Fit multiple linear models against a shared design matrix

The flagship batch regression function. Solves \(Y \approx X B\) where Y is a matrix whose columns are independent response variables. When no GPU backend is active the normal-equations or QR path runs on CPU. With an active GPU backend the QR path dispatches the factorization to the device and keeps intermediate results resident to minimise host round-trips.

Usage

many_lm(
  X,
  Y,
  weights = NULL,
  intercept = FALSE,
  include_fitted = FALSE,
  include_residuals = FALSE,
  cache = TRUE,
  method = c("normal", "qr")
)

Arguments

X

Numeric matrix or adgeMatrix of predictors, shape [n, p].

Y

Numeric matrix or adgeMatrix of responses, shape [n, q]. Each column is fitted independently against X.

weights

Optional numeric vector of length n with non-negative observation weights. When supplied, weighted least squares is used.

intercept

Logical. When TRUE, a column of ones is prepended to X before fitting.

include_fitted

Logical. When TRUE, fitted values are stored in the returned object.

include_residuals

Logical. When TRUE, residuals are stored in the returned object.

cache

Logical. When TRUE, the design-matrix factorization is cached for reuse when X is the same across calls.

method

Solver: "normal" (normal equations) or "qr" (QR decomposition). Ignored when weights is non-NULL and the weighted path is selected.

Value

An object of class "am_many_lm_fit", a named list containing:

coefficients

adgeMatrix of shape [p, q].

fitted.values

adgeMatrix [n, q] or NULL.

residuals

adgeMatrix [n, q] or NULL.

rss

Numeric vector of length q: residual sums of squares.

sigma2

Numeric vector of length q: residual variances.

rank

Integer model rank.

df.residual

Residual degrees of freedom.

See also

lm_fit, array_lm

Examples

X <- matrix(rnorm(100), nrow = 20)
Y <- matrix(rnorm(60), nrow = 20)
fit <- many_lm(X, Y, method = "qr")
dim(coef(fit))
#> [1] 5 3