o Qe @sddlZddlmZddlmZmZmZmZddlm Z m Z m Z ddl m Z ddlmZdd lmZdd lmZmZdd lmZdd lmZddlZddlZdd lmZddlmZddlmZmZgZ dZ!dZddZ"d[ddZ#d\ddZ$d]ddZ%d^ddZ&dZddZ'd_d d!Z(dZd"d#Z)d`d$d%Z*dad&d'Z+dbd(d)Z,dZd*d+Z-dcd-d.Z.ddd/d0Z/dZd1d2Z0dZd3d4Z1dZd5d6Z2dad7d8Z3dZd9d:Z4dedd?Z6dgd@dAZ7dZdBdCZ8dZdDdEZ9dZdFdGZ:dhdIdJZ;didLdMZdadRdSZ?dhdTdUZ@dkdVdWZAdldXdYZBdS)mN) LayerHelper)_varbase_creator_dygraph_tracerin_dygraph_mode_non_static_mode)check_variable_and_dtype check_type check_dtype)Variable)_in_legacy_dygraph)cast)multiplyadd) logical_not)full)core)VarDesc)_C_ops _legacy_C_ops c Cstr t||Strt|d|\}}|St|dgddt|dtt fdt |t r2t|}t |t |j krHt dt |j t |ft|D]\}}|t |j kret d|||t |j fqLtd it}||j}||j}|jdd |gi|g|gd d|id |S)a Permute the data dimensions of `input` according to `perm`. The `i`-th dimension of the returned tensor will correspond to the perm[i]-th dimension of `input`. Args: x (Tensor): The input Tensor. It is a N-D Tensor of data types bool, float32, float64, int32. perm (list|tuple): Permute the input according to the data of perm. name (str): The name of this layer. It is optional. Returns: Tensor: A transposed n-D Tensor, with data type being bool, float32, float64, int32, int64. For Example: .. code-block:: text x = [[[ 1 2 3 4] [ 5 6 7 8] [ 9 10 11 12]] [[13 14 15 16] [17 18 19 20] [21 22 23 24]]] shape(x) = [2,3,4] # Example 1 perm0 = [1,0,2] y_perm0 = [[[ 1 2 3 4] [13 14 15 16]] [[ 5 6 7 8] [17 18 19 20]] [[ 9 10 11 12] [21 22 23 24]]] shape(y_perm0) = [3,2,4] # Example 2 perm1 = [2,1,0] y_perm1 = [[[ 1 13] [ 5 17] [ 9 21]] [[ 2 14] [ 6 18] [10 22]] [[ 3 15] [ 7 19] [11 23]] [[ 4 16] [ 8 20] [12 24]]] shape(y_perm1) = [4,3,2] Examples: .. code-block:: python import paddle x = paddle.randn([2, 3, 4]) x_transposed = paddle.transpose(x, perm=[1, 0, 2]) print(x_transposed.shape) # [3L, 2L, 4L] axisx)boolfloat16float32float64int32int64 complex64 complex128 transposepermzInput(perm) is the permutation of dimensions of Input(x), its length should be equal to dimensions of Input(x), but received dimension of Input(x) is %s, the length of Input(perm) is %s.zEach element in Input(perm) should be less than Input(x)'s dimension, but %d-th element in Input(perm) is %d which exceeds Input(x)'s dimension %d. transpose2XOutZXShapetypeinputsoutputsattrsN)r")rrr"r rr$rr listtuple isinstancelenshape ValueError enumeraterlocals"create_variable_for_type_inferencedtype append_op) rr#nameout_idxdimhelperx_shaper?DD:\Projects\ConvertPro\env\Lib\site-packages\paddle/tensor/linalg.pyr"/sL2      r"Fc Cstr t||||Strd}tt|}|||d|d|S||d}dd}|||td it} | j|j d} | j d||dd | i|d | S) a1 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 # vector * vector x = paddle.rand([10]) y = paddle.rand([10]) z = paddle.matmul(x, y) print(z.shape) # [1] # matrix * vector x = paddle.rand([10, 5]) y = paddle.rand([5]) z = paddle.matmul(x, y) print(z.shape) # [10] # batched matrix * broadcasted vector x = paddle.rand([10, 5, 2]) y = paddle.rand([2]) z = paddle.matmul(x, y) print(z.shape) # [10, 5] # batched matrix * batched matrix x = paddle.rand([10, 5, 2]) y = paddle.rand([10, 2, 5]) z = paddle.matmul(x, y) print(z.shape) # [10, 5, 5] # batched matrix * broadcasted matrix x = paddle.rand([10, 1, 5, 2]) y = paddle.rand([1, 3, 2, 5]) z = paddle.matmul(x, y) print(z.shape) # [10, 3, 5, 5] matmul_v2trans_xtrans_yrBrCcSs2||d}|D] \}}t||gddq dS)N)ry)rrrr r!matmul)itemsr)rrE var_namesr8valr?r?r@ __check_inputs zmatmul..__check_inputr6r%Yr'r(N)rA) rrrFr getattrrrr4r5r6r7) rrEZ transpose_xZ transpose_yr8op_typeopr,rJr=r9r?r?r@rFs(^  rFfroc Csddd} ddd}d|dddfdd}d |ddfd d }|durX|durXt|tr>|d kr7|||||d Std|t|ttfrO|||||d|dStdt|t|trat|}t|trpt |dkrp|d}t|trt|tr|d kr||d||d|dStd|t|ttfr|||||d|dStd|t|trt |dkr|d kr|||||d S|t j ks|t j kr||||||dS|dkrtd|||||||dStd|)a5 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. Default 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 x = paddle.arange(24, dtype="float32").reshape([2, 3, 4]) - 12 # x: Tensor(shape=[2, 3, 4], dtype=float32, place=Place(cpu), stop_gradient=True, # [[[-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.linalg.norm(x, p='fro', axis=[0,1]) # out_fro: Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, # [17.43559647, 16.91153526, 16.73320007, 16.91153526]) # compute 2-order vector norm along last dimension. out_pnorm = paddle.linalg.norm(x, p=2, axis=-1) # out_pnorm: Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, # [[21.11871147, 13.19090557, 5.47722578 ], # [3.74165750 , 11.22497177, 19.13112640]]) # compute 