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OpenMx (version 2.7.9)

mxAlgebra: Create MxAlgebra Object

Description

This function creates a new MxAlgebra object.

Usage

mxAlgebra(expression, name = NA, dimnames = NA, ..., fixed = FALSE,
          joinKey=as.character(NA), joinModel=as.character(NA), verbose=0L)

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.
...
Not used. Forces argument ‘fixed’ to be specified by name.
fixed
If TRUE, this algebra will not be recomputed automatically when things it depends on change. mxComputeOnce can be used to force it to recompute.
joinKey
The name of the column in current model's raw data that is used as a foreign key to match against the primary key in joinModel's raw data.
joinModel
The name of the model that this matrix joins against.
verbose
For values greater than zero, enable runtime diagnostics.

Value

Returns a new MxAlgebra object.

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 mxFitFunctionAlgebra function. The mxFitFunctionAlgebra function must reference by name the MxAlgebra object to be evaluated. Note that, if the result for an MxAlgebra depends upon one or more "definition variables" (see mxMatrix()), then the value returned after the call to mxRun() will be computed using the values of those definition variables in the first (i.e., first before any automated sorting is done) row of the raw dataset. The following operators and functions are supported in mxAlgebra: Operators
solve()
Inversion
t()
Transposition
^
Elementwise powering
%^%
Kronecker powering
+
Addition
-
Subtraction
%*%
Matrix Multiplication
*
Elementwise product
/
Elementwise division
%x%
Kronecker product
%&%
Quadratic product: pre- and post-multiply B by A and its transpose t(A), i.e: A %&% B == A %*% B %*% t(A)
Functions
cov2cor
Convert covariance matrix to correlation matrix
chol
Cholesky Decomposition
cbind
Horizontal adhesion
rbind
Vertical adhesion
colSums
Matrix column sums as a column vector
rowSums
Matrix row sums as a column vector
det
Determinant
tr
Trace
sum
Sum
mean
Arithmetic mean
prod
Product
max
Maximum
min
Min
abs
Absolute value
sin
Sine
sinh
Hyperbolic sine
asin
Arcsine
asinh
Inverse hyperbolic sine
cos
Cosine
cosh
Hyperbolic cosine
acos
Arccosine
acosh
Inverse hyperbolic cosine
tan
Tangent
tanh
Hyperbolic tangent
atan
Arctangent
atanh
Inverse hyperbolic tangent
exp
Exponent
log
Natural Logarithm
sqrt
Square root
p2z
Standard-normal quantile
logp2z
Standard-normal quantile from log probabilities
lgamma
Log-gamma function
lgamma1p
Compute log(gamma(x+1)) accurately for small x
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
vech2full
Inverse half-vectorization
vechs2full
Inverse strict half-vectorization
vec2diag
Create matrix from a diagonal vector (similar to diag)
diag2vec
Extract diagonal from matrix (similar to diag)
expm
Matrix Exponential
logm
Matrix Logarithm
omxExponential
Matrix Exponential
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
omxSelectRows
Filter rows from a matrix
omxSelectCols
Filter columns from a matrix
omxSelectRowsAndCols
Filter rows and columns from a matrix
mxEvaluateOnGrid
Evaluate an algebra on an abscissa grid and collect column results
There are also several multiargument functions usable in MxAlgebras, which apply themselves elementwise to the matrix provided as their first argument. These functions have slightly different usage from their R counterparts. Their result is always a matrix with the same dimensions as that provided for their first argument. Values must be provided for ALL arguments of these functions, in order. Provide zeroes as logical values of FALSE, and non-zero numerical values as logical values of TRUE. For most of these functions, OpenMx cycles over values of arguments other than the first, by column (i.e., in column-major order), to the length of the first argument. Notable exceptions are the log, log.p, and lower.tail arguments to probability-distribution-related functions, for which only the [1,1] element is used. It is recommended that all arguments after the first be either (1) scalars, or (2) matrices with the same dimensions as the first argument.
Function Arguments Notes
besselI & besselK x,nu,expon.scaled Note that OpenMx does cycle over the elements of expon.scaled.
besselJ & besselY x,nu
dbeta x,shape1,shape2,ncp,log The algorithm for the non-central beta distribution is used for non-negative values of ncp. Negative ncp values are ignored, and the algorithm for the central beta distribution is used.
pbeta q,shape1,shape2,ncp,lower.tail,log.p Values of ncp are handled as with dbeta().
dbinom x,size,prob,log
pbinom q,size,prob,lower.tail,log.p
dcauchy x,location,scale,log
pcauchy q,location,scale,lower.tail,log.p
dchisq x,df,ncp,log The algorithm for the non-central chi-square distribution is used for non-negative values of ncp. Negative ncp values are ignored, and the algorithm for the central chi-square distribution is used.
pchisq q,df,ncp,lower.tail,log.p Values of ncp are handled as with dchisq().
omxDnbinom x,size,prob,mu,log Exactly one of arguments size, prob, and mu should be negative, and therefore ignored. Otherwise, mu is ignored, possibly with a warning, and the values of size and prob are used, irrespective of whether they are in the parameter space. If only prob is negative, the algorithm for the alternative size-mu parameterization is used. If size is negative, a value for size is calculated as mu*prob/(1-prob), and the algorithm for the size-prob parameterization is used (note that this approach is ill-advised when prob is very close to 0 or 1).
omxPnbinom q,size,prob,mu,lower.tail,log.p Arguments are handled as with omxDnbinom().
dpois x,lambda,log
ppois q,lambda,lower.tail,log.p

References

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

See Also

MxAlgebra for the S4 class created by mxAlgebra. mxFitFunctionAlgebra for an objective function 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.

Examples

Run this code

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(model="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(model="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

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