shape_base.pyc
1 o 2 [��cc� � @ s* d dl Z d dlm mZ d dlmZmZmZmZm Z m 3 Z 4 d dl m Z m Z d dlmZ d dlmZ d dlmZmZ d dlmZ d dlmZ d d lmZ d d 5 lmZ g d �Ze j ej d d �Z dd� Z dd� Z e e �dd� �Z dd� Z!e e!�dd� �Z"dd� Z#e e#�dd� �Z$d d � Z%e e%�d d � �Z&d d!� Z'e e'�d"d#� �Z(eZ)d$d%� Z*e e*�d&d'� �Z+d(d)� Z,e e,�d*d+� �Z-d,d-� Z.dJd.d/�Z/e e/�dKd0d1��Z0dJd2d3�Z1e e1�dKd4d5��Z2d6d7� Z3e e3�d8d9� �Z4e e3�d:d;� �Z5e e3�d<d=� �Z6d>d?� Z7d@dA� Z8dBdC� Z9e e9�dDdE� �Z:dFdG� Z;e e;�dHdI� �Z<dS )L� N)�asarray�zeros�outer� concatenate�array� 6 asanyarray)�reshape� transpose)�normalize_axis_index)� overrides)�vstack� 7 atleast_3d)�normalize_axis_tuple�� _arrays_for_stack_dispatcher)�ndindex)�matrix)� column_stack� row_stack�dstack� array_split�split�hsplit�vsplit�dsplit�apply_over_axes� expand_dims�apply_along_axis�kron�tile�get_array_wrap�take_along_axis�put_along_axis�numpy)�modulec C s� t �|jt j�s td��t| �|jkrtd��d|j }tt |��d g tt |d |j�� }g }t 8 || �D ])\}}|d u rD|� |� q6|d |� d ||d d � }|� t � |�� |�� q6t|�S )Nz"`indices` must be an integer arrayz;`indices` and `arr` must have the same number of dimensions�� r& )�����)�_nx� 9 issubdtype�dtype�integer� 10 IndexError�len�ndim� 11 ValueError�list�range�zip�append�aranger �tuple) � arr_shape�indices�axisZ 12 shape_onesZ dest_dimsZ fancy_index�dim�nZ ind_shape� r; ��C:\Users\Jacks.GUTTSPC\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.10_qbz5n2kfra8p0\LocalCache\local-packages\Python310\site-packages\numpy\lib\shape_base.py�_make_along_axis_idx s � 13 & r= c C � | |fS �Nr; )�arrr7 r8 r; r; r< �_take_along_axis_dispatcher4 � rA c C s@ |du r| j } t| �f}d}n t|| j�}| j}| t|||� S )aw 14 Take values from the input array by matching 1d index and data slices. 15 16 This iterates over matching 1d slices oriented along the specified axis in 17 the index and data arrays, and uses the former to look up values in the 18 latter. These slices can be different lengths. 19 20 Functions returning an index along an axis, like `argsort` and 21 `argpartition`, produce suitable indices for this function. 22 23 .. versionadded:: 1.15.0 24 25 Parameters 26 ---------- 27 arr : ndarray (Ni..., M, Nk...) 28 Source array 29 indices : ndarray (Ni..., J, Nk...) 30 Indices to take along each 1d slice of `arr`. This must match the 31 dimension of arr, but dimensions Ni and Nj only need to broadcast 32 against `arr`. 33 axis : int 34 The axis to take 1d slices along. If axis is None, the input array is 35 treated as if it had first been flattened to 1d, for consistency with 36 `sort` and `argsort`. 37 38 Returns 39 ------- 40 out: ndarray (Ni..., J, Nk...) 41 The indexed result. 42 43 Notes 44 ----- 45 This is equivalent to (but faster than) the following use of `ndindex` and 46 `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices:: 47 48 Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:] 49 J = indices.shape[axis] # Need not equal M 50 out = np.empty(Ni + (J,) + Nk) 51 52 for ii in ndindex(Ni): 53 for kk in ndindex(Nk): 54 a_1d = a [ii + s_[:,] + kk] 55 indices_1d = indices[ii + s_[:,] + kk] 56 out_1d = out [ii + s_[:,] + kk] 57 for j in range(J): 58 out_1d[j] = a_1d[indices_1d[j]] 59 60 Equivalently, eliminating the inner loop, the last two lines would be:: 61 62 out_1d[:] = a_1d[indices_1d] 63 64 See Also 65 -------- 66 take : Take along an axis, using the same indices for every 1d slice 67 put_along_axis : 68 Put values into the destination array by matching 1d index and data slices 69 70 Examples 71 -------- 72 73 For this sample array 74 75 >>> a = np.array([[10, 30, 20], [60, 40, 50]]) 76 77 We can sort either by using sort directly, or argsort and this function 78 79 >>> np.sort(a, axis=1) 80 array([[10, 20, 30], 81 [40, 50, 60]]) 82 >>> ai = np.argsort(a, axis=1); ai 83 array([[0, 2, 1], 84 [1, 2, 0]]) 85 >>> np.take_along_axis(a, ai, axis=1) 86 array([[10, 20, 30], 87 [40, 50, 60]]) 88 