2-order norm along [0,1] dimension. out_pnorm = paddle.linalg.norm(x, p=2, axis=[0,1]) # out_pnorm: Tensor(shape=[4], dtype=float32, place=Place(cpu), stop_gradient=True, # [17.43559647, 16.91153526, 16.73320007, 16.91153526]) # compute inf-order norm out_pnorm = paddle.linalg.norm(x, p=float("inf")) # out_pnorm = Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, # [12.]) out_pnorm = paddle.linalg.norm(x, p=float("inf"), axis=0) # out_pnorm: Tensor(shape=[3, 4], dtype=float32, place=Place(cpu), stop_gradient=True, # [[12., 11., 10., 9. ], # [8. , 7. , 6. , 7. ], # [8. , 9. , 10., 11.]]) # compute -inf-order norm out_pnorm = paddle.linalg.norm(x, p=-float("inf")) # out_pnorm: Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, # [0.]) out_pnorm = paddle.linalg.norm(x, p=-float("inf"), axis=0) # out_pnorm: Tensor(shape=[3, 4], dtype=float32, place=Place(cpu), stop_gradient=True, # [[0., 1., 2., 3.], # [4., 5., 6., 5.], # [4., 3., 2., 1.]]) NFc Ss|durt|trt|dkstdtr*|dur"t|g|dSt|||dStrE|dur:t|d|ddSt|d|d|ddS||dd }|durSd|d<t |d d d gd t dit }|j | d}|jd d|id|i|d|S)ab 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. NrzAThe dim of frobenius norm op should be None or two elements list!TFkeep_dim reduce_allr<r<rRrSinputrrfrobenius_normrKr%r'r()rV)r/r-r0r2rrrVr rrrr4r5 input_dtyper7)rUr<keepdimr8r,r=r9r?r?r@rVnsB   znorm..frobenius_normc Sstr|dur d}t|||d||Str)|durd}t|d|d|d|d| S|dur6t|dttfd|durAt|dtdt|d d d gd|durP|nd|durYt|nd ||dd }t dit }|j | d}|j dd|id|i|d|S)a| 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. Ng-q=porderrrXasvectorp_normrUrrg@)rrZrXr[epsilonrKr%r'r()r\)rrr\r rr floatintrrr4r5rWr7) rUrZrrXr[r8r,r=r9r?r?r@ vector_normsT   znorm..vector_normc SsJtrFt|}|dks|gks|dkrdnd}|dkr"|gkr"|ndg}|r1|gks1|dus1J|tdkr?t|||St|||Stdit}|j | d}|j dd|id |id |j | d} |dksv|gksv|dkrxdnd}|dkr|gkr|ndg}|tdkrd nd } |j | d|id | i|||d d| S)NTFrinfinf_normrKabsr%r'r)r*r+ reduce_max reduce_minrTr()rb) rrrcnprmaxminrr4r5rWr7) rUrZrrXr[r8r9rSr=Z reduce_outZ reduce_typer?r?r@rbs@  znorm..inf_norm?c Ss"tr"t|}t||}t||d|}t|td|}|Stdit} | j| d}| j| d}| j dd|id|id| j| d}| j d d|id|id |id | j| d}| j d d|id|i|||durvd nddd | j d d|id|id td|id |S)z NOTE: This function actually treats the matrix as flattened vector to calculate vector norm instead of matrix norm. NrjnormrKrcr%r'rdpowfactorr( reduce_sumTFrTrk) rrrcrlsumr^rr4r5rWr7) rUrZrrXr8abs_outpow_outsum_outr9blockr?r?r@ p_matrix_normsX   znorm..p_matrix_normrQ)r<rXr8z,only valid string values are 'fro', found {}T)rZrrXr[r8z.only valid p type is string or float, found {}r rr)rrZrXr[r8z:unspport p for p-order vector norm. except float, found {})rZrrXr8zIjust suport axis type int or list (length of list <=1) if p = 0, found {}z;except axis type int or list (length of list <=2), found {}NFN)NNFFN) r/strr2formatr_r^r)r.r-r0rgra) rprrXr8rVr`rbrur?r?r@rks W. < ,5        rkc Cstr t|||St|dddgdt|dddgdt|dttfdtd it}| |j }|g|gd}d|gi}dt|i}|j d|d|i|d|S) a 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 the absolute value of z. .. math:: ||z||_\infty=\max_i |z_i| When p = -inf, the negative-inf-norm of z is the minimum element of the absolute value 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 x = paddle.to_tensor([[3, 3],[3, 3]], dtype="float32") y = paddle.to_tensor([[3, 3],[3, 1]], dtype="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.] r6rrdistryrLr'r(N)rz) rrrzrr r^r_rr4r5r6r7) rrEryr8r=r9r*r+r,r?r?r@rzsR    rzc Csddd}ddgfdd}dgfd d }d d }t|j}t|dks.td dt||dkr4d}d|vr:dnd}|ddddtjtj fvr|t|d|t|dkr|dkrf|||ddS|} |dkrv|||| S|dkr||||| |S|dvr|||dgd|| |dgdS|tjtj fvr|||dgd|| |dgdSdStd|d|dvr|dkr|||ddS|||dStd|d)a Computes the condition number of a matrix or batches of matrices with respect to a matrix norm ``p``. Args: 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``. 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 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) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1.41421342]) # compute conditional number when order of the norm is 'fro' out_fro = paddle.linalg.cond(x, p='fro') # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [3.16227770]) # compute conditional number when order of the norm is 'nuc' out_nuc = paddle.linalg.cond(x, p='nuc') # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [9.24263859]) # compute conditional number when order of the norm is 1 out_1 = paddle.linalg.cond(x, p=1) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [2.]) # compute conditional number when order of