R: Create MxAlgebra Object

mxAlgebra {OpenMx}

R Documentation

Create MxAlgebra Object

Description

This function creates a new MxAlgebra object.

Usage

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

Arguments

`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.

Details

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

Value

Returns a new MxAlgebra object.

References

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

Examples


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]