linalg.py 92.2 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13
#   Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
14

myq406450149's avatar
myq406450149 已提交
15
import numpy as np
Z
Zhang Ting 已提交
16
from ..fluid.layer_helper import LayerHelper
17
from ..fluid.framework import in_dygraph_mode, _varbase_creator, Variable, _dygraph_tracer
H
huangxu96 已提交
18
from ..fluid.data_feeder import check_variable_and_dtype, check_type, check_dtype
19

20
from ..fluid.layers import transpose, cast  # noqa: F401
A
andyjpaddle 已提交
21 22
from ..fluid import layers
import paddle
23 24
from paddle.common_ops_import import core
from paddle.common_ops_import import VarDesc
W
wanghuancoder 已提交
25
from paddle import _C_ops
L
Lijunhui 已提交
26
import paddle
27

28 29
__all__ = []

30

S
ShenLiang 已提交
31
def matmul(x, y, transpose_x=False, transpose_y=False, name=None):
32
    """
33 34
    Applies matrix multiplication to two tensors. `matmul` follows
    the complete broadcast rules,
S
ShenLiang 已提交
35
    and its behavior is consistent with `np.matmul`.
S
swtkiwi 已提交
36

S
ShenLiang 已提交
37 38
    Currently, the input tensors' number of dimensions can be any, `matmul` can be used to
    achieve the `dot`, `matmul` and `batchmatmul`.
39 40 41 42 43

    The actual behavior depends on the shapes of :math:`x`, :math:`y` and the
    flag values of :attr:`transpose_x`, :attr:`transpose_y`. Specifically:

    - If a transpose flag is specified, the last two dimensions of the tensor
44 45
      are transposed. If the tensor is ndim-1 of shape, the transpose is invalid. If the tensor
      is ndim-1 of shape :math:`[D]`, then for :math:`x` it is treated as :math:`[1, D]`, whereas
S
ShenLiang 已提交
46 47 48 49 50 51 52 53
      for :math:`y` it is the opposite: It is treated as :math:`[D, 1]`.

    The multiplication behavior depends on the dimensions of `x` and `y`. Specifically:

    - If both tensors are 1-dimensional, the dot product result is obtained.

    - If both tensors are 2-dimensional, the matrix-matrix product is obtained.

54 55
    - If the `x` is 1-dimensional and the `y` is 2-dimensional,
      a `1` is prepended to its dimension in order to conduct the matrix multiply.
S
ShenLiang 已提交
56
      After the matrix multiply, the prepended dimension is removed.
57 58

    - If the `x` is 2-dimensional and `y` is 1-dimensional,
S
ShenLiang 已提交
59 60
      the matrix-vector product is obtained.

61 62 63 64 65 66 67 68 69
    - If both arguments are at least 1-dimensional and at least one argument
      is N-dimensional (where N > 2), then a batched matrix multiply is obtained.
      If the first argument is 1-dimensional, a 1 is prepended to its dimension
      in order to conduct the batched matrix multiply and removed after.
      If the second argument is 1-dimensional, a 1 is appended to its
      dimension for the purpose of the batched matrix multiple and removed after.
      The non-matrix (exclude the last two dimensions) dimensions are
      broadcasted according the broadcast rule.
      For example, if input is a (j, 1, n, m) tensor and the other is a (k, m, p) tensor,
S
ShenLiang 已提交
70
      out will be a (j, k, n, p) tensor.
71 72

    Args:
S
ShenLiang 已提交
73 74
        x (Tensor): The input tensor which is a Tensor.
        y (Tensor): The input tensor which is a Tensor.
75 76 77 78 79 80
        transpose_x (bool): Whether to transpose :math:`x` before multiplication.
        transpose_y (bool): Whether to transpose :math:`y` before multiplication.
        name(str|None): A name for this layer(optional). If set None, the layer
            will be named automatically.

    Returns:
S
ShenLiang 已提交
81
        Tensor: The output Tensor.
82 83 84

    Examples:

S
ShenLiang 已提交
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133
    .. code-block:: python

        import paddle
        import numpy as np

        # vector * vector
        x_data = np.random.random([10]).astype(np.float32)
        y_data = np.random.random([10]).astype(np.float32)
        x = paddle.to_tensor(x_data)
        y = paddle.to_tensor(y_data)
        z = paddle.matmul(x, y)
        print(z.numpy().shape)
        # [1]

        # matrix * vector
        x_data = np.random.random([10, 5]).astype(np.float32)
        y_data = np.random.random([5]).astype(np.float32)
        x = paddle.to_tensor(x_data)
        y = paddle.to_tensor(y_data)
        z = paddle.matmul(x, y)
        print(z.numpy().shape)
        # [10]

        # batched matrix * broadcasted vector
        x_data = np.random.random([10, 5, 2]).astype(np.float32)
        y_data = np.random.random([2]).astype(np.float32)
        x = paddle.to_tensor(x_data)
        y = paddle.to_tensor(y_data)
        z = paddle.matmul(x, y)
        print(z.numpy().shape)
        # [10, 5]

        # batched matrix * batched matrix
        x_data = np.random.random([10, 5, 2]).astype(np.float32)
        y_data = np.random.random([10, 2, 5]).astype(np.float32)
        x = paddle.to_tensor(x_data)
        y = paddle.to_tensor(y_data)
        z = paddle.matmul(x, y)
        print(z.numpy().shape)
        # [10, 5, 5]

        # batched matrix * broadcasted matrix
        x_data = np.random.random([10, 1, 5, 2]).astype(np.float32)
        y_data = np.random.random([1, 3, 2, 5]).astype(np.float32)
        x = paddle.to_tensor(x_data)
        y = paddle.to_tensor(y_data)
        z = paddle.matmul(x, y)
        print(z.numpy().shape)
        # [10, 3, 5, 5]
134 135

    """
S
ShenLiang 已提交
136 137
    op_type = 'matmul_v2'
    if in_dygraph_mode():
W
wanghuancoder 已提交
138
        op = getattr(_C_ops, op_type)
S
ShenLiang 已提交
139 140
        return op(x, y, 'trans_x', transpose_x, 'trans_y', transpose_y)

141
    attrs = {
S
ShenLiang 已提交
142 143
        'trans_x': transpose_x,
        'trans_y': transpose_y,
144 145 146 147 148
    }

    def __check_input(x, y):
        var_names = {'x': x, 'y': y}
        for name, val in var_names.items():
S
ShenLiang 已提交
149 150
            check_variable_and_dtype(
                val, name, ['float16', 'float32', 'float64'], 'matmul')
151 152 153

    __check_input(x, y)

S
ShenLiang 已提交
154
    helper = LayerHelper('matmul_v2', **locals())
155 156
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
S
ShenLiang 已提交
157
        type='matmul_v2',
158 159 160 161 162
        inputs={'X': x,
                'Y': y},
        outputs={'Out': out},
        attrs=attrs)
    return out
Z
Zhang Ting 已提交
163 164


myq406450149's avatar
myq406450149 已提交
165
def norm(x, p='fro', axis=None, keepdim=False, name=None):
166
    """
S
swtkiwi 已提交
167

168 169 170
    Returns the matrix norm (Frobenius) or vector norm (the 1-norm, the Euclidean
    or 2-norm, and in general the p-norm for p > 0) of a given tensor.

171 172 173 174 175 176
    .. note::
        This norm API is different from `numpy.linalg.norm`.
        This api supports high-order input tensors (rank >= 3), and certain axis need to be pointed out to calculate the norm.
        But `numpy.linalg.norm` only supports 1-D vector or 2-D matrix as input tensor.
        For p-order matrix norm, this api actually treats matrix as a flattened vector to calculate the vector norm, NOT REAL MATRIX NORM.

177
    Args:
myq406450149's avatar
myq406450149 已提交
178
        x (Tensor): The input tensor could be N-D tensor, and the input data
179
            type could be float32 or float64.
myq406450149's avatar
myq406450149 已提交
180
        p (float|string, optional): Order of the norm. Supported values are `fro`, `0`, `1`, `2`,
181
            `inf`, `-inf` and any positive real number yielding the corresponding p-norm. Not supported: ord < 0 and nuclear norm.
myq406450149's avatar
myq406450149 已提交
182
            Default value is `fro`.
myq406450149's avatar
myq406450149 已提交
183 184
        axis (int|list|tuple, optional): The axis on which to apply norm operation. If axis is int
            or list(int)/tuple(int)  with only one element, the vector norm is computed over the axis.
185
            If `axis < 0`, the dimension to norm operation is rank(input) + axis.
myq406450149's avatar
myq406450149 已提交
186
            If axis is a list(int)/tuple(int) with two elements, the matrix norm is computed over the axis.
myq406450149's avatar
myq406450149 已提交
187
            Defalut value is `None`.
188 189 190 191 192 193 194 195
        keepdim (bool, optional): Whether to reserve the reduced dimension in the
            output Tensor. The result tensor will have fewer dimension
            than the :attr:`input` unless :attr:`keepdim` is true, default
            value is False.
        name (str, optional): The default value is None. Normally there is no need for
            user to set this property. For more information, please refer to :ref:`api_guide_Name`.

    Returns:
myq406450149's avatar
myq406450149 已提交
196
        Tensor: results of norm operation on the specified axis of input tensor,
197
        it's data type is the same as input's Tensor.
198

199 200
    Examples:
        .. code-block:: python
201

202
            import paddle
myq406450149's avatar
myq406450149 已提交
203 204 205 206 207 208 209 210
            import numpy as np
            shape=[2, 3, 4]
            np_input = np.arange(24).astype('float32') - 12
            np_input = np_input.reshape(shape)
            x = paddle.to_tensor(np_input)
            #[[[-12. -11. -10.  -9.] [ -8.  -7.  -6.  -5.] [ -4.  -3.  -2.  -1.]]
            # [[  0.   1.   2.   3.] [  4.   5.   6.   7.] [  8.   9.  10.  11.]]]

211
            # compute frobenius norm along last two dimensions.
myq406450149's avatar
myq406450149 已提交
212 213 214
            out_fro = paddle.norm(x, p='fro', axis=[0,1])
            # out_fro.numpy() [17.435596 16.911535 16.7332   16.911535]

215 216
            # compute 2-order vector norm along last dimension.
            out_pnorm = paddle.norm(x, p=2, axis=-1)
myq406450149's avatar
myq406450149 已提交
217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234
            #out_pnorm.numpy(): [[21.118711  13.190906   5.477226]
            #                    [ 3.7416575 11.224972  19.131126]]

            # compute 2-order  norm along [0,1] dimension.
            out_pnorm = paddle.norm(x, p=2, axis=[0,1])
            #out_pnorm.numpy(): [17.435596 16.911535 16.7332   16.911535]

            # compute inf-order  norm
            out_pnorm = paddle.norm(x, p=np.inf)
            #out_pnorm.numpy()  = [12.]
            out_pnorm = paddle.norm(x, p=np.inf, axis=0)
            #out_pnorm.numpy(): [[12. 11. 10. 9.] [8. 7. 6. 7.] [8. 9. 10. 11.]]

