# `ulab.numpy` – Numerical approximation methods¶

`ulab.numpy.``interp`(x: ndarray, xp: ndarray, fp: ndarray, *, left: Optional[_float] = None, right: Optional[_float] = None)ndarray
Parameters
• x (ulab.numpy.ndarray) – The x-coordinates at which to evaluate the interpolated values.

• xp (ulab.numpy.ndarray) – The x-coordinates of the data points, must be increasing

• fp (ulab.numpy.ndarray) – The y-coordinates of the data points, same length as xp

• left – Value to return for `x < xp[0]`, default is `fp[0]`.

• right – Value to return for `x > xp[-1]`, default is `fp[-1]`.

Returns the one-dimensional piecewise linear interpolant to a function with given discrete data points (xp, fp), evaluated at x.

`ulab.numpy.``trapz`(y: ndarray, x: Optional[ndarray] = None, dx: _float = 1.0)_float
Parameters
• ulab.numpy.ndarray y (1D) – the values of the dependent variable

• ulab.numpy.ndarray x (1D) – optional, the coordinates of the independent variable. Defaults to uniformly spaced values.

• dx (float) – the spacing between sample points, if x=None

Returns the integral of y(x) using the trapezoidal rule.

`ulab.numpy.``_ArrayLike`
`ulab.numpy.``_DType`
`ulab.numpy.``_float`

Type alias of the bulitin float

`ulab.numpy.``_bool`

Type alias of the bulitin bool

`ulab.numpy.``int8` :_DType

Type code for signed integers in the range -128 .. 127 inclusive, like the ‘b’ typecode of `array.array`

`ulab.numpy.``int16` :_DType

Type code for signed integers in the range -32768 .. 32767 inclusive, like the ‘h’ typecode of `array.array`

`ulab.numpy.``float` :_DType

Type code for floating point values, like the ‘f’ typecode of `array.array`

`ulab.numpy.``uint8` :_DType

Type code for unsigned integers in the range 0 .. 255 inclusive, like the ‘H’ typecode of `array.array`

`ulab.numpy.``uint16` :_DType

Type code for unsigned integers in the range 0 .. 65535 inclusive, like the ‘h’ typecode of `array.array`

`ulab.numpy.``bool` :_DType

Type code for boolean values

`ulab.numpy.``argmax`(array: _ArrayLike, *, axis: Optional[int] = None)int

Return the index of the maximum element of the 1D array

`ulab.numpy.``argmin`(array: _ArrayLike, *, axis: Optional[int] = None)int

Return the index of the minimum element of the 1D array

`ulab.numpy.``argsort`(array: ndarray, *, axis: int = - 1)ndarray

Returns an array which gives indices into the input array from least to greatest.

`ulab.numpy.``cross`(a: ndarray, b: ndarray)ndarray

Return the cross product of two vectors of length 3

`ulab.numpy.``diff`(array: ndarray, *, n: int = 1, axis: int = - 1)ndarray

Return the numerical derivative of successive elements of the array, as an array. axis=None is not supported.

`ulab.numpy.``flip`(array: ndarray, *, axis: Optional[int] = None)ndarray

Returns a new array that reverses the order of the elements along the given axis, or along all axes if axis is None.

`ulab.numpy.``max`(array: _ArrayLike, *, axis: Optional[int] = None)_float

Return the maximum element of the 1D array

`ulab.numpy.``mean`(array: _ArrayLike, *, axis: Optional[int] = None)_float

Return the mean element of the 1D array, as a number if axis is None, otherwise as an array.

`ulab.numpy.``median`(array: ndarray, *, axis: int = - 1)ndarray

Find the median value in an array along the given axis, or along all axes if axis is None.

`ulab.numpy.``min`(array: _ArrayLike, *, axis: Optional[int] = None)_float

Return the minimum element of the 1D array

`ulab.numpy.``roll`(array: ndarray, distance: int, *, axis: Optional[int] = None)None

Shift the content of a vector by the positions given as the second argument. If the `axis` keyword is supplied, the shift is applied to the given axis. The array is modified in place.

`ulab.numpy.``sort`(array: ndarray, *, axis: int = - 1)ndarray

Sort the array along the given axis, or along all axes if axis is None. The array is modified in place.

`ulab.numpy.``std`(array: _ArrayLike, *, axis: Optional[int] = None, ddof: int = 0)_float

Return the standard deviation of the array, as a number if axis is None, otherwise as an array.

