Description Usage Arguments Details Value Note Author(s) See Also Examples

View source: R/family.basics.R

Maps the elements of an array containing symmetric positive-definite matrices to a matrix with sufficient columns to hold them (called matrix-band format.)

1 |

`j` |
Usually an integer from the set { |

`k` |
An integer from the set { |

`M` |
The number of linear/additive predictors. This is the dimension of each positive-definite symmetric matrix. |

`both` |
Logical. Return both the row and column indices? See below for more details. |

`diag` |
Logical. Return the indices for the diagonal elements?
If |

Suppose we have *n* symmetric positive-definite square matrices,
each *M* by *M*, and
these are stored in an `array`

of dimension `c(n,M,M)`

.
Then these can be more compactly represented by a
`matrix`

of dimension `c(n,K)`

where `K`

is an integer
between `M`

and `M*(M+1)/2`

inclusive.
The mapping between these two representations is given by this function.
It firstly enumerates by the diagonal elements, followed by the band
immediately above the diagonal, then the band above that one, etc.
The last element is `(1,M)`

.
This function performs the mapping from elements `(j,k)`

of symmetric positive-definite square matrices to the columns of
another matrix representing such.
This is called the *matrix-band* format and is used by
the VGAM package.

This function has a dual purpose depending on the value of `both`

.
If `both = FALSE`

then the column number corresponding
to the `j`

-`k`

element of the matrix is returned.
If `both = TRUE`

then `j`

and `k`

are ignored and a list
with the following components are returned.

`row.index` |
The row indices of the upper triangular part of the
matrix (This may or may not include the diagonal elements, depending
on the argument |

`col.index` |
The column indices of the upper triangular part of the
matrix (This may or may not include the diagonal elements, depending
on the argument |

This function is used in the `weight`

slot of many VGAM
family functions (see `vglmff-class`

), especially those
whose *M* is determined by the data, e.g., `dirichlet`

,
`multinomial`

.

T. W. Yee

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
iam(1, 2, M = 3) # The 4th column represents element (1,2) of a 3x3 matrix
iam(NULL, NULL, M = 3, both = TRUE) # Return the row and column indices
dirichlet()@weight
M <- 4
temp1 <- iam(NA, NA, M = M, both = TRUE)
mat1 <- matrix(NA, M, M)
mat1[cbind(temp1$row, temp1$col)] = 1:length(temp1$row)
mat1 # More commonly used
temp2 <- iam(NA, NA, M = M, both = TRUE, diag = FALSE)
mat2 <- matrix(NA, M, M)
mat2[cbind(temp2$row, temp2$col)] = 1:length(temp2$row)
mat2 # Rarely used
``` |

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