mxAlgebra {OpenMx} | R Documentation |

## Create MxAlgebra Object

### Description

This function creates a new MxAlgebra. The common use is to compute a value in a model: for instance a standardized value of a parameter, or a parameter which is a function of other values. It is also used in models with an mxFitFunctionAlgebra objective function.

**note**: Unless needed in the model objective, algebras are only computed twice: once at the
beginning and once at the end of running a model, so adding them doesn't often add a lot of overhead.

### Usage

```
mxAlgebra(expression, name = NA, dimnames = NA, ..., fixed = FALSE,
joinKey=as.character(NA), joinModel=as.character(NA),
verbose=0L, initial=matrix(as.numeric(NA),1,1),
recompute=c('always','onDemand'))
```

### 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 other arguments to be specified by name. |

`fixed` |
Deprecated. Use the ‘recompute’ argument instead. |

`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 the joinModel's raw data. |

`joinModel` |
The name of the model that this matrix joins against. |

`verbose` |
For values greater than zero, enable runtime diagnostics. |

`initial` |
a matrix. When |

`recompute` |
If ‘onDemand’, this algebra will not be recomputed automatically when things it depends on change. mxComputeOnce can be used to force it to recompute. |

### 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**: f 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

`mxRobustLog`

Robust 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

`mpinv`

Moore-Penrose Inverse

If `solve`

is used on an uninvertible square matrix in R, via
`mxEval()`

, it will fail with an error will; if
`solve`

is used on an uninvertible square matrix during
runtime, it will fail silently.

`mxRobustLog`

is the same as `log`

except that it returns -745
instead of -Inf for an argument of 0. The value -745 is less than
log(4.94066e-324), a good approximation of negative infinity because the
log of any number represented as a double will be of smaller absolute
magnitude.

There are also several multi-argument 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` | |

### Value

Returns a new MxAlgebra object.

### References

The OpenMx User's guide can be found at https://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

```
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
```

*OpenMx*version 2.21.11 Index]