89 The same works for max and min, if you expand the dimensions: 90 91 >>> np.expand_dims(np.max(a, axis=1), axis=1) 92 array([[30], 93 [60]]) 94 >>> ai = np.expand_dims(np.argmax(a, axis=1), axis=1) 95 >>> ai 96 array([[1], 97 [0]]) 98 >>> np.take_along_axis(a, ai, axis=1) 99 array([[30], 100 [60]]) 101 102 If we want to get the max and min at the same time, we can stack the 103 indices first 104 105 >>> ai_min = np.expand_dims(np.argmin(a, axis=1), axis=1) 106 >>> ai_max = np.expand_dims(np.argmax(a, axis=1), axis=1) 107 >>> ai = np.concatenate([ai_min, ai_max], axis=1) 108 >>> ai 109 array([[0, 1], 110 [1, 0]]) 111 >>> np.take_along_axis(a, ai, axis=1) 112 array([[10, 30], 113 [40, 60]]) 114 Nr ��flatr- r 115 r. �shaper= )r@ r7 r8 r6 r; r; r< r! 8 s i 116 r! c C s 117 | ||fS r? r; )r@ r7 �valuesr8 r; r; r< �_put_along_axis_dispatcher� s 118 rG c C sD |du r| j } d}t| �f}n t|| j�}| j}|| t|||�< dS )a 119 Put values into the destination array by matching 1d index and data slices. 120 121 This iterates over matching 1d slices oriented along the specified axis in 122 the index and data arrays, and uses the former to place values into the 123 latter. These slices can be different lengths. 124 125 Functions returning an index along an axis, like `argsort` and 126 `argpartition`, produce suitable indices for this function. 127 128 .. versionadded:: 1.15.0 129 130 Parameters 131 ---------- 132 arr : ndarray (Ni..., M, Nk...) 133 Destination array. 134 indices : ndarray (Ni..., J, Nk...) 135 Indices to change along each 1d slice of `arr`. This must match the 136 dimension of arr, but dimensions in Ni and Nj may be 1 to broadcast 137 against `arr`. 138 values : array_like (Ni..., J, Nk...) 139 values to insert at those indices. Its shape and dimension are 140 broadcast to match that of `indices`. 141 axis : int 142 The axis to take 1d slices along. If axis is None, the destination 143 array is treated as if a flattened 1d view had been created of it. 144 145 Notes 146 ----- 147 This is equivalent to (but faster than) the following use of `ndindex` and 148 `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices:: 149 150 Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:] 151 J = indices.shape[axis] # Need not equal M 152 153 for ii in ndindex(Ni): 154 for kk in ndindex(Nk): 155 a_1d = a [ii + s_[:,] + kk] 156 indices_1d = indices[ii + s_[:,] + kk] 157 values_1d = values [ii + s_[:,] + kk] 158 for j in range(J): 159 a_1d[indices_1d[j]] = values_1d[j] 160 161 Equivalently, eliminating the inner loop, the last two lines would be:: 162 163 a_1d[indices_1d] = values_1d 164 165 See Also 166 -------- 167 take_along_axis : 168 Take values from the input array by matching 1d index and data slices 169 170 Examples 171 -------- 172 173 For this sample array 174 175 >>> a = np.array([[10, 30, 20], [60, 40, 50]]) 176 177 We can replace the maximum values with: 178 179 >>> ai = np.expand_dims(np.argmax(a, axis=1), axis=1) 180 >>> ai 181 array([[1], 182 [0]]) 183 >>> np.put_along_axis(a, ai, 99, axis=1) 184 >>> a 185 array([[10, 99, 20], 186 [99, 40, 50]]) 187 188 Nr rC )r@ r7 rF r8 r6 r; r; r< r" � s J r" c O s |fS r? r; )�func1dr8 r@ �args�kwargsr; r; r< � _apply_along_axis_dispatcher � rK c 189 O s� t |�}|j}t||�}tt|��}t||d|� ||d d� |g �}t|jdd� �}dd� |D �}zt|�} W n t yM } 190 zt 191 d�d�d} 192 ~ 193 ww t | || g|�R i |���} t |jdd� | j | j �} tt| j��} | d|� | | j| j | j� | || j| j � }t | t�s�| �| �} | | | < |D ]}t | || g|�R i |���| |< q�t | t�s�| �| �} t| |�S t| |�}| �|�S )aU 194 Apply a function to 1-D slices along the given axis. 195 196 Execute `func1d(a, *args, **kwargs)` where `func1d` operates on 1-D arrays 197 and `a` is a 1-D slice of `arr` along `axis`. 