# Mathematical functions¶

## Trigonometric functions¶

 sin(x[, out]) Trigonometric sine, element-wise. cos(x[, out]) Cosine element-wise. tan(x[, out]) Compute tangent element-wise. arcsin(x[, out]) Inverse sine, element-wise. arccos(x[, out]) Trigonometric inverse cosine, element-wise. arctan(x[, out]) Trigonometric inverse tangent, element-wise. hypot(x1, x2[, out]) Given the “legs” of a right triangle, return its hypotenuse. arctan2(x1, x2[, out]) Element-wise arc tangent of x1/x2 choosing the quadrant correctly. degrees(x[, out]) Convert angles from radians to degrees. radians(x[, out]) Convert angles from degrees to radians. unwrap(p[, discont, axis]) Unwrap by changing deltas between values to 2*pi complement. deg2rad(x[, out]) Convert angles from degrees to radians. rad2deg(x[, out]) Convert angles from radians to degrees.

## Hyperbolic functions¶

 sinh(x[, out]) Hyperbolic sine, element-wise. cosh(x[, out]) Hyperbolic cosine, element-wise. tanh(x[, out]) Compute hyperbolic tangent element-wise. arcsinh(x[, out]) Inverse hyperbolic sine element-wise. arccosh(x[, out]) Inverse hyperbolic cosine, element-wise. arctanh(x[, out]) Inverse hyperbolic tangent element-wise.

## Rounding¶

 around(a[, decimals, out]) Evenly round to the given number of decimals. round_(a[, decimals, out]) Round an array to the given number of decimals. rint(x[, out]) Round elements of the array to the nearest integer. fix(x[, y]) Round to nearest integer towards zero. floor(x[, out]) Return the floor of the input, element-wise. ceil(x[, out]) Return the ceiling of the input, element-wise. trunc(x[, out]) Return the truncated value of the input, element-wise.

## Sums, products, differences¶

 prod(a[, axis, dtype, out, keepdims]) Return the product of array elements over a given axis. sum(a[, axis, dtype, out, keepdims]) Sum of array elements over a given axis. nansum(a[, axis, dtype, out, keepdims]) Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. cumprod(a[, axis, dtype, out]) Return the cumulative product of elements along a given axis. cumsum(a[, axis, dtype, out]) Return the cumulative sum of the elements along a given axis. diff(a[, n, axis]) Calculate the n-th order discrete difference along given axis. ediff1d(ary[, to_end, to_begin]) The differences between consecutive elements of an array. gradient(f, *varargs, **kwargs) Return the gradient of an N-dimensional array. cross(a, b[, axisa, axisb, axisc, axis]) Return the cross product of two (arrays of) vectors. trapz(y[, x, dx, axis]) Integrate along the given axis using the composite trapezoidal rule.

## Exponents and logarithms¶

 exp(x[, out]) Calculate the exponential of all elements in the input array. expm1(x[, out]) Calculate exp(x) - 1 for all elements in the array. exp2(x[, out]) Calculate 2**p for all p in the input array. log(x[, out]) Natural logarithm, element-wise. log10(x[, out]) Return the base 10 logarithm of the input array, element-wise. log2(x[, out]) Base-2 logarithm of x. log1p(x[, out]) Return the natural logarithm of one plus the input array, element-wise. logaddexp(x1, x2[, out]) Logarithm of the sum of exponentiations of the inputs. logaddexp2(x1, x2[, out]) Logarithm of the sum of exponentiations of the inputs in base-2.

## Other special functions¶

 i0(x) Modified Bessel function of the first kind, order 0. sinc(x) Return the sinc function.

## Floating point routines¶

 signbit(x[, out]) Returns element-wise True where signbit is set (less than zero). copysign(x1, x2[, out]) Change the sign of x1 to that of x2, element-wise. frexp(x[, out1, out2]) Decompose the elements of x into mantissa and twos exponent. ldexp(x1, x2[, out]) Returns x1 * 2**x2, element-wise.

## Arithmetic operations¶

 add(x1, x2[, out]) Add arguments element-wise. reciprocal(x[, out]) Return the reciprocal of the argument, element-wise. negative(x[, out]) Numerical negative, element-wise. multiply(x1, x2[, out]) Multiply arguments element-wise. divide(x1, x2[, out]) Divide arguments element-wise. power(x1, x2[, out]) First array elements raised to powers from second array, element-wise. subtract(x1, x2[, out]) Subtract arguments, element-wise. true_divide(x1, x2[, out]) Returns a true division of the inputs, element-wise. floor_divide(x1, x2[, out]) Return the largest integer smaller or equal to the division of the inputs. fmod(x1, x2[, out]) Return the element-wise remainder of division. mod(x1, x2[, out]) Return element-wise remainder of division. modf(x[, out1, out2]) Return the fractional and integral parts of an array, element-wise. remainder(x1, x2[, out]) Return element-wise remainder of division.

## Handling complex numbers¶

 angle(z[, deg]) Return the angle of the complex argument. real(val) Return the real part of the elements of the array. imag(val) Return the imaginary part of the elements of the array. conj(x[, out]) Return the complex conjugate, element-wise.

## Miscellaneous¶

 convolve(a, v[, mode]) Returns the discrete, linear convolution of two one-dimensional sequences. clip(a, a_min, a_max[, out]) Clip (limit) the values in an array. sqrt(x[, out]) Return the positive square-root of an array, element-wise. square(x[, out]) Return the element-wise square of the input. absolute(x[, out]) Calculate the absolute value element-wise. fabs(x[, out]) Compute the absolute values element-wise. sign(x[, out]) Returns an element-wise indication of the sign of a number. maximum(x1, x2[, out]) Element-wise maximum of array elements. minimum(x1, x2[, out]) Element-wise minimum of array elements. fmax(x1, x2[, out]) Element-wise maximum of array elements. fmin(x1, x2[, out]) Element-wise minimum of array elements. nan_to_num(x) Replace nan with zero and inf with finite numbers. real_if_close(a[, tol]) If complex input returns a real array if complex parts are close to zero. interp(x, xp, fp[, left, right, period]) One-dimensional linear interpolation.