#
# * The source code in this file is based on the soure code of CuPy.
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# Copyright (c) 2015 Preferred Infrastructure, Inc.
# Copyright (c) 2015 Preferred Networks, Inc.
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import nlcpy
import numpy
from nlcpy.request import request
# ----------------------------------------------------------------------------
# building matrices
# see: https://docs.scipy.org/doc/numpy/reference/routines.array-creation.html
# ----------------------------------------------------------------------------
[ドキュメント]def diag(v, k=0):
"""Extracts a diagonal or constructs a diagonal array.
Parameters
----------
v : array_like
If *v* is a 2-D array, return a copy of its *k-th* diagonal. If *v* is a 1-D
array, return a 2-D array with *v* on the k-th diagonal.
k : int, optional
Diagonal in question. The default is 0. Use *k>0* for diagonals above the main
diagonal, and *k<0* for diagonals below the main diagonal.
Returns
-------
out : ndarray
The extracted diagonal or constructed diagonal array.
See Also
--------
diagonal : Returns specified diagonals.
diagflat : Creates a two-dimensional array with the flattened input as a diagonal.
Examples
--------
>>> import nlcpy as vp
>>> x = vp.arange(9).reshape((3,3))
>>> x
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
>>> vp.diag(x)
array([0, 4, 8])
>>> vp.diag(x, k=1)
array([1, 5])
>>> vp.diag(x, k=-1)
array([3, 7])
>>> vp.diag(vp.diag(x))
array([[0, 0, 0],
[0, 4, 0],
[0, 0, 8]])
"""
if isinstance(v, nlcpy.ndarray):
ndim = v.ndim
else:
ndim = numpy.ndim(v)
if ndim == 1:
v = nlcpy.array(v)
if ndim == 2:
# to save bandwidth, don't copy non-diag elements to GPU
v = numpy.array(v)
if ndim == 1:
size = v.size + abs(k)
ret = nlcpy.zeros((size, size), dtype=v.dtype)
ret.diagonal(k)[:] = v
return ret
elif ndim == 2:
return v.diagonal(k).copy()
else:
raise ValueError('Input must be 1- or 2-d.')
[ドキュメント]def diagflat(v, k=0):
"""Creates a two-dimensional array with the flattened input as a diagonal.
Parameters
----------
v : array_like
Input data, which is flattened and set as the *k*-th diagonal of the output.
k : int, optional
Diagonal to set; 0, the default, corresponds to the "main" diagonal, a positive
(negative) *k* giving the number of the diagonal above (below) the main.
Returns
-------
out : ndarray
The 2-D output array.
See Also
--------
diag : Extracts a diagonal or construct a diagonal array.
diagonal : Returns specified diagonals.
Examples
--------
>>> import nlcpy as vp
>>> vp.diagflat([[1,2], [3,4]])
array([[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]])
>>> vp.diagflat([1,2], 1)
array([[0, 1, 0],
[0, 0, 2],
[0, 0, 0]])
"""
v = nlcpy.asanyarray(v).ravel()
return diag(v, k)
[ドキュメント]def tri(N, M=None, k=0, dtype=float):
"""An array with ones at and below the given diagonal and zeros elsewhere.
Parameters
----------
N : int
Number of rows in the array.
M : int, optional
Number of columns in the array. By default, *M* is taken equal to *N*.
k : int, optional
The sub-diagonal at and below which the array is filled. *k* = 0 is the main
diagonal, while *k* < 0 is below it, and *k* > 0 is above. The default is 0.
dtype : dtype, optional
Data type of the returned array. The default is float.
Returns
-------
tri : ndarray
Array with its lower triangle filled with ones and zero elsewhere; in other
words ``T[i,j] == 1`` for ``i <= j + k``, 0 otherwise.
Examples
--------
>>> import nlcpy as vp
>>> vp.tri(3, 5, 2, dtype=int)
array([[1, 1, 1, 0, 0],
[1, 1, 1, 1, 0],
[1, 1, 1, 1, 1]])
>>> vp.tri(3, 5, -1)
array([[0., 0., 0., 0., 0.],
[1., 0., 0., 0., 0.],
[1., 1., 0., 0., 0.]])
"""
if N < 0:
N = 0
else:
N = int(N)
if M is None:
M = N
elif M < 0:
M = 0
else:
M = int(M)
k = int(k)
out = nlcpy.empty([N, M], dtype=dtype)
if out.size:
request._push_request(
'nlcpy_tri',
'creation_op',
(out, k)
)
return out
[ドキュメント]def tril(m, k=0):
"""Lower triangle of an array.
Returns a copy of an array with elements above the *k*-th diagonal zeroed.
Parameters
----------
m : array_like
Input array.
k : int, optional
Diagonal above which to zero elements. *k* = 0 (the default) is the main
diagonal, *k* < 0 is below it and *k* > 0 is above.
Returns
-------
tri : ndarray
Lower triangle of *m*, of same shape and data-type as *m*.
See Also
--------
triu : Upper triangle of an array.
Examples
--------
>>> import nlcpy as vp
>>> vp.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 0, 0, 0],
[ 4, 0, 0],
[ 7, 8, 0],
[10, 11, 12]])
"""
m = nlcpy.asanyarray(m)
mask = nlcpy.tri(*m.shape[-2:], k=k, dtype=bool)
return nlcpy.where(mask, m, numpy.dtype(m.dtype).type(0))
[ドキュメント]def triu(m, k=0):
"""Upper triangle of an array.
Returns a copy of a matrix with the elements below the *k*-th diagonal zeroed.
Please refer to the documentation for tril for further details.
See Also
--------
tril : Lower triangle of an array.
Examples
--------
>>> import nlcpy as vp
>>> vp.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 1, 2, 3],
[ 4, 5, 6],
[ 0, 8, 9],
[ 0, 0, 12]])
"""
m = nlcpy.asanyarray(m)
mask = nlcpy.tri(*m.shape[-2:], k=k - 1, dtype=bool)
return nlcpy.where(mask, numpy.dtype(m.dtype).type(0), m)