Math Functions

Math Module

Directory List

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


AStar

Finds the optimal path using A*.
Compute the angle change needed to change a trajectory so that it
Generate a grid on a sphere
Generate right ascensions and declinations for a global grid.
Finds the cost for going from startNode to nextNode.
Finds successor nodes in a square grid.
Finds the cost of going from one node to another in a square grid.
Finds the cost for going from startNode to nextNode.
Finds the cost for going from startNode to nextNode in 3D.
Finds successor nodes.
Finds successor nodes in 3D.
Generate a grid on a sphere that is evenly spaced
Transforms between 2D and 1D coordinates.

Back To Top

Analysis

Use the Armijo rule to compute a stepsize, alpha:
Generates the autocorrelation function for the input sequence.
The binomial expansion of (x + y)^n
Computes the value of a continued fraction of the form
Generate a series of cosine harmonics of the arguments
Generate a series of cosine harmonics of the arguments
Find the solution for the Lyapunov equation apa' - p + q = 0
Given xF, find yF that best fits xF given the pair (x,y)
Generates the Fourier series coefficients of a signal
Heavside function. H = 1 x 0, otherwise = 0
Computes the value of the hypergeometric function
Computes the value of the ratio of hypergeometric functions
Computes the value of the confluent hypergeometric ratio
One dimensional interpolation and extrapolation on the rows of a.
One or two dimensional interpolation and extrapolation.
Performs a linear interpolation:
Interpolates between x1 and x2 when x1 and x2 lie in a circle. When
Converts cartesian to spherical coordinates.
Jacobian for converting from spherical to cartesian coordinates
This function computes the Jacobian matrix for a right hand-side.
This function computes the Jacobian matrix for a right hand-side.
log of base n.
Logistic function.
Solve the general Lyapunov equation ap + pa' + q = 0
Calculates the new standard deviation and average.
Solve an optimization problem with Newton's method.
Optimal trajectory using simplex
The first index is n and the second is m
Generates Associated Legendre Functions of the first kind and derivatives
Computes the Gaussian form of the Legendre functions.
Create a Pad approximant of exp(sT)
Generate a series of sine and cosine harmonics of the arguments
Generate a series of sine and cosine harmonics of the arguments
Compute a series a + sum(bn sin(n wo t)) + sum(cn cos(n wo t))
Generate a series of sine harmonics of the arguments
Generate a series of sine harmonics of the arguments
Uses the simplex method to minimize the cost when solving the problem
Computes the solution to the simplex problem with an optional maximum constraint.
Uses the simplex method to minimize the cost when solving the problem
Simplex slack variable scaling
Spherical coordinates Jacobian
Subtract two polynomials so that c = a - b.
Reorder columns to minimize the diagonal sum with a worst-first policy

Back To Top

Demos/AStar

Demonstrate A* for a close orbital maneuver.
Test AStarSearch using a grid with obstacles.
Test AStarSearch using a grid with obstacles.
Demonstrate A* for a close orbital maneuver.
Test AStarSearch using a grid with randomly placed obstacles.
Test AStarSearch using a grid with randomly placed obstacles.

Back To Top

Demos/FDIR

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

Back To Top

Demos/Math

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

Back To Top

Demos/Probability

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

Back To Top

FDIR

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

Back To Top

Geometry

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

Back To Top

Integration

Euler's method for numerical integration.
Second order Runge-Kutta.
Fourth order Runge-Kutta. Called function is of the form:
Fourth/fifth order Runge-Kutta.
Fourth order Runge-Kutta integration. RHS is time-independent (TI).
Uses 2D Simpson's Rule to integrate an area.

Back To Top

Linear

Generate a block diagonal matrix
Computes the right column compression of a matrix. Compresses the
Convert a matrix from complex to real.
Vector cross product for multicolum arrays.
Derivative of the unit vector for r.
Deletes leading zeros from a vector.
Dot product with support for arrays.
Duplicate vector n times
Computes the factorial matrix for a matrix.
Matrix inverse using Gauss-Jordan elimination with partial pivoting.
Subtract two matrices where NaN - NaN or inf - inf == 0
Inverse of a 3x3 matrix.
The product form of the inverse
Set = 0 if the matrix is all zeros.
Solves ax = b using the singular value decomposition
Weighted least squares curve fit
Magnitude of a set of vectors
Orthogonalize a matrix
Computes product of the terms in a vector
Computes the upper row compression of a matrix.
Multiplies a scalar times a vector.
Separate a matrix or vector based on the criteria entered in s.
Converts a vector into a skew symmetric matrix.
Computes the product of two skew symmetric matrices derive from vectors.
Converts a vector into a skew symmetric matrix
Always sums by column even if x is a single row.
Sum a set of vectors in a 3-by-n matrix
Unitize vectors by column.

Back To Top

MathUtils

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

Back To Top

Probability

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

Back To Top

Solvers

Use bisection method to find the zero crossing of a function.
Solves the problem ax = b when a is positive definite symmetric
Finds the solution to f(x) = 0 given derivative information.
Solves a set of equations for zero using Newton's method.
Wraps the Newton's method solver by trying several values.
Newton Raphson root finding method

Back To Top

Trigonometry

Inverse cosine with output in degrees.
Inverse cotangent
Inverse cotangent -180 deg < z < 180 deg
Inverse cotangent with output in degrees. -90 deg <= s <= 90 deg
Cosecant with output in degrees
Cosecant
Inverse sine with output in degrees
Inverse tangent -180 < z < 180
Inverse tangent with output in degrees. -90 < s < 90
Cosine with input in degrees
Computes the value of the cosine function.
Cotangent
Cosecant with input in degrees.
Find the angle between x and y.
Outputs 0 if the matrix is singular
Compute quad. coeff.s on cos(x) from linear eqn: A*sin(x)+B*cos(x)+C=0
Secant
Finds the solution to f(x) = 0 without derivatives.
Sine with input in degrees
Computes the value of the sine function given the argument in degrees.
Algebraically solve x for equation: a*sin(x) + b*cos(x) + c = 0
Tangent with input in degrees
Solve a*sin(beta) + b*cos(beta) = c.
Unwrap a vector of angular values to change continuously.
Produces a smoothly varying function from 0 to xMax.
Wrap a phase angle (or vector of angles) to keep it between -pi and +pi

Back To Top

SVN Revision: 42425


Back to API main page