table of Contents
Tensor calculation
tensorflow defines the basic tensor calculation lot, due to the special properties tensor, which arithmetic operations are mainly two types, one is based on the determinant / linear algebra, one is the calculation of the elemental-wise. The most common are:
Summation: tf.add
multiplication: tf.matmul,
inverse operation: tf.linalg.inv
Most are based on the definition in the calculation of linear algebra tf.linalg module. https://tensorflow.google.cn/api_docs/python/tf/linalg
tf.linalg module
Tensorflow linear algebra module provides a wealth of functions available for calls. In addition to the basic linear algebra determinant calculation, for example:
Adjoint (tf.linalg.adjoint)
value of the determinant of (tf.linalg.det)
is converted to a diagonal matrix (tf.linalg.diag)
eigenvalue and eigenvectors (tf.linalg.eigh)
determinant inversion ( tf.linalg.inv)
matrix multiplication (tf.linalg.matmul)
matrix transpose (tf.linalg.matrix_transpose)
the QR decomposition (tf.linalg.qr)
the SVD Singular value decomposition (tf.linalg.svd)
the LU decomposition (tf. linalg.lu)
determinant trace (tf.linalg.trace)
There are a number of advanced matrix analysis functions, such as adjoint matrix, the matrix cycle and so on.
class LinearOperator: Base class Defining A [BATCH of] Linear operator [S].
class LinearOperatorAdjoint: LinearOperator Representing The adjoint of Another operator adjoint.
class LinearOperatorBlockDiag:. Combines One or More LinearOperators in to A Block Diagonal Matrix block diagonal matrix
class LinearOperatorCirculant: LinearOperator acting like a circulant matrix circulant matrix.
class LinearOperatorCirculant2D: LinearOperator acting like circulant matrix block A block-circulant matrices.
class LinearOperatorCirculant3D: LinearOperator acting like circulant matrix block A nested inline block circulant matrix.
class LinearOperatorComposition: One composes or more LinearOperators. determinant may implement some of the user-defined operation
class LinearOperatorDiag: LinearOperator acting like a [batch] square diagonal matrix. 求batch的对角方阵
class LinearOperatorFullMatrix: LinearOperator that wraps a [batch] matrix.
class LinearOperatorHouseholder: LinearOperator acting like a [batch] of Householder transformations.
class LinearOperatorIdentity: LinearOperator acting like a [batch] square identity matrix.
class LinearOperatorInversion: LinearOperator representing the inverse of another operator.
class LinearOperatorKronecker: Kronecker product between two LinearOperators.Kronecker乘积
class LinearOperatorLowRankUpdate: Perturb a LinearOperator with a rank K update.
class LinearOperatorLowerTriangular: LinearOperator acting like a [batch] square lower triangular matrix.
class LinearOperatorScaledIdentity: LinearOperator acting like a scaled [batch] identity matrix A = c I.
class LinearOperatorToeplitz: LinearOperator acting like a [batch] of toeplitz matrices.
class LinearOperatorZeros: LinearOperator acting like a [batch] zero matrix.
tf.math module
Commonly used algebraic functions
In the math module, commonly used centralized algebra functions, e.g.
Absolute value (tf.math.abs)
of a given list of all tensor tensor elements do and element-wise accumulated (tf.accumulate_n)
trigonometric functions (tf.math.sin, tf.math.cos, tf. Math.tan)
inverse trigonometric functions (tf.math.acos, tf.math.asin, tf.math.atan)
hyperbolic functions (tf.math.sinh, tf.math.cosh, tf.math.tanh)
trans-bis Qu cosine function (tf.math.asinh, tf.math.acosh)
Bessel spline fitting (tf.math.bassel_i0, tf.bassel_i0e, tf.math.bessel_i1, tf.math.bassel_i1e )
rounding (tf.math .ceil, tf.math.floor)
operations carried out along a dimension (tf.math.reduce_any, tf.math.reduce_std, tf.math.reduce.mean, ... )
There are also a function of depth learning-related, such as:
Confusion matrix (tf.math.confusion_matrix)
tensor calculation certain data (tf.math.segment_ *)
tf.math.segment_*
Operation on the specified piece of data carried out tensor. There segment_max, segment_mean, segment_min, segment_prod, segment_sum. To segment_max example, where the direct use of tensorflow an example API documentation.
segment_ids=tf.constant([0,0,0,1,2,2,3,3])
v=tf.Variable([5,1,7,2,3,4,1,3])
m=tf.math.segment_max(v,segment_ids)
get:
m
Out[112]: <tf.Tensor: id=901, shape=(4,), dtype=int32, numpy=array([7, 2, 4, 3], dtype=int32)>
Intrinsic functions can be given segment_id, labe is calculated sequentially 0, 1, 2, the maximum value of the data segment, the image may show the calculation process is as follows:
c = tf.constant([[1,2,3,4], [4, 3, 2, 1], [5,6,7,8]])
segmax_c = tf.math.segment_max(c, tf.constant([0, 0, 1]))
print(segmax_c)
get:
tf.Tensor(
[[4 3 3 4]
[5 6 7 8]], shape=(2, 4), dtype=int32)
Here some slight understand. Indeed, where the tensor segment_id divided into two segments, [[1,2,3,4] [4,3,2,1]] is set, [5,6,7,8] is a group . After comparing each maximum value, the image of the "column" is drawing
Supplemental reading:
circulant: https: //www.cnblogs.com/torsor/p/8848641.html