            # compute -inf-order  norm
            out_pnorm = paddle.norm(x, p=-np.inf)
            #out_pnorm.numpy(): [0.]
            out_pnorm = paddle.norm(x, p=-np.inf, axis=0)
            #out_pnorm.numpy(): [[0. 1. 2. 3.] [4. 5. 6. 5.] [4. 3. 2. 1.]]
235 236
    """

myq406450149's avatar
myq406450149 已提交
237
    def frobenius_norm(input, dim=None, keepdim=False, name=None):
238 239 240 241 242 243 244 245 246 247 248
        """
        The frobenius norm OP is to calculate the frobenius norm of certain two dimensions of Tensor `input`.
        Args:
          input (Variable): Tensor, data type float32, float64.
          dim (list, optional): None for last two dimensions.
          keepdim (bool, optional): Whether keep the dimensions as the `input`, Default False.
        """
        if dim is not None and not (isinstance(dim, list) and len(dim) == 2):
            raise ValueError(
                "The dim of frobenius norm op should be None or two elements list!"
            )
myq406450149's avatar
myq406450149 已提交
249
        if in_dygraph_mode():
myq406450149's avatar
myq406450149 已提交
250
            if dim is None:
W
wanghuancoder 已提交
251 252 253 254
                return _C_ops.frobenius_norm(input, 'keep_dim', keepdim,
                                             'reduce_all', True)
            return _C_ops.frobenius_norm(input, 'dim', dim, 'keep_dim', keepdim,
                                         'reduce_all', False)
myq406450149's avatar
myq406450149 已提交
255 256
        attrs = {'dim': dim, 'keep_dim': keepdim, 'reduce_all': False}
        if dim is None:
257 258 259 260 261
            attrs['reduce_all'] = True
        check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                                 'frobenius_norm')

        helper = LayerHelper('frobenius_norm', **locals())
myq406450149's avatar
myq406450149 已提交
262 263
        out = helper.create_variable_for_type_inference(
            dtype=helper.input_dtype())
264 265 266 267 268 269 270 271 272 273 274 275

        helper.append_op(
            type='frobenius_norm',
            inputs={'X': input},
            outputs={'Out': out},
            attrs=attrs)
        return out

    def vector_norm(input,
                    porder=None,
                    axis=None,
                    keepdim=False,
myq406450149's avatar
myq406450149 已提交
276
                    asvector=False,
277 278 279 280 281 282 283 284 285
                    name=None):
        """
        Calculate the p-order vector norm for certain  dimension of Tensor `input`.
        Args:
          input (Variable): Tensor, data type float32, float64.
          porder (float, optional): None for porder=2.0.
          axis (int, optional): None for last dimension.
          keepdim (bool, optional): Whether keep the dimensions as the `input`, Default False.
        """
myq406450149's avatar
myq406450149 已提交
286 287
        if in_dygraph_mode():
            if axis is None: axis = -1
W
wanghuancoder 已提交
288 289
            return _C_ops.p_norm(input, 'porder', porder, 'axis', axis,
                                 'keepdim', keepdim, 'asvector', asvector)
290 291 292 293
        if porder is not None:
            check_type(porder, 'porder', (float, int), 'p_norm')
        if axis is not None:
            check_type(axis, 'axis', (int), 'p_norm')
myq406450149's avatar
myq406450149 已提交
294 295 296
        check_variable_and_dtype(input, 'input', ['float32', 'float64'],
                                 'p_norm')

297 298 299 300
        attrs = {
            'axis': axis if axis is not None else -1,
            'porder': float(porder) if porder is not None else 2.0,
            'keepdim': keepdim,
myq406450149's avatar
myq406450149 已提交
301
            'asvector': asvector,
302 303 304
            'epsilon': 1e-12,
        }
        helper = LayerHelper('p_norm', **locals())
myq406450149's avatar
myq406450149 已提交
305 306
        out = helper.create_variable_for_type_inference(
            dtype=helper.input_dtype())
307 308 309 310 311 312 313 314

        helper.append_op(
            type='p_norm',
            inputs={'X': input},
            outputs={'Out': out},
            attrs=attrs)
        return out

myq406450149's avatar
myq406450149 已提交
315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343
    def inf_norm(input,
                 porder=None,
                 axis=axis,
                 keepdim=False,
                 asvector=False,
                 name=None):
        helper = LayerHelper('frobenius_norm', **locals())
        out = helper.create_variable_for_type_inference(
            dtype=helper.input_dtype())
        helper.append_op(type='abs', inputs={'X': input}, outputs={'Out': out})
        reduce_out = helper.create_variable_for_type_inference(
            dtype=helper.input_dtype())

        reduce_all = True if axis == None or axis == [] or asvector == True else False
        axis = axis if axis != None and axis != [] else [0]

        reduce_type = 'reduce_max' if porder == np.float(
            'inf') else 'reduce_min'
        helper.append_op(
            type=reduce_type,
            inputs={'X': out},
            outputs={'Out': reduce_out},
            attrs={'dim': axis,
                   'keep_dim': keepdim,
                   'reduce_all': reduce_all})

        return reduce_out

    def p_matrix_norm(input, porder=1., axis=axis, keepdim=False, name=None):
344 345 346 347
        """
        NOTE:
            This function actually treats the matrix as flattened vector to calculate vector norm instead of matrix norm.
        """
myq406450149's avatar
myq406450149 已提交
348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381
        block = LayerHelper('norm', **locals())
        out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        abs_out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        block.append_op(
            type='abs', inputs={'X': input}, outputs={'Out': abs_out})
        pow_out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())

        block.append_op(
            type='pow',
            inputs={'X': abs_out},
            outputs={'Out': pow_out},
            attrs={'factor': porder})
        sum_out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        block.append_op(
            type='reduce_sum',
            inputs={'X': pow_out},
            outputs={'Out': sum_out},
            attrs={
                'dim': axis,
                'keep_dim': keepdim,
                'reduce_all': True if axis is None else False
            })
        porder
        block.append_op(
            type='pow',
            inputs={'X': sum_out},
            outputs={'Out': out},
            attrs={'factor': float(1. / porder)})
        return out

382 383 384
    if axis is None and p is not None:
        if isinstance(p, str):
            if p == "fro":
myq406450149's avatar
myq406450149 已提交
385
                return frobenius_norm(x, dim=axis, keepdim=keepdim, name=name)
386 387 388 389 390
            else:
                raise ValueError(
                    "only valid string values are 'fro', found {}".format(p))
        elif isinstance(p, (int, float)):
            return vector_norm(
myq406450149's avatar
myq406450149 已提交
391 392 393 394 395 396
                x,
                porder=p,
                axis=axis,
                keepdim=keepdim,
                asvector=True,
                name=name)
397 398 399 400
        else:
            raise ValueError("only valid p type is string or float, found {}".
                             format(type(p)))

myq406450149's avatar
myq406450149 已提交
401 402
    if isinstance(axis, tuple):
        axis = list(axis)
403 404 405 406 407
    if isinstance(axis, list) and len(axis) == 1:
        axis = axis[0]

    #calculate vector norm, where axis is int or list with only one integer
    if isinstance(axis, int):
myq406450149's avatar
myq406450149 已提交
408 409 410 411 412 413 414 415 416 417 418 419 420 421
        if isinstance(p, str):
            if p == "fro":
                return vector_norm(
                    x,
                    porder=2,
                    axis=axis,
                    keepdim=keepdim,
                    asvector=False,
                    name=name)

            else:
                raise ValueError(
                    "only valid string values are 'fro', found {}".format(p))
        elif isinstance(p, (int, float)):
422
            return vector_norm(
myq406450149's avatar
myq406450149 已提交
423 424 425 426 427 428
                x,
                axis=axis,
                porder=p,
                keepdim=keepdim,
                asvector=False,
                name=name)
429 430 431 432 433 434 435
        else:
            raise ValueError(
                "unspport p for p-order vector norm. except float, found {}".
                format(p))
    #calculate matrix norm, where axis is list with two integers
    elif isinstance(axis, list) and len(axis) == 2:
        if p == "fro":
myq406450149's avatar
myq406450149 已提交
436 437 438
            return frobenius_norm(x, dim=axis, keepdim=keepdim, name=name)
        elif p == np.inf or p == -np.inf:
            return inf_norm(x, porder=p, axis=axis, keepdim=keepdim, name=name)
myq406450149's avatar
myq406450149 已提交
439 440 441 442
        elif p == 0:
            raise ValueError(
                "just suport axis type int or list (length of list <=1) if p = 0, found {}".
                format(axis))
443
        else:
myq406450149's avatar
myq406450149 已提交
444 445
            return p_matrix_norm(
                x, porder=p, axis=axis, keepdim=keepdim, name=name)
446 447 448 449 450 451
    else:
        raise ValueError(
            "except axis type int or list (length of list <=2), found {}".
            format(axis))


452
def dist(x, y, p=2, name=None):
453
    r"""
S
swtkiwi 已提交
454

Z
Zhang Ting 已提交
455
    This OP returns the p-norm of (x - y). It is not a norm in a strict sense, only as a measure
456 457
    of distance. The shapes of x and y must be broadcastable. The definition is as follows, for
    details, please refer to the `numpy's broadcasting <https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html>`_:
Z
Zhang Ting 已提交
458

459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481
    - Each input has at least one dimension.
    - Match the two input dimensions from back to front, the dimension sizes must either be equal, one of them is 1, or one of them does not exist.

    Where, z = x - y, the shapes of x and y are broadcastable, then the shape of z can be
    obtained as follows:

    1. If the number of dimensions of x and y are not equal, prepend 1 to the dimensions of the
    tensor with fewer dimensions.

    For example, The shape of x is [8, 1, 6, 1], the shape of y is [7, 1, 5], prepend 1 to the
    dimension of y.

    x (4-D Tensor):  8 x 1 x 6 x 1

    y (4-D Tensor):  1 x 7 x 1 x 5

    2. Determine the size of each dimension of the output z: choose the maximum value from the
    two input dimensions.

    z (4-D Tensor):  8 x 7 x 6 x 5

    If the number of dimensions of the two inputs are the same, the size of the output can be
    directly determined in step 2. When p takes different values, the norm formula is as follows:
Z
Zhang Ting 已提交
482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507

    When p = 0, defining $0^0=0$, the zero-norm of z is simply the number of non-zero elements of z.

    .. math::

        ||z||_{0}=\lim_{p \\rightarrow 0}\sum_{i=1}^{m}|z_i|^{p}

    When p = inf, the inf-norm of z is the maximum element of z.

    .. math::

        ||z||_\infty=\max_i |z_i|

    When p = -inf, the negative-inf-norm of z is the minimum element of z.

    .. math::

        ||z||_{-\infty}=\min_i |z_i|

    Otherwise, the p-norm of z follows the formula,

    .. math::

        ||z||_{p}=(\sum_{i=1}^{m}|z_i|^p)^{\\frac{1}{p}}

    Args:
508 509
        x (Tensor): 1-D to 6-D Tensor, its data type is float32 or float64.
        y (Tensor): 1-D to 6-D Tensor, its data type is float32 or float64.
Z
Zhang Ting 已提交
510 511 512
        p (float, optional): The norm to be computed, its data type is float32 or float64. Default: 2.

    Returns:
513
        Tensor: Tensor that is the p-norm of (x - y).
Z
Zhang Ting 已提交
514 515 516 517 518 519 520

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

521 522 523 524
            x = paddle.to_tensor(np.array([[3, 3],[3, 3]]), "float32")
            y = paddle.to_tensor(np.array([[3, 3],[3, 1]]), "float32")
            out = paddle.dist(x, y, 0)
            print(out) # out = [1.]
Z
Zhang Ting 已提交
525

526 527
            out = paddle.dist(x, y, 2)
            print(out) # out = [2.]
Z
Zhang Ting 已提交
528

529 530
            out = paddle.dist(x, y, float("inf"))
            print(out) # out = [2.]
Z
Zhang Ting 已提交
531

532 533
            out = paddle.dist(x, y, float("-inf"))
            print(out) # out = [0.]
Z
Zhang Ting 已提交
534 535 536 537 538 539 540 541 542 543 544 545 546
    """
    check_variable_and_dtype(x, 'dtype', ['float32', 'float64'], 'dist')
    check_variable_and_dtype(y, 'dtype', ['float32', 'float64'], 'dist')
    check_type(p, 'p', (float, int), 'dist')
    helper = LayerHelper("dist", **locals())
    out = helper.create_variable_for_type_inference(x.dtype)

    inputs = {"X": [x], "Y": [y]}
    outputs = {'Out': [out]}
    attrs = {"p": float(p)}
    helper.append_op(
        type='dist', inputs=inputs, outputs={'Out': out}, attrs=attrs)
    return out
L
liuwei1031 已提交
547 548


549 550 551 552 553 554
def cond(x, p=None, name=None):
    """

    Computes the condition number of a matrix or batches of matrices with respect to a matrix norm ``p``.

    Args:
555 556
        x (Tensor): The input tensor could be tensor of shape ``(*, m, n)`` where ``*`` is zero or more batch dimensions
            for ``p`` in ``(2, -2)``, or of shape ``(*, n, n)`` where every matrix is invertible for any supported ``p``.
557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610
            And the input data type could be ``float32`` or ``float64``.
        p (float|string, optional): Order of the norm. Supported values are `fro`, `nuc`, `1`, `-1`, `2`, `-2`,
            `inf`, `-inf`. Default value is `None`, meaning that the order of the norm is `2`.
        name (str, optional): The default value is `None`. Normally there is no need for
            user to set this property. For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: computing results of condition number, its data type is the same as input Tensor ``x``.

