Math Module

Directory List

AStar	Analysis	Demos/AStar
Demos/FDIR	Demos/Math	Demos/Probability
FDIR	Geometry	Integration
Linear	MathUtils	Probability
Solvers	Trigonometry

AStar

AStarSearch	Finds the optimal path using A*.
DeltaAngleForNewRADec	Compute the angle change needed to change a trajectory so that it
GenerateGrid	Generate a grid on a sphere
GlobeGrid	Generate right ascensions and declinations for a global grid.
GridPathCost	Finds the cost for going from startNode to nextNode.
GridSuccessorNodes	Finds successor nodes in a square grid.
GridTraverseCost	Finds the cost of going from one node to another in a square grid.
ManeuverCost	Finds the cost for going from startNode to nextNode.
ManeuverCost3D	Finds the cost for going from startNode to nextNode in 3D.
ManeuverSuccessorNodes	Finds successor nodes.
ManeuverSuccessorNodes3D	Finds successor nodes in 3D.
SphericalGrid	Generate a grid on a sphere that is evenly spaced
TransformGridCoordinates	Transforms between 2D and 1D coordinates.

Analysis

Armijo	Use the Armijo rule to compute a stepsize, alpha:
AutoCorr	Generates the autocorrelation function for the input sequence.
Binomial	The binomial expansion of (x + y)^n
CFract	Computes the value of a continued fraction of the form
CHarm	Generate a series of cosine harmonics of the arguments
CHarmD	Generate a series of cosine harmonics of the arguments
DLyapG	Find the solution for the Lyapunov equation apa' - p + q = 0
FitPair	Given xF, find yF that best fits xF given the pair (x,y)
FourierSeries	Generates the Fourier series coefficients of a signal
Heavisde	Heavside function. H = 1 x 0, otherwise = 0
HypgF1	Computes the value of the hypergeometric function
HypgFr	Computes the value of the ratio of hypergeometric functions
HypgMr	Computes the value of the confluent hypergeometric ratio
IntExpR	One dimensional interpolation and extrapolation on the rows of a.
IntExt	One or two dimensional interpolation and extrapolation.
Interp1D	Performs a linear interpolation:
InterpolateCircle	Interpolates between x1 and x2 when x1 and x2 lie in a circle. When
JCart2Sp	Converts cartesian to spherical coordinates.
JSp2Cart	Jacobian for converting from spherical to cartesian coordinates
Jacobian	This function computes the Jacobian matrix for a right hand-side.
JacobianODE	This function computes the Jacobian matrix for a right hand-side.
LogBaseN	log of base n.
Logistic	Logistic function.
LyapG	Solve the general Lyapunov equation ap + pa' + q = 0
MakeDistribution	Generate a list of random variables with some specified distribution
NewStats	Calculates the new standard deviation and average.
NewtonsMethod	Solve an optimization problem with Newton's method.
OptimalTrajectory	Optimal trajectory using simplex
PAL	Generates the Associated Legendre Functions of the first kind
PDAL	Generates Associated Legendre Functions of the first kind and derivatives
PGauss	Computes the Gaussian form of the Legendre functions.
Pade	Create a Padé approximant of exp(sT)
SCHarm	Generate a series of sine and cosine harmonics of the arguments
SCHarmD	Generate a series of sine and cosine harmonics of the arguments
SCSeries	Compute a series a + sum(bn sin(n wo t)) + sum(cn cos(n wo t))
SHarm	Generate a series of sine harmonics of the arguments
SHarmD	Generate a series of sine harmonics of the arguments
Simplex	Uses the simplex method to minimize the cost when solving the problem
Simplex2	Computes the solution to the simplex problem with an optional maximum constraint.
SimplexOld	Uses the simplex method to minimize the cost when solving the problem
SimplexScaling	Simplex slack variable scaling
SphJacobian	Spherical coordinates Jacobian
SubPoly	Subtract two polynomials so that c = a - b.
WaveletMorlet	Performs a wavelet transform using a Morlet Wavelet
WorstFirstAssignment	Reorder columns to minimize the diagonal sum with a worst-first policy

Demos/AStar

AStarSearch3DManeuverDemo	Demonstrate A* for a close orbital maneuver.
AStarSearchGrid1Demo	Test AStarSearch using a grid with obstacles.
AStarSearchGrid2Demo	Test AStarSearch using a grid with obstacles.
AStarSearchManeuverDemo	Demonstrate A* for a close orbital maneuver.
AStarSearchOrderGridDemo	Test AStarSearch using a grid with randomly placed obstacles.
AStarSearchRandomGridDemo	Test AStarSearch using a grid with randomly placed obstacles.

