# norm¶

paddle.linalg. norm ( x, p='fro', axis=None, keepdim=False, name=None ) [source]

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.

Parameters
• 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 input unless 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 Name.

Returns

results of norm operation on the specified axis of input tensor, it’s data type is the same as input’s Tensor.

Return type

Tensor

Examples

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: 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: 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: 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  = Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
#                    [12.])

# 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