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

            x = paddle.to_tensor([[1., 0, -1], [0, 1, 0], [1, 0, 1]])

            # compute conditional number when p is None
            out = paddle.linalg.cond(x)
            # out.numpy() [1.4142135]

            # compute conditional number when order of the norm is 'fro'
            out_fro = paddle.linalg.cond(x, p='fro')
            # out_fro.numpy() [3.1622777]

            # compute conditional number when order of the norm is 'nuc'
            out_nuc = paddle.linalg.cond(x, p='nuc')
            # out_nuc.numpy() [9.2426405]

            # compute conditional number when order of the norm is 1
            out_1 = paddle.linalg.cond(x, p=1)
            # out_1.numpy() [2.]

            # compute conditional number when order of the norm is -1
            out_minus_1 = paddle.linalg.cond(x, p=-1)
            # out_minus_1.numpy() [1.]

            # compute conditional number when order of the norm is 2
            out_2 = paddle.linalg.cond(x, p=2)
            # out_2.numpy() [1.4142135]

            # compute conditional number when order of the norm is -1
            out_minus_2 = paddle.linalg.cond(x, p=-2)
            # out_minus_2.numpy() [0.70710677]

            # compute conditional number when order of the norm is inf
            out_inf = paddle.linalg.cond(x, p=np.inf)
            # out_inf.numpy() [2.]

            # compute conditional number when order of the norm is -inf
            out_minus_inf = paddle.linalg.cond(x, p=-np.inf)
            # out_minus_inf.numpy() [1.]

            a = paddle.to_tensor(np.random.randn(2, 4, 4).astype('float32'))
611
            # a.numpy()
612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865
            # [[[ 0.14063153 -0.996288    0.7996131  -0.02571543]
            #   [-0.16303636  1.5534962  -0.49919784 -0.04402903]
            #   [-1.1341571  -0.6022629   0.5445269   0.29154757]
            #   [-0.16816919 -0.30972657  1.7521842  -0.5402487 ]]
            #  [[-0.58081484  0.12402827  0.7229862  -0.55046535]
            #   [-0.15178485 -1.1604939   0.75810957  0.30971205]
            #   [-0.9669573   1.0940945  -0.27363303 -0.35416734]
            #   [-1.216529    2.0018666  -0.7773689  -0.17556527]]]
            a_cond_fro = paddle.linalg.cond(a, p='fro')
            # a_cond_fro.numpy()  [31.572273 28.120834]

            b = paddle.to_tensor(np.random.randn(2, 3, 4).astype('float64'))
            # b.numpy()
            # [[[ 1.61707487  0.46829144  0.38130416  0.82546736]
            #   [-1.72710298  0.08866375 -0.62518804  0.16128892]
            #   [-0.02822879 -1.67764516  0.11141444  0.3220113 ]]
            #  [[ 0.22524372  0.62474921 -0.85503233 -1.03960523]
            #   [-0.76620689  0.56673047  0.85064753 -0.45158196]
            #   [ 1.47595418  2.23646462  1.5701758   0.10497519]]]
            b_cond_2 = paddle.linalg.cond(b, p=2)
            # b_cond_2.numpy()  [3.30064451 2.51976252]

    """

    def mat_norm(input, porder=1., axis=None):
        """
        NOTE:
            Calculate the matrix norm of a square matrix or batches of square matrices,
            when porder is in (1, -1, inf, -inf)
        """
        reduce_all = True if axis is None or axis == [] else False
        axis = axis if axis != None and axis != [] else [0]
        keepdim = False

        if in_dygraph_mode():
            abs_out = _C_ops.abs(input)
            sum_out = _C_ops.reduce_sum(abs_out, 'dim', axis, 'keepdim',
                                        keepdim, 'reduce_all', reduce_all)
            if porder == 1 or porder == np.inf:
                return _C_ops.reduce_max(sum_out, 'dim', [-1], 'keepdim',
                                         keepdim, 'reduce_all', reduce_all)
            if porder == -1 or porder == -np.inf:
                return _C_ops.reduce_min(sum_out, 'dim', [-1], 'keepdim',
                                         keepdim, 'reduce_all', reduce_all)

        block = LayerHelper('norm', **locals())
        abs_out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        sum_out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        block.append_op(
            type='abs', inputs={'X': input}, outputs={'Out': abs_out})
        block.append_op(
            type='reduce_sum',
            inputs={'X': abs_out},
            outputs={'Out': sum_out},
            attrs={'dim': axis,
                   'keep_dim': keepdim,
                   'reduce_all': reduce_all})
        if porder == 1 or porder == np.inf:
            block.append_op(
                type='reduce_max',
                inputs={'X': sum_out},
                outputs={'Out': out},
                attrs={
                    'dim': [-1],
                    'keep_dim': keepdim,
                    'reduce_all': reduce_all
                })
        if porder == -1 or porder == -np.inf:
            block.append_op(
                type='reduce_min',
                inputs={'X': sum_out},
                outputs={'Out': out},
                attrs={
                    'dim': [-1],
                    'keep_dim': keepdim,
                    'reduce_all': reduce_all
                })
        return out

    def fro_norm(input, porder=2, axis=[-1]):
        """
        NOTE:
            Calculate the frobenius norm of a square matrix or batches of square matrices.
        """
        reduce_all = True if axis is None or axis == [] else False
        keepdim = False

        if in_dygraph_mode():
            pow_out = _C_ops.pow(input, 'factor', porder)
            sum_out_1 = _C_ops.reduce_sum(pow_out, 'dim', axis, 'keepdim',
                                          keepdim, 'reduce_all', reduce_all)
            sum_out_2 = _C_ops.reduce_sum(sum_out_1, 'dim', axis, 'keepdim',
                                          keepdim, 'reduce_all', reduce_all)
            return _C_ops.pow(sum_out_2, 'factor', float(1. / porder))

        block = LayerHelper('norm', **locals())
        pow_out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        sum_out_1 = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        sum_out_2 = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        block.append_op(
            type='pow',
            inputs={'X': input},
            outputs={'Out': pow_out},
            attrs={'factor': porder})
        block.append_op(
            type='reduce_sum',
            inputs={'X': pow_out},
            outputs={'Out': sum_out_1},
            attrs={'dim': axis,
                   'keep_dim': keepdim,
                   'reduce_all': reduce_all})
        block.append_op(
            type='reduce_sum',
            inputs={'X': sum_out_1},
            outputs={'Out': sum_out_2},
            attrs={'dim': axis,
                   'keep_dim': keepdim,
                   'reduce_all': reduce_all})
        block.append_op(
            type='pow',
            inputs={'X': sum_out_2},
            outputs={'Out': out},
            attrs={'factor': float(1. / porder)})
        return out

    def svd_norm(input, porder, axis=[-1]):
        """
        NOTE:
            Calculate the matrix norm, which is related to singular values, of a matrix
            or batches of matrices, including nuclear norm, 2-norm and (-2)-norm.
        """
        reduce_all = True if axis is None or axis == [] else False
        keepdim = False

        u, s, vh = svd(input, full_matrices=False)

        if in_dygraph_mode():
            if porder == "nuc":
                return _C_ops.reduce_sum(s, 'dim', axis, 'keepdim', keepdim,
                                         'reduce_all', reduce_all)
            max_out = _C_ops.reduce_max(s, 'dim', axis, 'keepdim', keepdim,
                                        'reduce_all', reduce_all)
            min_out = _C_ops.reduce_min(s, 'dim', axis, 'keepdim', keepdim,
                                        'reduce_all', reduce_all)
            if porder == 2:
                return _C_ops.elementwise_div(max_out, min_out, 'aixs', axis,
                                              'use_mkldnn', False)
            if porder == -2:
                return _C_ops.elementwise_div(min_out, max_out, 'aixs', axis,
                                              'use_mkldnn', False)

        block = LayerHelper('norm', **locals())
        out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        if porder == "nuc":
            block.append_op(
                type='reduce_sum',
                inputs={'X': s},
                outputs={'Out': out},
                attrs={
                    'dim': axis,
                    'keep_dim': keepdim,
                    'reduce_all': reduce_all
                })
            return out
        max_out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        min_out = block.create_variable_for_type_inference(
            dtype=block.input_dtype())
        block.append_op(
            type='reduce_max',
            inputs={'X': s},
            outputs={'Out': max_out},
            attrs={'dim': axis,
                   'keep_dim': keepdim,
                   'reduce_all': reduce_all})
        block.append_op(
            type='reduce_min',
            inputs={'X': s},
            outputs={'Out': min_out},
            attrs={'dim': axis,
                   'keep_dim': keepdim,
                   'reduce_all': reduce_all})
        if porder == 2:
            block.append_op(
                type='elementwise_div',
                inputs={'X': max_out,
                        'Y': min_out},
                outputs={'Out': out},
                attrs={'aixs': axis,
                       'use_mkldnn': False})
            return out
        if porder == -2:
            block.append_op(
                type='elementwise_div',
                inputs={'X': min_out,
                        'Y': max_out},
                outputs={'Out': out},
                attrs={'aixs': axis,
                       'use_mkldnn': False})
            return out

    def empty_tensor(input, shape):
        if in_dygraph_mode():
            return input.reshape(shape)
        raise ValueError("only support x is nonempty tensor in static mode")

    x_shape = list(x.shape)
    if not len(x_shape) >= 2:
        raise ValueError("input should be a matrix or batches of matrices, " +
                         "but the dimention of received input is {}".format(
                             len(x_shape)))
    if p == None:
        p = 2
    x_size = 0 if (0 in x_shape) else 1
    if p in ("fro", "nuc", 1, -1, np.inf, -np.inf):
        if x_shape[len(x_shape) - 1] == x_shape[len(x_shape) - 2]:
            if x_size == 0:
                return empty_tensor(x, x_shape[:-2])
            x_inv = x.inverse()
            if p == "fro":
                return fro_norm(x) * fro_norm(x_inv)
            if p == "nuc":
                return svd_norm(x, p) * svd_norm(x_inv, p)
            if p in (1, -1):
                return mat_norm(
                    x, porder=p, axis=[-2]) * mat_norm(
                        x_inv, porder=p, axis=[-2])
            if p in (np.inf, -np.inf):
                return mat_norm(
                    x, porder=p, axis=[-1]) * mat_norm(
                        x_inv, porder=p, axis=[-1])
        else:
            raise ValueError("only support p is {} when input is a ".format(p) +
                             "square matrix or batches of square matrices")
    elif p in (2, -2):
        if x_size == 0:
            return empty_tensor(x, x_shape[:-2])
        return svd_norm(x, porder=p)
    else:
        raise ValueError(
            "unsupported {} for p, only supporting ('fro', 'nuc', ".format(
                p) + "1, -1, 2, -2, inf, -inf) or none")


L
liuwei1031 已提交
866 867 868
def dot(x, y, name=None):
    """
    This operator calculates inner product for vectors.
869

L
liuwei1031 已提交
870
    .. note::
871 872
       Support 1-d and 2-d Tensor. When it is 2d, the first dimension of this matrix
       is the batch dimension, which means that the vectors of multiple batches are dotted.
L
liuwei1031 已提交
873 874

    Parameters:
S
ShenLiang 已提交
875 876
        x(Tensor): 1-D or 2-D ``Tensor``. Its dtype should be ``float32``, ``float64``, ``int32``, ``int64``
        y(Tensor): 1-D or 2-D ``Tensor``. Its dtype soulde be ``float32``, ``float64``, ``int32``, ``int64``
L
liuwei1031 已提交
877 878
        name(str, optional): Name of the output. Default is None. It's used to print debug info for developers. Details: :ref:`api_guide_Name`

879
    Returns:
880
        Tensor: the calculated result Tensor.
881

L
liuwei1031 已提交
882 883 884 885 886 887
    Examples:

    .. code-block:: python

        import paddle
        import numpy as np
888 889 890

        x_data = np.random.uniform(0.1, 1, [10]).astype(np.float32)
        y_data = np.random.uniform(1, 3, [10]).astype(np.float32)
S
ShenLiang 已提交
891 892
        x = paddle.to_tensor(x_data)
        y = paddle.to_tensor(y_data)
893
        z = paddle.dot(x, y)
894
        print(z)
L
liuwei1031 已提交
895 896 897

    """
    op_type = 'dot'
898 899
    # skip var type check in dygraph mode to improve efficiency
    if in_dygraph_mode():
W
wanghuancoder 已提交
900
        op = getattr(_C_ops, op_type)
901 902
        return op(x, y)

L
liuwei1031 已提交
903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920
    assert x is not None, 'x cannot be None in {}'.format(op_type)
    assert y is not None, 'y cannot be None in {}'.format(op_type)

    check_variable_and_dtype(x, 'x', ['float32', 'float64', 'int32', 'int64'],
                             op_type)
    check_variable_and_dtype(y, 'y', ['float32', 'float64', 'int32', 'int64'],
                             op_type)

    helper = LayerHelper(op_type, **locals())
    if name is None:
        out = helper.create_variable_for_type_inference(dtype=x.dtype)
    else:
        out = helper.create_variable(
            name=name, dtype=x.dtype, persistable=False)
    helper.append_op(
        type="dot", inputs={'X': x,
                            'Y': y}, attrs={}, outputs={"Out": out})
    return out
921 922 923 924


def t(input, name=None):
    """
925 926
    Transpose <=2-D tensor.
    0-D and 1-D tensors are returned as it is and 2-D tensor is equal to
927
    the paddle.transpose function which perm dimensions set 0 and 1.
928

929
    Args:
930
        input (Tensor): The input Tensor. It is a N-D (N<=2) Tensor of data types float16, float32, float64, int32.
931
        name(str, optional): The default value is None.  Normally there is no need for
932 933
            user to set this property.  For more information, please refer to :ref:`api_guide_Name`
    Returns:
934
        Tensor: A transposed n-D Tensor, with data type being float16, float32, float64, int32, int64.
935

936
    For Example:
937

938
        .. code-block:: text
939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954

             # Example 1 (0-D tensor)
             x = tensor([0.79])
             paddle.t(x) = tensor([0.79])

             # Example 2 (1-D tensor)
             x = tensor([0.79, 0.84, 0.32])
             paddle.t(x) = tensor([0.79, 0.84, 0.32])

             # Example 3 (2-D tensor)
             x = tensor([0.79, 0.84, 0.32],
                        [0.64, 0.14, 0.57])
             paddle.t(x) = tensor([0.79, 0.64],
                                  [0.84, 0.14],
                                  [0.32, 0.57])

955
     Examples:
956

957
        .. code-block:: python
958

959
            import paddle
960
            x = paddle.ones(shape=[2, 3], dtype='int32')
961
            x_transposed = paddle.t(x)
962 963
            print(x_transposed.shape)
            # [3, 2]
964 965 966 967 968 969 970 971 972 973 974
    """
    if len(input.shape) > 2:
        raise ValueError(
            "Input(input) only support N-D (N<=2) tensor, but received "
            "length of Input(input) is %s. Perhaps you can use paddle."
            "tensor.transpose() instead." % len(input.shape))
    if in_dygraph_mode():
        if len(input.shape) == 1:
            return input
        # 2-D tensor
        perm = [1, 0]
W
wanghuancoder 已提交
975
        out, _ = _C_ops.transpose2(input, 'axis', perm)
976 977 978
        return out

    check_variable_and_dtype(
979 980
        input, 'input', ['float16', 'float32', 'float64', 'int32',
                         'int64'], 'transpose')
981 982 983 984 985 986 987 988 989 990 991 992 993 994

    helper = LayerHelper('t', **locals())
    out = helper.create_variable_for_type_inference(input.dtype)
    input_shape = helper.create_variable_for_type_inference(input.dtype)
    if len(input.shape) == 1:
        out = input
    else:
        helper.append_op(
            type='transpose2',
            inputs={'X': [input]},
            outputs={'Out': [out],
                     'XShape': [input_shape]},
            attrs={'axis': [1, 0]})
    return out
995 996


997
def cross(x, y, axis=None, name=None):
998
    """
999
    Computes the cross product between two tensors along an axis.
1000

1001 1002
    Inputs must have the same shape, and the length of their axes should be equal to 3.
    If `axis` is not given, it defaults to the first axis found with the length 3.
1003

1004
    Args:
1005 1006
        x (Tensor): The first input tensor.
        y (Tensor): The second input tensor.
1007
        axis (int, optional): The axis along which to compute the cross product. It defaults to the first axis found with the length 3.
1008
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
1009 1010

    Returns:
1011
        Tensor. A Tensor with same data type as `x`.
1012

1013 1014
    Examples:
        .. code-block:: python
1015

1016
            import paddle
1017

Z
Zhou Wei 已提交
1018 1019 1020 1021 1022 1023
            x = paddle.to_tensor([[1.0, 1.0, 1.0],
                                  [2.0, 2.0, 2.0],
                                  [3.0, 3.0, 3.0]])
            y = paddle.to_tensor([[1.0, 1.0, 1.0],
                                  [1.0, 1.0, 1.0],
                                  [1.0, 1.0, 1.0]])
1024

1025 1026 1027 1028 1029 1030 1031 1032 1033
            z1 = paddle.cross(x, y)
            # [[-1. -1. -1.]
            #  [ 2.  2.  2.]
            #  [-1. -1. -1.]]

            z2 = paddle.cross(x, y, axis=1)
            # [[0. 0. 0.]
            #  [0. 0. 0.]
            #  [0. 0. 0.]]
1034 1035
    """
    if in_dygraph_mode():
1036
        if axis is not None:
W
wanghuancoder 已提交
1037
            return _C_ops.cross(x, y, 'dim', axis)
1038
        else:
W
wanghuancoder 已提交
1039
            return _C_ops.cross(x, y)
1040

1041 1042
    helper = LayerHelper("cross", **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
1043
    attrs = dict()
1044
    attrs['dim'] = axis
1045 1046 1047

    helper.append_op(
        type='cross',
1048 1049
        inputs={'X': x,
                'Y': y},
1050 1051 1052
        outputs={'Out': out},
        attrs=attrs)
    return out
1053 1054


1055
def cholesky(x, upper=False, name=None):
1056
    r"""
G
Guo Sheng 已提交
1057
    Computes the Cholesky decomposition of one symmetric positive-definite
1058 1059
    matrix or batches of symmetric positive-definite matrice.

G
Guo Sheng 已提交
1060 1061 1062 1063 1064 1065
    If `upper` is `True`, the decomposition has the form :math:`A = U^{T}U` ,
    and the returned matrix :math:`U` is upper-triangular. Otherwise, the
    decomposition has the form  :math:`A = LL^{T}` , and the returned matrix
    :math:`L` is lower-triangular.

    Args:
1066
        x (Tensor): The input tensor. Its shape should be `[*, M, M]`,
G
Guo Sheng 已提交
1067 1068 1069 1070 1071 1072 1073
            where * is zero or more batch dimensions, and matrices on the
            inner-most 2 dimensions all should be symmetric positive-definite.
            Its data type should be float32 or float64.
        upper (bool): The flag indicating whether to return upper or lower
            triangular matrices. Default: False.

    Returns:
1074
        Tensor: A Tensor with same shape and data type as `x`. It represents \
G
Guo Sheng 已提交
1075
            triangular matrices generated by Cholesky decomposition.
1076

G
Guo Sheng 已提交
1077 1078 1079 1080 1081 1082
    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

1083 1084 1085
            a = np.random.rand(3, 3)
            a_t = np.transpose(a, [1, 0])
            x_data = np.matmul(a, a_t) + 1e-03
1086
            x = paddle.to_tensor(x_data)
1087
            out = paddle.cholesky(x, upper=False)
1088
            print(out)
1089 1090 1091
            # [[1.190523   0.         0.        ]
            #  [0.9906703  0.27676893 0.        ]
            #  [1.25450498 0.05600871 0.06400121]]
G
Guo Sheng 已提交
1092 1093

    """
1094
    if in_dygraph_mode():
W
wanghuancoder 已提交
1095
        return _C_ops.cholesky(x, "upper", upper)
G
Guo Sheng 已提交
1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107
    check_variable_and_dtype(x, 'dtype', ['float32', 'float64'], 'cholesky')
    check_type(upper, 'upper', bool, 'cholesky')
    helper = LayerHelper('cholesky', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
        type='cholesky',
        inputs={'X': [x]},
        outputs={'Out': out},
        attrs={'upper': upper})
    return out


1108 1109 1110 1111
def matrix_rank(x, tol=None, hermitian=False, name=None):
    r"""
    Computes the rank of a matrix.

1112
    The rank of a matrix is the number of singular values that are greater than the specified `tol` threshold when hermitian=False,
1113
    or the number of eigenvalues in absolute value that are greater than the specified `tol` threshold when hermitian=True.
1114 1115

    Args:
1116 1117 1118 1119
        x (Tensor): The input tensor. Its shape should be `[..., m, n]`, where `...` is zero or more batch dimensions. If `x` is a batch
            of matrices then the output has the same batch dimensions. The data type of `x` should be float32 or float64.
        tol (float,Tensor,optional): the tolerance value. Default: None. If `tol` is not specified, and `sigma` is the largest
            singular value (or eigenvalues in absolute value), and `eps` is the epsilon value for the dtype of `x`, then `tol` is computed
1120
            with formula `tol=sigma * max(m,n) * eps`. Note that if `x` is a batch of matrices, `tol` is computed this way for every batch.
1121 1122
        hermitian (bool,optional): indicates whether `x` is Hermitian. Default: False. When hermitian=True, `x` is assumed to be Hermitian,
            enabling a more efficient method for finding eigenvalues, but `x` is not checked inside the function. Instead, We just use
1123
            the lower triangular of the matrix to compute.
1124 1125 1126 1127
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: Rank of tensor x.
1128

1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144
    Examples:
        .. code-block:: python

            import paddle

            a = paddle.eye(10)
            b = paddle.linalg.matrix_rank(a)
            print(b)
            # b = [10]

            c = paddle.ones(shape=[3, 4, 5, 5])
            d = paddle.linalg.matrix_rank(c, tol=0.01, hermitian=True)
            print(d)
            # d = [[1, 1, 1, 1],
            #      [1, 1, 1, 1],
            #      [1, 1, 1, 1]]
1145

1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193
    """

    if in_dygraph_mode():
        if tol is None:
            tol_tensor = None
            tol_attr = 0.0
            use_default_tol = True
        elif isinstance(tol, Variable):
            if tol.dtype != x.dtype:
                tol_tensor = cast(tol, x.dtype)
            else:
                tol_tensor = tol
            tol_attr = 0.0
            use_default_tol = False
        else:
            tol_tensor = None
            tol_attr = float(tol)
            use_default_tol = False
        return _C_ops.matrix_rank(x, tol_tensor, "tol", tol_attr, 'hermitian',
                                  hermitian, 'use_default_tol', use_default_tol)

    inputs = {}
    attrs = {}
    check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'matrix_rank')
    inputs['X'] = x
    if tol is None:
        attrs['use_default_tol'] = True
    elif isinstance(tol, Variable):
        check_variable_and_dtype(tol, 'tol', ['float32'], 'matrix_rank')
        attrs['use_default_tol'] = False
        if tol.dtype != x.dtype:
            inputs['TolTensor'] = cast(tol, x.dtype)
        else:
            inputs['TolTensor'] = tol
    else:
        check_type(tol, 'tol', float, 'matrix_rank')
        attrs['use_default_tol'] = False
        attrs['tol'] = tol
    check_type(hermitian, 'hermitian', bool, 'matrix_rank')
    attrs['hermitian'] = hermitian

    helper = LayerHelper('matrix_rank', **locals())
    out = helper.create_variable_for_type_inference(dtype='int32')
    helper.append_op(
        type='matrix_rank', inputs=inputs, outputs={'Out': out}, attrs=attrs)
    return out


1194 1195 1196 1197 1198 1199 1200 1201 1202
def bmm(x, y, name=None):
    """
    Applies batched matrix multiplication to two tensors.