the norm is -1 out_minus_1 = paddle.linalg.cond(x, p=-1) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1.]) # compute conditional number when order of the norm is 2 out_2 = paddle.linalg.cond(x, p=2) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1.41421342]) # compute conditional number when order of the norm is -1 out_minus_2 = paddle.linalg.cond(x, p=-2) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0.70710683]) # compute conditional number when order of the norm is inf out_inf = paddle.linalg.cond(x, p=float("inf")) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [2.]) # compute conditional number when order of the norm is -inf out_minus_inf = paddle.linalg.cond(x, p=-float("inf")) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1.]) a = paddle.randn([2, 4, 4]) # Tensor(shape=[2, 4, 4], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[[-0.06784091, -0.07095790, 1.31792855, -0.58959651], # [ 0.20818676, -0.85640615, -0.89998871, -1.47439921], # [-0.49132481, 0.42250812, -0.77383220, -2.19794774], # [-0.33551720, -1.70003879, -1.09795380, -0.63737559]], # [[ 1.12026262, -0.16119350, -1.21157813, 2.74383283], # [-0.15999718, 0.18798758, -0.69392562, 1.35720372], # [-0.53013402, -2.26304483, 1.40843511, -1.02288902], # [ 0.69533503, 2.05261683, -0.02251151, -1.43127477]]]) a_cond_fro = paddle.linalg.cond(a, p='fro') # Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [8.86691189 , 75.23817444]) b = paddle.randn([2, 3, 4]) # Tensor(shape=[2, 3, 4], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[[-0.43754861, 1.80796063, -0.78729683, -1.82264030], # [-0.27670753, 0.06620564, 0.29072434, -0.31155765], # [ 0.34123746, -0.05444612, 0.05001324, -1.46877074]], # [[-0.64331555, -1.51103854, -1.26277697, -0.68024760], # [ 2.59375715, -1.06665540, 0.96575671, -0.73330832], # [-0.47064447, -0.23945692, -0.95150250, -1.07125998]]]) b_cond_2 = paddle.linalg.cond(b, p=2) # Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [6.64228773, 3.89068866]) rjNc Ss|dus|gkr dnd}|dkr|gkr|ndg}d}trPt|}t||d|}|dks4|tjkr.mat_normrrYc Ss|dus|gkr dnd}d}tr1t||}t||d|}t||d|}t|td|Str]t|d|}t|d|d|d|}t|d|d|d|}t|dtd|St dit }|j | d }|j | d }|j | d }|j | d } |j d d |id |id|id|j dd |id |i|||dd|j dd |id |i|||dd|j d d |id | idtd|id| S)zr NOTE: Calculate the frobenius norm of a square matrix or batches of square matrices. NTFrjrmr<rXrSrkrKrlr%r'r(rnrTro)rrrlrpr^paddlein_dynamic_moderrnrr4r5rWr7) rUrZrrSrXrrZ sum_out_1Z sum_out_2rtr9r?r?r@fro_norms     zcond..fro_normc Ss,|dus|gkr dnd}d}t|dd\}}}tr|dkr4tr)t||d|St|d|d|d|StrZt|||}t|||} |d krOt || S|d krYt | |Sn2t |d|d|d|}t |d|d|d|} |d kr~t || d |d dS|d krt | |d |d dSt dit} | j| d} |dkr| jdd|id| i|||dd| S| j| d}| j| d} | jdd|id|i|||dd| jdd|id| i|||dd|d kr| jd|| dd| i|ddd| S|d kr| jd| |dd| i|ddd| SdS)z 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. NTF) full_matricesnucr<rXrSraixs use_mkldnnrkrKrnr%r'rTr(rerfelementwise_divrL)rrro)svdrrrrprrnrhridividererfrrr4r5rWr7) rUrZrrSrXusvhZmax_outZmin_outrtr9r?r?r@svd_norms         zcond..svd_normcSstr ||Std)Nz0only support x is nonempty tensor in static mode)r|r}reshaper2)rUr1r?r?r@ empty_tensorbs zcond..empty_tensorz1input should be a matrix or batches of matrices, z)but the dimention of received input is {}rr rQrrr rY)rZrz%only support p is {} when input is a z+square matrix or batches of square matrices)rr)rZz5unsupported {} for p, only supporting ('fro', 'nuc', z 1, -1, 2, -2, inf, -inf) or none)rjN)r-r1r0r2rxrgraZinverse) rryr8r{r~rrr>Zx_sizeZx_invr?r?r@conds\ dbJd     rcCstr t||Strt||Sd}|dusJd||dus*Jd|t|dgd|t|dgd|t|fit}|durQ|j |j d}n |j ||j d d }|j d||d id |id |S)af 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 # 1-D Tensor * 1-D Tensor x = paddle.to_tensor([1, 2, 3]) y = paddle.to_tensor([4, 5, 6]) z = paddle.dot(x, y) print(z) # [32] # 2-D Tensor * 2-D Tensor x = paddle.to_tensor([[1, 2, 3], [2, 4, 6]]) y = paddle.to_tensor([[4, 5, 6], [4, 5, 6]]) z = paddle.dot(x, y) print(z) # [[32], [64]] dotNzx cannot be None in {}zy cannot be None in {}r)rrrrrErKF)r8r6Z persistablerLr'r)r*r,r+) rrrr rrxrrr4r5r6Zcreate_variabler7)rrEr8rOr=r9r?r?r@rs.