Package 'lazymatrix'

Title: Perform Complex Matrix Operations Symbolically on Sparse Matrices
Description: Provides a framework for lazy computation on large sparse matrices. Enables lazy evaluation of normalized data matrices, preserving sparsity throughout operations without materializing dense intermediate objects. Implements statistical algorithms including LSQR for sparse least squares as described in Paige and Saunders (1982) <doi:10.1145/355984.355989> and partial singular value decomposition via the augmented implicitly restarted Lanczos bidiagonalization algorithm of Baglama and Reichel (2005) <doi:10.1137/04060593X>.
Authors: Viktor Segersall [aut, cre, cph]
Maintainer: Viktor Segersall <[email protected]>
License: GPL (>= 3)
Version: 0.1.0
Built: 2026-07-14 20:06:48 UTC
Source: https://github.com/cran/lazymatrix

Help Index

Vector Subtraction between regular vector and LazyColumn

Description

Subtracts a LazyColumn vector from a base vector.

Usage

## S4 method for signature 'ANY,LazyColumn'
e1 - e2

Arguments

e1

A LazyColumn object.
e2

A numeric vector.

Value

A numeric vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
b <- rnorm(nrow(mat_a))
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- lazy_a[, 2]
b - lazy_col

Vector subtraction between a LazyColumn vector and a regular R vector.

Description

Subtracts a numeric R vector from a LazyColumn vector.

Usage

## S4 method for signature 'LazyColumn,ANY'
e1 - e2

Arguments

e1

A LazyColumn object.
e2

A numeric vector.

Value

A numeric vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
b <- rnorm(nrow(mat_a))
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- lazy_a[,2]
lazy_col - b

Vector Subtraction between two LazyColumn vectors.

Description

Subtracts a LazyColumn vector from another LazyColumn vector.

Usage

## S4 method for signature 'LazyColumn,LazyColumn'
e1 - e2

Arguments

e1

A LazyColumn object.
e2

A LazyColumn object.

Value

A numeric vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow = 3, ncol = 4)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- lazy_a[, 2]
lazy_col_2 <- lazy_a[, 3]
lazy_col_2 - lazy_col

Multiply element-wise two LazyColumn vectors

Description

Computes the element-wise multiplication of two LazyColumn objects , preserving the lazy structure.

Usage

## S4 method for signature 'LazyColumn,LazyColumn'
e1 * e2

Arguments

e1

A LazyColumn object.
e2

A LazyColumn object.

Value

A numeric vector with the resulting vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
X <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- X[, 1]
lazy_col_2 <- X[, 2]
lazy_col_2 * lazy_col

Multiply a LazyColumn by a numeric scalar or vector

Description

Computes the element-wise multiplication of a LazyColumn object with a numeric value, preserving the lazy structure. If e2 is a scalar, scalar multiplication is performed. If e2 is a vector of the same length as the column, element-wise multiplication is performed.

Usage

## S4 method for signature 'LazyColumn,numeric'
e1 * e2

Arguments

e1

A LazyColumn object.
e2

A numeric scalar or vector.

Value

A numeric vector with the resulting vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
X <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- X[, 1]
lazy_col * 2
lazy_col * rnorm(nrow(X))

Multiply a numeric scalar or vector by a LazyColumn

Description

Computes the element-wise multiplication of a LazyColumn object with a numeric value, preserving the lazy structure. If e1 is a scalar, scalar multiplication is performed. If e1 is a vector of the same length as the column, element-wise multiplication is performed.

Usage

## S4 method for signature 'numeric,LazyColumn'
e1 * e2

Arguments

e1

A numeric scalar or vector.
e2

A LazyColumn object.

Value

A numeric vector with the resulting vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
X <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- X[, 1]
2* lazy_col
rnorm(nrow(X)) * lazy_col

Matrix multiplication for vector and LazyMatrix

Description

Multiplies a LazyMatrix object by a vector.

Usage

## S4 method for signature 'ANY,LazyMatrix'
x %*% y

Arguments

x

A numeric vector.
y

A LazyMatrix object.

Value

A Matrix object of class dgeMatrix.

Examples

mat_a <- base::matrix(rep(1, 6), nrow=2, ncol=3)
b <- c(1, 2)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
b %*% lazy_a

Perform the dot product between two LazyColumn vectors

Description

Computes the inner product between two LazyColumn objects.

Usage

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

Arguments

x

A LazyColumn object.
y

A LazyColumn object.