    Both of the two input tensors must be three-dementional and share the same batch size.

    if x is a (b, m, k) tensor, y is a (b, k, n) tensor, the output will be a (b, m, n) tensor.

    Args:
Y
yaoxuefeng 已提交
1203 1204
        x (Tensor): The input Tensor.
        y (Tensor): The input Tensor.
1205 1206 1207 1208
        name(str|None): A name for this layer(optional). If set None, the layer
            will be named automatically.

    Returns:
Y
yaoxuefeng 已提交
1209
        Tensor: The product Tensor.
1210 1211

    Examples:
S
sunzhongkai588 已提交
1212 1213 1214
        .. code-block:: python

            import paddle
Y
yaoxuefeng 已提交
1215

S
sunzhongkai588 已提交
1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228
            # In imperative mode:
            # size x: (2, 2, 3) and y: (2, 3, 2)
            x = paddle.to_tensor([[[1.0, 1.0, 1.0],
                                [2.0, 2.0, 2.0]],
                                [[3.0, 3.0, 3.0],
                                [4.0, 4.0, 4.0]]])
            y = paddle.to_tensor([[[1.0, 1.0],[2.0, 2.0],[3.0, 3.0]],
                                [[4.0, 4.0],[5.0, 5.0],[6.0, 6.0]]])
            out = paddle.bmm(x, y)
            #output size: (2, 2, 2)
            #output value:
            #[[[6.0, 6.0],[12.0, 12.0]],[[45.0, 45.0],[60.0, 60.0]]]
            out_np = out.numpy()
1229

1230
    """
Y
yaoxuefeng 已提交
1231 1232 1233 1234 1235 1236 1237 1238 1239 1240
    x_shape = x.shape
    y_shape = y.shape
    if not len(x_shape) == len(y_shape) == 3:
        raise ValueError(
            "x and y should be 3-dimensional. But received x's dimention: {}, y's dimention: {}".
            format(x_shape, y_shape))
    if x_shape[2] != y_shape[1]:
        raise ValueError(
            "x's width must be equal with y's height. But received x's shape: {}, y's shape: {}".
            format(x_shape, y_shape))
1241 1242 1243 1244
    if x_shape[0] != y_shape[0]:
        raise ValueError(
            "x's batch (shape[0]) must be equal with y's batch (shape[0]). But received x's shape: {}, y's shape: {}".
            format(x_shape, y_shape))
1245

1246
    if in_dygraph_mode():
W
wanghuancoder 已提交
1247
        return _C_ops.bmm(x, y)
1248 1249

    helper = LayerHelper('bmm', **locals())
1250 1251 1252
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(type='bmm', inputs={'X': x, 'Y': y}, outputs={'Out': out})
    return out
Q
Qi Li 已提交
1253 1254


1255
def histogram(input, bins=100, min=0, max=0, name=None):
Q
Qi Li 已提交
1256
    """
1257
    Computes the histogram of a tensor. The elements are sorted into equal width bins between min and max.
Q
Qi Li 已提交
1258 1259 1260
    If min and max are both zero, the minimum and maximum values of the data are used.

    Args:
1261
        input (Tensor): A Tensor(or LoDTensor) with shape :math:`[N_1, N_2,..., N_k]` . The data type of the input Tensor
Q
Qi Li 已提交
1262 1263 1264 1265 1266 1267
            should be float32, float64, int32, int64.
        bins (int): number of histogram bins
        min (int): lower end of the range (inclusive)
        max (int): upper end of the range (inclusive)

    Returns:
1268
        Tensor: data type is int64, shape is (nbins,).
Q
Qi Li 已提交
1269

1270
    Examples:
Q
Qi Li 已提交
1271
        .. code-block:: python
1272

Q
Qi Li 已提交
1273
            import paddle
1274

1275
            inputs = paddle.to_tensor([1, 2, 1])
1276 1277
            result = paddle.histogram(inputs, bins=4, min=0, max=3)
            print(result) # [0, 2, 1, 0]
Q
Qi Li 已提交
1278 1279
    """
    if in_dygraph_mode():
W
wanghuancoder 已提交
1280
        return _C_ops.histogram(input, "bins", bins, "min", min, "max", max)
Q
Qi Li 已提交
1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293

    helper = LayerHelper('histogram', **locals())
    check_variable_and_dtype(
        input, 'X', ['int32', 'int64', 'float32', 'float64'], 'histogram')
    out = helper.create_variable_for_type_inference(VarDesc.VarType.INT64)
    helper.append_op(
        type='histogram',
        inputs={'X': input},
        outputs={'Out': out},
        attrs={'bins': bins,
               'min': min,
               'max': max})
    return out
S
smallv0221 已提交
1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346


def bincount(x, weights=None, minlength=0, name=None):
    """
    Computes frequency of each value in the input tensor. 

    Args:
        x (Tensor): A Tensor with non-negative integer. Should be 1-D tensor.
        weights (Tensor, optional): Weight for each value in the input tensor. Should have the same shape as input. Default is None.
        minlength (int, optional): Minimum number of bins. Should be non-negative integer. Default is 0.
        name(str, optional): The default value is None.  Normally there is no need for user to set this
            property.  For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: The tensor of frequency.

    Examples:
        .. code-block:: python

            import paddle

            x = paddle.to_tensor([1, 2, 1, 4, 5])
            result1 = paddle.bincount(x)
            print(result1) # [0, 2, 1, 0, 1, 1]

            w = paddle.to_tensor([2.1, 0.4, 0.1, 0.5, 0.5])
            result2 = paddle.bincount(x, weights=w)
            print(result2) # [0., 2.19999981, 0.40000001, 0., 0.50000000, 0.50000000]
    """
    if x.dtype not in [paddle.int32, paddle.int64]:
        raise TypeError("Elements in Input(x) should all be integers")

    if in_dygraph_mode():
        return _C_ops.bincount(x, weights, "minlength", minlength)

    helper = LayerHelper('bincount', **locals())

    check_variable_and_dtype(x, 'X', ['int32', 'int64'], 'bincount')

    if weights is not None:
        check_variable_and_dtype(weights, 'Weights',
                                 ['int32', 'int64', 'float32', 'float64'],
                                 'bincount')
        out = helper.create_variable_for_type_inference(dtype=weights.dtype)
    else:
        out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
        type='bincount',
        inputs={'X': x,
                'Weights': weights},
        outputs={'Out': out},
        attrs={'minlength': minlength})
    return out
1347 1348 1349 1350 1351 1352 1353


def mv(x, vec, name=None):
    """
    Performs a matrix-vector product of the matrix x and the vector vec.

    Args:
F
furnace 已提交
1354
        x (Tensor): A tensor with shape :math:`[M, N]` , The data type of the input Tensor x
1355
            should be one of float32, float64.
F
furnace 已提交
1356
        vec (Tensor): A tensor with shape :math:`[N]` , The data type of the input Tensor x
1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379
            should be one of float32, float64.
        name(str, optional): The default value is None.  Normally there is no need for user to set this
            property.  For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: The tensor which is producted by x and vec.

    Examples:
        .. code-block:: python

            # x: [M, N], vec: [N]
            # paddle.mv(x, vec)  # out: [M]

            import numpy as np
            import paddle

            x_data = np.array([[2, 1, 3], [3, 0, 1]]).astype("float64")
            x = paddle.to_tensor(x_data)
            vec_data = np.array([3, 5, 1])
            vec = paddle.to_tensor(vec_data).astype("float64")
            out = paddle.mv(x, vec)
    """
    if in_dygraph_mode():
W
wanghuancoder 已提交
1380
        out = _C_ops.mv(x, vec)
1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405
        return out

    def __check_input(x, vec):
        var_names = {'x': x, 'vec': vec}
        for name, val in var_names.items():
            check_variable_and_dtype(val, name, ['float32', 'float64'], 'mv')
        x_shape = list(x.shape)
        vec_shape = list(vec.shape)
        if len(x_shape) != 2:
            raise ValueError(
                "x should be 2-dimensional. But received x's dimention: {}".
                format(x_shape))
        if len(vec_shape) != 1:
            raise ValueError(
                "vec should be 1-dimensional. But received vec's dimention: {}".
                format(vec_shape))

    __check_input(x, vec)

    helper = LayerHelper('mv', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
        type='mv', inputs={'X': x,
                           'Vec': vec}, outputs={'Out': out})
    return out
1406 1407


1408
def det(x, name=None):
H
huangxu96 已提交
1409 1410 1411 1412 1413 1414 1415 1416
    """
    Calculates determinant value of a square matrix or batches of square matrices.
    Args:
        x (Tensor): input (Tensor): the input matrix of size `(n, n)` or the batch of matrices of size
                    `(*, n, n)` where `*` is one or more batch dimensions.
    Returns:
        y (Tensor):the determinant value of a square matrix or batches of square matrices.

1417
    Examples:
H
huangxu96 已提交
1418 1419 1420 1421 1422 1423
        .. code-block:: python

        import paddle

        x =  paddle.randn([3,3,3])

1424
        A = paddle.linalg.det(x)
H
huangxu96 已提交
1425 1426

        print(A)
1427

H
huangxu96 已提交
1428 1429
        # [ 0.02547996,  2.52317095, -6.15900707])

1430

H
huangxu96 已提交
1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455
    """
    if in_dygraph_mode():
        return core.ops.determinant(x)

    check_dtype(x.dtype, 'Input', ['float32', 'float64'], 'det')

    input_shape = list(x.shape)
    assert len(input_shape) >= 2,                     \
            "The x must be at least 2-dimensional, "   \
            "but received Input x's dimensional: %s.\n" %  \
            len(input_shape)

    assert (input_shape[-1] == input_shape[-2]),    \
            "Expect squared input," \
            "but received %s by %s matrix.\n" \
            %(input_shape[-2], input_shape[-1]) \

    helper = LayerHelper('determinant', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)

    helper.append_op(
        type='determinant', inputs={'Input': [x]}, outputs={'Out': [out]})
    return out


1456
def slogdet(x, name=None):
H
huangxu96 已提交
1457 1458 1459
    """
    Calculates the sign and natural logarithm of the absolute value of a square matrix's or batches square matrices' determinant.
    The determinant can be computed with ``sign * exp(logabsdet)
1460

H
huangxu96 已提交
1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471
    Supports input of float, double

    Note that for matrices that have zero determinant, this returns ``(0, -inf)``
    Args:
        x (Tensor): the batch of matrices of size :math:`(*, n, n)`
            where math:`*` is one or more batch dimensions.

    Returns:
        y (Tensor): A tensor containing the sign of the determinant and the natural logarithm
        of the absolute value of determinant, respectively.

1472
    Examples:
H
huangxu96 已提交
1473 1474 1475 1476 1477 1478
    .. code-block:: python

        import paddle

        x =  paddle.randn([3,3,3])

1479
        A = paddle.linalg.slogdet(x)
H
huangxu96 已提交
1480 1481

        print(A)
1482

H
huangxu96 已提交
1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510
        # [[ 1.        ,  1.        , -1.        ],
        # [-0.98610914, -0.43010661, -0.10872950]])

    """
    if in_dygraph_mode():
        return core.ops.slogdeterminant(x)

    check_dtype(x.dtype, 'Input', ['float32', 'float64'], 'slogdet')

    input_shape = list(x.shape)
    assert len(input_shape) >= 2,                     \
            "The x must be at least 2-dimensional, "   \
            "but received Input x's dimensional: %s.\n" %  \
            len(input_shape)

    assert (input_shape[-1] == input_shape[-2]),    \
            "Expect squared input," \
            "but received %s by %s matrix.\n" \
            %(input_shape[-2], input_shape[-1]) \

    helper = LayerHelper('slogdeterminant', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)

    helper.append_op(
        type='slogdeterminant', inputs={'Input': [x]}, outputs={'Out': [out]})
    return out


1511 1512
def svd(x, full_matrices=False, name=None):
    r"""
1513 1514 1515 1516 1517
    Computes the singular value decomposition of one matrix or a batch of regular matrices.

