math_atoms: Standard R Functions for CVXR Expressions

In CVXR: Disciplined Convex Optimization

Standard R Functions for CVXR Expressions

Description

CVXR registers methods so that standard R functions create the appropriate atoms when applied to Expression objects.

For CVXR expressions, computes the norm atom with the same meaning as base R norm for every type: a vector is a one-column or one-row matrix. For any other input the call is forwarded as written to Matrix::norm, so the result is exactly base R's (including its default type "O").

For CVXR expressions, computes the standard deviation atom (ddof=0 by default, matching CVXPY/numpy convention). For numeric inputs, falls through to sd.

For CVXR expressions, computes the variance atom (ddof=0 by default). For numeric inputs, falls through to var.

For CVXR expressions, computes the outer product of two vectors. For other inputs, falls through to outer.

For CVXR expressions, dispatches to DiagVec (vector to diagonal matrix) or DiagMat (extract diagonal from matrix), matching CVXPY's cp.diag() behavior. For other inputs, falls through to Matrix::diag, called exactly as written, which dispatches via S4 for both Matrix and base matrix objects.

Usage

norm(x, type = "2", ...)

sd(x, ...)

var(x, ...)

outer(X, Y, ...)

diag(x = 1, nrow, ncol, names = TRUE, k = NULL)

Arguments

x	An Expression, matrix, vector, or scalar.
type	Norm type, as in base R: "O"/"o"/"1" (maximum absolute column sum), "I"/"i" (maximum absolute row sum), "F"/"f"/"E"/"e" (Frobenius), "M"/"m" (largest absolute entry), "2" (largest singular value; the default for an expression only). For an expression, any other value is passed to cvxr_norm as p.
...	For non-Expression inputs: passed to outer. For expressions, only FUN = "*" is accepted; any other FUN or argument is an error.
X	An Expression or numeric.
Y	An Expression or numeric.
nrow	For non-Expression: passed to Matrix::diag; an error with an Expression.
ncol	For non-Expression: passed to Matrix::diag; an error with an Expression.
names	For non-Expression: passed to Matrix::diag; an error with an Expression.
k	Integer diagonal offset for Expressions only. NULL (default) means 0, the main diagonal.

Details

The k parameter (off-diagonal offset) is only available for Expression inputs; giving it with a non-Expression x is an error.

Value

An Expression or numeric value.

An Expression or numeric value.

An Expression or numeric value.

An Expression or matrix.

An Expression, matrix, or vector.

Math group (elementwise, via S3 group generic)

abs(x)

Absolute value (convex, nonneg)

exp(x)

Exponential (convex, positive)

log(x)

Natural logarithm (concave, domain x >= 0)

sqrt(x)

Square root via power(x, 0.5) (concave)

log1p(x)

log(1+x) compound expression (concave)

log2(x), log10(x)

Base-2/10 logarithm

cumsum(x)

Cumulative sum (affine)

cummax(x)

Cumulative max (convex)

cumprod(x)

Cumulative product

ceiling(x), floor(x)

Round up/down (quasilinear, DQCP). As in CVXPY, the value rounds x to 4 decimal places first, so floor(-3e-10) of an expression is 0, not -1.

sign(x)

Sign (quasilinear for a scalar, DQCP). As in CVXPY, it is -1 for x <= 0, so sign(0) of an expression is -1, not 0.

On a matrix expression, cumsum(), cummax() and cumprod() run down each column, as in CVXPY; use cumsum_axis(x, axis = NULL) for all entries in column-major order.

Summary group (via S3 group generic)

sum(x)

Sum all entries (affine)

max(x)

Maximum entry (convex)

min(x)

Minimum entry (concave)

prod(x)

Product of entries

Each also takes axis and keepdims, as in CVXPY: sum(x, axis = 2) is sum_entries(x, axis = 2), and likewise max_entries, min_entries and prod_entries.

S3 generic methods

mean(x)

Arithmetic mean; pass axis/keepdims via ...

diff(x)

First-order differences; also cvxr_diff

Masking wrappers

These mask the base/stats versions and dispatch on argument type:

norm(x)

2-norm; use type for "1", "I" (infinity), "F" (Frobenius)

sd(x)

Standard deviation (ddof=0 for expressions)

var(x)

Variance (ddof=0 for expressions)

outer(X, Y)

Outer product of two vector expressions

Advanced usage

For axis-aware reductions, keepdims, or other options not available through the standard interface, use the explicit functions: cvxr_norm, cvxr_mean, cvxr_diff, cvxr_std, cvxr_var, cvxr_outer.

See Also

power, sum_entries, max_entries, min_entries

cvxr_norm for the full-featured version with axis and keepdims arguments

cvxr_std for the full-featured version

cvxr_var for the full-featured version

cvxr_outer for the CVXR-specific version

DiagVec, DiagMat

CVXR documentation built on Oct. 19, 2026, 5:07 p.m.