198 199 This is equivalent to (but faster than) the following use of `ndindex` and 200 `s_`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of indices:: 201 202 Ni, Nk = a.shape[:axis], a.shape[axis+1:] 203 for ii in ndindex(Ni): 204 for kk in ndindex(Nk): 205 f = func1d(arr[ii + s_[:,] + kk]) 206 Nj = f.shape 207 for jj in ndindex(Nj): 208 out[ii + jj + kk] = f[jj] 209 210 Equivalently, eliminating the inner loop, this can be expressed as:: 211 212 Ni, Nk = a.shape[:axis], a.shape[axis+1:] 213 for ii in ndindex(Ni): 214 for kk in ndindex(Nk): 215 out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk]) 216 217 Parameters 218 ---------- 219 func1d : function (M,) -> (Nj...) 220 This function should accept 1-D arrays. It is applied to 1-D 221 slices of `arr` along the specified axis. 222 axis : integer 223 Axis along which `arr` is sliced. 224 arr : ndarray (Ni..., M, Nk...) 225 Input array. 226 args : any 227 Additional arguments to `func1d`. 228 kwargs : any 229 Additional named arguments to `func1d`. 230 231 .. versionadded:: 1.9.0 232 233 234 Returns 235 ------- 236 out : ndarray (Ni..., Nj..., Nk...) 237 The output array. The shape of `out` is identical to the shape of 238 `arr`, except along the `axis` dimension. This axis is removed, and 239 replaced with new dimensions equal to the shape of the return value 240 of `func1d`. So if `func1d` returns a scalar `out` will have one 241 fewer dimensions than `arr`. 242 243 See Also 244 -------- 245 apply_over_axes : Apply a function repeatedly over multiple axes. 246 247 Examples 248 -------- 249 >>> def my_func(a): 250 ... """Average first and last element of a 1-D array""" 251 ... return (a[0] + a[-1]) * 0.5 252 >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) 253 >>> np.apply_along_axis(my_func, 0, b) 254 array([4., 5., 6.]) 255 >>> np.apply_along_axis(my_func, 1, b) 256 array([2., 5., 8.]) 257 258 For a function that returns a 1D array, the number of dimensions in 259 `outarr` is the same as `arr`. 260 261 >>> b = np.array([[8,1,7], [4,3,9], [5,2,6]]) 262 >>> np.apply_along_axis(sorted, 1, b) 263 array([[1, 7, 8], 264 [3, 4, 9], 265 [2, 5, 6]]) 266 267 For a function that returns a higher dimensional array, those dimensions 268 are inserted in place of the `axis` dimension. 269 270 >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) 271 >>> np.apply_along_axis(np.diag, -1, b) 272 array([[[1, 0, 0], 273 [0, 2, 0], 274 [0, 0, 3]], 275 [[4, 0, 0], 276 [0, 5, 0], 277 [0, 0, 6]], 278 [[7, 0, 0], 279 [0, 8, 0], 280 [0, 0, 9]]]) 281 Nr& r' c s s � | ]}|t f V qd S r? )�Ellipsis)�.0�indr; r; r< � <genexpr>r s � z#apply_along_axis.<locals>.<genexpr>z;Cannot apply_along_axis when any iteration dimensions are 0r )r r. r 282 r0 r1 r r rE �next� StopIterationr/ r r* � 283 isinstancer �__array_prepare__�__array_wrap__)rH r8 r@ rI rJ �ndZin_dimsZ 284 inarr_view�indsZind0�e�res�buffZ buff_dimsZ buff_permuterO �out_arrr; r; r< r sH \ 285 ( ���� 286 ��� 287 288 $ 289 290 291 292 293 r c C s |fS r? r; )�func�a�axesr; r; r< �_apply_over_axes_dispatcher� rL r_ c C s� t |�}|j}t|�jdkr|f}|D ],}|dk r || }||f}| |� }|j|jkr.|}qt||�}|j|jkr<|}qtd��|S )ay 294 Apply a function repeatedly over multiple axes. 295 296 `func` is called as `res = func(a, axis)`, where `axis` is the first 297 element of `axes`. The result `res` of the function call must have 298 either the same dimensions as `a` or one less dimension. If `res` 299 has one less dimension than `a`, a dimension is inserted before 300 `axis`. The call to `func` is then repeated for each axis in `axes`, 301 with `res` as the first argument. 302 303 Parameters 304 ---------- 305 func : function 306 This function must take two arguments, `func(a, axis)`. 307 a : array_like 308 Input array. 309 axes : array_like 310 Axes over which `func` is applied; the elements must be integers. 311 312 Returns 313 ------- 314 apply_over_axis : ndarray 315 The output array. The number of dimensions is the same as `a`, 316 but the shape can be different. This depends on whether `func` 317 changes the shape of its output with respect to its input. 