cond¶
- paddle.linalg. cond ( x, p=None, name=None ) [source]
-
Computes the condition number of a matrix or batches of matrices with respect to a matrix norm
p.- Parameters
-
x (Tensor) – The input tensor could be tensor of shape
(*, m, n)where*is zero or more batch dimensions forpin(2, -2), or of shape(*, n, n)where every matrix is invertible for any supportedp. And the input data type could befloat32orfloat64.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 Name.
- Returns
-
computing results of condition number, its data type is the same as input Tensor
x. - Return type
-
Tensor
Examples
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')) # a.numpy() # [[[ 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]