# 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. import numpy as np from ..fluid.layer_helper import LayerHelper from ..fluid.data_feeder import check_variable_and_dtype, check_type from ..fluid.framework import in_dygraph_mode, _varbase_creator, Variable from ..fluid.layers import transpose, cast # noqa: F401 from paddle.common_ops_import import core from paddle.common_ops_import import VarDesc from paddle import _C_ops __all__ = [] def matmul(x, y, transpose_x=False, transpose_y=False, name=None): """ Applies matrix multiplication to two tensors. `matmul` follows the complete broadcast rules, and its behavior is consistent with `np.matmul`. Currently, the input tensors' number of dimensions can be any, `matmul` can be used to achieve the `dot`, `matmul` and `batchmatmul`. 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 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 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. - 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. After the matrix multiply, the prepended dimension is removed. - If the `x` is 2-dimensional and `y` is 1-dimensional, the matrix-vector product is obtained. - 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, out will be a (j, k, n, p) tensor. Args: x (Tensor): The input tensor which is a Tensor. y (Tensor): The input tensor which is a Tensor. 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: Tensor: The output Tensor. Examples: .. 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] """ op_type = 'matmul_v2' if in_dygraph_mode(): op = getattr(_C_ops, op_type) return op(x, y, 'trans_x', transpose_x, 'trans_y', transpose_y) attrs = { 'trans_x': transpose_x, 'trans_y': transpose_y, } def __check_input(x, y): var_names = {'x': x, 'y': y} for name, val in var_names.items(): check_variable_and_dtype( val, name, ['float16', 'float32', 'float64'], 'matmul') __check_input(x, y) helper = LayerHelper('matmul_v2', **locals()) out = helper.create_variable_for_type_inference(dtype=x.dtype) helper.append_op( type='matmul_v2', inputs={'X': x, 'Y': y}, outputs={'Out': out}, attrs=attrs) return out def norm(x, p='fro', axis=None, keepdim=False, name=None): """ 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. .. 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. Args: x (Tensor): The input tensor could be N-D tensor, and the input data type could be float32 or float64. p (float|string, optional): Order of the norm. Supported values are `fro`, `0`, `1`, `2`, `inf`, `-inf` and any positive real number yielding the corresponding p-norm. Not supported: ord < 0 and nuclear norm. Default value is `fro`. 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. If `axis < 0`, the dimension to norm operation is rank(input) + axis. If axis is a list(int)/tuple(int) with two elements, the matrix norm is computed over the axis. Defalut value is `None`. 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: Tensor: results of norm operation on the specified axis of input tensor, it's data type is the same as input's Tensor. Examples: .. code-block:: python import paddle 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.]]] # compute frobenius norm along last two dimensions. out_fro = paddle.norm(x, p='fro', axis=[0,1]) # out_fro.numpy() [17.435596 16.911535 16.7332 16.911535] # compute 2-order vector norm along last dimension. out_pnorm = paddle.norm(x, p=2, axis=-1) #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.]] """ def frobenius_norm(input, dim=None, keepdim=False, name=None): """ 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!" ) if in_dygraph_mode(): if dim is None: 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) attrs = {'dim': dim, 'keep_dim': keepdim, 'reduce_all': False} if dim is None: attrs['reduce_all'] = True check_variable_and_dtype(input, 'input', ['float32', 'float64'], 'frobenius_norm') helper = LayerHelper('frobenius_norm', **locals()) out = helper.create_variable_for_type_inference( dtype=helper.input_dtype()) 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, asvector=False, 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. """ if in_dygraph_mode(): if axis is None: axis = -1 return _C_ops.p_norm(input, 'porder', porder, 'axis', axis, 'keepdim', keepdim, 'asvector', asvector) 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') check_variable_and_dtype(input, 'input', ['float32', 'float64'], 'p_norm') attrs = { 'axis': axis if axis is not None else -1, 'porder': float(porder) if porder is not None else 2.0, 'keepdim': keepdim, 'asvector': asvector, 'epsilon': 1e-12, } helper = LayerHelper('p_norm', **locals()) out = helper.create_variable_for_type_inference( dtype=helper.input_dtype()) helper.append_op( type='p_norm', inputs={'X': input}, outputs={'Out': out}, attrs=attrs) return out 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): """ NOTE: This function actually treats the matrix as flattened vector to calculate vector norm instead of matrix norm. """ 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 if axis is None and p is not None: if isinstance(p, str): if p == "fro": return frobenius_norm(x, dim=axis, keepdim=keepdim, name=name) else: raise