# linear¶

paddle.nn.functional.common. linear ( x, weight, bias=None, name=None ) [source]

Fully-connected linear transformation operator. For each input \(X\) , the equation is:

\[Out = XW + b\]

where \(W\) is the weight and \(b\) is the bias.

If the weight is a 2-D tensor of shape \([in\_features, out\_features]\) , input should be a multi-dimensional tensor of shape \([batch\_size, *, in\_features]\) , where \(*\) means any number of additional dimensions. The linear operator multiplies input tensor with weight and produces an output tensor of shape \([batch\_size, *, out\_features]\) , If \(bias\) is not None, the bias should be a 1-D tensor of shape \([out\_features]\) and will be added to the output.

Parameters
• x (Tensor) – Input tensor. The data type should be float16, float32 or float64.

• weight (Tensor) – Weight tensor. The data type should be float16, float32 or float64.

• bias (Tensor, optional) – Bias tensor. The data type should be float16, float32 or float64. If it is set to None, no bias will be added to the output units.

• name (str, optional) – Normally there is no need for user to set this parameter. For detailed information, please refer to Name .

Returns

Tensor, the shape is \([batch\_size, *, out\_features]\) and the data type is the same with input \(x\) .

Examples

```import paddle

x = paddle.randn((3, 2), dtype="float32")
# x: [[-0.32342386 -1.200079  ]
#     [ 0.7979031  -0.90978354]
#     [ 0.40597573  1.8095392 ]]
weight = paddle.full(shape=[2, 4], fill_value="0.5", dtype="float32", name="weight")
# weight: [[0.5 0.5 0.5 0.5]
#          [0.5 0.5 0.5 0.5]]
bias = paddle.ones(shape=[4], dtype="float32", name="bias")
# bias: [1. 1. 1. 1.]
y = paddle.nn.functional.linear(x, weight, bias)
# y: [[0.23824859 0.23824859 0.23824859 0.23824859]
#     [0.9440598  0.9440598  0.9440598  0.9440598 ]
#     [2.1077576  2.1077576  2.1077576  2.1077576 ]]
```