bd_wproduct

LINEAR_ALGEBRA

1 Description

Compute weighted operations using a diagonal weight from w: Inputs may be base numeric matrices .

2 Usage

bd_wproduct(X, w, op)

3 Arguments

Parameter	Description
`X`	Numeric matrix (n x p).
`w`	Numeric weight vector (length or ), or a 1D matrix coerced to a vector.
`op`	Character string (case-insensitive): one of , , , .

4 Value

Numeric matrix with dimensions depending on : for , for , and for /.

5 Details

w is interpreted as the diagonal of a weight matrix; its required length depends on the operation: rows for "xtwx" and "wx", columns for "xwxt" and "xw".

6 Examples

set.seed(1)
n <- 10; p <- 5
X <- matrix(rnorm(n * p), n, p)
u <- runif(n); w <- u * (1 - u)
bd_wproduct(X, w, "xtwx")  # p x p
bd_wproduct(X, w, "wx")    # n x p (row scaling)

v <- runif(p)
bd_wproduct(X, v, "xw")    # n x p (col scaling)
bd_wproduct(X, v, "xwxt")  # n x n

---
title: "bd_wproduct"
subtitle: "bd_wproduct"
---

<span class="category-badge linear_algebra">LINEAR_ALGEBRA</span>

## Description

Compute weighted operations using a diagonal weight from `w`:
\itemize{
\item `"xtwx"`: \eqn{X' diag(w) X}  (row weights; `length(w) = nrow(X)`)
\item `"xwxt"`: \eqn{X diag(w) X'}  (column weights; `length(w) = ncol(X)`)
\item `"xw"`  : \eqn{X diag(w)}     (column scaling; `length(w) = ncol(X)`)
\item `"wx"`  : \eqn{diag(w) X}     (row scaling;    `length(w) = nrow(X)`)
}
Inputs may be base numeric matrices .

## Usage

```r
bd_wproduct(X, w, op)
```
## Arguments

::: {.param-table}
| Parameter | Description |
|-----------|-------------|
| `X` | Numeric matrix (n x p). |
| `w` | Numeric weight vector (length \code{n} or \code{p}), or a 1D matrix coerced to a vector. |
| `op` | Character string (case-insensitive): one of   \code{"XtwX"/"xtwx"}, \code{"XwXt"/"xwxt"}, \code{"Xw"/"xw"}, \code{"wX"/"wx"}.  |
:::

## Value

::: {.return-value}
Numeric matrix with dimensions depending on \code{op}:
\code{p x p} for \code{"xtwx"}, \code{n x n} for \code{"xwxt"}, and \code{n x p} for \code{"xw"}/\code{"wx"}.

:::
## Details

`w` is interpreted as the diagonal of a weight matrix; its required length depends on the operation:
rows for `"xtwx"` and `"wx"`, columns for `"xwxt"` and `"xw"`.

## Examples
```{r}
#| eval: false
#| warning: false

set.seed(1)
n <- 10; p <- 5
X <- matrix(rnorm(n * p), n, p)
u <- runif(n); w <- u * (1 - u)
bd_wproduct(X, w, "xtwx")  # p x p
bd_wproduct(X, w, "wx")    # n x p (row scaling)

v <- runif(p)
bd_wproduct(X, v, "xw")    # n x p (col scaling)
bd_wproduct(X, v, "xwxt")  # n x n

```