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: $\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^x e^{-t^2}\,\mathrm dt$ .

	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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2. Overview Mathematic¶