# Mathematical 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
 where indices selection nonzero indices selection argwhere indices selection from_indices biulder from indices
 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
 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
 pow power function sqrt square root function cbrt cubic root function hypot hypotenuse function
 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
 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
 erf error function erfc complementary error function tgamma gamma function lgamma natural logarithm of the gamma function
 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
 isfinite checks for finite values isinf checks for infinite values isnan checks for NaN values isclose element-wise closeness detection allclose closeness reduction
 sum sum of elements over given axes prod product of elements over given axes mean mean of elements over given axes 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
 cumsum cumulative sum of elements over a given axis cumprod cumulative product of elements over given axes
 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