`ulab.numpy.``sum`(array: _ArrayLike, *, axis: Optional[int] = None)Union[_float, int, ndarray]

Return the sum of the array, as a number if axis is None, otherwise as an array.

class `ulab.numpy.``ndarray`
`ulab.numpy.``get_printoptions`()Dict[str, int]

Get printing options

`ulab.numpy.``set_printoptions`(threshold: Optional[int] = None, edgeitems: Optional[int] = None)None

Set printing options

`ulab.numpy.``ndinfo`(array: ndarray)None
`ulab.numpy.``array`(values: Union[ndarray, Iterable[Union[_float, _bool, Iterable[Any]]]], *, dtype: _DType = ulab.numpy.float)ndarray

alternate constructor function for `ulab.numpy.ndarray`. Mirrors numpy.array

`ulab.numpy.``trace`(m: ndarray)_float
Parameters

m – a square matrix

Compute the trace of the matrix, the sum of its diagonal elements.

`ulab.numpy.``dot`(m1: ndarray, m2: ndarray)Union[ndarray, _float]
Parameters
• m1 (ndarray) – a matrix, or a vector

• m2 (ndarray) – a matrix, or a vector

Computes the product of two matrices, or two vectors. In the letter case, the inner product is returned.

`ulab.numpy.``acos`(a: _ArrayLike)ndarray

Computes the inverse cosine function

`ulab.numpy.``acosh`(a: _ArrayLike)ndarray

Computes the inverse hyperbolic cosine function

`ulab.numpy.``asin`(a: _ArrayLike)ndarray

Computes the inverse sine function

`ulab.numpy.``asinh`(a: _ArrayLike)ndarray

Computes the inverse hyperbolic sine function

`ulab.numpy.``around`(a: _ArrayLike, *, decimals: int = 0)ndarray

Returns a new float array in which each element is rounded to `decimals` places.

`ulab.numpy.``atan`(a: _ArrayLike)ndarray

Computes the inverse tangent function; the return values are in the range [-pi/2,pi/2].

`ulab.numpy.``arctan2`(ya: _ArrayLike, xa: _ArrayLike)ndarray

Computes the inverse tangent function of y/x; the return values are in the range [-pi, pi].

`ulab.numpy.``atanh`(a: _ArrayLike)ndarray

Computes the inverse hyperbolic tangent function

`ulab.numpy.``ceil`(a: _ArrayLike)ndarray

Rounds numbers up to the next whole number

`ulab.numpy.``cos`(a: _ArrayLike)ndarray

Computes the cosine function

`ulab.numpy.``cosh`(a: _ArrayLike)ndarray

Computes the hyperbolic cosine function

`ulab.numpy.``degrees`(a: _ArrayLike)ndarray

Converts angles from radians to degrees

`ulab.numpy.``erf`(a: _ArrayLike)ndarray

Computes the error function, which has applications in statistics

`ulab.numpy.``erfc`(a: _ArrayLike)ndarray

Computes the complementary error function, which has applications in statistics

`ulab.numpy.``exp`(a: _ArrayLike)ndarray

Computes the exponent function.

`ulab.numpy.``expm1`(a: _ArrayLike)ndarray

Computes \$e^x-1\$. In certain applications, using this function preserves numeric accuracy better than the `exp` function.

`ulab.numpy.``floor`(a: _ArrayLike)ndarray

Rounds numbers up to the next whole number

`ulab.numpy.``gamma`(a: _ArrayLike)ndarray

Computes the gamma function

`ulab.numpy.``lgamma`(a: _ArrayLike)ndarray

Computes the natural log of the gamma function

`ulab.numpy.``log`(a: _ArrayLike)ndarray

Computes the natural log

`ulab.numpy.``log10`(a: _ArrayLike)ndarray

Computes the log base 10

`ulab.numpy.``log2`(a: _ArrayLike)ndarray

Computes the log base 2

`ulab.numpy.``radians`(a: _ArrayLike)ndarray

Converts angles from degrees to radians

`ulab.numpy.``sin`(a: _ArrayLike)ndarray

Computes the sine function

`ulab.numpy.``sinh`(a: _ArrayLike)ndarray

Computes the hyperbolic sine

`ulab.numpy.``sqrt`(a: _ArrayLike)ndarray

Computes the square root

`ulab.numpy.``tan`(a: _ArrayLike)ndarray

Computes the tangent

`ulab.numpy.``tanh`(a: _ArrayLike)ndarray

Computes the hyperbolic tangent

`ulab.numpy.``vectorize`(f: Union[Callable[[int], _float], Callable[[_float], _float]], *, otypes: Optional[_DType] = None)Callable[[_ArrayLike], ndarray]
Parameters
• f (callable) – The function to wrap

• otypes – List of array types that may be returned by the function. None is interpreted to mean the return value is float.

Wrap a Python function `f` so that it can be applied to arrays. The callable must return only values of the types specified by `otypes`, or the result is undefined.