# Mathematical functions

- Operators and related functions

operator+ | identity
operator- | opposite
operator+ | addition
operator- | substraction
operator* | multiplication
operator/ | division
operator|| | logical or
operator&& | logical and
operator! | logical not
where | ternary selection
any | return true if any value is truthy
all | return true if all the values are truthy
operator< | element-wise lesser than
operator<= | element-wise less or equal
operator> | element-wise greater than
operator>= | element-wise greater or equal
operator== | expression equality
operator!= | expression inequality
equal | element-wise equality
not_equal | element-wise inequality
less | element-wise lesser than
less_equal | element-wise less or equal
greater | element-wise greater than
greater_equal | element-wise greater or equal
cast | element-wise static_cast
operator& | bitwise and
operator| | bitwise or
operator^ | bitwise xor
operator~ | bitwise not
left_shift | bitwise shift left
right_shift | bitwise shift right
operator<< | bitwise shift left
operator>> | bitwise shift right

- Index related functions

where | indices selection
nonzero | indices selection
argwhere | indices selection
from_indices | biulder from indices

- Basic functions

abs | absolute value
fabs | absolute value
fmod | remainder of the floating point division operation
remainder | signed remainder of the division operation
fma | fused multiply-add operation
minimum | element-wise minimum
maximum | element-wise maximum
fmin | element-wise minimum for floating point values
fmax | element-wise maximum for floating point values
fdim | element-wise positive difference
clip | element-wise clipping operation
sign | element-wise indication of the sign

- Exponential functions

exp | natural exponential function
exp2 | base 2 exponential function
expm1 | natural exponential function, minus one
log | natural logarithm function
log2 | base 2 logarithm function
log10 | base 10 logarithm function
log1p | natural logarithm of one plus function

- Power functions

pow | power function
sqrt | square root function
cbrt | cubic root function
hypot | hypotenuse function

- Trigonometric functions

sin | sine function
cos | cosine function
tan | tangent function
asin | arc sine function
acos | arc cosine function
atan | arc tangent function
atan2 | arc tangent function, determining quadrants

- Hyperbolic functions

sinh | hyperbolic sine function
cosh | hyperbolic cosine function
tanh | hyperbolic tangent function
asinh | inverse hyperbolic sine function
acosh | inverse hyperbolic cosine function
atanh | inverse hyperbolic tangent function

- Error and gamma functions

erf | error function
erfc | complementary error function
tgamma | gamma function
lgamma | natural logarithm of the gamma function

- Nearest integer floating point operations

ceil | nearest integers not less
floor | nearest integers not greater
trunc | nearest integers not greater in magnitude
round | nearest integers, rounding away from zero
nearbyint | nearest integers using current rounding mode
rint | nearest integers using current rounding mode

- Classification functions

isfinite | checks for finite values
isinf | checks for infinite values
isnan | checks for NaN values
isclose | element-wise closeness detection
allclose | closeness reduction

- Reducing functions

sum | sum of elements over given axes
prod | product of elements over given axes
mean | mean of elements over given axes
average | weighted average along the specified axis
variance | variance of elements over given axes
stddev | standard deviation of elements over given axes
diff | Calculate the n-th discrete difference along the given axis
amax | amax of elements over given axes
amin | amin of elements over given axes
trapz | Integrate along the given axis using the composite trapezoidal rule
norm_l0 | L0 pseudo-norm over given axes
norm_l1 | L1 norm over given axes
norm_sq | Squared L2 norm over given axes
norm_l2 | L2 norm over given axes
norm_linf | Infinity norm over given axes
norm_lp_to_p | p_th power of Lp norm over given axes
norm_lp | Lp norm over given axes
norm_induced_l1 | Induced L1 norm of a matrix
norm_induced_linf | Induced L-infinity norm of a matrix

- Accumulating functions

cumsum | cumulative sum of elements over a given axis
cumprod | cumulative product of elements over given axes

- NaN functions

nan_to_num | convert NaN and +/- inf to finite numbers
nansum | sum of elements over a given axis, replacing NaN with 0
nanprod | product of elements over given axes, replacing NaN with 1
nancumsum | cumsum of elements over a given axis, replacing NaN with 0
nancumprod | cumprod of elements over given axes, replacing NaN with 1