Value

A numeric value with the resulting scalar.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
X <- LazyMatrix(mat_a, "sd", "mean")
b <- rnorm(nrow(X))
lazy_col <- X[, 1]
lazy_col_2 <- X[, 2]
lazy_col %*% lazy_col_2

Perform the dot product between a LazyColumn and a numeric vector

Description

Computes the inner product of a LazyColumn object and a numeric vector. If y is a scalar, scalar multiplication is performed. If y is a vector of the same length as the column, the dot product is performed.

Usage

## S4 method for signature 'LazyColumn,numeric'
x %*% y

Arguments

x

A LazyColumn object.
y

A numeric scalar or vector.

Value

A numeric value with the resulting scalar.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
X <- LazyMatrix(mat_a, "sd", "mean")
b <- rnorm(nrow(X))
lazy_col <- X[, 1]
lazy_col %*% b

Matrix multiplication for LazyMatrix and vector

Description

Multiplies a LazyMatrix object by a vector.

Usage

## S4 method for signature 'LazyMatrix,ANY'
x %*% y

Arguments

x

A LazyMatrix object.
y

A numeric vector.

Value

A numeric matrix.

Examples

mat_a <- base::matrix(rep(1, 6), nrow=2, ncol=3)
b <- c(1, 2, 3)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_a %*% b

Matrix multiplication for LazyMatrix and matrix-object.

Description

Multiplies a LazyMatrix object by a matrix

Usage

## S4 method for signature 'LazyMatrix,matrix'
x %*% y

Arguments

x

A LazyMatrix object.
y

A matrix-object.

Value

A matrix-object with the product of the lazy and non lazy object.

Examples

mat_a <- matrix(rep(1, 6), nrow = 2, ncol = 3)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
set.seed(123)
m <- matrix(rnorm(6), nrow = 3, ncol = 2)
lazy_a %*% m

Perform the dot product between a numeric vectorand a LazyColumn

Description

Computes the inner product of a numeric vector and a LazyColumn object. If x is a scalar, scalar multiplication is performed. If x is a vector of the same length as the column, the dot product is performed.

Usage

## S4 method for signature 'numeric,LazyColumn'
x %*% y

Arguments

x

A numeric scalar or vector.
y

A LazyColumn object.

Value

A numeric value with the resulting scalar.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
X <- LazyMatrix(mat_a, "sd", "mean")
b <- rnorm(nrow(X))
lazy_col <- X[, 1]
b %*% lazy_col

Vector Addition between regular vector and LazyColumn

Description

Sums a regular base vector and a LazyColumn vector.

Usage

## S4 method for signature 'ANY,LazyColumn'
e1 + e2

Arguments

e1

A numeric vector.
e2

A LazyColumn object.

Value

A numeric vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
b <- rnorm(nrow(mat_a))
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- lazy_a[, 2]
b + lazy_col

Vector Addition between LazyColumn and regular vector

Description

Sums a LazyColumn vector and a regular base vector.

Usage

## S4 method for signature 'LazyColumn,ANY'
e1 + e2

Arguments

e1

A LazyColumn object.
e2

A numeric vector.

Value

A numeric vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
b <- rnorm(nrow(mat_a))
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- lazy_a[,2]
lazy_col + b

Vector Addition between two LazyColumn vectors.

Description

Sums two LazyColumn vectors.

Usage

## S4 method for signature 'LazyColumn,LazyColumn'
e1 + e2

Arguments

e1

A LazyColumn object.
e2

A LazyColumn object.

Value

A numeric vector.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- lazy_a[,2]
lazy_col_2 <- lazy_a[, 3]
lazy_col_2 + lazy_col

Retrieve or set the row or column names of a LazyMatrix object.

Description

Retrieve or set the row or column names of a LazyMatrix object.

Usage

## S4 method for signature 'LazyMatrix'
colnames(x)

Arguments

x

A LazyMatrix object.

Value

A character vector of column names, or NULL if the matrix has no column names.

Examples

mat_a <- base::matrix(rep(1, 6), nrow=2, ncol=3)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
colnames(lazy_a)

Comparison operators for LazyColumn

Description

Enables logical comparisons (>, <, >=, <=, ==, !=) on a LazyColumn, comparing against its scaled values.

Usage

## S4 method for signature 'LazyColumn,numeric'
Compare(e1, e2)

Arguments

e1

A LazyColumn or numeric.
e2

A LazyColumn or numeric.

Value

A logical vector.