318 319 See Also 320 -------- 321 apply_along_axis : 322 Apply a function to 1-D slices of an array along the given axis. 323 324 Notes 325 ----- 326 This function is equivalent to tuple axis arguments to reorderable ufuncs 327 with keepdims=True. Tuple axis arguments to ufuncs have been available since 328 version 1.7.0. 329 330 Examples 331 -------- 332 >>> a = np.arange(24).reshape(2,3,4) 333 >>> a 334 array([[[ 0, 1, 2, 3], 335 [ 4, 5, 6, 7], 336 [ 8, 9, 10, 11]], 337 [[12, 13, 14, 15], 338 [16, 17, 18, 19], 339 [20, 21, 22, 23]]]) 340 341 Sum over axes 0 and 2. The result has same number of dimensions 342 as the original array: 343 344 >>> np.apply_over_axes(np.sum, a, [0,2]) 345 array([[[ 60], 346 [ 92], 347 [124]]]) 348 349 Tuple axis arguments to ufuncs are equivalent: 350 351 >>> np.sum(a, axis=(0,2), keepdims=True) 352 array([[[ 60], 353 [ 92], 354 [124]]]) 355 356 r z7function is not returning an array of the correct shape)r r. r r r/ )r\ r] r^ �val�Nr8 rI rY r; r; r< r � s B 357 r c C s | fS r? r; )r] r8 r; r; r< �_expand_dims_dispatcher� rL rb c sv t | t�r 358 t| �} nt| �} t� �ttfvr� f� t� �| j }t � |�� t 359 | j ��� �fdd�t |�D �}| � |�S )a. 360 Expand the shape of an array. 361 362 Insert a new axis that will appear at the `axis` position in the expanded 363 array shape. 364 365 Parameters 366 ---------- 367 a : array_like 368 Input array. 369 axis : int or tuple of ints 370 Position in the expanded axes where the new axis (or axes) is placed. 371 372 .. deprecated:: 1.13.0 373 Passing an axis where ``axis > a.ndim`` will be treated as 374 ``axis == a.ndim``, and passing ``axis < -a.ndim - 1`` will 375 be treated as ``axis == 0``. This behavior is deprecated. 376 377 .. versionchanged:: 1.18.0 378 A tuple of axes is now supported. Out of range axes as 379 described above are now forbidden and raise an `AxisError`. 380 381 Returns 382 ------- 383 result : ndarray 384 View of `a` with the number of dimensions increased. 385 386 See Also 387 -------- 388 squeeze : The inverse operation, removing singleton dimensions 389 reshape : Insert, remove, and combine dimensions, and resize existing ones 390 doc.indexing, atleast_1d, atleast_2d, atleast_3d 391 392 Examples 393 -------- 394 >>> x = np.array([1, 2]) 395 >>> x.shape 396 (2,) 397 398 The following is equivalent to ``x[np.newaxis, :]`` or ``x[np.newaxis]``: 399 400 >>> y = np.expand_dims(x, axis=0) 401 >>> y 402 array([[1, 2]]) 403 >>> y.shape 404 (1, 2) 405 406 The following is equivalent to ``x[:, np.newaxis]``: 407 408 >>> y = np.expand_dims(x, axis=1) 409 >>> y 410 array([[1], 411 [2]]) 412 >>> y.shape 413 (2, 1) 414 415 ``axis`` may also be a tuple: 416 417 >>> y = np.expand_dims(x, axis=(0, 1)) 418 >>> y 419 array([[[1, 2]]]) 420 421 >>> y = np.expand_dims(x, axis=(2, 0)) 422 >>> y 423 array([[[1], 424 [2]]]) 425 426 Note that some examples may use ``None`` instead of ``np.newaxis``. These 427 are the same objects: 428 429 >>> np.newaxis is None 430 True 431 432 c s g | ] }|� v r 433 d nt ���qS r% )rQ )rN �ax�r8 Zshape_itr; r< � 434 <listcomp>X s z expand_dims.<locals>.<listcomp>)rS r r r �typer5 r0 r- r. r �iterrE r1 r )r] r8 Zout_ndimrE r; rd r< r s 435 L 436 437 438 439 r c C � t | �S r? r ��tupr; r; r< �_column_stack_dispatcher` rB rk c C sZ t js t| dd� g }| D ]}t|�}|jdk r!t|dddd�j}|�|� q t� |d�S )a� 440 Stack 1-D arrays as columns into a 2-D array. 441 442 Take a sequence of 1-D arrays and stack them as columns 443 to make a single 2-D array. 2-D arrays are stacked as-is, 444 just like with `hstack`. 1-D arrays are turned into 2-D columns 445 first. 446 447 Parameters 448 ---------- 449 tup : sequence of 1-D or 2-D arrays. 450 Arrays to stack. All of them must have the same first dimension. 451 452 Returns 453 ------- 454 stacked : 2-D array 455 The array formed by stacking the given arrays. 