#    rTcCsd}t|jdkst|jdkrtdt|jt|dddgd|}t|jdkr0|d}|s=|jd dkr=|}d }|jd} |d ur||j}t|jdkr^td t|j|jd | krptd | |jd | d krtd | t |t |dkstd|d ur||j} t| jdkrtdt|jt|dddgd|jd | krtd| |jd | d krtd| |d ur|| }n| }t j | |jd} |d us|d ur|} | d krtd|d ur||} | jdd| } n |jdd| } |} |d ur3|d ur3|dkr3| ||| }n| |}|d krDt j d |jd}|| d}t || }t ||}|S)u  Estimate the covariance matrix of the input variables, given data and weights. A covariance matrix is a square matrix, indicate the covariance of each pair variables in the input matrix. For example, for an N-dimensional samples X=[x1,x2,…xN]T, then the covariance matrix element Cij is the covariance of xi and xj. The element Cii is the variance of xi itself. Parameters: x(Tensor): A N-D(N<=2) Tensor containing multiple variables and observations. By default, each row of x represents a variable. Also see rowvar below. rowvar(Bool, optional): If rowvar is True (default), then each row represents a variable, with observations in the columns. Default: True ddof(Bool, optional): If ddof=True will return the unbiased estimate, and ddof=False will return the simple average. Default: True fweights(Tensor, optional): 1-D Tensor of integer frequency weights; The number of times each observation vector should be repeated. Default: None aweights(Tensor, optional): 1-D Tensor of observation vector weights. How important of the observation vector, larger data means this element is more important. Default: None 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 covariance matrix Tensor of the variables. Examples: .. code-block:: python import paddle xt = paddle.rand((3,4)) paddle.linalg.cov(xt) ''' Tensor(shape=[3, 3], dtype=float64, place=CUDAPlace(0), stop_gradient=True, [[0.07918842, 0.06127326, 0.01493049], [0.06127326, 0.06166256, 0.00302668], [0.01493049, 0.00302668, 0.01632146]]) ''' covrr z]Input(x) only support N-D (1<=N<=2) tensor in cov, but received length of Input(input) is %s.r6rrrrNz`Input(fweights) only support N-D (N<=1) tensor in cov, but received shape of Input(input) is %s.ziThe number of Input(fweights) should equal to x's dim[1]: {}, but received size of Input(fweights) is {}.zZThe value of Input(fweights) cannot be negtive, but received min of Input(fweights) is {}.z Input(fweights) must be integer zaInput(aweights) only support N-D (N<=1) tensor in cov, but received length of Input(input) is %s.ziThe number of Input(aweights) should equal to x's dim[1]: {}, but received size of Input(aweights) is {}.zZThe value of Input(aweights) cannot be negtive, but received min of Input(aweights) is {}.rKz0The sum of weights is zero, can't be normalized.)rT)r0r1r2rrtZastyper6rxrir|allround to_tensorrpitem unsqueezemmconjrZsqueeze)rrowvarZddofZfweightsZaweightsr8rOnxwZobservation_numZawZw_sumZnx_wZavgZ norm_factorZxxtrr?r?r@rs#               rcCst|jdkrtdt|jtr(t|jdkr|Sddg}t||}|StrCt|jdkr4|Sddg}t|d|\}}|St |dgddt dit }| |j }| |j }t|jdkrk|}|S|jd d |gi|g|gd dddgid |S)al 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 float32, float64, int32, int64. 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. Examples: .. code-block:: python :name: code-example import paddle # Example 1 (0-D tensor) x = paddle.to_tensor([0.79]) paddle.t(x) # [0.79] # Example 2 (1-D tensor) x = paddle.to_tensor([0.79, 0.84, 0.32]) paddle.t(x) # [0.79000002, 0.83999997, 0.31999999] paddle.t(x).shape # [3] # Example 3 (2-D tensor) x = paddle.to_tensor([[0.79, 0.84, 0.32], [0.64, 0.14, 0.57]]) x.shape # [2, 3] paddle.t(x) # [[0.79000002, 0.63999999], # [0.83999997, 0.14000000], # [0.31999999, 0.56999999]] paddle.t(x).shape # [3, 2] rzInput(input) only support N-D (N<=2) tensor, but received length of Input(input) is %s. Perhaps you can use paddle.tensor.transpose() instead.r rrrU)rrrrrr"rr$r%r&r(N)r)r0r1r2rrr"r rr$rrr4r5r6r7)rUr8r#r9r:r= input_shaper?r?r@rMsJ'     rcCstr|dur tn|}t|||Str'|dur!t||d|St||Stdit}||j }t }||d<|j d||dd|i|d|S)aC 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 be 9 which indicates using 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.]] Nr<crossrLr'r()r) r K_DEFAULT_DIMrrr rrr4r5r6dictr7)rrErr8r=r9r,r?r?r@rs$&  rcCstr t||Strt|d|St|dddgdt|dtdtd it }|j |j d}|j dd|gid|id|id |S) a Computes the Cholesky decomposition of one symmetric positive-definite matrix or batches of symmetric positive-definite matrice. If `upper` is `True`, the decomposition has the form :math:`A = U^{T}U` , and the returned matrix :math:`U` is upper-triangular. Otherwise, the decomposition has the form :math:`A = LL^{T}` , and the returned matrix :math:`L` is lower-triangular. Args: x (Tensor): The input tensor. Its shape should be `[*, M, M]`, where * is zero or more batch dimensions, and matrices on the inner-most 2 dimensions all should be symmetric positive-definite. Its data type should be float32 or float64. upper (bool): The flag indicating whether to return upper or lower triangular matrices. Default: False. name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: Tensor, A Tensor with same shape and data type as `x`. It represents triangular matrices generated by Cholesky decomposition. Examples: .. code-block:: python import paddle a = paddle.rand([3, 3], dtype="float32") a_t = paddle.transpose(a, [1, 0]) x = paddle.matmul(a, a_t) + 1e-03 out = paddle.linalg.cholesky(x, upper=False) print(out) upperr6rrcholeskyrKr%r'r(N)r) rrrr rrr rrr4r5r6r7)rrr8r=r9r?r?r@rs$ rc Cstr8t|tr!