    Let :math:`X` be the input matrix or a batch of input matrices, the output should satisfies:

    .. math::
1518 1519
        X = U * diag(S) * VT

1520 1521
    Args:
        x (Tensor): The input tensor. Its shape should be `[..., N, M]`,
1522
            where `...` is zero or more batch dimensions. N and M can be arbitraty
1523 1524 1525 1526
            positive number. Note that if x is sigular matrices, the grad is numerical
            instable. The data type of x should be float32 or float64.
        full_matrices (bool): A flag to control the behavor of svd.
            If full_matrices = True, svd op will compute full U and V matrics,
1527
            which means shape of U is `[..., N, N]`, shape of V is `[..., M, M]`. K = min(M, N).
1528
            If full_matrices = False, svd op will use a economic method to store U and V.
1529
            which means shape of U is `[..., N, K]`, shape of V is `[..., M, K]`. K = min(M, N).
1530
        name (str, optional): Name for the operation (optional, default is None).
1531
            For more information, please refer to :ref:`api_guide_Name`.
1532 1533

    Returns:
1534
        Tuple of 3 tensors: (U, S, VH). VH is the conjugate transpose of V. S is the singlar value vectors of matrics with shape `[..., K]`
1535

1536 1537 1538 1539
    Examples:
        .. code-block:: python

            import paddle
1540 1541 1542

            x = paddle.to_tensor([[1.0, 2.0], [1.0, 3.0], [4.0, 6.0]]).astype('float64')
            x = x.reshape([3, 2])
1543
            u, s, vh = paddle.linalg.svd(x)
1544 1545 1546 1547 1548
            print (u)
            #U = [[ 0.27364809, -0.21695147  ],
            #      [ 0.37892198, -0.87112408 ],
            #      [ 0.8840446 ,  0.44053933 ]]

1549
            print (s)
1550
            #S = [8.14753743, 0.78589688]
1551
            print (vh)
1552 1553
            #VT= [[ 0.51411221,  0.85772294],
            #     [ 0.85772294, -0.51411221]]
1554

1555
            # one can verify : U * S * VT == X
1556
            #                  U * UH == I
1557
            #                  V * VH == I
1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579
    """

    if in_dygraph_mode():
        return _C_ops.svd(x, 'full_matrices', full_matrices)
    check_variable_and_dtype(x, 'dtype', ['float32', 'float64'], 'svd')
    check_type(full_matrices, 'full_matrices', bool, 'svd')
    helper = LayerHelper('svd', **locals())
    u = helper.create_variable_for_type_inference(dtype=x.dtype)
    vh = helper.create_variable_for_type_inference(dtype=x.dtype)
    s = helper.create_variable_for_type_inference(dtype=x.dtype)
    attrs = dict()
    attrs['full_matrices'] = full_matrices
    helper.append_op(
        type='svd',
        inputs={'X': [x]},
        outputs={'U': u,
                 'VH': vh,
                 'S': s},
        attr=attrs, )
    return u, s, vh


1580 1581 1582
def matrix_power(x, n, name=None):
    r"""
    Computes the n-th power of a square matrix or a batch of square matrices.
1583

1584 1585 1586 1587 1588
    Let :math:`X` be a sqaure matrix or a batch of square matrices, :math:`n` be
    an exponent, the equation should be:

    .. math::
        Out = X ^ {n}
1589

1590 1591 1592 1593
    Specifically,

    - If `n > 0`, it returns the matrix or a batch of matrices raised to the power
    of `n`.
1594

1595 1596 1597 1598 1599 1600 1601 1602 1603 1604
    - If `n = 0`, it returns the identity matrix or a batch of identity matrices.

    - If `n < 0`, it returns the inverse of each matrix (if invertible) raised to
    the power of `abs(n)`.

    Args:
        x (Tensor): A square matrix or a batch of square matrices to be raised
            to power `n`. Its shape should be `[*, M, M]`, where `*` is zero or
            more batch dimensions. Its data type should be float32 or float64.
        n (int): The exponent. It can be any positive, negative integer or zero.
1605
        name (str, optional): Name for the operation (optional, default is None).
1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: The n-th power of the matrix (or the batch of matrices) `x`. Its
            data type should be the same as that of `x`.

    Examples:
        .. code-block:: python

            import paddle

            x = paddle.to_tensor([[1, 2, 3],
                                  [1, 4, 9],
                                  [1, 8, 27]], dtype='float64')
1620
            print(paddle.linalg.matrix_power(x, 2))
1621 1622 1623 1624
            # [[6.  , 34. , 102.],
            #  [14. , 90. , 282.],
            #  [36. , 250., 804.]]

1625
            print(paddle.linalg.matrix_power(x, 0))
1626 1627 1628 1629
            # [[1., 0., 0.],
            #  [0., 1., 0.],
            #  [0., 0., 1.]]

1630
            print(paddle.linalg.matrix_power(x, -2))
1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647
            # [[ 12.91666667, -12.75000000,  2.83333333 ],
            #  [-7.66666667 ,  8.         , -1.83333333 ],
            #  [ 1.80555556 , -1.91666667 ,  0.44444444 ]]
    """
    if in_dygraph_mode():
        return core.ops.matrix_power(x, "n", n)

    check_variable_and_dtype(x, 'dtype', ['float32', 'float64'], 'matrix_power')
    check_type(n, 'n', int, 'matrix_power')
    helper = LayerHelper('matrix_power', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
        type='matrix_power',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'n': n})
    return out
1648 1649


1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713
def qr(x, mode="reduced", name=None):
    r"""
    Computes the QR decomposition of one matrix or batches of matrice (backward is unsupported now).

    Args:
        x (Tensor): The input tensor. Its shape should be `[..., M, N]`,
            where ... is zero or more batch dimensions. M and N can be arbitrary
            positive number. The data type of x should be float32 or float64. 
        mode (str, optional): A flag to control the behavior of qr, the default is "reduced". 
            Suppose x's shape is `[..., M, N]` and denoting `K = min(M, N)`:
            If mode = "reduced", qr op will return reduced Q and R matrices, 
            which means Q's shape is `[..., M, K]` and R's shape is `[..., K, N]`.
            If mode = "complete", qr op will return complete Q and R matrices, 
            which means Q's shape is `[..., M, M]` and R's shape is `[..., M, N]`.
            If mode = "r", qr op will only return reduced R matrix, which means
            R's shape is `[..., K, N]`.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.
            
    Returns:
        If mode = "reduced" or mode = "complete", qr will return a two tensor-tuple, which represents Q and R. 
        If mode = "r", qr will return a tensor which represents R.
        
    Examples:            
        .. code-block:: python

            import paddle 

            x = paddle.to_tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]).astype('float64')
            q, r = paddle.linalg.qr(x)
            print (q)
            print (r)

            # Q = [[-0.16903085,  0.89708523],
            #      [-0.50709255,  0.27602622],
            #      [-0.84515425, -0.34503278]])

            # R = [[-5.91607978, -7.43735744],
            #      [ 0.        ,  0.82807867]])
            
            # one can verify : X = Q * R ;     
    """
    if in_dygraph_mode():
        q, r = _C_ops.qr(x, 'mode', mode)
        if mode == "r":
            return r
        else:
            return q, r
    check_variable_and_dtype(x, 'dtype', ['float32', 'float64'], 'qr')
    check_type(mode, 'mode', str, 'qr')
    helper = LayerHelper('qr', **locals())
    q = helper.create_variable_for_type_inference(dtype=x.dtype)
    r = helper.create_variable_for_type_inference(dtype=x.dtype)
    attrs = dict()
    attrs['mode'] = mode
    helper.append_op(
        type='qr', inputs={'X': [x]}, outputs={'Q': q,
                                               'R': r}, attrs=attrs)
    if mode == "r":
        return r
    else:
        return q, r


L
Lijunhui 已提交
1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779
def eig(x, name=None):
    """
    This API performs the eigenvalue decomposition of a square matrix or a batch of square matrices.

    .. note::
        If the matrix is a Hermitian or a real symmetric matrix, please use :ref:`paddle.linalg.eigh` instead, which is much faster.
        If only eigenvalues is needed, please use :ref:`paddle.linalg.eigvals` instead.
        If the matrix is of any shape, please use :ref:`paddle.linalg.svd`.
        This API is only supported on CPU device.
        The output datatype is always complex for both real and complex input.

    Args:
        x (Tensor): A tensor with shape math:`[*, N, N]`, The data type of the x should be one of ``float32``,
            ``float64``, ``compplex64`` or ``complex128``.
        name (str, optional): The default value is `None`. Normally there is no need for user to set 
            this property. For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Eigenvalues(Tensors): A tensor with shape math:`[*, N]` refers to the eigen values.
        Eigenvectors(Tensors): A tensor with shape math:`[*, N, N]` refers to the eigen vectors.

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

            paddle.device.set_device("cpu")

            x_data = np.array([[1.6707249, 7.2249975, 6.5045543],
                               [9.956216,  8.749598,  6.066444 ],
                               [4.4251957, 1.7983172, 0.370647 ]]).astype("float32")
            x = paddle.to_tensor(x_data)
            w, v = paddle.linalg.eig(x)
            print(w)
            # Tensor(shape=[3, 3], dtype=complex128, place=CPUPlace, stop_gradient=False,
            #       [[(-0.5061363550800655+0j) , (-0.7971760990842826+0j) ,
            #         (0.18518077798279986+0j)],
            #        [(-0.8308237755993192+0j) ,  (0.3463813401919749+0j) ,
            #         (-0.6837005269141947+0j) ],
            #        [(-0.23142567697893396+0j),  (0.4944999840400175+0j) ,
            #         (0.7058765252952796+0j) ]])

            print(v)
            # Tensor(shape=[3], dtype=complex128, place=CPUPlace, stop_gradient=False,
            #       [ (16.50471283351188+0j)  , (-5.5034820550763515+0j) ,
            #         (-0.21026087843552282+0j)])
    """
    if in_dygraph_mode():
        w, v = _C_ops.eig(x)
        return w, v

    check_variable_and_dtype(
        x, 'X', ['float32', 'float64', 'complex64', 'complex128'], 'eig')
    helper = LayerHelper('eig', **locals())

    w = helper.create_variable_for_type_inference(x.dtype)
    v = helper.create_variable_for_type_inference(x.dtype)

    inputs = {'X': x}
    outputs = {'Eigenvalues': w, 'Eigenvectors': v}
    helper.append_op(type='eig', inputs=inputs, outputs=outputs)

    return w, v


1780 1781 1782
def eigvals(x, name=None):
    """
    Compute the eigenvalues of one or more general matrices.
1783 1784 1785

    Warning:
        The gradient kernel of this operator does not yet developed.
1786 1787 1788 1789
        If you need back propagation through this operator, please replace it with paddle.linalg.eig.

    Args:
        x (Tensor): A square matrix or a batch of square matrices whose eigenvalues will be computed.
1790
            Its shape should be `[*, M, M]`, where `*` is zero or more batch dimensions.
1791
            Its data type should be float32, float64, complex64, or complex128.
1792
        name (str, optional): Name for the operation (optional, default is None).
1793
            For more information, please refer to :ref:`api_guide_Name`.
1794
            
1795
    Returns:
1796
        Tensor: A tensor containing the unsorted eigenvalues which has the same batch dimensions with `x`.
1797 1798 1799 1800 1801 1802
            The eigenvalues are complex-valued even when `x` is real.

    Examples:
        .. code-block:: python

            import paddle
1803

1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816
            paddle.set_device("cpu")
            paddle.seed(1234)

            x = paddle.rand(shape=[3, 3], dtype='float64')
            # [[0.02773777, 0.93004224, 0.06911496],
            #  [0.24831591, 0.45733623, 0.07717843],
            #  [0.48016702, 0.14235102, 0.42620817]])

            print(paddle.linalg.eigvals(x))
            # [(-0.27078833542132674+0j), (0.29962280156230725+0j), (0.8824477020120244+0j)] #complex128
    """

    check_variable_and_dtype(x, 'dtype',
1817 1818
                             ['float32', 'float64', 'complex64',
                              'complex128'], 'eigvals')
1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839

    x_shape = list(x.shape)
    if len(x_shape) < 2:
        raise ValueError(
            "The dimension of Input(x) should be at least 2, but received x's dimention = {}, x's shape = {}".
            format(len(x_shape), x_shape))

    if x_shape[-1] != x_shape[-2]:
        raise ValueError(
            "The last two dimensions of Input(x) should be equal, but received x's shape = {}".
            format(x_shape))

    if in_dygraph_mode():
        return _C_ops.eigvals(x)

    helper = LayerHelper('eigvals', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(type='eigvals', inputs={'X': x}, outputs={'Out': out})
    return out


1840 1841 1842 1843
def multi_dot(x, name=None):
    """
    Multi_dot is an operator that calculates multiple matrix multiplications.