456 457 See Also 458 -------- 459 stack, hstack, vstack, concatenate 460 461 Examples 462 -------- 463 >>> a = np.array((1,2,3)) 464 >>> b = np.array((2,3,4)) 465 >>> np.column_stack((a,b)) 466 array([[1, 2], 467 [2, 3], 468 [3, 4]]) 469 470 � �� 471 stacklevelFT��copy�subok�ndminr& ) 472 r �ARRAY_FUNCTION_ENABLEDr r r. r �Tr3 r( r )rj �arrays�vr@ r; r; r< r d s " 473 r c C rh r? r ri r; r; r< �_dstack_dispatcher� rB rw c C s6 t js t| dd� t| � }t|t�s|g}t�|d�S )a� 474 Stack arrays in sequence depth wise (along third axis). 475 476 This is equivalent to concatenation along the third axis after 2-D arrays 477 of shape `(M,N)` have been reshaped to `(M,N,1)` and 1-D arrays of shape 478 `(N,)` have been reshaped to `(1,N,1)`. Rebuilds arrays divided by 479 `dsplit`. 480 481 This function makes most sense for arrays with up to 3 dimensions. For 482 instance, for pixel-data with a height (first axis), width (second axis), 483 and r/g/b channels (third axis). The functions `concatenate`, `stack` and 484 `block` provide more general stacking and concatenation operations. 485 486 Parameters 487 ---------- 488 tup : sequence of arrays 489 The arrays must have the same shape along all but the third axis. 490 1-D or 2-D arrays must have the same shape. 491 492 Returns 493 ------- 494 stacked : ndarray 495 The array formed by stacking the given arrays, will be at least 3-D. 496 497 See Also 498 -------- 499 concatenate : Join a sequence of arrays along an existing axis. 500 stack : Join a sequence of arrays along a new axis. 501 block : Assemble an nd-array from nested lists of blocks. 502 vstack : Stack arrays in sequence vertically (row wise). 503 hstack : Stack arrays in sequence horizontally (column wise). 504 column_stack : Stack 1-D arrays as columns into a 2-D array. 505 dsplit : Split array along third axis. 506 507 Examples 508 -------- 509 >>> a = np.array((1,2,3)) 510 >>> b = np.array((2,3,4)) 511 >>> np.dstack((a,b)) 512 array([[[1, 2], 513 [2, 3], 514 [3, 4]]]) 515 516 >>> a = np.array([[1],[2],[3]]) 517 >>> b = np.array([[2],[3],[4]]) 518 >>> np.dstack((a,b)) 519 array([[[1, 2]], 520 [[2, 3]], 521 [[3, 4]]]) 522 523 rl rm )r rs r r rS r0 r( r )rj �arrsr; r; r< r � s 5 524 r c C sv t t| ��D ]2}t�| | �dkr tjd| | jd�| |< qt�t�t�| | �d��r8tjd| | jd�| |< q| S )Nr �r* ) r1 r- r( r. �emptyr* �sometrue�equalrE )�sub_arys�ir; r; r< �_replace_zero_by_x_arrays� s �r c C r> r? r; ��ary�indices_or_sectionsr8 r; r; r< �_array_split_dispatcher� rB r� c C s z| j | }W n ty t| �}Y nw zt|�d }dgt|� |g }W n8 ty_ t|�}|dkr;td�d�t||�\}}dg||d g || |g }tj |tj 525 d�� � }Y nw g } t� | |d�} 526 t |�D ]} || } || d } | �t� | 527 | | � |d�� qm| S )a 528 529 Split an array into multiple sub-arrays. 530 531 Please refer to the ``split`` documentation. The only difference 532 between these functions is that ``array_split`` allows 533 `indices_or_sections` to be an integer that does *not* equally 534 divide the axis. For an array of length l that should be split 535 into n sections, it returns l % n sub-arrays of size l//n + 1 536 and the rest of size l//n. 537 538 See Also 539 -------- 540 split : Split array into multiple sub-arrays of equal size. 541 542 Examples 543 -------- 544 >>> x = np.arange(8.0) 545 >>> np.array_split(x, 3) 546 [array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7.])] 547 548 >>> x = np.arange(9) 549 >>> np.array_split(x, 4) 550 [array([0, 1, 2]), array([3, 4]), array([5, 6]), array([7, 8])] 551 552 r& r z&number sections must be larger than 0.Nry )rE �AttributeErrorr- r0 � TypeError�intr/ �divmodr( r �intp�cumsum�swapaxesr1 r3 )r� r� r8 ZNtotalZ NsectionsZ 553 div_pointsZ Neach_section�extrasZ section_sizesr} Zsaryr~ �st�endr; r; r< r � s6 � 554 � �� r c C r> r? r; r� r; r; r< �_split_dispatcher rB r� c C sL zt |� W n ty |}| j| }|| r td�d�Y nw t| ||�S )a� 555 Split an array into multiple sub-arrays as views into `ary`. 