TensorFlow 2 version |
Math Operations.
TensorFlow provides a variety of math functions including:
- Basic arithmetic operators and trigonometric functions.
- Special math functions (like:
tf.math.igamma
andtf.math.zeta
) - Complex number functions (like:
tf.math.imag
andtf.math.angle
) - Reductions and scans (like:
tf.math.reduce_mean
andtf.math.cumsum
) - Segment functions (like:
tf.math.segment_sum
)
See: tf.linalg
for matrix and tensor functions.
About Segmentation
TensorFlow provides several operations that you can use to perform common
math computations on tensor segments.
Here a segmentation is a partitioning of a tensor along
the first dimension, i.e. it defines a mapping from the first dimension onto
segment_ids
. The segment_ids
tensor should be the size of
the first dimension, d0
, with consecutive IDs in the range 0
to k
,
where k<d0
.
In particular, a segmentation of a matrix tensor is a mapping of rows to
segments.
For example:
c = tf.constant([[1,2,3,4], [-1,-2,-3,-4], [5,6,7,8]])
tf.math.segment_sum(c, tf.constant([0, 0, 1]))
# ==> [[0 0 0 0]
# [5 6 7 8]]
The standard segment_*
functions assert that the segment indices are sorted.
If you have unsorted indices use the equivalent unsorted_segment_
function.
Thses functions take an additional argument num_segments
so that the output
tensor can be efficiently allocated.
c = tf.constant([[1,2,3,4], [-1,-2,-3,-4], [5,6,7,8]])
tf.math.unsorted_segment_sum(c, tf.constant([0, 1, 0]), num_segments=2)
# ==> [[ 6, 8, 10, 12],
# [-1, -2, -3, -4]]
Functions
abs(...)
: Computes the absolute value of a tensor.
accumulate_n(...)
: Returns the element-wise sum of a list of tensors.
acos(...)
: Computes acos of x element-wise.
acosh(...)
: Computes inverse hyperbolic cosine of x element-wise.
add(...)
: Returns x + y element-wise.
add_n(...)
: Adds all input tensors element-wise.
angle(...)
: Returns the element-wise argument of a complex (or real) tensor.
argmax(...)
: Returns the index with the largest value across axes of a tensor. (deprecated arguments)
argmin(...)
: Returns the index with the smallest value across axes of a tensor. (deprecated arguments)
asin(...)
: Computes the trignometric inverse sine of x element-wise.
asinh(...)
: Computes inverse hyperbolic sine of x element-wise.
atan(...)
: Computes the trignometric inverse tangent of x element-wise.
atan2(...)
: Computes arctangent of y/x
element-wise, respecting signs of the arguments.
atanh(...)
: Computes inverse hyperbolic tangent of x element-wise.
bessel_i0(...)
: Computes the Bessel i0 function of x
element-wise.
bessel_i0e(...)
: Computes the Bessel i0e function of x
element-wise.
bessel_i1(...)
: Computes the Bessel i1 function of x
element-wise.
bessel_i1e(...)
: Computes the Bessel i1e function of x
element-wise.
betainc(...)
: Compute the regularized incomplete beta integral \(I_x(a, b)\).
bincount(...)
: Counts the number of occurrences of each value in an integer array.
ceil(...)
: Returns element-wise smallest integer not less than x.
confusion_matrix(...)
: Computes the confusion matrix from predictions and labels.
conj(...)
: Returns the complex conjugate of a complex number.
cos(...)
: Computes cos of x element-wise.
cosh(...)
: Computes hyperbolic cosine of x element-wise.
count_nonzero(...)
: Computes number of nonzero elements across dimensions of a tensor. (deprecated arguments) (deprecated arguments)
cumprod(...)
: Compute the cumulative product of the tensor x
along axis
.
cumsum(...)
: Compute the cumulative sum of the tensor x
along axis
.
cumulative_logsumexp(...)
: Compute the cumulative log-sum-exp of the tensor x
along axis
.
digamma(...)
: Computes Psi, the derivative of Lgamma (the log of the absolute value of
divide(...)
: Computes Python style division of x
by y
.
divide_no_nan(...)
: Computes an unsafe divide which returns 0 if the y is zero.
equal(...)
: Returns the truth value of (x == y) element-wise.
erf(...)
: Computes the Gauss error function of x
element-wise.
erfc(...)
: Computes the complementary error function of x
element-wise.
exp(...)
: Computes exponential of x element-wise. \(y = e^x\).
expm1(...)
: Computes exp(x) - 1
element-wise.
floor(...)
: Returns element-wise largest integer not greater than x.
floordiv(...)
: Divides x / y
elementwise, rounding toward the most negative integer.
floormod(...)
: Returns element-wise remainder of division. When x < 0
xor y < 0
is
greater(...)
: Returns the truth value of (x > y) element-wise.
greater_equal(...)
: Returns the truth value of (x >= y) element-wise.
igamma(...)
: Compute the lower regularized incomplete Gamma function P(a, x)
.
igammac(...)
: Compute the upper regularized incomplete Gamma function Q(a, x)
.
imag(...)
: Returns the imaginary part of a complex (or real) tensor.
in_top_k(...)
: Says whether the targets are in the top K
predictions.
invert_permutation(...)
: Computes the inverse permutation of a tensor.
is_finite(...)
: Returns which elements of x are finite.
is_inf(...)
: Returns which elements of x are Inf.
is_nan(...)
: Returns which elements of x are NaN.
is_non_decreasing(...)
: Returns True
if x
is non-decreasing.
is_strictly_increasing(...)
: Returns True
if x
is strictly increasing.
l2_normalize(...)
