diff options
Diffstat (limited to 'numpy/lib/twodim_base.py')
| -rw-r--r-- | numpy/lib/twodim_base.py | 79 |
1 files changed, 58 insertions, 21 deletions
diff --git a/numpy/lib/twodim_base.py b/numpy/lib/twodim_base.py index 91df1f4f8..fe3066377 100644 --- a/numpy/lib/twodim_base.py +++ b/numpy/lib/twodim_base.py @@ -3,14 +3,17 @@ """ from __future__ import division, absolute_import, print_function -__all__ = ['diag', 'diagflat', 'eye', 'fliplr', 'flipud', 'rot90', 'tri', 'triu', - 'tril', 'vander', 'histogram2d', 'mask_indices', - 'tril_indices', 'tril_indices_from', 'triu_indices', 'triu_indices_from', +__all__ = ['diag', 'diagflat', 'eye', 'fliplr', 'flipud', 'rot90', 'tri', + 'triu', 'tril', 'vander', 'histogram2d', 'mask_indices', + 'tril_indices', 'tril_indices_from', 'triu_indices', + 'triu_indices_from', ] -from numpy.core.numeric import asanyarray, equal, subtract, arange, \ - zeros, greater_equal, multiply, ones, asarray, alltrue, where, \ - empty, diagonal +from numpy.core.numeric import ( + asanyarray, subtract, arange, zeros, greater_equal, multiply, ones, + asarray, where, + ) + def fliplr(m): """ @@ -62,6 +65,7 @@ def fliplr(m): raise ValueError("Input must be >= 2-d.") return m[:, ::-1] + def flipud(m): """ Flip array in the up/down direction. @@ -115,6 +119,7 @@ def flipud(m): raise ValueError("Input must be >= 1-d.") return m[::-1, ...] + def rot90(m, k=1): """ Rotate an array by 90 degrees in the counter-clockwise direction. @@ -167,6 +172,7 @@ def rot90(m, k=1): # k == 3 return fliplr(m.swapaxes(0, 1)) + def eye(N, M=None, k=0, dtype=float): """ Return a 2-D array with ones on the diagonal and zeros elsewhere. @@ -218,6 +224,7 @@ def eye(N, M=None, k=0, dtype=float): m[:M-k].flat[i::M+1] = 1 return m + def diag(v, k=0): """ Extract a diagonal or construct a diagonal array. @@ -288,6 +295,7 @@ def diag(v, k=0): else: raise ValueError("Input must be 1- or 2-d.") + def diagflat(v, k=0): """ Create a two-dimensional array with the flattened input as a diagonal. @@ -346,6 +354,7 @@ def diagflat(v, k=0): return res return wrap(res) + def tri(N, M=None, k=0, dtype=float): """ An array with ones at and below the given diagonal and zeros elsewhere. @@ -388,6 +397,7 @@ def tri(N, M=None, k=0, dtype=float): m = greater_equal(subtract.outer(arange(N), arange(M)), -k) return m.astype(dtype) + def tril(m, k=0): """ Lower triangle of an array. @@ -424,6 +434,7 @@ def tril(m, k=0): out = multiply(tri(m.shape[0], m.shape[1], k=k, dtype=m.dtype), m) return out + def triu(m, k=0): """ Upper triangle of an array. @@ -450,13 +461,16 @@ def triu(m, k=0): out = multiply((1 - tri(m.shape[0], m.shape[1], k - 1, dtype=m.dtype)), m) return out -# borrowed from John Hunter and matplotlib -def vander(x, N=None): + +# Originally borrowed from John Hunter and matplotlib +def vander(x, N=None, order='decreasing'): """ - Generate a Van der Monde matrix. + Generate a Vandermonde matrix. - The columns of the output matrix are decreasing powers of the input - vector. Specifically, the `i`-th output column is the input vector + 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. @@ -466,14 +480,22 @@ def vander(x, N=None): x : array_like 1-D input array. N : int, optional - Order of (number of columns in) the output. If `N` is not specified, - a square array is returned (``N = len(x)``). + 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'. Returns ------- out : ndarray - Van der Monde matrix of order `N`. The first column is ``x^(N-1)``, - the second ``x^(N-2)`` and so forth. + 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)``. + + See Also + -------- + polynomial.polynomial.polyvander Examples -------- @@ -497,6 +519,11 @@ def vander(x, N=None): [ 8, 4, 2, 1], [ 27, 9, 3, 1], [125, 25, 5, 1]]) + >>> np.vander(x, order='increasing') + array([[ 1, 1, 1, 1], + [ 1, 2, 4, 8], + [ 1, 3, 9, 27], + [ 1, 5, 25, 125]]) The determinant of a square Vandermonde matrix is the product of the differences between the values of the input vector: @@ -507,13 +534,22 @@ def vander(x, N=None): 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) - X = ones( (len(x), N), x.dtype) - for i in range(N - 1): - X[:, i] = x**(N - i - 1) - return X + N = len(x) + if order == "decreasing": + powers = arange(N - 1, -1, -1) + else: + powers = arange(N) + + V = x.reshape(-1, 1) ** powers + + return V def histogram2d(x, y, bins=10, range=None, normed=False, weights=None): @@ -530,7 +566,8 @@ def histogram2d(x, y, bins=10, range=None, normed=False, weights=None): The bin specification: * If int, the number of bins for the two dimensions (nx=ny=bins). - * If [int, int], the number of bins in each dimension (nx, ny = bins). + * If [int, int], the number of bins in each dimension + (nx, ny = bins). * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins). * If [array, array], the bin edges in each dimension |