diff options
Diffstat (limited to 'numpy/lib/polynomial.py')
| -rw-r--r-- | numpy/lib/polynomial.py | 72 |
1 files changed, 40 insertions, 32 deletions
diff --git a/numpy/lib/polynomial.py b/numpy/lib/polynomial.py index 0fd9bbd79..6aa708861 100644 --- a/numpy/lib/polynomial.py +++ b/numpy/lib/polynomial.py @@ -152,9 +152,8 @@ def poly(seq_of_zeros): return 1.0 dt = seq_of_zeros.dtype a = ones((1,), dtype=dt) - for k in range(len(seq_of_zeros)): - a = NX.convolve(a, array([1, -seq_of_zeros[k]], dtype=dt), - mode='full') + for zero in seq_of_zeros: + a = NX.convolve(a, array([1, -zero], dtype=dt), mode='full') if issubclass(a.dtype.type, NX.complexfloating): # if complex roots are all complex conjugates, the roots are real. @@ -489,16 +488,19 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False): default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned. w : array_like, shape (M,), optional - Weights to apply to the y-coordinates of the sample points. For - gaussian uncertainties, use 1/sigma (not 1/sigma**2). + Weights. If not None, the weight ``w[i]`` applies to the unsquared + residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are + chosen so that the errors of the products ``w[i]*y[i]`` all have the + same variance. When using inverse-variance weighting, use + ``w[i] = 1/sigma(y[i])``. The default value is None. cov : bool or str, optional If given and not `False`, return not just the estimate but also its covariance matrix. By default, the covariance are scaled by - chi2/dof, where dof = M - (deg + 1), i.e., the weights are presumed - to be unreliable except in a relative sense and everything is scaled - such that the reduced chi2 is unity. This scaling is omitted if - ``cov='unscaled'``, as is relevant for the case that the weights are - 1/sigma**2, with sigma known to be a reliable estimate of the + chi2/dof, where dof = M - (deg + 1), i.e., the weights are presumed + to be unreliable except in a relative sense and everything is scaled + such that the reduced chi2 is unity. This scaling is omitted if + ``cov='unscaled'``, as is relevant for the case that the weights are + w = 1/sigma, with sigma known to be a reliable estimate of the uncertainty. Returns @@ -508,13 +510,19 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False): coefficients for `k`-th data set are in ``p[:,k]``. residuals, rank, singular_values, rcond - Present only if `full` = True. Residuals is sum of squared residuals - of the least-squares fit, the effective rank of the scaled Vandermonde - coefficient matrix, its singular values, and the specified value of - `rcond`. For more details, see `linalg.lstsq`. + These values are only returned if ``full == True`` + + - residuals -- sum of squared residuals of the least squares fit + - rank -- the effective rank of the scaled Vandermonde + coefficient matrix + - singular_values -- singular values of the scaled Vandermonde + coefficient matrix + - rcond -- value of `rcond`. + + For more details, see `numpy.linalg.lstsq`. V : ndarray, shape (M,M) or (M,M,K) - Present only if `full` = False and `cov`=True. The covariance + Present only if ``full == False`` and ``cov == True``. The covariance matrix of the polynomial coefficient estimates. The diagonal of this matrix are the variance estimates for each coefficient. If y is a 2-D array, then the covariance matrix for the `k`-th data set @@ -525,7 +533,7 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False): ----- RankWarning The rank of the coefficient matrix in the least-squares fit is - deficient. The warning is only raised if `full` = False. + deficient. The warning is only raised if ``full == False``. The warnings can be turned off by @@ -542,7 +550,7 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False): ----- The solution minimizes the squared error - .. math :: + .. math:: E = \\sum_{j=0}^k |p(x_j) - y_j|^2 in the equations:: @@ -678,7 +686,7 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False): "to scale the covariance matrix") # note, this used to be: fac = resids / (len(x) - order - 2.0) # it was deciced that the "- 2" (originally justified by "Bayesian - # uncertainty analysis") is not was the user expects + # uncertainty analysis") is not what the user expects # (see gh-11196 and gh-11197) fac = resids / (len(x) - order) if y.ndim == 1: @@ -708,8 +716,8 @@ def polyval(p, x): ``p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]`` - If `x` is a sequence, then `p(x)` is returned for each element of `x`. - If `x` is another polynomial then the composite polynomial `p(x(t))` + If `x` is a sequence, then ``p(x)`` is returned for each element of ``x``. + If `x` is another polynomial then the composite polynomial ``p(x(t))`` is returned. Parameters @@ -767,8 +775,8 @@ def polyval(p, x): else: x = NX.asanyarray(x) y = NX.zeros_like(x) - for i in range(len(p)): - y = y * x + p[i] + for pv in p: + y = y * x + pv return y @@ -1037,7 +1045,7 @@ def polydiv(u, v): return poly1d(q), poly1d(r) return q, r -_poly_mat = re.compile(r"[*][*]([0-9]*)") +_poly_mat = re.compile(r"\*\*([0-9]*)") def _raise_power(astr, wrap=70): n = 0 line1 = '' @@ -1270,14 +1278,14 @@ class poly1d: s = s[:-5] return s - for k in range(len(coeffs)): - if not iscomplex(coeffs[k]): - coefstr = fmt_float(real(coeffs[k])) - elif real(coeffs[k]) == 0: - coefstr = '%sj' % fmt_float(imag(coeffs[k])) + for k, coeff in enumerate(coeffs): + if not iscomplex(coeff): + coefstr = fmt_float(real(coeff)) + elif real(coeff) == 0: + coefstr = '%sj' % fmt_float(imag(coeff)) else: - coefstr = '(%s + %sj)' % (fmt_float(real(coeffs[k])), - fmt_float(imag(coeffs[k]))) + coefstr = '(%s + %sj)' % (fmt_float(real(coeff)), + fmt_float(imag(coeff))) power = (N-k) if power == 0: @@ -1394,9 +1402,9 @@ class poly1d: def __getitem__(self, val): ind = self.order - val if val > self.order: - return 0 + return self.coeffs.dtype.type(0) if val < 0: - return 0 + return self.coeffs.dtype.type(0) return self.coeffs[ind] def __setitem__(self, key, val): |