1844
    Supports inputs of float16(only GPU support), float32 and float64 dtypes. This function does not
1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885
    support batched inputs.

    The input tensor in [x] must be 2-D except for the first and last can be 1-D.
    If the first tensor is a 1-D vector of shape(n, ) it is treated as row vector
    of shape(1, n), similarly if the last tensor is a 1D vector of shape(n, ), it
    is treated as a column vector of shape(n, 1).

    If the first and last tensor are 2-D matrix, then the output is also 2-D matrix,
    otherwise the output is a 1-D vector.

    Multi_dot will select the lowest cost multiplication order for calculation. The
    cost of multiplying two matrices with shapes (a, b) and (b, c) is a * b * c.
    Given matrices A, B, C with shapes (20, 5), (5, 100), (100, 10) respectively,
    we can calculate the cost of different multiplication orders as follows:
    - Cost((AB)C) = 20x5x100 + 20x100x10 = 30000
    - Cost(A(BC)) = 5x100x10 + 20x5x10 = 6000

    In this case, multiplying B and C first, then multiply A, which is 5 times faster
    than sequential calculation.

    Args:
        x ([Tensor]): The input tensors which is a list Tensor.
        name(str|None): A name for this layer(optional). If set None, the layer
            will be named automatically.

    Returns:
        Tensor: The output Tensor.


    Examples:

    .. code-block:: python

        import paddle
        import numpy as np

        # A * B
        A_data = np.random.random([3, 4]).astype(np.float32)
        B_data = np.random.random([4, 5]).astype(np.float32)
        A = paddle.to_tensor(A_data)
        B = paddle.to_tensor(B_data)
1886
        out = paddle.linalg.multi_dot([A, B])
1887 1888 1889 1890 1891 1892 1893 1894 1895 1896
        print(out.numpy().shape)
        # [3, 5]

        # A * B * C
        A_data = np.random.random([10, 5]).astype(np.float32)
        B_data = np.random.random([5, 8]).astype(np.float32)
        C_data = np.random.random([8, 7]).astype(np.float32)
        A = paddle.to_tensor(A_data)
        B = paddle.to_tensor(B_data)
        C = paddle.to_tensor(C_data)
1897
        out = paddle.linalg.multi_dot([A, B, C])
1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917
        print(out.numpy().shape)
        # [10, 7]

    """
    if in_dygraph_mode():
        return _C_ops.multi_dot(x)

    check_type(x, 'x', (list, tuple), 'multi_dot')
    for id, item in enumerate(x):
        check_variable_and_dtype(item, 'x[' + str(id) + ']',
                                 ['float16', 'float32', 'float64'], 'multi_dot')
        if item.dtype != x[0].dtype:
            raise TypeError(
                "All the Tensors in the input must have the same data type.")

    helper = LayerHelper('multi_dot', **locals())
    dtype = helper.input_dtype(input_param_name='x')
    out = helper.create_variable_for_type_inference(dtype)
    helper.append_op(type='multi_dot', inputs={"X": x}, outputs={"Out": out})
    return out
1918 1919 1920 1921


def eigh(x, UPLO='L', name=None):
    """
1922
    Compute the eigenvalues and eigenvectors of a
1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945
    complex Hermitian (conjugate symmetric) or a real symmetric matrix.

    Args:
        x (Tensor): A tensor with shape :math:`[*, N, N]` , The data type of the input Tensor x
            should be one of float32, float64, complex64, complex128.
        UPLO(str, optional): (string, default 'L'), 'L' represents the lower triangular matrix,
                        "'U' represents the upper triangular matrix.".
        name(str, optional): The default value is None.  Normally there is no need for user to set this
            property.  For more information, please refer to :ref:`api_guide_Name`.

    Returns:

        out_value(Tensor):  A Tensor with shape [*, N] and data type of float32 and float64. The eigenvalues of eigh op.
        out_vector(Tensor): A Tensor with shape [*, N, N] and data type of float32,float64,complex64 and complex128. The eigenvectors of eigh op.

    Examples:
        .. code-block:: python

            import numpy as np
            import paddle

            x_data = np.array([[1, -2j], [2j, 5]])
            x = paddle.to_tensor(x_data)
1946
            out_value, out_vector = paddle.linalg.eigh(x, UPLO='L')
1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966
            print(out_value)
            #[0.17157288, 5.82842712]
            print(out_vector)
            #[(-0.9238795325112867+0j), (-0.3826834323650898+0j)],
            #[ 0.3826834323650898j    , -0.9238795325112867j    ]]

    """
    if in_dygraph_mode():
        return _C_ops.eigh(x, 'UPLO', UPLO)

    def __check_input(x, UPLO):
        x_shape = list(x.shape)
        if len(x.shape) < 2:
            raise ValueError(
                "Input(input) only support >=2 tensor, but received "
                "length of Input(input) is %s." % len(x.shape))
        if x_shape[-1] != x_shape[-2]:
            raise ValueError(
                "The input matrix must be batches of square matrices. But received x's dimention: {}".
                format(x_shape))
1967
        if UPLO != 'L' and UPLO != 'U':
1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
            raise ValueError(
                "UPLO must be L or U. But received UPLO is: {}".format(UPLO))

    __check_input(x, UPLO)

    helper = LayerHelper('eigh', **locals())
    check_variable_and_dtype(
        x, 'dtype', ['float32', 'float64', 'complex64', 'complex128'], 'eigh')

    out_value = helper.create_variable_for_type_inference(dtype=x.dtype)
    out_vector = helper.create_variable_for_type_inference(dtype=x.dtype)

    helper.append_op(
        type='eigh',
        inputs={'X': x},
        outputs={'Eigenvalues': out_value,
                 'Eigenvectors': out_vector},
        attrs={'UPLO': UPLO})
    return out_value, out_vector
A
andyjpaddle 已提交
1987 1988 1989 1990


def pinv(x, rcond=1e-15, hermitian=False, name=None):
    r"""
1991
    Calculate pseudo inverse via SVD(singular value decomposition)
A
andyjpaddle 已提交
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
    of one matrix or batches of regular matrix.

    .. math::

        if hermitian == False:
            x = u * s * vt  (SVD)
            out = v * 1/s * ut
        else:
            x = u * s * ut  (eigh)
            out = u * 1/s * u.conj().transpose(-2,-1)
2002

A
andyjpaddle 已提交
2003 2004 2005
    If x is hermitian or symmetric matrix, svd will be replaced with eigh.

    Args:
2006 2007 2008
        x(Tensor): The input tensor. Its shape should be (*, m, n)
            where * is zero or more batch dimensions. m and n can be
            arbitraty positive number. The data type of x should be
A
andyjpaddle 已提交
2009 2010 2011 2012
            float32 or float64 or complex64 or complex128. When data
            type is complex64 or cpmplex128, hermitian should be set
            True.

2013 2014 2015 2016
        rcond(Tensor, optional): the tolerance value to determine
            when is a singular value zero. Defalut:1e-15.

        hermitian(bool, optional): indicates whether x is Hermitian
A
andyjpaddle 已提交
2017
            if complex or symmetric if real. Default: False.
2018 2019

        name(str|None): A name for this layer(optional). If set None,
A
andyjpaddle 已提交
2020
            the layer will be named automatically.
2021

A
andyjpaddle 已提交
2022
    Returns:
2023
        Tensor: The tensor with same data type with x. it represents
A
andyjpaddle 已提交
2024
        pseudo inverse of x. Its shape should be (*, n, m).
2025

A
andyjpaddle 已提交
2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184
    Examples:
        .. code-block:: python

            import paddle

            x = paddle.arange(15).reshape((3, 5)).astype('float64')
            input = paddle.to_tensor(x)
            out = paddle.linalg.pinv(input)
            print(input)
            print(out)

            # input:
            # [[0. , 1. , 2. , 3. , 4. ],
            # [5. , 6. , 7. , 8. , 9. ],
            # [10., 11., 12., 13., 14.]]

            # out:
            # [[-0.22666667, -0.06666667,  0.09333333],
            # [-0.12333333, -0.03333333,  0.05666667],
            # [-0.02000000,  0.00000000,  0.02000000],
            # [ 0.08333333,  0.03333333, -0.01666667],
            # [ 0.18666667,  0.06666667, -0.05333333]]

            # one can verify : x * out * x = x ;
            # or              out * x * out = x ;
    """

    if in_dygraph_mode():
        if not hermitian:
            # combine svd and matmul op
            u, s, vt = _C_ops.svd(x, 'full_matrices', False)
            max_singular_val = _C_ops.reduce_max(s, 'dim', [-1], 'keep_dim', True, \
                'reduce_all', False)
            rcond = paddle.to_tensor(rcond, dtype=x.dtype)
            cutoff = rcond * max_singular_val
            y = float('inf')
            y = paddle.to_tensor(y, dtype=x.dtype)

            condition = s > cutoff
            cond_int = layers.cast(condition, s.dtype)
            cond_not_int = layers.cast(layers.logical_not(condition), s.dtype)
            out1 = layers.elementwise_mul(1 / s, cond_int)
            out2 = layers.elementwise_mul(1 / y, cond_not_int)
            singular = layers.elementwise_add(out1, out2)
            st, _ = _C_ops.unsqueeze2(singular, 'axes', [-2])

            dims = list(range(len(vt.shape)))
            perm = dims[:-2] + [dims[-1]] + [dims[-2]]
            v, _ = _C_ops.transpose2(vt, 'axis', perm)

            out_1 = v * st
            out_2 = _C_ops.matmul_v2(out_1, u, 'trans_x', False, 'trans_y',
                                     True)
            return out_2
        else:
            # combine eigh and matmul op
            s, u = _C_ops.eigh(x, 'UPLO', 'L')
            s_abs = paddle.abs(s)
            max_singular_val = _C_ops.reduce_max(s_abs, 'dim', [-1], 'keep_dim', True, \
                'reduce_all', False)
            rcond = paddle.to_tensor(rcond, dtype=s.dtype)
            cutoff = rcond * max_singular_val
            y = float('inf')
            y = paddle.to_tensor(y, dtype=s.dtype)

            condition = s_abs > cutoff
            cond_int = layers.cast(condition, s.dtype)
            cond_not_int = layers.cast(layers.logical_not(condition), s.dtype)
            out1 = layers.elementwise_mul(1 / s, cond_int)
            out2 = layers.elementwise_mul(1 / y, cond_not_int)
            singular = layers.elementwise_add(out1, out2)
            st, _ = _C_ops.unsqueeze2(singular, 'axes', [-2])

            out_1 = u * st
            u_conj = _C_ops.conj(u)
            out_2 = _C_ops.matmul_v2(out_1, u_conj, 'trans_x', False, 'trans_y',
                                     True)
            return out_2
    else:
        if not hermitian:
            helper = LayerHelper('pinv', **locals())
            dtype = x.dtype
            check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'pinv')

            u = helper.create_variable_for_type_inference(dtype)
            s = helper.create_variable_for_type_inference(dtype)
            vt = helper.create_variable_for_type_inference(dtype)
            helper.append_op(
                type='svd',
                inputs={'X': [x]},
                outputs={'U': u,
                         'VH': vt,
                         'S': s},
                attrs={'full_matrices': False}, )

            max_singular_val = helper.create_variable_for_type_inference(dtype)
            helper.append_op(
                type='reduce_max',
                inputs={'X': s},
                outputs={'Out': max_singular_val},
                attrs={'dim': [-1],
                       'keep_dim': True,
                       'reduce_all': False})

