Theano-0.4.0.zip

.. currentmodule:: tensor =========================== Basic Tensor Functionality =========================== Theano supports any kind of Python object, but its focus is support for symbolic matrix expressions. When you type, >>> x = T.fmatrix() the ``x`` is a :class:`TensorVariable` instance. The ``T.fmatrix`` object itself is an instance of :class:`TensorType`. Theano knows what type of variable ``x`` is because ``x.type`` points back to ``T.fmatrix``. This chapter explains the various ways of creating tensor variables, the attributes and methods of :class:`TensorVariable` and :class:`TensorType`, and various basic symbolic math and arithmetic that Theano supports for tensor variables. .. _libdoc_tensor_creation: Creation ======== Theano provides a list of predefined tensor types that can be used to create a tensor variables. Variables can be named to facilitate debugging, and all of these constructors accept an optional ``name`` argument. For example, the following each produce a TensorVariable instance that stands for a 0-dimensional ndarray of integers with the name ``'myvar'``: >>> x = scalar('myvar', dtype='int32') >>> x = iscalar('myvar') >>> x = TensorType(dtype='int32', broadcastable=())('myvar') Constructors with optional dtype ---------------------------------------- These are the simplest and often-preferred methods for creating symbolic variables in your code. By default, they produce floating-point variables (with dtype determined by config.floatX, see :attr:`floatX`) so if you use these constructors it is easy to switch your code between different levels of floating-point precision. .. function:: scalar(name=None, dtype=config.floatX) Return a Variable for a 0-dimensional ndarray .. function:: vector(name=None, dtype=config.floatX) Return a Variable for a 1-dimensional ndarray .. function:: row(name=None, dtype=config.floatX) Return a Variable for a 2-dimensional ndarray in which the number of rows is guaranteed to be 1. .. function:: col(name=None, dtype=config.floatX) Return a Variable for a 2-dimensional ndarray in which the number of columns is guaranteed to be 1. .. function:: matrix(name=None, dtype=config.floatX) Return a Variable for a 2-dimensional ndarray .. function:: tensor3(name=None, dtype=config.floatX) Return a Variable for a 3-dimensional ndarray .. function:: tensor4(name=None, dtype=config.floatX) Return a Variable for a 4-dimensional ndarray .. #COMMENT Each of the types described above can be constructed by two methods: a singular version (e.g., :ref:`dmatrix <libdoc_tensor_creation>`) and a plural version (:ref:`dmatrices <libdoc_tensor_creation>`). When called, the singular version takes a single argument which is the name of the *Variable* we want to make and it makes a single Variable of that type. The plural version can either take All Fully-Typed Constructors ---------------------------- The following TensorType instances are provided in the theano.tensor module. They are all callable, and accept an optional ``name`` argument. So for example: .. code-block:: python from theano.tensor import * x = dmatrix() # creates one Variable with no name x = dmatrix('x') # creates one Variable with name 'x' xyz = dmatrix('xyz') # creates one Variable with name 'xyz' .. #COMMENT table generated by $ python Theano/doc/generate_dtype_tensor_table.py ============ =========== ==== =========== ================================= Constructor dtype ndim shape broadcastable ============ =========== ==== =========== ================================= bscalar int8 0 () () bvector int8 1 (?,) (False,) brow int8 2 (1,?) (True, False) bcol int8 2 (?,1) (False, True) bmatrix int8 2 (?,?) (False, False) btensor3 int8 3 (?,?,?) (False, False, False) btensor4 int8 4 (?,?,?,?) (False, False, False, False) wscalar int16 0 () () wvector int16 1 (?,) (False,) wrow int16 2 (1,?) (True, False) wcol int16 2 (?,1) (False, True) wmatrix int16 2 (?,?) (False, False) wtensor3 int16 3 (?,?,?) (False, False, False) wtensor4 int16 4 (?,?,?,?) (False, False, False, False) iscalar int32 0 () () ivector int32 1 (?,) (False,) irow int32 2 (1,?) (True, False) icol int32 2 (?,1) (False, True) imatrix int32 2 (?,?) (False, False) itensor3 int32 3 (?,?,?) (False, False, False) itensor4 int32 4 (?,?,?,?) (False, False, False, False) lscalar int64 0 () () lvector int64 1 (?,) (False,) lrow int64 2 (1,?) (True, False) lcol int64 2 (?,1) (False, True) lmatrix int64 2 (?,?) (False, False) ltensor3 int64 3 (?,?,?) (False, False, False) ltensor4 int64 4 (?,?,?,?) (False, False, False, False) dscalar float64 0 () () dvector float64 1 (?,) (False,) drow float64 2 (1,?) (True, False) dcol float64 2 (?,1) (False, True) dmatrix float64 2 (?,?) (False, False) dtensor3 float64 3 (?,?,?) (False, False, False) dtensor4 float64 4 (?,?,?,?) (False, False, False, False) fscalar float32 0 () () fvector float32 1 (?,) (False,) frow float32 2 (1,?) (True, False) fcol float32 2 (?,1) (False, True) fmatrix float32 2 (?,?) (False, False) ftensor3 float32 3 (?,?,?) (False, False, False) ftensor4 float32 4 (?,?,?,?) (False, False, False, False) cscalar complex64 0 () () cvector complex64 1 (?,) (False,) crow complex64 2 (1,?) (True, False) ccol complex64 2 (?,1) (False, True) cmatrix complex64 2 (?,?) (False, False) ctensor3 complex64 3 (?,?,?) (False, False, False) ctensor4 complex64 4 (?,?,?,?) (False, False, False, False) zscalar complex128 0 () () zvector complex128 1 (?,) (False,) zrow complex128 2 (1,?) (True, False) zcol complex128 2 (?,1) (False, True) zmatrix complex128 2 (?,?) (False, False) ztensor3 complex128 3 (?,?,?) (False, False, False) ztensor4 complex128 4 (?,?,?,?) (False, False, False, False) ============ =========== ==== =========== ================================= Plural Constructors -------------------------- There are several constructors that can produce multiple variables at once. These are not frequently used in practice, but often used in tutorial examples to save space! .. function:: iscalars, lscalars, fscalars, dscalars Return one or more scalar variables. .. function:: ivectors, lvectors, fvectors, dvectors Return one or more vector variables. .. function:: irows, lrows, frows, drows Return one or more row variables. .. function:: icols, lcols, fcols, dcols Return one or more col variables. .. function:: imatrices, lmatrices, fmatrices, dmatrices Return one o