ADmatrix: AD matrix methods (sparse and dense)

In RTMB: 'R' Bindings for 'TMB'

AD matrix methods (sparse and dense)

Description

Matrices (base package) and sparse matrices (Matrix package) can be used inside the RTMB objective function as part of the calculations. Behind the scenes these R objects are converted to AD representations when needed. AD objects have a temporary lifetime, so you probably won't see them / need to know them. The only important thing is which methods work for the objects.

Usage

## S3 method for class 'advector'
chol(x, ...)

## S3 method for class 'advector'
determinant(x, logarithm = TRUE, ...)

## S4 method for signature 'adcomplex'
eigen(x, symmetric, only.values = FALSE, EISPACK = FALSE)

## S4 method for signature 'advector'
eigen(x, symmetric, only.values = FALSE, EISPACK = FALSE)

## S4 method for signature 'advector'
svd(x, nu, nv, LINPACK = FALSE)

## S3 method for class 'adsparse'
t(x)

## S3 method for class 'adsparse'
x[...]

## S3 replacement method for class 'adsparse'
x[...] <- value

## S4 method for signature 'adsparse,missing,missing'
diag(x)

## S4 method for signature 'advector'
expm(x)

## S4 method for signature 'adsparse'
expm(x)

## S4 method for signature 'adsparse'
dim(x)

## S4 method for signature 'anysparse,ad'
x %*% y

## S4 method for signature 'ad,anysparse'
x %*% y

## S4 method for signature 'adsparse,adsparse'
x %*% y

## S4 method for signature 'ad,ad'
x %*% y

## S4 method for signature 'ad,ad.'
tcrossprod(x, y)

## S4 method for signature 'ad,ad.'
crossprod(x, y)

## S4 method for signature 'advector'
cov2cor(V)

## S4 method for signature 'ad,ad.'
solve(a, b)

## S4 method for signature 'num,num.'
solve(a, b)

## S4 method for signature 'anysparse,ad.'
solve(a, b)

## S4 method for signature 'advector'
colSums(x, na.rm, dims)

## S4 method for signature 'advector'
rowSums(x, na.rm, dims)

## S3 method for class 'advector'
cbind(...)

## S3 method for class 'advector'
rbind(...)

Arguments

x	matrix (sparse or dense)
...	As cbind
logarithm	Not used
symmetric	Logical; Is input matrix symmetric (Hermitian) ?
only.values	Ignored
EISPACK	Ignored
nu	Ignored
nv	Ignored
LINPACK	Ignored
value	Replacement value
y	matrix (sparse or dense)
V	Covariance matrix
a	matrix
b	matrix, vector or missing
na.rm	Logical; Remove NAs while taping.
dims	Same as colSums and rowSums.

Value

List (vectors/values) with adcomplex components.

List (vectors/values) with advector components in symmetric case and adcomplex components otherwise.

Object of class advector with a dimension attribute for dense matrix operations; Object of class adsparse for sparse matrix operations.

Functions

• chol(advector): AD matrix cholesky

• determinant(advector): AD log determinant

• eigen(adcomplex): General AD eigen decomposition for complex matrices. Note that argument symmetric is not auto-detected so must be specified.

• eigen(advector): AD eigen decomposition for real matrices. The non-symmetric case is redirected to the adcomplex method. Note that argument symmetric is not auto-detected so must be specified.

• svd(advector): AD svd decomposition for real matrices.

• t(adsparse): AD sparse matrix transpose. Re-directs to t,CsparseMatrix-method.

• [: AD sparse matrix subsetting. Re-directs to [-methods.

• `[`(adsparse) <- value: AD sparse matrix subset assignment. Re-directs to [<–methods.

• diag(x = adsparse, nrow = missing, ncol = missing): AD sparse matrix diagonal extract. Re-directs to diag,CsparseMatrix-method.

• expm(advector): AD matrix exponential

• expm(adsparse): AD matrix exponential

• dim(adsparse): AD sparse matrix dimension

• x %*% y: AD matrix multiply

• x %*% y: AD matrix multiply

• x %*% y: AD matrix multiply

• x %*% y: AD matrix multiply

• tcrossprod(x = ad, y = ad.): AD matrix multiply

• crossprod(x = ad, y = ad.): AD matrix multiply

• cov2cor(advector): AD matrix cov2cor

• solve(a = ad, b = ad.): AD matrix inversion and solve

• solve(a = num, b = num.): AD matrix inversion and solve

• solve(a = anysparse, b = ad.): Sparse AD matrix solve (not yet implemented)

• colSums(advector): AD matrix (or array) colsums

• rowSums(advector): AD matrix (or array) rowsums

• cbind(advector): AD matrix column bind

• rbind(advector): AD matrix row bind

Examples

F <- MakeTape(function(x) matrix(1:9,3,3) %*% x, numeric(3))
F$jacobian(1:3)
F <- MakeTape(function(x) Matrix::expm(matrix(x,2,2)), numeric(4))
F$jacobian(1:4)
F <- MakeTape(det, diag(2)) ## Indirectly available via 'determinant'
F$jacobian(matrix(1:4,2))

RTMB documentation built on Sept. 12, 2024, 6:45 a.m.