556 557 Parameters 558 ---------- 559 ary : ndarray 560 Array to be divided into sub-arrays. 561 indices_or_sections : int or 1-D array 562 If `indices_or_sections` is an integer, N, the array will be divided 563 into N equal arrays along `axis`. If such a split is not possible, 564 an error is raised. 565 566 If `indices_or_sections` is a 1-D array of sorted integers, the entries 567 indicate where along `axis` the array is split. For example, 568 ``[2, 3]`` would, for ``axis=0``, result in 569 570 - ary[:2] 571 - ary[2:3] 572 - ary[3:] 573 574 If an index exceeds the dimension of the array along `axis`, 575 an empty sub-array is returned correspondingly. 576 axis : int, optional 577 The axis along which to split, default is 0. 578 579 Returns 580 ------- 581 sub-arrays : list of ndarrays 582 A list of sub-arrays as views into `ary`. 583 584 Raises 585 ------ 586 ValueError 587 If `indices_or_sections` is given as an integer, but 588 a split does not result in equal division. 589 590 See Also 591 -------- 592 array_split : Split an array into multiple sub-arrays of equal or 593 near-equal size. Does not raise an exception if 594 an equal division cannot be made. 595 hsplit : Split array into multiple sub-arrays horizontally (column-wise). 596 vsplit : Split array into multiple sub-arrays vertically (row wise). 597 dsplit : Split array into multiple sub-arrays along the 3rd axis (depth). 598 concatenate : Join a sequence of arrays along an existing axis. 599 stack : Join a sequence of arrays along a new axis. 600 hstack : Stack arrays in sequence horizontally (column wise). 601 vstack : Stack arrays in sequence vertically (row wise). 602 dstack : Stack arrays in sequence depth wise (along third dimension). 603 604 Examples 605 -------- 606 >>> x = np.arange(9.0) 607 >>> np.split(x, 3) 608 [array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7., 8.])] 609 610 >>> x = np.arange(8.0) 611 >>> np.split(x, [3, 5, 6, 10]) 612 [array([0., 1., 2.]), 613 array([3., 4.]), 614 array([5.]), 615 array([6., 7.]), 616 array([], dtype=float64)] 617 618 z0array split does not result in an equal divisionN)r- r� rE r/ r )r� r� r8 �sectionsra r; r; r< r s C 619 ���� r c C r> r? r; �r� r� r; r; r< �_hvdsplit_dispatcherm rB r� c C s8 t �| �dkr td��| jdkrt| |d�S t| |d�S )a] 620 Split an array into multiple sub-arrays horizontally (column-wise). 621 622 Please refer to the `split` documentation. `hsplit` is equivalent 623 to `split` with ``axis=1``, the array is always split along the second 624 axis except for 1-D arrays, where it is split at ``axis=0``. 625 626 See Also 627 -------- 628 split : Split an array into multiple sub-arrays of equal size. 629 630 Examples 631 -------- 632 >>> x = np.arange(16.0).reshape(4, 4) 633 >>> x 634 array([[ 0., 1., 2., 3.], 635 [ 4., 5., 6., 7.], 636 [ 8., 9., 10., 11.], 637 [12., 13., 14., 15.]]) 638 >>> np.hsplit(x, 2) 639 [array([[ 0., 1.], 640 [ 4., 5.], 641 [ 8., 9.], 642 [12., 13.]]), 643 array([[ 2., 3.], 644 [ 6., 7.], 645 [10., 11.], 646 [14., 15.]])] 647 >>> np.hsplit(x, np.array([3, 6])) 648 [array([[ 0., 1., 2.], 649 [ 4., 5., 6.], 650 [ 8., 9., 10.], 651 [12., 13., 14.]]), 652 array([[ 3.], 653 [ 7.], 654 [11.], 655 [15.]]), 656 array([], shape=(4, 0), dtype=float64)] 657 658 With a higher dimensional array the split is still along the second axis. 659 660 >>> x = np.arange(8.0).reshape(2, 2, 2) 661 >>> x 662 array([[[0., 1.], 663 [2., 3.]], 664 [[4., 5.], 665 [6., 7.]]]) 666 >>> np.hsplit(x, 2) 667 [array([[[0., 1.]], 668 [[4., 5.]]]), 669 array([[[2., 3.]], 670 [[6., 7.]]])] 671 672 With a 1-D array, the split is along axis 0. 673 674 >>> x = np.array([0, 1, 2, 3, 4, 5]) 675 >>> np.hsplit(x, 2) 676 [array([0, 1, 2]), array([3, 4, 5])] 677 678 r z3hsplit only works on arrays of 1 or more dimensionsr& �r( r. r/ r r� r; r; r< r q s 679 > 680 r c C �" t �| �dk r td��t| |d�S )a 681 Split an array into multiple sub-arrays vertically (row-wise). 