Mathematical functions#

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.

asin(x, /[, out, where, casting, order, ...])

Inverse sine, element-wise.

arccos(x, /[, out, where, casting, order, ...])

Trigonometric inverse cosine, element-wise.

acos(x, /[, out, where, casting, order, ...])

Trigonometric inverse cosine, element-wise.

arctan(x, /[, out, where, casting, order, ...])

Trigonometric inverse tangent, element-wise.

atan(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.

atan2(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.

asinh(x, /[, out, where, casting, order, ...])

Inverse hyperbolic sine element-wise.

arccosh(x, /[, out, where, casting, order, ...])

Inverse hyperbolic cosine, element-wise.

acosh(x, /[, out, where, casting, order, ...])

Inverse hyperbolic cosine, element-wise.

arctanh(x, /[, out, where, casting, order, ...])

Inverse hyperbolic tangent element-wise.

atanh(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.

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, ...])

Returns the lowest common multiple of |x1| and |x2|

gcd(x1, x2, /[, out, where, casting, order, ...])

Returns the greatest common divisor of |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.

pow(x1, x2, /[, out, where, casting, order, ...])

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.

bitwise_count(x, /[, out, where, casting, ...])

Computes the number of 1-bits in the absolute value of x.