diff options
Diffstat (limited to 'numpy/lib/twodim_base.py')
| -rw-r--r-- | numpy/lib/twodim_base.py | 48 |
1 files changed, 34 insertions, 14 deletions
diff --git a/numpy/lib/twodim_base.py b/numpy/lib/twodim_base.py index 91df1f4f8..cdb0a4f5b 100644 --- a/numpy/lib/twodim_base.py +++ b/numpy/lib/twodim_base.py @@ -450,13 +450,15 @@ 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 +468,18 @@ 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)``. Examples -------- @@ -497,6 +503,11 @@ 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 +518,22 @@ 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): |