682 683 Please refer to the ``split`` documentation. ``vsplit`` is equivalent 684 to ``split`` with `axis=0` (default), the array is always split along the 685 first axis regardless of the array dimension. 686 687 See Also 688 -------- 689 split : Split an array into multiple sub-arrays of equal size. 690 691 Examples 692 -------- 693 >>> x = np.arange(16.0).reshape(4, 4) 694 >>> x 695 array([[ 0., 1., 2., 3.], 696 [ 4., 5., 6., 7.], 697 [ 8., 9., 10., 11.], 698 [12., 13., 14., 15.]]) 699 >>> np.vsplit(x, 2) 700 [array([[0., 1., 2., 3.], 701 [4., 5., 6., 7.]]), array([[ 8., 9., 10., 11.], 702 [12., 13., 14., 15.]])] 703 >>> np.vsplit(x, np.array([3, 6])) 704 [array([[ 0., 1., 2., 3.], 705 [ 4., 5., 6., 7.], 706 [ 8., 9., 10., 11.]]), array([[12., 13., 14., 15.]]), array([], shape=(0, 4), dtype=float64)] 707 708 With a higher dimensional array the split is still along the first axis. 709 710 >>> x = np.arange(8.0).reshape(2, 2, 2) 711 >>> x 712 array([[[0., 1.], 713 [2., 3.]], 714 [[4., 5.], 715 [6., 7.]]]) 716 >>> np.vsplit(x, 2) 717 [array([[[0., 1.], 718 [2., 3.]]]), array([[[4., 5.], 719 [6., 7.]]])] 720 721 rl z3vsplit only works on arrays of 2 or more dimensionsr r� r� r; r; r< r � s , r c C r� )am 722 Split array into multiple sub-arrays along the 3rd axis (depth). 723 724 Please refer to the `split` documentation. `dsplit` is equivalent 725 to `split` with ``axis=2``, the array is always split along the third 726 axis provided the array dimension is greater than or equal to 3. 727 728 See Also 729 -------- 730 split : Split an array into multiple sub-arrays of equal size. 731 732 Examples 733 -------- 734 >>> x = np.arange(16.0).reshape(2, 2, 4) 735 >>> x 736 array([[[ 0., 1., 2., 3.], 737 [ 4., 5., 6., 7.]], 738 [[ 8., 9., 10., 11.], 739 [12., 13., 14., 15.]]]) 740 >>> np.dsplit(x, 2) 741 [array([[[ 0., 1.], 742 [ 4., 5.]], 743 [[ 8., 9.], 744 [12., 13.]]]), array([[[ 2., 3.], 745 [ 6., 7.]], 746 [[10., 11.], 747 [14., 15.]]])] 748 >>> np.dsplit(x, np.array([3, 6])) 749 [array([[[ 0., 1., 2.], 750 [ 4., 5., 6.]], 751 [[ 8., 9., 10.], 752 [12., 13., 14.]]]), 753 array([[[ 3.], 754 [ 7.]], 755 [[11.], 756 [15.]]]), 757 array([], shape=(2, 2, 0), dtype=float64)] 758 � z3dsplit only works on arrays of 3 or more dimensionsrl r� r� r; r; r< r � s ( r c G �* t dd� t| �D ��}|r|d d S dS )��Find the wrapper for the array with the highest priority. 759 760 In case of ties, leftmost wins. If no wrapper is found, return None 761 c s �4 � | ]\}}t |d �rt|dd�| |jfV qdS )rT �__array_priority__r N)�hasattr�getattrrT �rN r~ �xr; r; r< rP � � � �z$get_array_prepare.<locals>.<genexpr>r' N��sorted� enumerate�rI �wrappersr; r; r< �get_array_prepare � � r� c G r� )r� c s r� )rU r� r N)r� r� rU r� r; r; r< rP % r� z!get_array_wrap.<locals>.<genexpr>r' Nr� r� r; r; r< r r� r c C r> r? r; )r] �br; r; r< �_kron_dispatcher- rB r� c C s^ t |�}t| dd|jd�} t| t�pt|t�}|j| j}}t||�}|dks+|dkr1t�| |�S | j}|j}| j j 762 s@t | |�} |j j 763 sIt ||�}dtd|| � | }dtd|| � | }t | t t|| ��d�}t |t t|| ��d�} t |t td|d d��d�}t | t td|d d��d�} tj|| | d �} 764 | 765 � t�||��} 766 |s�| 767 S t| 768 dd 769 �S ) a 770 Kronecker product of two arrays. 771 772 Computes the Kronecker product, a composite array made of blocks of the 773 second array scaled by the first. 774 775 Parameters 776 ---------- 777 a, b : array_like 778 779 Returns 780 ------- 781 out : ndarray 782 783 See Also 784 -------- 785 outer : The outer product 786 787 Notes 788 ----- 789 The function assumes that the number of dimensions of `a` and `b` 790 are the same, if necessary prepending the smallest with ones. 791 If ``a.shape = (r0,r1,..,rN)`` and ``b.shape = (s0,s1,...,sN)``, 792 the Kronecker product has shape ``(r0*s0, r1*s1, ..., rN*SN)``. 