Demos/FDIR

DCMotorSim	Simulates 2 DC Motors with failure detection logic.
DetectionFilterBuilderDemo	Simulate a detection filter using the DetectionFilterBuilder GUI.
FDIROLASim	Test Fault Diagnosis using online approximators.
OrbitFDIRDemo	Demonstrate an orbit detection filter for a spacecraft with one thruster.
OrbitFDIRPulseDemo	Demonstrate an orbit detection filter with random thrust pulses.
SpinnerFDIRDemo	Demonstrate a detection filter for a spinning spacecraft.

Demos/Math

SimplexConstraintRelaxationDemo	Solve an infeasible LP with simplex through constraint relaxation
SimplexScalingDemo	Solve a linear program with Simplex. Illustrate the need for scaling.
THyperG	Demonstrate hypergeometric functions.

Demos/Probability

DoggyProblem	Demonstrate the BinomialTheorem for the doggy problem.
GunProblem	Demonstrate the BinomialTheorem for the gun problem.

FDIR

BuildLinearDF	Create a detection filter for a fully measured system.
DCMotorDetectionFilter	Implements a DC motor detection filter. Uses Euler integration.
DCMotorFailures	Triggers a failure at time tFail.
DCMotorParitySpace	Computes the residuals for two DC motors.
DetectionFilter	Implement a detection filter for a fully measured system.
DetectionFilterBuild	Algorithm to compute detection filter gains.
DetectionFilterBuilder	GUI to build detection filters.
DetectionFilterSimulation	Simulate a detection filter using a state space model.
DetectionFilterUnnormalized	Create a unnormalized detection filter for a fully measured system.
DualDCMotors	Simulates two DC motors.
NonlinearEstimator	Implements an online approximator for a spring mass damper system.
NonlinearSpring	Right-hand-side of a nonlinear spring dynamics model.
NonlinearSpringFault	Nonlinear spring fault.
NormalizeMatrix	Normalizes a state space system for use with a detection filter.
OnlineApproximator	Implements an online approximator, f( y, theta ).
ProbabilityOfFailure	Computes the probability of failure.
RadialBasisFunction	Implements a radial basis function for online estimators.
TMatrix	Compute a transformation matrix from a statespace

Geometry

AngleSepFromRotation	Compute angular separation between 2 vectors by rotating about an axis
BilinearInterpolation	Apply bilinear interpolation on 4 data points.
FindValidAngleRange	Find valid range of rotation angles that satisfy separation constraints
FitEllipse	Fit an ellipse.
InsideAngleRange	Determine whether an angle is inside an angular range.
IntersectLineAndCone	Compute the intersection of a line and a cone.
IntersectLineAndEllipsoid	Compute the intersection of a line and ellipsoid.
MergeAngleRange	Merge two angular ranges. Returns the intersection.
Perpendicular	Finds perpendicular vectors to a such that Dot(b,a) = 0.
PointInGridInTriangle	Determine whether points p are in triangle v.
PointInPolygon	Determine whether points p are in polygon v.
PointInTriangle	Determine whether points p are in triangle v.
SegmentIntersection	Compute whether and where two 2D line segments intersect
SurfaceAreaEllipsoid	Compute the surface area of an ellipsoid.
UnitVectorAverage	Average unit vector.

Integration

Euler	EULER Euler's method for numerical integration.
FracDI	Fractional order derivative or integral
RK2	Second order Runge-Kutta.
RK4	Fourth order Runge-Kutta. Called function is of the form:
RK45	Fourth/fifth order Runge-Kutta.
RK4TI	Fourth order Runge-Kutta integration. RHS is time-independent (TI).
TwoDSimpsonIntegration	Uses 2D Simpson's Rule to integrate an area.

