Math functions

The goal

Matrices alone are useless. We need some math functions to act upon them.

I will focus on the important ones. Those will get a link.

Trigonometric functions

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

Hyperbolic functions

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

Rounding

round(a[, decimals, out])	Evenly round to the given number of decimals.
around(a[, decimals, out])	Round an array to the given number of decimals.
rint(x, /[, out, where, casting, order, …])	Round elements of the array to the nearest integer.
fix(x[, out])	Round to nearest integer towards zero.
floor(x, /[, out, where, casting, order, …])	Return the floor of the input, element-wise.
ceil(x, /[, out, where, casting, order, …])	Return the ceiling of the input, element-wise.
trunc(x, /[, out, where, casting, order, …])	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.
nanprod(a[, axis, dtype, out, keepdims, …])	Return the product of array elements over a given axis treating Not a Numbers (NaNs) as ones.
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.
nancumprod(a[, axis, dtype, out])	Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one.
nancumsum(a[, axis, dtype, out])	Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero.
diff(a[, n, axis, prepend, append])	Calculate the n-th discrete difference along the given axis.
ediff1d(ary[, to_end, to_begin])	The differences between consecutive elements of an array.
gradient(f, *varargs[, axis, edge_order])	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, where, casting, order, …])	Calculate the exponential of all elements in the input array.
expm1(x, /[, out, where, casting, order, …])	Calculate exp(x) - 1 for all elements in the array.
exp2(x, /[, out, where, casting, order, …])	Calculate 2**p for all p in the input array.
log(x, /[, out, where, casting, order, …])	Natural logarithm, element-wise.
log10(x, /[, out, where, casting, order, …])	Return the base 10 logarithm of the input array, element-wise.
log2(x, /[, out, where, casting, order, …])	Base-2 logarithm of x.
log1p(x, /[, out, where, casting, order, …])	Return the natural logarithm of one plus the input array, element-wise.
logaddexp(x1, x2, /[, out, where, casting, …])	Logarithm of the sum of exponentiations of the inputs.
logaddexp2(x1, x2, /[, out, where, casting, …])	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 normalized sinc function.

Floating point routines

signbit(x, /[, out, where, casting, order, …])	Returns element-wise True where signbit is set (less than zero).
copysign(x1, x2, /[, out, where, casting, …])	Change the sign of x1 to that of x2, element-wise.
frexp(x[, out1, out2], / [[, out, where, …])	Decompose the elements of x into mantissa and twos exponent.
ldexp(x1, x2, /[, out, where, casting, …])	Returns x1 * 2**x2, element-wise.
nextafter(x1, x2, /[, out, where, casting, …])	Return the next floating-point value after x1 towards x2, element-wise.
spacing(x, /[, out, where, casting, order, …])	Return the distance between x and the nearest adjacent number.

Rational routines

lcm(x1, x2, /[, out, where, casting, order, …])	x1\| and \|x2\|
gcd(x1, x2, /[, out, where, casting, order, …])	x1\| and \|x2\|

Arithmetic operations

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

Handling complex numbers

angle(z[, deg])	Return the angle of the complex argument.
real(val)	Return the real part of the complex argument.
imag(val)	Return the imaginary part of the complex argument.
conj(x, /[, out, where, casting, order, …])	Return the complex conjugate, element-wise.
conjugate(x, /[, out, where, casting, …])	Return the complex conjugate, element-wise.

Extrema Finding

maximum(x1, x2, /[, out, where, casting, …])	Element-wise maximum of array elements.
max(a[, axis, out, keepdims, initial, where])	Return the maximum of an array or maximum along an axis.
amax(a[, axis, out, keepdims, initial, where])	Return the maximum of an array or maximum along an axis.
fmax(x1, x2, /[, out, where, casting, …])	Element-wise maximum of array elements.
nanmax(a[, axis, out, keepdims, initial, where])	Return the maximum of an array or maximum along an axis, ignoring any NaNs.
minimum(x1, x2, /[, out, where, casting, …])	Element-wise minimum of array elements.
min(a[, axis, out, keepdims, initial, where])	Return the minimum of an array or minimum along an axis.
amin(a[, axis, out, keepdims, initial, where])	Return the minimum of an array or minimum along an axis.
fmin(x1, x2, /[, out, where, casting, …])	Element-wise minimum of array elements.
nanmin(a[, axis, out, keepdims, initial, where])	Return minimum of an array or minimum along an axis, ignoring any NaNs.

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, where, casting, order, …])	Return the non-negative square-root of an array, element-wise.
cbrt(x, /[, out, where, casting, order, …])	Return the cube-root of an array, element-wise.
square(x, /[, out, where, casting, order, …])	Return the element-wise square of the input.
absolute(x, /[, out, where, casting, order, …])	Calculate the absolute value element-wise.
fabs(x, /[, out, where, casting, order, …])	Compute the absolute values element-wise.
sign(x, /[, out, where, casting, order, …])	Returns an element-wise indication of the sign of a number.
heaviside(x1, x2, /[, out, where, casting, …])	Compute the Heaviside step function.
nan_to_num(x[, copy, nan, posinf, neginf])	Replace NaN with zero and infinity with large finite numbers (default behaviour) or with the numbers defined by the user using the nan, posinf and/or neginf keywords.
real_if_close(a[, tol])	If input is complex with all imaginary parts close to zero, return real parts.
interp(x, xp, fp[, left, right, period])	One-dimensional linear interpolation for monotonically increasing sample points.