793 The elements are products of elements from `a` and `b`, organized 794 explicitly by:: 795 796 kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN] 797 798 where:: 799 800 kt = it * st + jt, t = 0,...,N 801 802 In the common 2-D case (N=1), the block structure can be visualized:: 803 804 [[ a[0,0]*b, a[0,1]*b, ... , a[0,-1]*b ], 805 [ ... ... ], 806 [ a[-1,0]*b, a[-1,1]*b, ... , a[-1,-1]*b ]] 807 808 809 Examples 810 -------- 811 >>> np.kron([1,10,100], [5,6,7]) 812 array([ 5, 6, 7, ..., 500, 600, 700]) 813 >>> np.kron([5,6,7], [1,10,100]) 814 array([ 5, 50, 500, ..., 7, 70, 700]) 815 816 >>> np.kron(np.eye(2), np.ones((2,2))) 817 array([[1., 1., 0., 0.], 818 [1., 1., 0., 0.], 819 [0., 0., 1., 1.], 820 [0., 0., 1., 1.]]) 821 822 >>> a = np.arange(100).reshape((2,5,2,5)) 823 >>> b = np.arange(24).reshape((2,3,4)) 824 >>> c = np.kron(a,b) 825 >>> c.shape 826 (2, 10, 6, 20) 827 >>> I = (1,3,0,2) 828 >>> J = (0,2,1) 829 >>> J1 = (0,) + J # extend to ndim=4 830 >>> S1 = (1,) + b.shape 831 >>> K = tuple(np.array(I) * np.array(S1) + np.array(J1)) 832 >>> c[K] == a[I]*b[J] 833 True 834 835 FTro r r% )r8 r& rl )rq )rp )r r r. rS r �maxr( �multiplyrE �flags� 836 contiguousr r r5 r1 ) r] r� Z 837 is_any_mat�ndb�ndarV �as_�bs�a_arrZb_arr�resultr; r; r< r 1 s, N 838 839 840 r c C r> r? r; )�A�repsr; r; r< �_tile_dispatcher� rB r� c C s� zt |�}W n ty |f}Y nw t|�}tdd� |D ��r/t| tj�r/tj| dd|d�S tj| dd|d�}||jk rFd|j| | }t dd� t |j 841 |�D ��}|j }|dkrwt |j 842 |�D ]\}}|d krr|� d 843 |�� |d�}|| }q`|� |�S ) a 844 Construct an array by repeating A the number of times given by reps. 845 846 If `reps` has length ``d``, the result will have dimension of 847 ``max(d, A.ndim)``. 848 849 If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new 850 axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication, 851 or shape (1, 1, 3) for 3-D replication. If this is not the desired 852 behavior, promote `A` to d-dimensions manually before calling this 853 function. 854 855 If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it. 856 Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as 857 (1, 1, 2, 2). 858 859 Note : Although tile may be used for broadcasting, it is strongly 860 recommended to use numpy's broadcasting operations and functions. 861 862 Parameters 863 ---------- 864 A : array_like 865 The input array. 866 reps : array_like 867 The number of repetitions of `A` along each axis. 868 869 Returns 870 ------- 871 c : ndarray 872 The tiled output array. 873 874 See Also 875 -------- 876 repeat : Repeat elements of an array. 877 broadcast_to : Broadcast an array to a new shape 878 879 Examples 880 -------- 881 >>> a = np.array([0, 1, 2]) 882 >>> np.tile(a, 2) 883 array([0, 1, 2, 0, 1, 2]) 884 >>> np.tile(a, (2, 2)) 885 array([[0, 1, 2, 0, 1, 2], 886 [0, 1, 2, 0, 1, 2]]) 887 >>> np.tile(a, (2, 1, 2)) 888 array([[[0, 1, 2, 0, 1, 2]], 889 [[0, 1, 2, 0, 1, 2]]]) 890 891 >>> b = np.array([[1, 2], [3, 4]]) 892 >>> np.tile(b, 2) 893 array([[1, 2, 1, 2], 894 [3, 4, 3, 4]]) 895 >>> np.tile(b, (2, 1)) 896 array([[1, 2], 897 [3, 4], 898 [1, 2], 899 [3, 4]]) 900 901 >>> c = np.array([1,2,3,4]) 902 >>> np.tile(c,(4,1)) 903 array([[1, 2, 3, 4], 904 [1, 2, 3, 4], 905 [1, 2, 3, 4], 906 [1, 2, 3, 4]]) 907 c s s � | ]}|d kV qdS )r& Nr; )rN r� r; r; r< rP � s � ztile.<locals>.<genexpr>Tro Fr% c s s � | ] \}}|| V qd S r? r; )rN �s�tr; r; r< rP � s � r r& r' )r5 r� r- �allrS r( �ndarrayr r. r2 rE �sizer �repeat) r� r� rj �d�c� shape_outr: Zdim_in�nrepr; r; r< r � s& C 908 � 909 910 911 r r? )r )=� functools�numpy.core.numeric�core�numericr( r r r r r r �numpy.core.fromnumericr r �numpy.core.multiarrayr 912 � 913 numpy.corer r r r �numpy.core.shape_baser �numpy.lib.index_tricksr �numpy.matrixlib.defmatrixr �__all__�partial�array_function_dispatchr= rA r! rG r" rK r r_ r rb r r rk r rw r r r� r r� r r� r r r r� r r� r r� r r; r; r; r< �<module> sz � 914 t 915 U 916 917 V 918 \ 919 . 920 > 921 922 7 M 923 E 924 0 925 + 926 q