Linear

BlockDiagonal	Generate a block diagonal matrix
ColCompR	Computes the right column compression of a matrix. Compresses the
ComplexToReal	Convert a matrix from complex to real.
Cross	Vector cross product for multicolum arrays.
DUnit	Derivative of the unit vector for r.
DelLZ	Deletes leading zeros from a vector.
Dot	Dot product with support for arrays.
DupVect	Duplicate vector n times
Factorl	Computes the factorial matrix for a matrix.
GJInv	Matrix inverse using Gauss-Jordan elimination with partial pivoting.
GenSub	Subtract two matrices where NaN - NaN or inf - inf == 0
Inv3x3	Inverse of a 3x3 matrix.
InvP	The product form of the inverse
IsSing	Outputs 0 if the matrix is singular
IsZero	Set = 0 if the matrix is all zeros.
LeastSq	Weighted least squares curve fit
Mag	Magnitude of a set of vectors
Orthogonalize	Orthogonalize a matrix
Product	Computes product of the terms in a vector
RowCompU	Computes the upper row compression of a matrix.
SXV	Multiplies a scalar times a vector.
Sep	Separate a matrix or vector based on the criteria entered in s.
Skew	Converts a vector into a skew symmetric matrix.
SkewSq	Computes the product of two skew symmetric matrices derive from vectors.
SkewSymm	Converts a vector into a skew symmetric matrix
SumC	Always sums by column even if x is a single row.
SumV	Sum a set of vectors in a 3-by-n matrix
Unit	Unitize vectors by column.

MathUtils

DeltaEig	Computes the delta eigenvalues for a given a small perturbation of a, e
FTrunc	Simulates floating point truncation to -.
FindIfInBetween	Determines if x is in between odd-even pairs.
FloatToTwosComplement	Converts a float to two's complement array.
Odd	1 if the value is odd
R2P5	Rounds towards zero to the nearest 1/2.
Ramp	Generate a ramp signal at t0 from value v0 to vF in time interval t
Ramps	Generates ramps for any number of inputs. Since version 10.
RoundN	Round to n decimal places
TriangleWave	Generates a triangle wave. 0 is the beginning and 2*pi is the end.
TwosComplementToFloat	Converts a two's complement array to float.

Probability

BinomialTheorem	Computes the binomial theorem.
CRand	Covariance matrix transformation
CableTensionExample	Cable tension example.
Combinations	The number of combinations of r articles in n samples.
ConfidenceInterval	Computes the confidence interval.
CovarianceRHS	Generates the covariance derivative.
EMarkov	Find the correlation time and the mean squared value for a Markov sequence.
ErrorCombination	Combine errors given a function.
GaussianCPDF	Cumulative probability density function for a Gaussian
GaussianPDF	Compute the probability density function for a Gaussian distribution.
GaussianRSG	Gaussian Random Sequence Generator Using the Box-Mueller Transform
Markov	Generate random output from a Gauss-Markov process.
NormalDistribution	Matrix normal or Gaussian distribution.
RMarkov	Generates the autocorrelation function for a Markov Process.
RandP	Generate a Poission random matrix.
RandPM	Generates uniform random matrices between -1 and +1
RandPN	Generate a Poission random matrix using a normal approximation.
Random	Compute a random nxm matrix
SMarkov	Generates the spectral function for a Markov Process.
SignTest	Compare the relative accuracy of two signals.

Solvers

BisectionZero	Use bisection method to find the zero crossing of a function.
LEPDS	Solves the problem ax = b when a is positive definite symmetric
LSSVD	Solves ax = b using the singular value decomposition
ModNewt	Finds the solution to f(x) = 0 given derivative information.
NLEqSolver	Solves a set of equations for zero using Newton's method.
NLEqSolverWrapper	Wraps the Newton's method solver by trying several values.
NewtRaph	Newton Raphson root finding method
Secant	Finds the solution to f(x) = 0 without derivatives.

Trigonometry

ACosD	Inverse cosine with output in degrees.
ACot2	Inverse cotangent
ACot2D	Inverse cotangent -180 deg < z < 180 deg
ACotD	Inverse cotangent with output in degrees. -90 deg <= s <= 90 deg
ACscD	Cosecant with output in degrees
ASecD	Cosecant
ASinD	Inverse sine with output in degrees
ATan2D	Inverse tangent -180 < z < 180
ATanD	Inverse tangent with output in degrees. -90 < s < 90
CosD	Cosine with input in degrees
CosX	Computes the value of the cosine function.
CotD	Cotangent
CscD	Cosecant with input in degrees.
DeltCirc	Find the angle between x and y.
LinearSinCosToQuadCos	Compute quadratic coefficients on cos(x) from linear eqn
SecD	Secant
SinD	Sine with input in degrees
SinX	Computes the value of the sine function given the argument in degrees.
SolveLinearSinCos	Algebraically solve x for equation: asin(x) + bcos(x) + c = 0
TanD	Tangent with input in degrees
TrigReduction	Solve asin(beta) + bcos(beta) = c.
UnwrapPhase	Unwrap a vector of angular values to change continuously.
VerSin	Produces a smoothly varying function from 0 to xMax.
WrapPhase	Wrap a phase angle (or vector of angles) to keep it between -pi and +pi

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