: Normalizes along dimension axis
using an L2 norm. (deprecated arguments)
lbeta(...)
: Computes \(ln(|Beta(x)|)\), reducing along the last dimension.
less(...)
: Returns the truth value of (x < y) element-wise.
less_equal(...)
: Returns the truth value of (x <= y) element-wise.
lgamma(...)
: Computes the log of the absolute value of Gamma(x)
element-wise.
log(...)
: Computes natural logarithm of x element-wise.
log1p(...)
: Computes natural logarithm of (1 + x) element-wise.
log_sigmoid(...)
: Computes log sigmoid of x
element-wise.
log_softmax(...)
: Computes log softmax activations. (deprecated arguments)
logical_and(...)
: Returns the truth value of x AND y element-wise.
logical_not(...)
: Returns the truth value of NOT x element-wise.
logical_or(...)
: Returns the truth value of x OR y element-wise.
logical_xor(...)
: Logical XOR function.
maximum(...)
: Returns the max of x and y (i.e. x > y ? x : y) element-wise.
minimum(...)
: Returns the min of x and y (i.e. x < y ? x : y) element-wise.
mod(...)
: Returns element-wise remainder of division. When x < 0
xor y < 0
is
multiply(...)
: Returns x * y element-wise.
multiply_no_nan(...)
: Computes the product of x and y and returns 0 if the y is zero, even if x is NaN or infinite.
negative(...)
: Computes numerical negative value element-wise.
nextafter(...)
: Returns the next representable value of x1
in the direction of x2
, element-wise.
not_equal(...)
: Returns the truth value of (x != y) element-wise.
polygamma(...)
: Compute the polygamma function \(\psi^{(n)}(x)\).
polyval(...)
: Computes the elementwise value of a polynomial.
pow(...)
: Computes the power of one value to another.
real(...)
: Returns the real part of a complex (or real) tensor.
reciprocal(...)
: Computes the reciprocal of x element-wise.
reciprocal_no_nan(...)
: Performs a safe reciprocal operation, element wise.
reduce_all(...)
: Computes the "logical and" of elements across dimensions of a tensor. (deprecated arguments)
reduce_any(...)
: Computes the "logical or" of elements across dimensions of a tensor. (deprecated arguments)
reduce_euclidean_norm(...)
: Computes the Euclidean norm of elements across dimensions of a tensor.
reduce_logsumexp(...)
: Computes log(sum(exp(elements across dimensions of a tensor))). (deprecated arguments)
reduce_max(...)
: Computes the maximum of elements across dimensions of a tensor. (deprecated arguments)
reduce_mean(...)
: Computes the mean of elements across dimensions of a tensor.
reduce_min(...)
: Computes the minimum of elements across dimensions of a tensor. (deprecated arguments)
reduce_prod(...)
: Computes the product of elements across dimensions of a tensor. (deprecated arguments)
reduce_std(...)
: Computes the standard deviation of elements across dimensions of a tensor.
reduce_sum(...)
: Computes the sum of elements across dimensions of a tensor. (deprecated arguments)
reduce_variance(...)
: Computes the variance of elements across dimensions of a tensor.
rint(...)
: Returns element-wise integer closest to x.
round(...)
: Rounds the values of a tensor to the nearest integer, element-wise.
rsqrt(...)
: Computes reciprocal of square root of x element-wise.
scalar_mul(...)
: Multiplies a scalar times a Tensor
or IndexedSlices
object.
segment_max(...)
: Computes the maximum along segments of a tensor.
segment_mean(...)
: Computes the mean along segments of a tensor.
segment_min(...)
: Computes the minimum along segments of a tensor.
segment_prod(...)
: Computes the product along segments of a tensor.
segment_sum(...)
: Computes the sum along segments of a tensor.
sigmoid(...)
: Computes sigmoid of x
element-wise.
sign(...)
: Returns an element-wise indication of the sign of a number.
sin(...)
: Computes sine of x element-wise.
sinh(...)
: Computes hyperbolic sine of x element-wise.
softmax(...)
: Computes softmax activations. (deprecated arguments)
softplus(...)
: Computes softplus: log(exp(features) + 1)
.
softsign(...)
: Computes softsign: features / (abs(features) + 1)
.
sqrt(...)
: Computes square root of x element-wise.
square(...)
: Computes square of x element-wise.
squared_difference(...)
: Returns (x - y)(x - y) element-wise.
subtract(...)
: Returns x - y element-wise.
tan(...)
: Computes tan of x element-wise.
tanh(...)
: Computes hyperbolic tangent of x
element-wise.
top_k(...)
: Finds values and indices of the k
largest entries for the last dimension.
truediv(...)
: Divides x / y elementwise (using Python 3 division operator semantics).
unsorted_segment_max(...)
: Computes the maximum along segments of a tensor.
unsorted_segment_mean(...)
: Computes the mean along segments of a tensor.
unsorted_segment_min(...)
: Computes the minimum along segments of a tensor.
unsorted_segment_prod(...)
: Computes the product along segments of a tensor.
unsorted_segment_sqrt_n(...)
: Computes the sum along segments of a tensor divided by the sqrt(N).
unsorted_segment_sum(...)
: Computes the sum along segments of a tensor.
xdivy(...)
: Returns 0 if x == 0, and x / y otherwise, elementwise.
xlogy(...)
: Returns 0 if x == 0, and x * log(y) otherwise, elementwise.
zero_fraction(...)
: Returns the fraction of zeros in value
.
zeta(...)
: Compute the Hurwitz zeta function \(\zeta(x, q)\).