cond

paddle.linalg. cond ( x, p=None, name=None ) [源代码]

根据范数种类 p 计算一个或一批矩阵的条件数，也可以通过 paddle.cond 来调用。

参数：

  • x (Tensor) : 输入可以是形状为 (*, m, n) 的矩阵Tensor， * 为零或更大的批次维度，此时 p 为 2 或 -2 ；也可以是形状为 (*, n, n) 的可逆（批）方阵Tensor，此时 p 为任意已支持的值。数据类型为 float32 或 float64 。

  • p (float|string，可选) : 范数种类。目前支持的值为 fro 、 nuc 、 1 、 -1 、 2 、 -2 、 inf 、 -inf 。默认值为 None ，即范数种类为 2 。

  • name (str，可选) - 默认值为 None ，一般无需设置，具体用法请参见 Name 。

返回：

  • Tensor， 条件数的计算结果， 数据类型和输入 x 的一致。

代码示例：

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]