params <-
list(family = "red")

## ----setup, include=FALSE-----------------------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(multivarious)

## ----pca_example--------------------------------------------------------------
# Load iris dataset and select numeric columns
data(iris)
X <- as.matrix(iris[, 1:4])

# 1. Define a pre-processor (center the data)
preproc <- center()

# 2. Fit PCA using svd_wrapper, keeping 3 components
#    The pre-processor is applied internally.
fit <- pca(X, ncomp = 3, preproc = preproc)

# The result 'fit' is a bi_projector
print(fit)

# 3. Access results
iris_scores <- scores(fit) # Scores of the centered training data (150 x 3)
iris_loadings <- loadings(fit) # Loadings (4 x 3)
cat("\nDimensions of Scores:", dim(iris_scores), "\n")
cat("Dimensions of Loadings:", dim(iris_loadings), "\n")

# 4. Project new data
# Create some new iris-like samples (5 samples, 4 variables)
set.seed(123)
new_iris_data <- matrix(rnorm(5 * 4, mean = colMeans(X), sd = apply(X, 2, sd)), 
                        nrow = 5, byrow = TRUE)

# Project the new data into the PCA space defined by 'fit'
# Pre-processing (centering using training data means) is applied automatically.
projected_new_scores <- project(fit, new_iris_data)
cat("\nDimensions of Projected New Data Scores:", dim(projected_new_scores), "\n")
print(head(projected_new_scores))

# 5. Reconstruct approximated original data from scores
# Reconstruct the first few original samples
reconstructed_X_approx <- reconstruct(fit, comp=1:3) # uses scores(fit) by default
cat("\nReconstructed Approximation of Original Data (first 5 rows):\n")
print(head(reconstructed_X_approx))

print(head(X)) # Original data for comparison


## ----project_vars_example-----------------------------------------------------
# Using the 'fit' object from the PCA example above

# Create a new variable (column) with the same number of samples as original data
set.seed(456)
new_variable <- rnorm(nrow(X))

# Project this new variable into the component space defined by the PCA scores (fit$s)
# Result shows how the new variable relates to the principal components.
projected_variable_loadings <- project_vars(fit, new_variable)
cat("\nProjection of new variable onto components:", projected_variable_loadings, "\n")