Comparison operators for LazyColumn

Description

Enables logical comparisons (>, <, >=, <=, ==, !=) on a LazyColumn, comparing against its scaled values.

Usage

## S4 method for signature 'numeric,LazyColumn'
Compare(e1, e2)

Arguments

e1

A LazyColumn or numeric.
e2

A LazyColumn or numeric.

Value

A logical vector.

Crossproduct for LazyMatrix

Description

Computes the crossproduct of a LazyMatrix object as it's Gram matrix or computes the transposed matrix-vector multiplication.

Usage

## S4 method for signature 'LazyMatrix,ANY'
crossprod(x, y = NULL)

Arguments

x

A LazyMatrix object.
y

An optional numeric vector or matrix. If NULL, computes the Gram matrix of x.

Value

A matrix: the Gram matrix if y is NULL, otherwise the crossproduct result.

Examples

mat_a <- matrix(rep(1, 6), nrow=2, ncol=3)
b <- c(1, 2)
lazy_a <- LazyMatrix(mat_a, scale="sd", location="mean")
crossprod(lazy_a)
crossprod(lazy_a, b)

Returns the dimension of a LazyMarix Object.

Description

Returns the dimension of a LazyMarix Object.

Usage

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

Arguments

x

A LazyMatrix object.

Value

For an array (and hence in particular, for a matrix) dim retrieves the dim attribute of the object. It is NULL or a vector of mode integer. The replacement method changes the "dim" attribute (provided the new value is compatible) and removes any "dimnames" and "names" attributes.

Examples

mat_a <- base::matrix(rep(1, 6), nrow=2, ncol=3)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
dim(lazy_a)

Fast crossprod for LazyMatrix (dense case)

Description

Fast crossprod for LazyMatrix (dense case)

Usage

lazy_crossprod_vec(x, s, c, y)

Arguments

x

Dense matrix
s

Column scale inverse vector (1 / col_scales)
c

Column location vector (col_locations)
y

Vector to multiply

Value

Vector result of t(X_tilde) * y

Fast crossprod for LazyMatrix (sparse case)

Description

Fast crossprod for LazyMatrix (sparse case)

Usage

lazy_crossprod_vec_sp(x, s, c, y)

Arguments

x

Sparse matrix (dgCMatrix)
s

Column scale inverse vector (1 / col_scales)
c

Column location vector (col_locations)
y

Vector to multiply

Value

Vector result of t(X_tilde) * y

LazyColumn S4 class

Description

An S4 class to represent a column vector as a subset of a LazyMatrix-object

Value

An object of class LazyColumn with slots data (numeric vector), scale (numeric scalar), and location (numeric scalar); represents a column of a LazyMatrix (scaled via scale and location).

Slots

data

The underlying data column vector.

scale

Numeric scalar containing column-scale parameter.

location

Numeric scalar containing the column-location parameter.

Examples

mat <- matrix(1:6, nrow = 2, ncol = 3)
lazy_mat <- LazyMatrix(mat, "sd", "mean")
lazy_column <- lazy_mat[, 2]

Constructs a LazyMatrix object.

Description

Constructs a LazyMatrix object.

Usage

LazyMatrix(data, scale = NULL, location = NULL)

Arguments

data

a matrix object.
scale

optional scaling parameter.
location

optional location parameter.

Value

A LazyMatrix object.

Examples

mat_a <- matrix(1:6, nrow=3, ncol=2)
lazy_a <- LazyMatrix(mat_a, scale="sd", location="mean")
lazy_a

LazyMatrix S4 class

Description

An S4 class to represent a lazily transformed matrix with scaling and location parameters.

Value

An object of class LazyMatrix with slots data (matrix, possibly sparse), col_scales, row_scales, col_locations, row_locations. Represents the original data matrix plus stored scaling/centering parameters used for lazy operations

Slots

data

The underlying matrix.

col_scales

Numeric vector of column scales.

row_scales

Numeric vector of row scales.

col_locations

Numeric vector of column locations.

row_locations

Numeric vector of row locations.

Examples

mat <- matrix(1:6, nrow=2, ncol=3)
obj <- LazyMatrix(mat, "sd", "mean")

Get the length of a LazyColumn

Description

Get the length of a LazyColumn

Usage

## S4 method for signature 'LazyColumn'
length(x)

Arguments

x

A LazyColumn object.

Value

An integer value containing the number of elements within the vector.

