mxAlgebra {OpenMx} | R Documentation |

This function creates a new MxAlgebra object.

mxAlgebra(expression, name = NA, dimnames = NA)

`expression` |
An R expression of OpenMx-supported matrix operators and matrix functions. |

`name` |
An optional character string indicating the name of the object. |

`dimnames` |
list. The dimnames attribute for the algebra: a list of length 2 giving the row and column names respectively. An empty list is treated as NULL, and a list of length one as row names. The list can be named, and the list names will be used as names for the dimensions. |

The mxAlgebra function is used to create algebraic expressions that operate on one or more MxMatrix objects. To evaluate an MxAlgebra object, it must be placed in an MxModel object, along with all referenced `MxMatrix`

objects and the `mxAlgebraObjective`

function. The `mxAlgebraObjective`

function must reference the `MxAlgebra`

object to be evaluated by name.

The following operators are supported in mxAlgebra:

`solve()`

Inversion

`t()`

Transposition

`^`

Elementwise powering

`%^%`

Kronecker powering

`+`

Addition

`-`

Subtraction

`%*%`

Matrix Multiplication

`*`

Element or dot product

`/`

Element division

`%x%`

Kronecker product

`%&%`

Quadratic product

The following functions are supported in mxAlgebra:

`cbind`

Horizontal adhesion

`rbind`

Vertical adhesion

`det`

Determinant

`tr`

Trace

`sum`

Sum

`prod`

Product

`max`

Maximum

`min`

Min

`abs`

Absolute value

`sin`

Sine

`sinh`

Hyperbolic sine

`cos`

Cosine

`cosh`

Hyperbolic cosine

`tan`

Tangent

`tanh`

Hyperbolic tangent

`exp`

Exponent

`log`

Natural Logarithm

`sqrt`

Square root

`eigenval`

Eigenvalues of a square matrix. Usage: eigenval(x); eigenvec(x); ieigenval(x); ieigenvec(x)

`rvectorize`

Vectorize by row

`cvectorize`

Vectorize by column

`vech`

Half-vectorization

`vechs`

Strict half-vectorization

`vec2diag`

Create a diagonal matrix

`diag2vec`

Extract diagonal from matrix

`omxMnor`

Multivariate Normal Integration

`omxAllInt`

All cells Multivariate Normal Integration

`omxNot`

Perform unary negation on a matrix

`omxAnd`

Perform binary and on two matrices

`omxOr`

Perform binary or on two matrices

`omxGreaterThan`

Perform binary greater on two matrices

`omxLessThan`

Perform binary less than on two matrices

`omxApproxEquals`

Perform binary equals to (within a specified epsilon) on two matrices

`omxExponential`

Matrix Exponential

Returns a new MxAlgebra object.

The OpenMx User's guide can be found at http://openmx.psyc.virginia.edu/documentation.

MxAlgebra for the S4 class created by mxAlgebra. mxAlgebraObjective for an objective functions which takes an MxAlgebra or MxMatrix object as the function to be minimized. MxMatrix and mxMatrix for objects which may be entered in the 'expression' argument and the function that creates them. More information about the OpenMx package may be found here.

A <- mxMatrix("Full", nrow = 3, ncol = 3, values=2, name = "A") # Simple example: algebra B simply evaluates to the matrix A B <- mxAlgebra(A, name = "B") # Compute A + B C <- mxAlgebra(A + B, name = "C") # Compute sin(C) D <- mxAlgebra(sin(C), name = "D") # Make a model and evaluate the mxAlgebra object 'D' A <- mxMatrix("Full", nrow = 3, ncol = 3, values=2, name = "A") model <- mxModel("AlgebraExample", A, B, C, D ) fit <- mxRun(model) mxEval(D, fit) # Numbers in mxAlgebras are upgraded to 1x1 matrices # Example of Kronecker powering (%^%) and multiplication (%*%) A <- mxMatrix(type="Full", nrow=3, ncol=3, value=c(1:9), name="A") m1 <- mxModel("kron", A, mxAlgebra(A %^% 2, name="KroneckerPower")) mxRun(m1)$KroneckerPower # Running kron # mxAlgebra 'KroneckerPower' # @formula: A %^% 2 # @result: # [,1] [,2] [,3] # [1,] 1 16 49 # [2,] 4 25 64 # [3,] 9 36 81

[Package *OpenMx* version 1.2.0-1931 Index]