|j|jkrt||j}n|}d}t||||S|dur*d}d}nt|}d}t||||St rs|durFd}d}d}n!t|tr_|j|jkrXt||j}n|}d}d}nd}t|}d}t ||d|d|d|Si}i}t |dd d gd ||d <|durd|d<n,t|trd|d<|j|jkrt||j|d <n||d <nt |dtd d|d<||d<t |dt d ||d<tdit} | jdd} | jd |d| i|d| S)a 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 eigenvalues 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, enabling a more efficient method for finding eigenvalues, 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]] FNgTtol hermitianuse_default_tolrrr matrix_rankr%Z TolTensorrrKr'r()r)rr/r r6rrZmatrix_rank_tolr^rr rrr rrr4r5r7) rrrr8Z tol_tensorrZtol_attrr*r,r=r9r?r?r@rsz'           rcCs|j}|j}t|t|krdksntd|||d|dkr-td|||d|dkr=td||trFt||StrPt ||St dit }|j |j d }|jd||d d |id |S)a 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: .. code-block:: python 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) # Tensor(shape=[2, 2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, # [[[6. , 6. ], # [12., 12.]], # [[45., 45.], # [60., 60.]]]) zRx and y should be 3-dimensional. But received x's dimention: {}, y's dimention: {}rr zRx's width must be equal with y's height. But received x's shape: {}, y's shape: {}rzgx's batch (shape[0]) must be equal with y's batch (shape[0]). But received x's shape: {}, y's shape: {}bmmrKrLr'rdN)r)r1r0r2rxrrrr|r}rrr4r5r6r7)rrEr8r>Zy_shaper=r9r?r?r@rs8'  rdc Cstr t||||Strt|d|d|d|Std it}t|dgdd|t j j }|j dd|id|i|||dd |S) a 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, optional): number of histogram bins. min (int, optional): lower end of the range (inclusive). max (int, optional): upper end of the range (inclusive). name (str, optional): For details, please refer to :ref:`api_guide_Name`. Generally, no setting is required. Default: None. 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] binsrirh histogramr%rrrrr')rrirhr(N)r) rrrr rrr4rr5rZVarTypeZINT64r7)rUrrirhr8r=r9r?r?r@rs$  rcCs|jtjtjfvr tdtrt||d|Stdit }t |dddgd|dur>t |dgd d|j |jd }n|j |jd }|j d||d d |id|id |S)a 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] z+Elements in Input(x) should all be integers minlengthbincountr%rrNWeightsrrK)r%rr'r()r) r6r|rr TypeErrorrrrrr4rr5r7)rweightsrr8r=r9r?r?r@rs,rcCsvtr t||Strt||}|Sdd}|||td it}|j|jd}|j d||dd|id|S) aK 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 paddle x = paddle.to_tensor([[2, 1, 3], [3, 0, 1]]).astype("float64") vec = paddle.to_tensor([3, 5, 1]).astype("float64") out = paddle.mv(x, vec) print(out) # Tensor(shape=[2], dtype=float64, place=Place(cpu), stop_gradient=True, # [14., 10.]) cSsz||d}|D] \}}t||ddgdq t|j}t|j}t|dkr.td|t|dkr;td|dS) N)rvecrrmvrz9x should be 2-dimensional. But received x's dimention: {}r z=vec should be 1-dimensional. But received vec's dimention: {})rGrr-r1r0r2rx)rrrHr8rIr>Z vec_shaper?r?r@rJZs(      zmv..__check_inputrrK)r%ZVecr'rdN)r) rrrr rrr4r5r6r7)rrr8r9rJr=r?r?r@r4s   rcCstrt|Strt|St|jdddgdt|j }t |dks-Jdt ||d|dksAJd |d|dft dit }|j |jd }|jd d|gid |gid |S)af 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: Tensor, the determinant value of a square matrix or batches of square matrices. Examples: .. code-block:: python import paddle x = paddle.randn([3,3,3]) A = paddle.linalg.det(x) print(A) # [ 0.02547996, 2.52317095, -6.15900707]) InputrrdetrNThe x must be at least 2-dimensional, but received Input x's dimensional: %s. rYr3Expect squared input,but received %s by %s matrix. determinantrKr'rdN)r)rrrr rrr r6r-r1r0rr4r5r7rr8rr=r9r?r?r@rys.   rcCstrt|Strt|St|jdddgdt |j }t |dks.Jdt ||d|dksBJd |d|dft dit }|j|jd }|jd d|gid |gid |S)a 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) 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. Examples: .. code-block:: python import paddle x = paddle.randn([3,3,3]) A = paddle.linalg.slogdet(x) print(A) # [[ 1. , 1. , -1. ], # [-0.98610914, -0.43010661, -0.10872950]]) rrrslogdetrrrYrrslogdeterminantrKr'rdN)r)rrrr|r}rrr r6r-r1r0rr4r5r7rr?r?r@rs.   rcCstr t||Strt|d|St|dddgdt|dtdtd it }|j |j d}|j |j d}|j |j d}t }||d<|j dd|gi|||d|d |||fS) a 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:: X = U * diag(S) * VT 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 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, which means shape of U is `[..., N, N]`, shape of V is `[..., M, M]`. K = min(M, N). 