ValueError( "only valid string values are 'fro', found {}".format(p)) elif isinstance(p, (int, float)): return vector_norm( x, porder=p, axis=axis, keepdim=keepdim, asvector=True, name=name) else: raise ValueError("only valid p type is string or float, found {}". format(type(p))) if isinstance(axis, tuple): axis = list(axis) 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): 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)): return vector_norm( x, axis=axis, porder=p, keepdim=keepdim, asvector=False, name=name) 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": 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) elif p == 0: raise ValueError( "just suport axis type int or list (length of list <=1) if p = 0, found {}". format(axis)) else: return p_matrix_norm( x, porder=p, axis=axis, keepdim=keepdim, name=name) else: raise ValueError( "except axis type int or list (length of list <=2), found {}". format(axis)) def dist(x, y, p=2): r""" This OP returns the p-norm of (x - y). It is not a norm in a strict sense, only as a measure 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 `_: - 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: 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: 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. p (float, optional): The norm to be computed, its data type is float32 or float64. Default: 2. Returns: Tensor: Tensor that is the p-norm of (x - y). Examples: .. code-block:: python import paddle import numpy as np 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.] out = paddle.dist(x, y, 2) print(out) # out = [2.] out = paddle.dist(x, y, float("inf")) print(out) # out = [2.] out = paddle.dist(x, y, float("-inf")) print(out) # out = [0.] """ 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 def dot(x, y, name=None): """ This operator calculates inner product for vectors. .. note:: 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. Parameters: 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`` name(str, optional): Name of the output. Default is None. It's used to print debug info for developers. Details: :ref:`api_guide_Name` Returns: Tensor: the calculated result Tensor. Examples: .. code-block:: python import paddle import numpy as np x_data = np.random.uniform(0.1, 1, [10]).astype(np.float32) y_data = np.random.uniform(1, 3, [10]).astype(np.float32) x = paddle.to_tensor(x_data) y = paddle.to_tensor(y_data) z = paddle.dot(x, y) print(z) """ op_type = 'dot' # skip var type check in dygraph mode to improve efficiency if in_dygraph_mode(): op = getattr(_C_ops, op_type) return op(x, y) 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 def t(input, name=None): """ Transpose <=2-D tensor. 0-D and 1-D tensors are returned as it is and 2-D tensor is equal to the paddle.transpose function which perm dimensions set 0 and 1. Args: input (Tensor): The input Tensor. It is a N-D (N<=2) Tensor of data types float16, float32, float64, int32. 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: A transposed n-D Tensor, with data type being float16, float32, float64, int32, int64. For Example: .. code-block:: text # 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]) Examples: .. code-block:: python import paddle x = paddle.ones(shape=[2, 3], dtype='int32') x_transposed = paddle.t(x) print(x_transposed.shape) # [3, 2] """ 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] out, _ = _C_ops.transpose2(input, 'axis', perm) return out check_variable_and_dtype( input, 'input', ['float16', 'float32', 'float64', 'int32', 'int64'], 'transpose') 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 def cross(x, y, axis=None, name=None): """ Computes the cross product between two tensors along an axis. 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. Args: x (Tensor): The first input tensor. y (Tensor): The second input tensor. axis (int, optional): The axis along which to compute the cross product. It defaults to the first axis found with the length 3. name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor. A Tensor with same data type as `x`. Examples: .. code-block:: python import paddle 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]]) 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.]] """ if in_dygraph_mode(): if axis is not None: return _C_ops.cross(x, y, 'dim', axis) else: return _C_ops.cross(x, y) helper = LayerHelper("cross", **locals()) out = helper.create_variable_for_type_inference(x.dtype) attrs = dict() attrs['dim'] = axis helper.append_op( type='cross', inputs={'X': x, 'Y': y}, outputs={'Out': out}, attrs=attrs) return out def cholesky(x, upper=False, name=None): r""" Computes the Cholesky decomposition of one symmetric positive-definite matrix or batches of symmetric positive-definite matrice. 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: x (Tensor): The input tensor. Its shape should be `[*, M, M]`, 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: Tensor: A Tensor with same shape and data type as `x`. It represents \ triangular matrices generated by Cholesky decomposition. Examples: .. code-block:: python import paddle import numpy as np a = np.random.rand(3, 3) a_t = np.transpose(a, [1, 0]) x_data = np.matmul(a, a_t) + 1e-03 x = paddle.to_tensor(x_data) out = paddle.cholesky(x, upper=False) print(out) # [[1.190523 0. 