Math Module 

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. 
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 handside. 
JacobianODE  This function computes the Jacobian matrix for a right handside. 
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 worstfirst policy 
AStarSearch3DManeuverDemo  Demonstrate A* for a close orbital maneuver. 
AStarSearchGrid1Demo  Test AStarSearch using a grid with obstacles. 
AStarSearchGrid2Demo  Test AStarSearch using a grid with more 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. 
SimplexConstraintRelaxationDemo  Solve an infeasible LP with simplex through constraint relaxation 
SimplexScalingDemo  Solve a linear program with Simplex. Illustrate the need for scaling. 
SimplexScalingDemoData.mat  Example problem data 
THyperG  Demonstrate hypergeometric functions. 
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. 
DoggyProblem  Demonstrate the BinomialTheorem for the doggy problem. 
GunProblem  Demonstrate the BinomialTheorem for the gun problem. 
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. 
FDIRTest.mat  Sample data created by DetectionFilterBuilderDemo. 
NonlinearEstimator  Implements an online approximator for a spring mass damper system. 
NonlinearSpring  Righthandside 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 
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. 
Euler  EULER Euler's method for numerical integration. 
FracDI  Fractional order derivative or integral 
RK2  Second order RungeKutta. 
RK4  Fourth order RungeKutta. Called function is of the form: 
RK45  Fourth/fifth order RungeKutta. 
RK4TI  Fourth order RungeKutta integration. RHS is timeindependent (TI). 
TwoDSimpsonIntegration  Uses 2D Simpson's Rule to integrate an area. 
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 GaussJordan 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 3byn matrix 
Unit  Unitize vectors by column. 
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 oddeven 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. 
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 BoxMueller Transform 
Markov  Generate random output from a GaussMarkov 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. 
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. 
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: a*sin(x) + b*cos(x) + c = 0 
TanD  Tangent with input in degrees 
TrigReduction  Solve a*sin(beta) + b*cos(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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