diff options
Diffstat (limited to 'numpy/lib/twodim_base.py')
| -rw-r--r-- | numpy/lib/twodim_base.py | 175 |
1 files changed, 103 insertions, 72 deletions
diff --git a/numpy/lib/twodim_base.py b/numpy/lib/twodim_base.py index 12c0f9bb3..a8925592a 100644 --- a/numpy/lib/twodim_base.py +++ b/numpy/lib/twodim_base.py @@ -11,8 +11,23 @@ __all__ = ['diag', 'diagflat', 'eye', 'fliplr', 'flipud', 'rot90', 'tri', from numpy.core.numeric import ( asanyarray, subtract, arange, zeros, greater_equal, multiply, ones, - asarray, where, + asarray, where, less, int8, int16, int32, int64, empty, promote_types ) +from numpy.core import iinfo + + +i1 = iinfo(int8) +i2 = iinfo(int16) +i4 = iinfo(int32) +def _min_int(low, high): + """ get small int that fits the range """ + if high <= i1.max and low >= i1.min: + return int8 + if high <= i2.max and low >= i2.min: + return int16 + if high <= i4.max and low >= i4.min: + return int32 + return int64 def fliplr(m): @@ -25,7 +40,7 @@ def fliplr(m): Parameters ---------- m : array_like - Input array. + Input array, must be at least 2-D. Returns ------- @@ -40,8 +55,7 @@ def fliplr(m): Notes ----- - Equivalent to A[:,::-1]. Does not require the array to be - two-dimensional. + Equivalent to A[:,::-1]. Requires the array to be at least 2-D. Examples -------- @@ -373,6 +387,7 @@ def tri(N, M=None, k=0, dtype=float): dtype : dtype, optional Data type of the returned array. The default is float. + Returns ------- tri : ndarray of shape (N, M) @@ -394,8 +409,14 @@ def tri(N, M=None, k=0, dtype=float): """ if M is None: M = N - m = greater_equal(subtract.outer(arange(N), arange(M)), -k) - return m.astype(dtype) + + m = greater_equal.outer(arange(N, dtype=_min_int(0, N)), + arange(-k, M-k, dtype=_min_int(-k, M - k))) + + # Avoid making a copy if the requested type is already bool + m = m.astype(dtype, copy=False) + + return m def tril(m, k=0): @@ -431,8 +452,7 @@ def tril(m, k=0): """ m = asanyarray(m) - out = multiply(tri(m.shape[0], m.shape[1], k=k, dtype=m.dtype), m) - return out + return multiply(tri(*m.shape[-2:], k=k, dtype=bool), m, dtype=m.dtype) def triu(m, k=0): @@ -458,22 +478,20 @@ def triu(m, k=0): """ m = asanyarray(m) - out = multiply((1 - tri(m.shape[0], m.shape[1], k - 1, dtype=m.dtype)), m) - return out + return multiply(~tri(*m.shape[-2:], k=k-1, dtype=bool), m, dtype=m.dtype) # Originally borrowed from John Hunter and matplotlib -def vander(x, N=None, order='decreasing'): +def vander(x, N=None, increasing=False): """ Generate a Vandermonde matrix. - The columns of the output matrix are powers of the input vector. The - order of the powers is determined by the `order` argument, either - "decreasing" (the default) or "increasing". Specifically, when - `order` is "decreasing", the `i`-th output column is the input vector - raised element-wise to the power of ``N - i - 1``. Such a matrix with - a geometric progression in each row is named for Alexandre-Theophile - Vandermonde. + The columns of the output matrix are powers of the input vector. The + order of the powers is determined by the `increasing` boolean argument. + Specifically, when `increasing` is False, the `i`-th output column is + the input vector raised element-wise to the power of ``N - i - 1``. Such + a matrix with a geometric progression in each row is named for Alexandre- + Theophile Vandermonde. Parameters ---------- @@ -482,16 +500,18 @@ def vander(x, N=None, order='decreasing'): N : int, optional Number of columns in the output. If `N` is not specified, a square array is returned (``N = len(x)``). - order : str, optional - Order of the powers of the columns. Must be either 'decreasing' - (the default) or 'increasing'. + increasing : bool, optional + Order of the powers of the columns. If True, the powers increase + from left to right, if False (the default) they are reversed. + + .. versionadded:: 1.9.0 Returns ------- out : ndarray - Vandermonde matrix. If `order` is "decreasing", the first column is - ``x^(N-1)``, the second ``x^(N-2)`` and so forth. If `order` is - "increasing", the columns are ``x^0, x^1, ..., x^(N-1)``. + Vandermonde matrix. If `increasing` is False, the first column is + ``x^(N-1)``, the second ``x^(N-2)`` and so forth. If `increasing` is + True, the columns are ``x^0, x^1, ..., x^(N-1)``. See Also -------- @@ -519,7 +539,7 @@ def vander(x, N=None, order='decreasing'): [ 8, 4, 2, 1], [ 27, 9, 3, 1], [125, 25, 5, 1]]) - >>> np.vander(x, order='increasing') + >>> np.vander(x, increasing=True) array([[ 1, 1, 1, 1], [ 1, 2, 4, 8], [ 1, 3, 9, 27], @@ -534,22 +554,22 @@ def vander(x, N=None, order='decreasing'): 48 """ - if order not in ['decreasing', 'increasing']: - raise ValueError("Invalid order %r; order must be either " - "'decreasing' or 'increasing'." % (order,)) x = asarray(x) if x.ndim != 1: raise ValueError("x must be a one-dimensional array or sequence.") if N is None: N = len(x) - if order == "decreasing": - powers = arange(N - 1, -1, -1) - else: - powers = arange(N) - V = x.reshape(-1, 1) ** powers + v = empty((len(x), N), dtype=promote_types(x.dtype, int)) + tmp = v[:, ::-1] if not increasing else v + + if N > 0: + tmp[:, 0] = 1 + if N > 1: + tmp[:, 1:] = x[:, None] + multiply.accumulate(tmp[:, 1:], out=tmp[:, 1:], axis=1) - return V + return v def histogram2d(x, y, bins=10, range=None, normed=False, weights=None): @@ -559,9 +579,11 @@ def histogram2d(x, y, bins=10, range=None, normed=False, weights=None): Parameters ---------- x : array_like, shape (N,) - An array containing the x coordinates of the points to be histogrammed. + An array containing the x coordinates of the points to be + histogrammed. y : array_like, shape (N,) - An array containing the y coordinates of the points to be histogrammed. + An array containing the y coordinates of the points to be + histogrammed. bins : int or [int, int] or array_like or [array, array], optional The bin specification: @@ -579,13 +601,13 @@ def histogram2d(x, y, bins=10, range=None, normed=False, weights=None): ``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range will be considered outliers and not tallied in the histogram. normed : bool, optional - If False, returns the number of samples in each bin. If True, returns - the bin density, i.e. the bin count divided by the bin area. + If False, returns the number of samples in each bin. If True, + returns the bin density ``bin_count / sample_count / bin_area``. weights : array_like, shape(N,), optional - An array of values ``w_i`` weighing each sample ``(x_i, y_i)``. Weights - are normalized to 1 if `normed` is True. If `normed` is False, the - values of the returned histogram are equal to the sum of the weights - belonging to the samples falling into each bin. + An array of values ``w_i`` weighing each sample ``(x_i, y_i)``. + Weights are normalized to 1 if `normed` is True. If `normed` is + False, the values of the returned histogram are equal to the sum of + the weights belonging to the samples falling into each bin. Returns ------- @@ -605,20 +627,15 @@ def histogram2d(x, y, bins=10, range=None, normed=False, weights=None): Notes ----- - When `normed` is True, then the returned histogram is the sample density, - defined such that: - - .. math:: - \\sum_{i=0}^{nx-1} \\sum_{j=0}^{ny-1} H_{i,j} \\Delta x_i \\Delta y_j = 1 - - where `H` is the histogram array and :math:`\\Delta x_i \\Delta y_i` - the area of bin ``{i,j}``. + When `normed` is True, then the returned histogram is the sample + density, defined such that the sum over bins of the product + ``bin_value * bin_area`` is 1. Please note that the histogram does not follow the Cartesian convention - where `x` values are on the abcissa and `y` values on the ordinate axis. - Rather, `x` is histogrammed along the first dimension of the array - (vertical), and `y` along the second dimension of the array (horizontal). - This ensures compatibility with `histogramdd`. + where `x` values are on the abscissa and `y` values on the ordinate + axis. Rather, `x` is histogrammed along the first dimension of the + array (vertical), and `y` along the second dimension of the array + (horizontal). This ensures compatibility with `histogramdd`. Examples -------- @@ -650,14 +667,14 @@ def histogram2d(x, y, bins=10, range=None, normed=False, weights=None): >>> fig = plt.figure(figsize=(7, 3)) >>> ax = fig.add_subplot(131) - >>> ax.set_title('imshow:\nequidistant') + >>> ax.set_title('imshow: equidistant') >>> im = plt.imshow(H, interpolation='nearest', origin='low', - extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) + extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) pcolormesh can display exact bin edges: >>> ax = fig.add_subplot(132) - >>> ax.set_title('pcolormesh:\nexact bin edges') + >>> ax.set_title('pcolormesh: exact bin edges') >>> X, Y = np.meshgrid(xedges, yedges) >>> ax.pcolormesh(X, Y, H) >>> ax.set_aspect('equal') @@ -665,7 +682,7 @@ def histogram2d(x, y, bins=10, range=None, normed=False, weights=None): NonUniformImage displays exact bin edges with interpolation: >>> ax = fig.add_subplot(133) - >>> ax.set_title('NonUniformImage:\ninterpolated') + >>> ax.set_title('NonUniformImage: interpolated') >>> im = mpl.image.NonUniformImage(ax, interpolation='bilinear') >>> xcenters = xedges[:-1] + 0.5 * (xedges[1:] - xedges[:-1]) >>> ycenters = yedges[:-1] + 0.5 * (yedges[1:] - yedges[:-1]) @@ -761,17 +778,24 @@ def mask_indices(n, mask_func, k=0): return where(a != 0) -def tril_indices(n, k=0): +def tril_indices(n, k=0, m=None): """ - Return the indices for the lower-triangle of an (n, n) array. + Return the indices for the lower-triangle of an (n, m) array. Parameters ---------- n : int - The row dimension of the square arrays for which the returned + The row dimension of the arrays for which the returned indices will be valid. k : int, optional Diagonal offset (see `tril` for details). + m : int, optional + .. versionadded:: 1.9.0 + + The column dimension of the arrays for which the returned + arrays will be valid. + By default `m` is taken equal to `n`. + Returns ------- @@ -831,7 +855,7 @@ def tril_indices(n, k=0): [-10, -10, -10, -10]]) """ - return mask_indices(n, tril, k) + return where(tri(n, m, k=k, dtype=bool)) def tril_indices_from(arr, k=0): @@ -857,14 +881,14 @@ def tril_indices_from(arr, k=0): .. versionadded:: 1.4.0 """ - if not (arr.ndim == 2 and arr.shape[0] == arr.shape[1]): - raise ValueError("input array must be 2-d and square") - return tril_indices(arr.shape[0], k) + if arr.ndim != 2: + raise ValueError("input array must be 2-d") + return tril_indices(arr.shape[-2], k=k, m=arr.shape[-1]) -def triu_indices(n, k=0): +def triu_indices(n, k=0, m=None): """ - Return the indices for the upper-triangle of an (n, n) array. + Return the indices for the upper-triangle of an (n, m) array. Parameters ---------- @@ -873,6 +897,13 @@ def triu_indices(n, k=0): be valid. k : int, optional Diagonal offset (see `triu` for details). + m : int, optional + .. versionadded:: 1.9.0 + + The column dimension of the arrays for which the returned + arrays will be valid. + By default `m` is taken equal to `n`. + Returns ------- @@ -934,12 +965,12 @@ def triu_indices(n, k=0): [ 12, 13, 14, -1]]) """ - return mask_indices(n, triu, k) + return where(~tri(n, m, k=k-1, dtype=bool)) def triu_indices_from(arr, k=0): """ - Return the indices for the upper-triangle of a (N, N) array. + Return the indices for the upper-triangle of arr. See `triu_indices` for full details. @@ -964,6 +995,6 @@ def triu_indices_from(arr, k=0): .. versionadded:: 1.4.0 """ - if not (arr.ndim == 2 and arr.shape[0] == arr.shape[1]): - raise ValueError("input array must be 2-d and square") - return triu_indices(arr.shape[0], k) + if arr.ndim != 2: + raise ValueError("input array must be 2-d") + return triu_indices(arr.shape[-2], k=k, m=arr.shape[-1]) |