            rcond = layers.fill_constant(shape=[1], value=rcond, dtype=dtype)
            cutoff = rcond * max_singular_val
            y = float('inf')
            y = layers.fill_constant(shape=[1], value=y, dtype=dtype)

            condition = s > cutoff
            cond_int = layers.cast(condition, dtype)
            cond_not_int = layers.cast(layers.logical_not(condition), dtype)
            out1 = layers.elementwise_mul(1 / s, cond_int)
            out2 = layers.elementwise_mul(1 / y, cond_not_int)
            singular = layers.elementwise_add(out1, out2)

            st = helper.create_variable_for_type_inference(dtype=dtype)
            st_shape = helper.create_variable_for_type_inference(dtype=dtype)
            helper.append_op(
                type='unsqueeze2',
                inputs={'X': singular},
                attrs={'axes': [-2]},
                outputs={'Out': st,
                         'XShape': st_shape})

            dims = list(range(len(vt.shape)))
            perm = dims[:-2] + [dims[-1]] + [dims[-2]]
            v = helper.create_variable_for_type_inference(dtype)
            v_shape = helper.create_variable_for_type_inference(dtype)
            helper.append_op(
                type='transpose2',
                inputs={'X': [vt]},
                outputs={'Out': [v],
                         'XShape': [v_shape]},
                attrs={'axis': perm})

            out_1 = helper.create_variable_for_type_inference(dtype)
            helper.append_op(
                type='elementwise_mul',
                inputs={'X': v,
                        'Y': st},
                outputs={'Out': out_1},
                attrs={'axis': -1,
                       'use_mkldnn': False})
            out_1 = helper.append_activation(out_1)

            out_2 = helper.create_variable_for_type_inference(dtype)
            helper.append_op(
                type='matmul_v2',
                inputs={'X': out_1,
                        'Y': u},
                outputs={'Out': out_2},
                attrs={'trans_x': False,
                       'trans_y': True}, )
            return out_2
        else:
            helper = LayerHelper('pinv', **locals())
            dtype = x.dtype
            check_variable_and_dtype(
2185 2186
                x, 'dtype', ['float32', 'float64', 'complex64',
                             'complex128'], 'pinv')
A
andyjpaddle 已提交
2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258

            if dtype == paddle.complex128:
                s_type = 'float64'
            elif dtype == paddle.complex64:
                s_type = 'float32'
            else:
                s_type = dtype

            u = helper.create_variable_for_type_inference(dtype)
            s = helper.create_variable_for_type_inference(s_type)
            helper.append_op(
                type='eigh',
                inputs={'X': x},
                outputs={'Eigenvalues': s,
                         'Eigenvectors': u},
                attrs={'UPLO': 'L'})
            s_abs = helper.create_variable_for_type_inference(s_type)
            helper.append_op(
                type='abs', inputs={'X': s}, outputs={'Out': s_abs})
            max_singular_val = helper.create_variable_for_type_inference(s_type)
            helper.append_op(
                type='reduce_max',
                inputs={'X': s_abs},
                outputs={'Out': max_singular_val},
                attrs={'dim': [-1],
                       'keep_dim': True,
                       'reduce_all': False})

            rcond = layers.fill_constant(shape=[1], value=rcond, dtype=s_type)
            cutoff = rcond * max_singular_val
            y = float('inf')
            y = layers.fill_constant(shape=[1], value=y, dtype=s_type)

            condition = s_abs > cutoff
            cond_int = layers.cast(condition, s_type)
            cond_not_int = layers.cast(layers.logical_not(condition), s_type)
            out1 = layers.elementwise_mul(1 / s, cond_int)
            out2 = layers.elementwise_mul(1 / y, cond_not_int)
            singular = layers.elementwise_add(out1, out2)

            st = helper.create_variable_for_type_inference(dtype=s_type)
            st_shape = helper.create_variable_for_type_inference(dtype=s_type)
            helper.append_op(
                type='unsqueeze2',
                inputs={'X': singular},
                attrs={'axes': [-2]},
                outputs={'Out': st,
                         'XShape': st_shape})

            out_1 = helper.create_variable_for_type_inference(dtype)
            helper.append_op(
                type='elementwise_mul',
                inputs={'X': u,
                        'Y': st},
                outputs={'Out': out_1},
                attrs={'axis': -1,
                       'use_mkldnn': False})
            out_1 = helper.append_activation(out_1)

            u_conj = helper.create_variable_for_type_inference(dtype)
            helper.append_op(
                type='conj', inputs={'X': u}, outputs={'Out': [u_conj]})

            out_2 = helper.create_variable_for_type_inference(dtype)
            helper.append_op(
                type='matmul_v2',
                inputs={'X': out_1,
                        'Y': u_conj},
                outputs={'Out': out_2},
                attrs={'trans_x': False,
                       'trans_y': True}, )
            return out_2
W
Weilong Wu 已提交
2259 2260 2261 2262 2263 2264 2265


def solve(x, y, name=None):
    r"""
    Computes the solution of a square system of linear equations with a unique solution for input 'X' and 'Y'.
    Let :math: `X` be a sqaure matrix or a batch of square matrices, :math:`Y` be
    a vector/matrix or a batch of vectors/matrices, the equation should be:
2266

W
Weilong Wu 已提交
2267 2268 2269 2270
    .. math::
        Out = X^-1 * Y
    Specifically,
    - This system of linear equations has one solution if and only if input 'X' is invertible.
2271

W
Weilong Wu 已提交
2272 2273 2274 2275 2276
    Args:
        x (Tensor): A square matrix or a batch of square matrices. Its shape should be `[*, M, M]`, where `*` is zero or
            more batch dimensions. Its data type should be float32 or float64.
        y (Tensor): A vector/matrix or a batch of vectors/matrices. Its shape should be `[*, M, K]`, where `*` is zero or
            more batch dimensions. Its data type should be float32 or float64.
2277
        name(str, optional): Name for the operation (optional, default is None).
W
Weilong Wu 已提交
2278
            For more information, please refer to :ref:`api_guide_Name`.
2279

W
Weilong Wu 已提交
2280
    Returns:
2281
        Tensor: The solution of a square system of linear equations with a unique solution for input 'x' and 'y'.
W
Weilong Wu 已提交
2282
        Its data type should be the same as that of `x`.
2283

W
Weilong Wu 已提交
2284 2285
    Examples:
    .. code-block:: python
2286

W
Weilong Wu 已提交
2287 2288 2289
        # a square system of linear equations:
        # 2*X0 + X1 = 9
        # X0 + 2*X1 = 8
2290

W
Weilong Wu 已提交
2291 2292
        import paddle
        import numpy as np
2293

W
Weilong Wu 已提交
2294 2295 2296 2297 2298
        np_x = np.array([[3, 1],[1, 2]])
        np_y = np.array([9, 8])
        x = paddle.to_tensor(np_x, dtype="float64")
        y = paddle.to_tensor(np_y, dtype="float64")
        out = paddle.linalg.solve(x, y)
2299

W
Weilong Wu 已提交
2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315
        print(out)
        # [2., 3.])
    """
    if in_dygraph_mode():
        return _C_ops.solve(x, y)

    inputs = {"X": [x], "Y": [y]}
    helper = LayerHelper("solve", **locals())
    check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'solve')
    check_variable_and_dtype(y, 'y', ['float32', 'float64'], 'solve')
    out = helper.create_variable_for_type_inference(dtype=x.dtype)

    helper.append_op(
        type="solve", inputs={"X": x,
                              "Y": y}, outputs={"Out": out})
    return out
2316 2317


2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390
def triangular_solve(x,
                     y,
                     upper=True,
                     transpose=False,
                     unitriangular=False,
                     name=None):
    r"""
    Computes the solution of a system of equations with a triangular coefficient matrix `x` and
    multiple right-hand sides `y` .

    Input `x` and `y` is 2D matrices or batches of 2D matrices. If the inputs are batches, the outputs
    is also batches.

    Args:
        x (Tensor): The input triangular coefficient matrix. Its shape should be `[*, M, M]`, where `*` is zero or
            more batch dimensions. Its data type should be float32 or float64.
        y (Tensor): Multiple right-hand sides of system of equations. Its shape should be `[*, M, K]`, where `*` is 
            zero or more batch dimensions. Its data type should be float32 or float64.
        upper (bool, optional): Whether to solve the upper-triangular system of equations (default) or the lower-triangular 
            system of equations. Default: True.
        transpose (bool, optional): whether `x` should be transposed before calculation. Default: False.
        unitriangular (bool, optional): whether `x` is unit triangular. If True, the diagonal elements of `x` are assumed 
            to be 1 and not referenced from `x` . Default: False.
        name(str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: The solution of the system of equations. Its data type should be the same as that of `x`.

    Examples:
    .. code-block:: python

        # a square system of linear equations:
        # x1 +   x2  +   x3 = 0
        #      2*x2  +   x3 = -9
        #               -x3 = 5

        import paddle
        import numpy as np

        x = paddle.to_tensor([[1, 1, 1], 
                              [0, 2, 1],
                              [0, 0,-1]], dtype="float64")
        y = paddle.to_tensor([[0], [-9], [5]], dtype="float64")
        out = paddle.linalg.triangular_solve(x, y, upper=True)

        print(out)
        # [7, -2, -5]
    """
    if in_dygraph_mode():
        return _C_ops.triangular_solve(x, y, 'upper', upper, 'transpose',
                                       transpose, 'unitriangular',
                                       unitriangular)

    inputs = {"X": [x], "Y": [y]}
    helper = LayerHelper("triangular_solve", **locals())
    check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'triangular_solve')
    check_variable_and_dtype(y, 'y', ['float32', 'float64'], 'triangular_solve')
    out = helper.create_variable_for_type_inference(dtype=x.dtype)

    helper.append_op(
        type='triangular_solve',
        inputs={'X': x,
                'Y': y},
        outputs={'Out': out},
        attrs={
            'upper': upper,
            'transpose': transpose,
            'unitriangular': unitriangular
        })
    return out


2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455
def eigvalsh(x, UPLO='L', name=None):
    """
    Computes the eigenvalues of a 
    complex Hermitian (conjugate symmetric) or a real symmetric matrix.

    Args:
        x (Tensor): A tensor with shape :math:`[_, M, M]` , The data type of the input Tensor x
            should be one of float32, float64, complex64, complex128.
        UPLO(str, optional): Lower triangular part of a (‘L’, default) or the upper triangular part (‘U’).
        name(str, optional): The default value is None.  Normally there is no need for user to set this
            property.  For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: The tensor eigenvalues in ascending order.

    Examples:
        .. code-block:: python

            import numpy as np
            import paddle

            x_data = np.array([[1, -2j], [2j, 5]])
            x = paddle.to_tensor(x_data)
            out_value = paddle.eigvalsh(x, UPLO='L')
            print(out_value)
            #[0.17157288, 5.82842712]
    """
    if in_dygraph_mode():
        is_test = x.stop_gradient
        values, _ = _C_ops.eigvalsh(x, 'UPLO', UPLO, 'is_test', is_test)
        return values

    def __check_input(x, UPLO):
        x_shape = list(x.shape)
        if len(x.shape) < 2:
            raise ValueError(
                "Input(input) only support >=2 tensor, but received "
                "length of Input(input) is %s." % len(x.shape))
        if x_shape[-1] != x_shape[-2]:
            raise ValueError(
                "The input matrix must be batches of square matrices. But received x's dimention: {}".
                format(x_shape))
        if UPLO is not 'L' and UPLO is not 'U':
            raise ValueError(
                "UPLO must be L or U. But received UPLO is: {}".format(UPLO))

    __check_input(x, UPLO)

    helper = LayerHelper('eigvalsh', **locals())
    check_variable_and_dtype(x, 'dtype',
                             ['float32', 'float64', 'complex64', 'complex128'],
                             'eigvalsh')

    out_value = helper.create_variable_for_type_inference(dtype=x.dtype)
    out_vector = helper.create_variable_for_type_inference(dtype=x.dtype)

    is_test = x.stop_gradient
    helper.append_op(
        type='eigvalsh',
        inputs={'X': x},
        outputs={'Eigenvalues': out_value,
                 'Eigenvectors': out_vector},
        attrs={'UPLO': UPLO,
               'is_test': is_test})
    return out_value