X := GenerateSignal( 3 * sin(t) + cos(2*t), t = 0 .. 4 * Pi, 100 );

sample_rate, Times, Signal := GenerateSignal( t * exp(-t), t = 0 .. 5, 10^3, 'output' = ['samplerate','times','signal'] );

R := GenerateSignal( t / (1+t^2), t = 0 .. 4, 2^10, 'noisetype' = 'additive', 'noisedeviation' = 0.01, 'output' = 'record' ):

R['signalplot'];

R['periodogram'];

X := GenerateSignal( 5 + sqrt(1-(t-1)^4), t = 0 .. 2, 200, 'mirror' = 'antisymmetric', 'copies' = 4 ):

Y := GenerateSignal( 6 - abs(t-1), t = 0 .. 2, 200, 'mirror' = 'antisymmetric', 'copies' = 4 ):

R := DynamicTimeWarping( X, Y, 'compiled', 'output' = 'record' ):

R['unwarpedplot'];

R['warpedplot'];

R['cost'];

$28.7505811441736654$

R['rmse'];

$0.0220493272388582497$

f := piecewise( t < Pi  or t > 3 * Pi, sin(4*t) + 5, 1/10 * sin(40*t) + 5 );
a, b := 0, 4 * Pi;
n := 2^14;

$f≔\left\{\begin{array}{cc}\sin \left(4t\right)+5& t<\mathrm{\pi }\mathbf{or}3\mathrm{\pi }<t\\ \frac{\sin \left(40t\right)}{10}+5& \mathrm{otherwise}\end{array}\right.$

$a,b≔0,4\mathrm{\pi }$

$n≔16384$

( dt, T, X ) := GenerateSignal( f, t = a .. b, n, 'includefinishtime' = 'false', 'output' = ['timestep','times','signal'] ):

DX := DifferentiateData( X, 1, 'step' = dt, 'method' = 'spectral', 'extrapolation' = 'periodic' ):

dataplot( T, [X,DX], 'style' = 'line', 'color' = ['red','blue'], 'legend' = ["Signal","First derivative"], 'size' = [500,250] );

f := (x,y) -> sqrt( 1 + sin( Pi * ( x^2 + 3 * y^2 ) ) );
a, b, c, d := 0.0, 1.0, -0.5, 1.5;

$f≔\left(x\&comma;y\right)\mapsto \sqrt{1+\sin \left(\mathrm{\pi }\cdot \left(x^2+3\cdot y^2\right)\right)}$

$a,b,c,d≔0.,1.0,\mathrm{-0.5},1.5$

plot3d( f, a .. b, c .. d );

m, n := 100, 100;
dx, dy := evalhf( (b-a) / (m-1) ), evalhf( (d-c) / (n-1) );

$m,n≔100,100$

$\mathrm{dx},\mathrm{dy}≔0.0101010101010101019,0.0202020202020202037$

X := Vector( m, i -> evalhf( a + (i-1) * dx ), 'datatype' = 'float[8]' ):
Y := Vector( n, j -> evalhf( c + (j-1) * dy ), 'datatype' = 'float[8]' ):
Z := Matrix( m, n, (i,j) -> evalhf( f( X[i], Y[i] ) ), 'datatype' = 'float[8]' );

IntegrateData2D( X, Y, Z, 'uniform', 'compiled', 'method' = 'simpson' );

$2.09312887784632640$

X := LinearAlgebra:-RandomVector( 5, 'generator' = -1.0 - 1.0 * I .. 1.0 + 1.0 * I, 'datatype' = 'complex[8]' );

$X≔\left[\begin{array}{c}\mathrm{-0.170954922213783}-0.0703201167497254\mathrm{I}\\ 0.998983240195409-0.424301310369726\mathrm{I}\\ 0.0799641980758583+0.413834838645526\mathrm{I}\\ \mathrm{-0.763689603106579}+0.976835857569961\mathrm{I}\\ \mathrm{-0.338342009593391}+0.796972275668599\mathrm{I}\end{array}\right]$

Y := RealPart( X );

$Y≔\left[\begin{array}{c}\mathrm{-0.170954922213783}\\ 0.998983240195409\\ 0.0799641980758583\\ \mathrm{-0.763689603106579}\\ \mathrm{-0.338342009593391}\end{array}\right]$

Z := ImaginaryPart( X );

$Z≔\left[\begin{array}{c}\mathrm{-0.0703201167497254}\\ \mathrm{-0.424301310369726}\\ 0.413834838645526\\ 0.976835857569961\\ 0.796972275668599\end{array}\right]$

ComplexToReal( X );

$\left[\begin{array}{c}\mathrm{-0.170954922213783}\\ 0.998983240195409\\ 0.0799641980758583\\ \mathrm{-0.763689603106579}\\ \mathrm{-0.338342009593391}\end{array}\right],\left[\begin{array}{c}\mathrm{-0.0703201167497254}\\ \mathrm{-0.424301310369726}\\ 0.413834838645526\\ 0.976835857569961\\ 0.796972275668599\end{array}\right]$

n := 2^10;

$n≔1024$

X := GenerateSignal( sin(4*t) + 5, t = 0 .. 2 * Pi, n, 'includefinishtime' = 'false' ):

SignalPlot( X, 'view' = ['DEFAULT',0..10], 'color' = 'blue' );

Y := GenerateSignal( 1/10 * sin(40*t) + 5, t = 0 .. 2 * Pi, n, 'includefinishtime' = 'false' ):

SignalPlot( Y, 'view' = ['DEFAULT',0..10], 'color' = 'blue' );

Insert( X, floor(n/2) + 1, Y, 'inplace' ):

SignalPlot( X, 'view' = ['DEFAULT',0..10], 'color' = 'blue' );

X := < -5, 12, 6, 7, 3, 15, -10 >;

$X≔\left[\begin{array}{c}\mathrm{-5}\\ 12\\ 6\\ 7\\ 3\\ 15\\ \mathrm{-10}\end{array}\right]$

FindPeakPoints( X, 'output' = 'plot', 'plotincludepoints' = ['peaks','regular','valleys'], 'gridlines' );

FindPeakPoints( X, 'output' = ['peakindices','valleyindices'] );

$\left[\begin{array}{c}2\\ 4\\ 6\end{array}\right],\left[\begin{array}{c}1\\ 3\\ 5\\ 7\end{array}\right]$

n := 10^5;
r := 1.0 + 1.0 * I;
dt := 'complex[8]';
X := LinearAlgebra:-RandomVector( n, 'generator' = -r .. r, 'datatype' = dt ):
Y := LinearAlgebra:-RandomVector( n, 'generator' = -r .. r, 'datatype' = dt ):

$n≔100000$

$r≔1.0+\mathrm{I}$

$\mathrm{dt}≔{\mathrm{complex}}_8$

tests := 25;
CodeTools:-Usage( RootMeanSquareError( X, Y ), 'iterations' = tests );
CodeTools:-Usage( RelativeRootMeanSquareError( X, Y ), 'iterations' = tests );

$\mathrm{tests}≔25$

memory used=16.36KiB, alloc change=0 bytes, cpu time=3.12ms, real time=3.56ms, gc time=0ns

$1.15349306481481761$

memory used=44.40KiB, alloc change=0 bytes, cpu time=7.48ms, real time=7.20ms, gc time=0ns

$1.41397255876189520$