Examples

mat_a <- base::matrix(rep(1, 6), nrow=2, ncol=3)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_col <- lazy_a[, 2]
length(lazy_col)

Performs least squares estimation on LazyMatrix object using the iterative lsqr algorithm.

Description

Performs least squares estimation on LazyMatrix object using the iterative lsqr algorithm.

Usage

lsqr(x, y, ...)

## S4 method for signature 'LazyMatrix'
lsqr(x, y)

Arguments

x

A LazyMatrix object.
y

A response vector.
...

Additional arguments (currently unused).

Value

A Matrix-object with the regression coefficients of the covariates.

Examples

set.seed(123)
mat_a <- base::matrix(rnorm(500), nrow = 50, ncol = 10)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
response_vector <- rnorm(nrow(mat_a))
lsqr(lazy_a, response_vector)

Returns the number of columns of the data matrix

Description

Returns the number of columns of the data matrix

Usage

## S4 method for signature 'LazyMatrix'
ncol(x)

Arguments

x

A LazyMatrix object.

Value

an integer of length 1 or NULL.

Examples

mat_a <- base::matrix(rep(1, 6), nrow=2, ncol=3)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
ncol(lazy_a)

Compute the norm of a LazyMatrix or LazyColumn

Description

Dispatches to the appropriate method based on the class of x.

Usage

norm(x, ...)

Arguments

x

A LazyMatrix or LazyColumn object.
...

Additional arguments passed to methods, such as type.

Value

For LazyColumn, a numeric scalar containing the Euclidean norm. For LazyMatrix, a numeric scalar containing the Frobenius norm.

Perform the norm of a LazyColumn vector

Description

Computes the norm of a LazyColumn object.

Usage

## S4 method for signature 'LazyColumn'
norm(x, type = "2")

Arguments

x

A LazyColumn object.
type

A character value defining type of norm. Default is Euclidean norm.

Value

A numeric value with the resulting scalar.

Examples

mat_a <- base::matrix(rnorm(12), nrow=3, ncol=4)
X <- LazyMatrix(mat_a, "sd", "mean")
b <- rnorm(nrow(X))
lazy_col <- X[, 1]
norm(lazy_col)

Computes the Frobenius norm of a LazyMatrix object.

Description

Computes the Frobenius norm of a LazyMatrix object.

Usage

## S4 method for signature 'LazyMatrix'
norm(x)

Arguments

x

A LazyMatrix object.

Value

A numeric scalar representing the Frobenius norm of the matrix.

Examples

mat_a <- base::matrix(rnorm(50), nrow = 10, ncol = 5)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
norm(lazy_a)

Returns the number of rows of the data matrix

Description

Returns the number of rows of the data matrix

Usage

## S4 method for signature 'LazyMatrix'
nrow(x)

Arguments

x

A LazyMatrix object.

Value

an integer of length 1 or NULL.

Examples

mat_a <- base::matrix(rep(1, 6), nrow=2, ncol=3)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
nrow(lazy_a)

Performs a principal component analysis on the LazyMatrix object using irlba:s sparse svd.

Description

Performs a principal component analysis on the LazyMatrix object using irlba:s sparse svd.

Usage

## S4 method for signature 'LazyMatrix'
prcomp(x, retx = TRUE, tol = NULL, rank. = NULL, ...)

Arguments

x

a LazyMatrix object.
retx

a logical value indicating whether the rotated variables should be returned.
tol

a value indicating the magnitude below which components should be omitted. (Components are omitted if their standard deviations are less than or equal to tol times the standard deviation of the first component.) With the default null setting, no components are omitted (unless rank. is specified less than min(dim(x)).). Other settings for tol could be tol = 0 or tol = sqrt(.Machine$double.eps), which would omit essentially constant components.
rank.

optionally, a number specifying the maximal rank, i.e., maximal number of principal components to be used. Can be set as alternative or in addition to tol, useful notably when the desired rank is considerably smaller than the dimensions of the matrix.
...

Additional arguments passed to underlying methods.

Value

A list of class \"prcomp\" containing:

sdev

The standard deviations of the principal components (i.e., the square roots of the eigenvalues of the covariance/correlation matrix, calculated using the singular values of the data matrix).
rotation

The matrix of variable loadings (columns are eigenvectors).
x

If retx is TRUE, the value of the rotated data (centered and optionally scaled, multiplied by the rotation matrix).
center

The centering used, or FALSE.
scale

The scaling applied to the data, or FALSE

Examples

set.seed(123)
mat_a <- matrix(rnorm(500), nrow=50, ncol=10)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
pca_lazy <- prcomp(lazy_a)

Set names for a LazyColumn

Description

Assigns names to the underlying data of a LazyColumn, returning a new LazyColumn with the same scale and location as the original. This enables name-based subsetting via [ on LazyColumn objects, mirroring stats::setNames() for ordinary vectors.

