.empty(dlen + 1, dtype=z1.dtype) @@ -244,16 +244,16 @@ def _zseries_div(z1, z2): quo[i] = z1[i] quo[dlen - i] = r tmp = r*z2 - z1[i:i+len2] -= tmp - z1[j:j+len2] -= tmp + z1[i:i+lc2] -= tmp + z1[j:j+lc2] -= tmp i += 1 j -= 1 r = z1[i] quo[i] = r tmp = r*z2 - z1[i:i+len2] -= tmp + z1[i:i+lc2] -= tmp quo /= scl - rem = z1[i+1:i-1+len2].copy() + rem = z1[i+1:i-1+lc2].copy() return quo, rem @@ -541,21 +541,7 @@ def chebfromroots(roots): array([1.5+0.j, 0. +0.j, 0.5+0.j]) """ - if len(roots) == 0: - return np.ones(1) - else: - [roots] = pu.as_series([roots], trim=False) - roots.sort() - p = [chebline(-r, 1) for r in roots] - n = len(p) - while n > 1: - m, r = divmod(n, 2) - tmp = [chebmul(p[i], p[i+m]) for i in range(m)] - if r: - tmp[0] = chebmul(tmp[0], p[-1]) - p = tmp - n = m - return p[0] + return pu._fromroots(chebline, chebmul, roots) def chebadd(c1, c2): @@ -597,15 +583,7 @@ def chebadd(c1, c2): array([4., 4., 4.]) """ - # c1, c2 are trimmed copies - [c1, c2] = pu.as_series([c1, c2]) - if len(c1) > len(c2): - c1[:c2.size] += c2 - ret = c1 - else: - c2[:c1.size] += c1 - ret = c2 - return pu.trimseq(ret) + return pu._add(c1, c2) def chebsub(c1, c2): @@ -649,16 +627,7 @@ def chebsub(c1, c2): array([ 2., 0., -2.]) """ - # c1, c2 are trimmed copies - [c1, c2] = pu.as_series([c1, c2]) - if len(c1) > len(c2): - c1[:c2.size] -= c2 - ret = c1 - else: - c2 = -c2 - c2[:c1.size] += c1 - ret = c2 - return pu.trimseq(ret) + return pu._sub(c1, c2) def chebmulx(c): @@ -807,6 +776,7 @@ def chebdiv(c1, c2): if c2[-1] == 0: raise ZeroDivisionError() + # note: this is more efficient than `pu._div(chebmul, c1, c2)` lc1 = len(c1) lc2 = len(c2) if lc1 < lc2: @@ -856,6 +826,9 @@ def chebpow(c, pow, maxpower=16): array([15.5, 22. , 16. , ..., 12.5, 12. , 8. ]) """ + # note: this is more efficient than `pu._pow(chebmul, c1, c2)`, as it + # avoids converting between z and c series repeatedly + # c is a trimmed copy [c] = pu.as_series([c]) power = int(pow) @@ -940,14 +913,10 @@ def chebder(c, m=1, scl=1, axis=0): c = np.array(c, ndmin=1, copy=1) if c.dtype.char in '?bBhHiIlLqQpP': c = c.astype(np.double) - cnt, iaxis = [int(t) for t in [m, axis]] - - if cnt != m: - raise ValueError("The order of derivation must be integer") + cnt = pu._deprecate_as_int(m, "the order of derivation") + iaxis = pu._deprecate_as_int(axis, "the axis") if cnt < 0: raise ValueError("The order of derivation must be non-negative") - if iaxis != axis: - raise ValueError("The axis must be integer") iaxis = normalize_axis_index(iaxis, c.ndim) if cnt == 0: @@ -1063,10 +1032,8 @@ def chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0): c = c.astype(np.double) if not np.iterable(k): k = [k] - cnt, iaxis = [int(t) for t in [m, axis]] - - if cnt != m: - raise ValueError("The order of integration must be integer") + cnt = pu._deprecate_as_int(m, "the order of integration") + iaxis = pu._deprecate_as_int(axis, "the axis") if cnt < 0: raise ValueError("The order of integration must be non-negative") if len(k) > cnt: @@ -1075,8 +1042,6 @@ def chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0): raise ValueError("lbnd must be a scalar.") if np.ndim(scl) != 0: raise ValueError("scl must be a scalar.") - if iaxis != axis: - raise ValueError("The axis must be integer") iaxis = normalize_axis_index(iaxis, c.ndim) if cnt == 0: @@ -1238,14 +1203,7 @@ def chebval2d(x, y, c): .. versionadded:: 1.7.0 """ - try: - x, y = np.array((x, y), copy=0) - except Exception: - raise ValueError('x, y are incompatible') - - c = chebval(x, c) - c = chebval(y, c, tensor=False) - return c + return pu._valnd(chebval, c, x, y) def chebgrid2d(x, y, c): @@ -1298,9 +1256,7 @@ def chebgrid2d(x, y, c): .. versionadded:: 1.7.0 """ - c = chebval(x, c) - c = chebval(y, c) - return c + return pu._gridnd(chebval, c, x, y) def chebval3d(x, y, z, c): @@ -1351,15 +1307,7 @@ def chebval3d(x, y, z, c): .. versionadded:: 1.7.0 """ - try: - x, y, z = np.array((x, y, z), copy=0) - except Exception: - raise ValueError('x, y, z are incompatible') - - c = chebval(x, c) - c = chebval(y, c, tensor=False) - c = chebval(z, c, tensor=False) - return c + return pu._valnd(chebval, c, x, y, z) def chebgrid3d(x, y, z, c): @@ -1415,10 +1363,7 @@ def chebgrid3d(x, y, z, c): .. versionadded:: 1.7.0 """ - c = chebval(x, c) - c = chebval(y, c) - c = chebval(z, c) - return c + return pu._gridnd(chebval, c, x, y, z) def chebvander(x, deg): @@ -1456,9 +1401,7 @@ def chebvander(x, deg): the converted `x`. """ - ideg = int(deg) - if ideg != deg: - raise ValueError("deg must be integer") + ideg = pu._deprecate_as_int(deg, "deg") if ideg < 0: raise ValueError("deg must be non-negative") @@ -1526,17 +1469,7 @@ def chebvander2d(x, y, deg): .. versionadded:: 1.7.0 """ - ideg = [int(d) for d in deg] - is_valid = [id == d and id >= 0 for id, d in zip(ideg, deg)] - if is_valid != [1, 1]: - raise ValueError("degrees must be non-negative integers") - degx, degy = ideg - x, y = np.array((x, y), copy=0) + 0.0 - - vx = chebvander(x, degx) - vy = chebvander(y, degy) - v = vx[..., None]*vy[..., None,:] - return v.reshape(v.shape[:-2] + (-1,)) + return pu._vander2d(chebvander, x, y, deg) def chebvander3d(x, y, z, deg): @@ -1590,18 +1523,7 @@ def chebvander3d(x, y, z, deg): .. versionadded:: 1.7.0 """ - ideg = [int(d) for d in deg] - is_valid = [id == d and id >= 0 for id, d in zip(ideg, deg)] - if is_valid != [1, 1, 1]: - raise ValueError("degrees must be non-negative integers") - degx, degy, degz = ideg - x, y, z = np.array((x, y, z), copy=0) + 0.0 - - vx = chebvander(x, degx) - vy = chebvander(y, degy) - vz = chebvander(z, degz) - v = vx[..., None, None]*vy[..., None,:, None]*vz[..., None, None,:] - return v.reshape(v.shape[:-3] + (-1,)) + return pu._vander3d(chebvander, x, y, z, deg) def chebfit(x, y, deg, rcond=None, full=False, w=None): @@ -1723,81 +1645,7 @@ def chebfit(x, y, deg, rcond=None, full=False, w=None): -------- """ - x = np.asarray(x) + 0.0 - y = np.asarray(y) + 0.0 - deg = np.asarray(deg) - - # check arguments. - if deg.ndim > 1 or deg.dtype.kind not in 'iu' or deg.size == 0: - raise TypeError("deg must be an int or non-empty 1-D array of int") - if deg.min() < 0: - raise ValueError("expected deg >= 0") - if x.ndim != 1: - raise TypeError("expected 1D vector for x") - if x.size == 0: - raise TypeError("expected non-empty vector for x") - if y.ndim < 1 or y.ndim > 2: - raise TypeError("expected 1D or 2D array for y") - if len(x) != len(y): - raise TypeError("expected x and y to have same length") - - if deg.ndim == 0: - lmax = deg - order = lmax + 1 - van = chebvander(x, lmax) - else: - deg = np.sort(deg) - lmax = deg[-1] - order = len(deg) - van = chebvander(x, lmax)[:, deg] - - # set up the least squares matrices in transposed form - lhs = van.T - rhs = y.T - if w is not None: - w = np.asarray(w) + 0.0 - if w.ndim != 1: - raise TypeError("expected 1D vector for w") - if len(x) != len(w): - raise TypeError("expected x and w to have same length") - # apply weights. Don't use inplace operations as they - # can cause problems with NA. - lhs = lhs * w - rhs = rhs * w - - # set rcond - if rcond is None: - rcond = len(x)*np.finfo(x.dtype).eps - - # Determine the norms of the design matrix columns. - if issubclass(lhs.dtype.type, np.complexfloating): - scl = np.sqrt((np.square(lhs.real) + np.square(lhs.imag)).sum(1)) - else: - scl = np.sqrt(np.square(lhs).sum(1)) - scl[scl == 0] = 1 - - # Solve the least squares problem. - c, resids, rank, s = la.lstsq(lhs.T/scl, rhs.T, rcond) - c = (c.T/scl).T - - # Expand c to include non-fitted coefficients which are set to zero - if deg.ndim > 0: - if c.ndim == 2: - cc = np.zeros((lmax + 1, c.shape[1]), dtype=c.dtype) - else: - cc = np.zeros(lmax + 1, dtype=c.dtype) - cc[deg] = c - c = cc - - # warn on rank reduction - if rank != order and not full: - msg = "The fit may be poorly conditioned" - warnings.warn(msg, pu.RankWarning, stacklevel=2) - - if full: - return c, [resids, rank, s, rcond] - else: - return c + return pu._fit(chebvander, x, y, deg, rcond, full, w) def chebcompanion(c): @@ -1895,7 +1743,8 @@ def chebroots(c): if len(c) == 2: return np.array([-c[0]/c[1]]) - m = chebcompanion(c) + # rotated companion matrix reduces error + m = chebcompanion(c)[::-1,::-1] r = la.eigvals(m) r.sort() return r @@ -2003,9 +1852,9 @@ def chebgauss(deg): .. math:: w_i = \\pi / n """ - ideg = int(deg) - if ideg != deg or ideg < 1: - raise ValueError("deg must be a non-negative integer") + ideg = pu._deprecate_as_int(deg, "deg") + if ideg <= 0: + raise ValueError("deg must be a positive integer") x = np.cos(np.pi * np.arange(1, 2*ideg, 2) / (2.0*ideg)) w = np.ones(ideg)*(np.pi/ideg) |