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]`. K = min(M, N). name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: 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]` Examples: .. code-block:: python import paddle 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, vh = paddle.linalg.svd(x) print (u) #U = [[ 0.27364809, -0.21695147 ], # [ 0.37892198, -0.87112408 ], # [ 0.8840446 , 0.44053933 ]] print (s) #S = [8.14753743, 0.78589688] print (vh) #VT= [[ 0.51411221, 0.85772294], # [ 0.85772294, -0.51411221]] # one can verify : U * S * VT == X # U * UH == I # V * VH == I rr6rrrrKr%UZVHSr(N)r)rrrr rrr rrr4r5r6rr7)rrr8r=rrrr,r?r?r@rs&0   rcCstr t||Strt|d|St|dddgdt|dtdtd it }|j |j d}|j dd|id|id|id |S) a 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.linalg.matrix_power(x, 2)) # [[6. , 34. , 102.], # [14. , 90. , 282.], # [36. , 250., 804.]] print(paddle.linalg.matrix_power(x, 0)) # [[1., 0., 0.], # [0., 1., 0.], # [0., 0., 1.]] print(paddle.linalg.matrix_power(x, -2)) # [[ 12.91666667, -12.75000000, 2.83333333 ], # [-7.66666667 , 8. , -1.83333333 ], # [ 1.80555556 , -1.91666667 , 0.44444444 ]] nr6rr matrix_powerrKr%r'r(N)r) rrrr rrr r_rr4r5r6r7)rrr8r=r9r?r?r@r2s5 rreducedcCstrt||\}}|dkr|S||fStr+t|d|\}}|dkr'|S||fSt|dddgdt|dtdtd it }|j |j d}|j |j d}t }||d<|j dd|gi||d |d |dkrm|S||fS) a. 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 ; rmoder6rrqrrKr%)QRr(N)r)rrrr rrr rwrr4r5r6rr7)rrr8qrr=r,r?r?r@rzs.*rc Cstr t||\}}}nItrt|d|\}}}n:t|dddgdtd it}|j |j d}|j dd}|j dd}t }||d<|j dd|i|||d |d |r]|||fS||fS) uF Computes the LU factorization of an N-D(N>=2) matrix x. Returns the LU factorization(inplace x) and Pivots. low triangular matrix L and upper triangular matrix U are combined to a single LU matrix. Pivoting is done if pivot is set to True. P mat can be get by pivots: .. code-block:: text ones = eye(rows) #eye matrix of rank rows for i in range(cols): swap(ones[i], ones[pivots[i]]) return ones Args: X (Tensor): the tensor to factor of N-dimensions(N>=2). pivot (bool, optional): controls whether pivoting is done. Default: True. get_infos (bool, optional): if set to True, returns an info IntTensor. Default: False. name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: factorization (Tensor), LU matrix, the factorization of input X. pivots (IntTensor), the pivots of size(∗(N-2), min(m,n)). `pivots` stores all the intermediate transpositions of rows. The final permutation `perm` could be reconstructed by this, details refer to upper example. infos (IntTensor, optional), if `get_infos` is `True`, this is a tensor of size (∗(N-2)) where non-zero values indicate whether factorization for the matrix or each minibatch has succeeded or failed. Examples: .. code-block:: python import paddle x = paddle.to_tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]).astype('float64') lu,p,info = paddle.linalg.lu(x, get_infos=True) # >>> lu: # Tensor(shape=[3, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True, # [[5. , 6. ], # [0.20000000, 0.80000000], # [0.60000000, 0.50000000]]) # >>> p # Tensor(shape=[2], dtype=int32, place=CUDAPlace(0), stop_gradient=True, # [3, 3]) # >>> info # Tensor(shape=[], dtype=int32, place=CUDAPlace(0), stop_gradient=True, # 0) P,L,U = paddle.linalg.lu_unpack(lu,p) # >>> P # (Tensor(shape=[3, 3], dtype=float64, place=CUDAPlace(0), stop_gradient=True, # [[0., 1., 0.], # [0., 0., 1.], # [1., 0., 0.]]), # >>> L # Tensor(shape=[3, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True, # [[1. , 0. ], # [0.20000000, 1. ], # [0.60000000, 0.50000000]]), # >>> U # Tensor(shape=[2, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True, # [[5. , 6. ], # [0. , 0.80000000]])) # one can verify : X = P @ L @ U ; pivotr6rrlurKr_r%)r'PivotsZInfosr(N)r) rrrr|r}rrrr4r5r6rr7) rr get_infosr8rryinfor=r,r?r?r@rs(P    rc Cstrt||||\}}}|||fStr)t||d|d|\}}}|||fSt|dddgdtd it}|j |j d} |j |j d} |j |j d} t } || d<|| d<|j d||d| | | d | d | | | fS) a Unpack L U and P to single matrix tensor . unpack L and U matrix from LU, unpack permutation matrix P from Pivtos . P mat can be get by pivots: .. code-block:: text ones = eye(rows) #eye matrix of rank rows for i in range(cols): swap(ones[i], ones[pivots[i]]) Args: