5.3Other Functions

F

Name of actual function or inline function in form

Input:

F(P1,P2,...)

DF

Derivative value as matrix, name of derivative function or

inline function in form DF(P1,P2,...).

INDEX

Index of parameter of interest. DF should Calculate the

derivative with recpect to parameter Pn, where n is the

index.

Output:

D0

Actual derivative

D1

Estimated derivative

F

NxN Feedback matrix

Input:

L

NxL Noise effect matrix (optional, default identity)

Qc

LxL Diagonal Spectral Density (optional, default zeros)

dt

Time Step (optional, default 1)

Output:

A

Transition matrix

Q

Discrete Process Covariance

Syntax:

[L,def] = schol(A)

Input:

A

Symmetric pos.semi.def matrix to be factorized

Output:

L

Lower triangular matrix such that A=L*L’ if def>=0.

def

Value 1,0,-1 denoting that A was positive definite, positive

X

Dx1 value or N values as DxN matrix

Input:

M

Dx1 mean of distibution or N values as DxN matrix.

S

DxD covariance matrix

Output:

P

Probability of X.

E

Negative logarithm of P

M

Dx1 mean of distibution or K values as DxK matrix.

Input:

S

DxD covariance matrix

N

Number of samples (optional, default 1)

Output:

X

Dx(K*N) matrix of samples.

f

Name of function in form f(x,P(:)) or inline function tak-

ing the same parameters. In chained case the function

should be f(x,y,P(:)).

Input:

dt

Delta time as scalar.

x

Value of x from the previous time step.

P1

Values of parameters of the function at initial time t as a

cell array (or single plain value). Defaults to empty array

(no parameters).

P2

Values of parameters of the function at time t+dt/2 as a

cell array (or single plain value). Defaults to P1 and each

empty (or missing) value in the cell array is replaced with

the corresponding value in P1.

P3

Values of parameters of the function at time t+dt. Defaults

to P2 similarly to above.

Y

Cell array of partial results y1,y2,y3,y4 in the RK algo-

rithm of the second parameter in the interated function.

This can be used for chaining the integrators. Defaults to

empty.

Output:

x

Next value of X

Y

Cell array of partial results in Runge-Kutta algorithm.