2. Overview Mathematic¶

Miscellaneous

get_math_lib

get_math_lib returns the name of the enabled math libray.

ode

ode computes the solution of ordinary differential equation of the first order.

set_math_lib

set_math_lib sets the math library.

solve

solve calculates the solution of a non linear system.

Interpolation

akimaspline

akimaspline computes an akima spline for a given x- and y-vector.

detect_peaks

detect_peaks finds peaks and valleys in a given noisy signal. Only local minima and maxima detected where the difference between adjacent extreme values are greater than the threshold.

fspline

fspline computes a fit spline for a given x- and y-vector.

interpol

The interpol function executes a linear interpolation or cosine interpolation for the given x-coordinates.

moving_average

The moving_average function calculates a moving average. This filter can be used to reduce random noise.

moving_median

The moving_median function calculates a moving median. The function operates over a moving window of values. For each window, the middle value found in the window is used.

nonlin

nonlin computes the parameters of a given (non linear) function so that the deviation of the function for the given data points is minimized.

polyfit

polyfit finds the coefficients of a polynomial of degree N using the least squares method.

polyval

polyval calculates the y coordinates of a polynomial of degree n evaluated at x.

pspline

pspline computes a spline under tension for a given x and y vector. In contrast to the fspline function, the x-elements do not have to be sorted in increasing order.

rspline

rspline computes a rational spline under tension for a given x and y vector.

sgolayfilt

sgolayfilt computes a moving average using the Savitzky-Golay algorithm.

2D-Interpolation

akimaspline2

akimaspline2 executes a 2-dimensional “matrix to matrix” interpolation.

fspline2

fspline2 executes a 2-dimensional “matrix to matrix” interpolation.

griddata

griddata creates a regular grid of arbitrarily distributed data triples.

interpol2

interpol2 executes a 2-dimensional “matrix to matrix” interpolation.

nonlin

nonlin computes the parameters of a given (non linear) function so that the deviation of the function for the given data points is minimized.

reduce3d

reduce3d removes data points from an x/y/z dataset.

rspline2

rspline2 executes a 2-dimensional “matrix to matrix” interpolation.

smooth2

smooth2 is a function to smooth a matrix using the Savitzky-Golay algorthim.

spline2

spline2 executes a 2-dimensional “matrix to matrix” interpolation.

FFT

conv

The conv function combines two signals to form a new signal, for example, calculates the output signal for an input signal and the impulse response signal.

deconv

The deconv performs the deconvolution of vector u and vector v.

fft

The fft function computes the complex Fourier Transformation.

ifft

Calculates the Inverse Fourier Transformation.

upfirdn

upfirdn is a polyphase FIR resampling function.

Elementary Functions

abs

abs calculates the absolute value of its argument.

all

all checks if all elements of a vector or matrix are other than zero (0).

angle

angle calculates the phase angles in radinas for each element of a complex array.

any

any checks if any elements of a vector or matrix are zero.

ceil

Calculates the ceiling of a value.

conj

conj returns the complex conjugate of its parameter.

cumprod

cumprod returns the cumulative product of each column of a matrix.

cumsum

cumsum returns the cumulative sums of each column of a matrix.

diff

diff computes differences such as the following: [x[2] - x[1], x[3] - x[2], … , x[n] - x[n-1]]

exp

exp returns the exponential value of its parameter.

floor

Returns the largest interger that is less than or equal to its argument.

fround

fround rounds the elements of a matrix. The number of significant digits can be specified.

histc

histc calculates a histogram.

histogram

histogram calculates the histogram of a vector.

imag

imag returns the imaginary part of a complex number.

log

log returns the natural logarithm of its parameter.

log10

log10 returns the base-10 logarithm of its parameter.

mean

mean returns the mean of its parameter. When the argument is a matrix, a row vector will be created containing the mean values of the matrix columns.

merge

merge merges two sorted vectors and returns a single sorted vector.

quantile

quantile returns quantile of a data vector rvX for the cumulative probability rvP in the interval 0 to 1. For rvP = 0.5 the median is returned. For rvP = 1 the maximum is returned.

real

real returns the real part of its argument.

remove

remove removes all elements with the value 0 or rsRemove from a real vector. In case of a matrix all rows with the value 0 or rsRemove in the first column will be removed.

round

Is replaced by fround.

sort

sort performs a sort from a real, complex or string matrix or vector.

sqrt

sqrt calculate the square root of a matrix.

std

std returns the standard deviation of its parameter.

sum

sum computes the sum of all elements for a real or complex vector. Strings from string vectors will be appended to a scalar string. When the argument is a matrix, a row vector will be created containing the sum of the matrix columns.

Trigonometric Functions

acos

acosh calculates the arccosine.

acosh

acosh calculates the hyperbolic arccosine.

acot

acot calculates the arccotangent.

asin

asin calculates the ac arcsine.

asinh

asinh calculates the hyperbolic arcsine.

atan

atan2 calculates the four-quadrant inverse tangent.

atanh

atanh calculates the hyperbolic arctangent.

cos

cos returns the cosine of its parameter.

cosh

cosh returns the hyperbolic cosine of its parameter.

sin

sin returns the sine of m.

sinh

sinh returns the hyperbolic sine of its parameter.

tan

tan returns the tangent of its parameter.

tanh

tanh returns the hyperbolic tangent of its parameter.

Special Functions

besseli

Modified Bessel function of the first kind.

besselj

Bessel function of the first kind.

erf

erf calculates the error function: .

Matrix Creation

diag

diag creates a diagonal-matrix or a row-vector.

eye

eye returns an identity matrix.

ones

ones creates a real matrix with all elements set to the value 1.0.

rand

rand returns random numbers with uniform distribution.

zeros

The zeros function creates a real matrix with all elements set to the value 0.0.

Linear Algebra

cond

cond calculates the condition number of a matrix.

det

det computes the determinant of a square matrix.

eig

eig calculates the eigenvalues and eigenvectors of a square matrix.

integral

integral computes an approximation of the integral via the trapezoidal method.

inv

inv calculates the inverse of a square matrix.

norm

norm calculates various matrix norms.

pinv

pinv calculates the pseudoinverse of a given matrix.

svd

Singular value decomposition.

Random Numbers

rand

rand returns random numbers with uniform distribution.

srand

srand sets a start value for the random generator.

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