x (Tensor): The LU tensor get from paddle.linalg.lu, which is combined by L and U. y (Tensor): Pivots get from paddle.linalg.lu. unpack_ludata (bool,optional): whether to unpack L and U from x. Default: True. unpack_pivots (bool, optional): whether to unpack permutation matrix P from Pivtos. Default: True. name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Returns: P (Tensor), Permutation matrix P of lu factorization. L (Tensor), The lower triangular matrix tensor of lu factorization. U (Tensor), The upper triangular matrix tensor of lu factorization. Examples: .. code-block:: python import paddle x = paddle.to_tensor([[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]).astype('float64') lu,p,info = paddle.linalg.lu(x, get_infos=True) # >>> lu: # Tensor(shape=[3, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True, # [[5. , 6. ], # [0.20000000, 0.80000000], # [0.60000000, 0.50000000]]) # >>> p # Tensor(shape=[2], dtype=int32, place=CUDAPlace(0), stop_gradient=True, # [3, 3]) # >>> info # Tensor(shape=[], dtype=int32, place=CUDAPlace(0), stop_gradient=True, # 0) P,L,U = paddle.linalg.lu_unpack(lu,p) # >>> P # (Tensor(shape=[3, 3], dtype=float64, place=CUDAPlace(0), stop_gradient=True, # [[0., 1., 0.], # [0., 0., 1.], # [1., 0., 0.]]), # >>> L # Tensor(shape=[3, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True, # [[1. , 0. ], # [0.20000000, 1. ], # [0.60000000, 0.50000000]]), # >>> U # Tensor(shape=[2, 2], dtype=float64, place=CUDAPlace(0), stop_gradient=True, # [[5. , 6. ], # [0. , 0.80000000]])) # one can verify : X = P @ L @ U ; unpack_ludata unpack_pivotsr6rr lu_unpackrK)r%r)ZPmatLrr(N)r) rrrr|r}rrrr4r5r6rr7) rrErrr8Prrr=rylrr,r?r?r@r( s.I     rcCstrt|Strt|\}}||fSt|dgddtdit}| |j }| |j }d|i}||d}|j d||d||fS)a 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 paddle.device.set_device("cpu") x = paddle.to_tensor([[1.6707249, 7.2249975, 6.5045543], [9.956216, 8.749598, 6.066444 ], [4.4251957, 1.7983172, 0.370647 ]]) w, v = paddle.linalg.eig(x) print(v) # 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(w) # Tensor(shape=[3], dtype=complex128, place=CPUPlace, stop_gradient=False, # [ (16.50471283351188+0j) , (-5.5034820550763515+0j) , # (-0.21026087843552282+0j)]) r%rrr r!eigZ EigenvaluesZ EigenvectorsrdN)r) rrrr|r}rrrr4r5r6r7)rr8rvr=r*r+r?r?r@r s.     rcCst|dgddt|j}t|dkrtdt|||d|dkr-td|tr5t|St r>t |St dit }|j|jd }|jdd |id |id |S)aj Compute the eigenvalues of one or more general matrices. Warning: The gradient kernel of this operator does not yet developed. 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. Its shape should be `[*, M, M]`, where `*` is zero or more batch dimensions. Its data type should be float32, float64, complex64, or complex128. 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 containing the unsorted eigenvalues which has the same batch dimensions with `x`. The eigenvalues are complex-valued even when `x` is real. Examples: .. code-block:: python import paddle 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 r6reigvalsrz_The dimension of Input(x) should be at least 2, but received x's dimention = {}, x's shape = {}rYrzPThe last two dimensions of Input(x) should be equal, but received x's shape = {}rKr%r'rdN)r)rr-r1r0r2rxrrrr|r}rrr4r5r6r7)rr8r>r=r9r?r?r@r s0$     rcCstrt|Strt|St|dttfdt|D]\}}t |dt |dgdd|j |dj kr=2 tensor, but received length of Input(input) is %s.rYrzSThe input matrix must be batches of square matrices. But received x's dimention: {}rrz-UPLO must be L or U. But received UPLO is: {}r-r1r0r2rxrrr>r?r?r@rJ $ zeigh..__check_inputeighr6rrKr%rr(N)r) rrrr rrr4rr5r6r7)rrr8rJr= out_value out_vectorr?r?r@r` s&!   rV瞯.__check_inputeigvalshr6rrKr%r)rrr(N)r) rrrZ stop_gradientr|r}rrr4rr5r6r7) rrr8valuesr:rrJr=rrr?r?r@r s4 rc Cspt}|dkr|dvrtd||durdn|}nd|vr4|dvr+td||dur1d n|}ntd |j|jkrH|jtjtjfvrHntd |durw|jtjkrdd t|j d |j d}n|jtjkrwdt|j d |j d}t rt rt ||||\}}}} nt ||d|d|\}}}} |d krtjdgtjd}tjdg|jd} n |dkrtjdg|jd} |||| fStdit} t|dgddt|dgdd| j|jd}| j|jd}| jtjd}| j|jd} | jd||d|||| d||dd|d kr$tjjddgd}tjjddgd} n|dkr2tjjddgd} |||| fS) uK Computes a solution to the least squares problem of a system of linear equations. Args: x (Tensor): A tensor with shape ``(*, M, N)`` , the data type of the input Tensor ``x`` should be one of float32, float64. y (Tensor): A tensor with shape ``(*, M, K)`` , the data type of the input Tensor ``y`` should be one of float32, float64. rcond(float, optional): The default value is None. A float pointing number used to determine the effective rank of ``x``. If ``rcond`` is None, it will be set to max(M, N) times the machine precision of x_dtype. driver(str, optional): The default value is None. The name of LAPACK method to be used. For CPU inputs the valid values are ‘gels’, ‘gelsy’, ‘gelsd, ‘gelss’. For CUDA input, the only valid driver is ‘gels’. If ``driver`` is None, ‘gelsy’ is used for CPU inputs and ‘gels’ for CUDA inputs. 