0. ] # [0.9906703 0.27676893 0. ] # [1.25450498 0.05600871 0.06400121]] """ if in_dygraph_mode(): return _C_ops.cholesky(x, "upper", upper) 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 def matrix_rank(x, tol=None, hermitian=False, name=None): r""" Computes the rank of a matrix. The rank of a matrix is the number of singular values that are greater than the specified tol threshold when hermitian=False, or the number of eigenvalues in absolute value that are greater than the specified tol threshold when hermitian=True. Args: 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 eigenvalue in absolute value), and eps is the epsilon value for the dtype of x, then tol is computed 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. hermitian (bool,optional): indicates whether x is Hermitian. Default: False. When hermitian=True, x is assumed to be Hermitian, but x is not checked inside the function. Instead, We just use the lower triangular of the matrix to compute. 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. 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]] """ 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 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: x (Tensor): The input Tensor. y (Tensor): The input Tensor. name(str|None): A name for this layer(optional). If set None, the layer will be named automatically. Returns: Tensor: The product Tensor. Examples: import paddle # 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() """ 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)) 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)) if in_dygraph_mode(): return _C_ops.bmm(x, y) helper = LayerHelper('bmm', **locals()) 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 def histogram(input, bins=100, min=0, max=0): """ Computes the histogram of a tensor. The elements are sorted into equal width bins between min and max. If min and max are both zero, the minimum and maximum values of the data are used. Args: input (Tensor): A Tensor(or LoDTensor) with shape :math:`[N_1, N_2,..., N_k]` . The data type of the input Tensor 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: Tensor: data type is int64, shape is (nbins,). Examples: .. code-block:: python import paddle inputs = paddle.to_tensor([1, 2, 1]) result = paddle.histogram(inputs, bins=4, min=0, max=3) print(result) # [0, 2, 1, 0] """ if in_dygraph_mode(): return _C_ops.histogram(input, "bins", bins, "min", min, "max", max) 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 def mv(x, vec, name=None): """ Performs a matrix-vector product of the matrix x and the vector vec. Args: x (Tensor): A tensor with shape :math:`[M, N]` , The data type of the input Tensor x should be one of float32, float64. vec (Tensor): A tensor with shape :math:`[N]` , The data type of the input Tensor x 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(): out = _C_ops.mv(x, vec) 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 def svd(x, full_matrices=False, name=None): r""" Computes the singular value decomposition of one matrix or batches of regular matrice. Args: x (Tensor): The input tensor. Its shape should be `[..., N, M]`, where ... is zero or more batch dimensions. N and M can be arbitraty positive number. Note that if x is sigular matrices, the grad is numerical instability. 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, which means shape of U is `[..., N, N]`, shape of V is `[..., M, M]`. If full_matrices = False, svd op will use a economic method to store U and V. which means shape of U is `[..., N, K]`, shape of V is `[..., M, K]` Returns: Tensor: Tensor U, the shape of U is controlled by full_matrices flag. Tensor: Tensor S, the singular value of X. the shape of S is [..., K] Tensor: Tensor VH, the conjugate transpose of V. the shape of V is controlled by full_matrices flag. import numpy as np x = paddle.to_tensor([[1.0, 2.0], [1.0, 3.0], [4.0, 6.0]]).astype('float64') x = x.reshape([3, 2]) u, s, vt = paddle.linalg.svd(x) print (u) print (s) print (vt) #U = [[ 0.27364809, -0.21695147 ], # [ 0.37892198, -0.87112408 ], # [ 0.8840446 , 0.44053933 ]] #S = [8.14753743, 0.78589688] #VT= [[ 0.51411221, 0.85772294], # [ 0.85772294, -0.51411221]] # one can verify : U * S * VT = X ; # U * UH = I ; # V * VH = I """ 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 def matrix_power(x, n, name=None): r""" Computes the n-th power of a square matrix or a batch of square matrices. 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} Specifically, - If `n > 0`, it returns the matrix or a batch of matrices raised to the power of `n`. - 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. name (str, optional): Name for the operation (optional, default is None). 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') print(paddle.matrix_power(x, 2)) # [[6. , 34. , 102.], # [14. , 90. , 282.], # [36. , 250., 804.]] print(paddle.matrix_power(x, 0)) # [[1., 0., 0.], # [0., 1., 0.], # [0., 0., 1.]] print(paddle.matrix_power(x, -2)) # [[ 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