# chainer.functions.linear¶

chainer.functions.linear(x, W, b=None, n_batch_axes=1)[source]

Linear function, or affine transformation.

It accepts two or three arguments: an input minibatch x, a weight matrix W, and optionally a bias vector b. It computes

$y_i = W x_i + b.$
Parameters
• x (Variable or N-dimensional array) – Input variable, which is a $$(s_1, s_2, ..., s_n)$$-shaped float array. Its first n_batch_axes dimensions are handled as minibatch dimensions. The other dimensions are handled as concatenated one dimension whose size must be $$(s_{\rm n\_batch\_axes} * ... * s_n = N)$$.

• W (Variable or N-dimensional array) – Weight variable of shape $$(M, N)$$, where $$(N = s_{\rm n\_batch\_axes} * ... * s_n)$$.

• b (Variable or N-dimensional array) – Bias variable (optional) of shape $$(M,)$$.

• n_batch_axes (int) – The number of batch axes. The default is 1. The input variable is reshaped into ($${\rm n\_batch\_axes} + 1$$)-dimensional tensor. This should be greater than 0.

Returns

Output variable. A float array with shape of $$(s_1, ..., s_{\rm n\_batch\_axes}, M)$$.

Return type

Variable

Example

>>> x = np.random.uniform(0, 1, (3, 4)).astype(np.float32)
>>> W = np.random.uniform(0, 1, (5, 4)).astype(np.float32)
>>> b = np.random.uniform(0, 1, (5,)).astype(np.float32)
>>> y = F.linear(x, W, b)
>>> y.shape
(3, 5)