Usage

## S4 method for signature 'LazyColumn,character'
setNames(object = nm, nm)

Arguments

object

A LazyColumn object.
nm

A character vector of names, with length equal to length(object@data).

Value

A new LazyColumn with named data, preserving the original scale and location.

Examples

set.seed(123)
mat_a <- matrix(rnorm(500), nrow = 50, ncol = 10)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_c <- lazy_a[, 2]
lazy_named <- setNames(lazy_c[1:26], letters[1:26])
lazy_named["a"]

Subset a LazyColumn

Description

Subsets a LazyColumn object using standard R indexing rules: positive integers, negative integers, logical vectors (with recycling), character vectors (if named), zero, or missing (nothing).

Usage

## S4 method for signature 'LazyColumn,ANY,ANY,ANY'
x[i, j, ..., drop = TRUE]

Arguments

x

A LazyColumn object.
i

Index: positive integers, negative integers, logical vector, character vector (if named), zero, or missing (nothing).
j

Not used for LazyColumn (1-dimensional). Must be missing.
...

Additional arguments (ignored).
drop

Logical. Currently ignored — single element extraction always returns a plain scaled numeric, consistent with vector subsetting.

Value

A LazyColumn when multiple elements are selected, or a scaled numeric value when a single element is selected.

Examples

set.seed(123)
mat_a <- matrix(rnorm(500), nrow = 50, ncol = 10)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_c <- lazy_a[, 2]

# Single element → plain scaled numeric
lazy_c[2]

# Multiple elements → LazyColumn
lazy_c[c(1, 3, 5)]

Subset a LazyMatrix by columns

Description

Subsets a LazyMatrix object by columns, returning either a LazyColumn or a new LazyMatrix depending on the number of columns selected. Row subsetting is not yet supported.

Usage

## S4 method for signature 'LazyMatrix,ANY,ANY,ANY'
x[i, j, ..., drop = TRUE]

Arguments

x

A LazyMatrix object.
i

Row index. Must be missing as row subsetting is not yet supported.
j

Column index. Either a single integer returning a LazyColumn, or a vector of integers returning a LazyMatrix.
...

Additional arguments (ignored).
drop

Logical. Currently ignored.

Value

A LazyColumn if a single column is selected, or a LazyMatrix if multiple columns are selected.

Examples

A <- Matrix::sparseMatrix(i = c(1,2,3), j = c(1,2,3), x = c(1,2,3))
lazy_m <- LazyMatrix(A, "sd", "mean")

# Single column → LazyColumn
lazy_col <- lazy_m[, 2]

# Multiple columns → LazyMatrix
lazy_subset <- lazy_m[, 1:3]

Singular Value decomposition for LazyMatrix.

Description

Performs lazy SVD using irlba for partial Singular value decomposition on sparse matrices.

Usage

## S4 method for signature 'LazyMatrix'
svd(x, nu = min(n, p), nv = min(n, p))

Arguments

x

A LazyMatrix object.
nu

number of left singular vectors to estimate (defaults to nv).
nv

number of right singular vectors to estimate.

Value

A list with entries:

d

max(nu, nv) approximate singular values
u

nu approximate left singular vectors (only when right_only=FALSE)
v

nv approximate right singular vectors
iter

The number of Lanczos iterations carried out
mprod

The total number of matrix vector products carried out

Examples

set.seed(123)
mat_a <- matrix(rnorm(500), nrow = 50, ncol = 10)
lazy_a <-LazyMatrix(mat_a, scale = "sd", location = "mean")
S <- svd(lazy_a)
# Receive singular values with
S$d

Given a LazyMatrix x, t returns the transpose of x.

Description

Given a LazyMatrix x, t returns the transpose of x.

Usage

## S4 method for signature 'LazyMatrix'
t(x)

Arguments

x

A LazyMatrix object.

Value

A LazyMatrix object with the transposed data matrix.

Examples

mat_a <- base::matrix(rep(1, 6), nrow=2, ncol=3)
lazy_a <- LazyMatrix(mat_a, "sd", "mean")
lazy_t <- t(lazy_a)