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: Tuple: A tuple of 4 Tensors which is (``solution``, ``residuals``, ``rank``, ``singular_values``). ``solution`` is a tensor with shape ``(*, N, K)``, meaning the least squares solution. ``residuals`` is a tensor with shape ``(*, K)``, meaning the squared residuals of the solutions, which is computed when M > N and every matrix in ``x`` is full-rank, otherwise return an empty tensor. ``rank`` is a tensor with shape ``(*)``, meaning the ranks of the matrices in ``x``, which is computed when ``driver`` in (‘gelsy’, ‘gelsd’, ‘gelss’), otherwise return an empty tensor. ``singular_values`` is a tensor with shape ``(*, min(M, N))``, meaning singular values of the matrices in ``x``, which is computed when ``driver`` in (‘gelsd’, ‘gelss’), otherwise return an empty tensor. Examples: .. code-block:: python import paddle paddle.set_device("cpu") x = paddle.to_tensor([[1, 3], [3, 2], [5, 6.]]) y = paddle.to_tensor([[3, 4, 6], [5, 3, 4], [1, 2, 1.]]) results = paddle.linalg.lstsq(x, y, driver="gelsd") print(results[0]) # [[ 0.78350395, -0.22165027, -0.62371236], # [-0.11340097, 0.78866047, 1.14948535]] print(results[1]) # [19.81443405, 10.43814468, 30.56185532]) print(results[2]) # 2 print(results[3]) # [9.03455734, 1.54167950] x = paddle.to_tensor([[10, 2, 3], [3, 10, 5], [5, 6, 12.]]) y = paddle.to_tensor([[4, 2, 9], [2, 0, 3], [2, 5, 3.]]) results = paddle.linalg.lstsq(x, y, driver="gels") print(results[0]) # [[ 0.39386186, 0.10230173, 0.93606132], # [ 0.10741687, -0.29028133, 0.11892585], # [-0.05115091, 0.51918161, -0.19948854]] print(results[1]) # [] cpu)NgelsZgelssZgelsdgelsyzaOnly support valid driver is 'gels', 'gelss', 'gelsd', 'gelsy' or None for CPU inputs. But got {}NrZgpu)NrzGOnly support valid driver is 'gels' or None for CUDA inputs. But got {}rz.Only support lstsq api for CPU or CUDA device.zIOnly support x and y have the same dtype such as 'float32' and 'float64'.gHz>rrYrrdriverr)r1r6lstsqr6rrKrL)ZSolutionZ ResidualsZRankZSingularValues)rrr(rank)r8r1singular_values)r)r|Z get_devicer2rx RuntimeErrorr6rrrhr1rrrrremptyrrr4rr5r7staticdata) rrErrr8ZdeviceZsolutionZ residualsrrr=r?r?r@r s;          rcCst|jdkst|jdkrtdt|jt|dddgdt||}|jdkr.||St|}t|r<| }t |}||d d d f}||d d d f}t|rnt t | d dt | d dSt |d d}|S) u A correlation coefficient matrix indicate the correlation of each pair variables in the input matrix. For example, for an N-dimensional samples X=[x1,x2,…xN]T, then the correlation coefficient matrix element Rij is the correlation of xi and xj. The element Rii is the covariance of xi itself. The relationship between the correlation coefficient matrix `R` and the covariance matrix `C`, is .. math:: R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } } The values of `R` are between -1 and 1. Parameters: x(Tensor): A N-D(N<=2) Tensor containing multiple variables and observations. By default, each row of x represents a variable. Also see rowvar below. rowvar(Bool, optional): If rowvar is True (default), then each row represents a variable, with observations in the columns. Default: True. 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: The correlation coefficient matrix of the variables. Examples: .. code-block:: python import paddle xt = paddle.rand((3,4)) print(paddle.linalg.corrcoef(xt)) # Tensor(shape=[3, 3], dtype=float32, place=Place(cpu), stop_gradient=True, # [[ 1. , -0.73702252, 0.66228950], # [-0.73702258, 1. , -0.77104872], # [ 0.66228974, -0.77104825, 1. ]]) rr zbInput(x) only support N-D (1<=N<=2) tensor in corrcoef, but received length of Input(input) is %s.r6rrcorrcoefrNrY)r0r1r2rrndimr|ZdiagZ is_complexrealsqrtcomplexZclipimag)rrr8cdZstddevr?r?r@r s,&       r)N)FFN)rQNFN)rN)NN)TTNNN)rN)FNrv)rrrN)NrN)rN)TFN)TTN)rN)rFN)TFFN)NNN)TN)CnumpyrgZ frameworkrrrrrZfluid.data_feederrr r rr Zfluid.frameworkr Z manipulationrmathrrZlogicrZcreationrr|warningsZpaddle.common_ops_importrrrr__all__rr"rFrkrzrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr?r?r?r@sx          f  u d & A { S > 7 p H / 8 E 8 < E H F h e C B N L I; O 5 L