Package 'testmath'

Do you expect a matrix to be diagonal?

Description

Do you expect a matrix to be diagonal?

Usage

expect_diagonal(matrix, tolerance = testthat::testthat_tolerance(), ...)

Arguments

matrix	matrix. The matrix you are checking to be diagonal.
tolerance	numeric. The tolerance of difference between compared entries. Defaults to testthat's default tolerance.
...	Additional arguments passed to waldo::compare().

See Also

Other matrix properties: expect_orthogonal(), expect_psd(), expect_spd(), expect_symmetric()

Examples

mat_diag <- diag(c(1, 5, 3))
mat_not_diag <- matrix(c(1, 2, 0, 3), nrow = 2)

expect_diagonal(mat_diag)
testthat::expect_failure(expect_diagonal(mat_not_diag))

---

Do you expect a function to be idempotent?

Description

This function tests whether applying a function twice yields the same result as applying it once.

Usage

expect_idempotent(f, x, tolerance = testthat::testthat_tolerance(), ...)

Arguments

f	function. The function you are testing.
x	parameter(s). The value under which you test the function.
tolerance	Passed on to waldo::compare(). If non-null, ignores small floating point differences
...	Additional arguments passed into waldo::compare()

See Also

Other function properties: expect_involutory(), expect_n_idempotent(), expect_n_involutory(), expect_periodic()

Examples

x <- c(2, 1, 3)
expect_idempotent(mean, x)

---

Do you expect a function to be involutory?

Description

This function tests whether a function, $f$ is its own inverse for a given value of $x$.

Usage

expect_involutory(f, x, tolerance = testthat::testthat_tolerance(), ...)

Arguments

f	function. The function you are testing to be involutory
x	parameter(s). The value under which you test the function.
tolerance	Passed on to waldo::compare(). If non-null, ignores small floating point differences
...	Additional arguments passed into waldo::compare()

Details

Tests that $f(f(x)) = x$. A function is called involutory (or a self-inverse function) if this applies at each element in its domain.

See Also

Other function properties: expect_idempotent(), expect_n_idempotent(), expect_n_involutory(), expect_periodic()

Examples

x <- c(2, 1, 3)
expect_involutory(rev, x) # passes
testthat::expect_failure(expect_involutory(sort, x)) # fails

---

Do you expect a function to be $n$-idempotent?

Description

This function tests whether a function, $f$, applied $n$ times on $x$ yields the same result as applying it a single time.

Usage

expect_n_idempotent(f, x, n, tolerance = testthat::testthat_tolerance(), ...)

Arguments

f	function. The function you are testing.
x	parameter(s). The value under which you test the function f.
n	integer. The expected order of idempotence.
tolerance	Passed on to waldo::compare(). If non-null, ignores small floating point differences
...	Additional arguments passed into waldo::compare()

Details

Tests that $f^n(x) = f(x)$. For n = 2, this is equivalent to expect_idempotent.

See Also

Other function properties: expect_idempotent(), expect_involutory(), expect_n_involutory(), expect_periodic()

Examples

# A function that reaches its fixed/stable state after 3 steps
custom_func <- function(x) {
  pmin(pmax(x, 0), 1) # e.g., clipping logic
}

expect_n_idempotent(custom_func, -5:5, n = 3)

---

Do you expect a function to be $n$-involutory?

Description

This function tests whether a function, $f$, applied $n$ times on $x$ returns $x$.

Usage

expect_n_involutory(f, x, n, tolerance = testthat::testthat_tolerance(), ...)

Arguments

f	function. The function you are testing.
x	parameter(s). The value under which you test the function f.
n	integer. The expected order of involution.
tolerance	Passed on to waldo::compare(). If non-null, ignores small floating point differences
...	Additional arguments passed into waldo::compare()

Details

Tests that $f^n(x) = x$. For n = 2, this is equivalent to expect_involutory.

See Also

Other function properties: expect_idempotent(), expect_involutory(), expect_n_idempotent(), expect_periodic()

Examples

mult_by_im <- function(x) {
  x * 1i
}

expect_n_involutory(mult_by_im, 1, n = 4)

---

Do you expect a matrix to be orthogonal?

Description

Do you expect a matrix to be orthogonal?

Usage

expect_orthogonal(matrix, tolerance = testthat::testthat_tolerance(), ...)

Arguments

matrix	matrix. The matrix you are checking for orthogonality.
tolerance	numeric. The tolerance of difference between compared entries. Defaults to testthat's default tolerance.
...	Additional arguments passed to waldo::compare().

See Also

Other matrix properties: expect_diagonal(), expect_psd(), expect_spd(), expect_symmetric()

Examples

# Rotation matrix is orthogonal
theta <- pi / 4
R <- matrix(c(cos(theta), -sin(theta), sin(theta), cos(theta)), nrow = 2)
expect_orthogonal(R)

# Non-orthogonal matrix
mat_bad <- matrix(1:4, nrow = 2)
testthat::expect_failure(expect_orthogonal(mat_bad))

---

Do you expect a function to be periodic?

Description

This function tests whether a function, $f$, is periodic on $x$ with period $T$

Usage

expect_periodic(f, x, period, tolerance = testthat::testthat_tolerance(), ...)

Arguments

f	function. The function you are testing to be periodic.
x	parameter(s). The value under which you test the function f.
period	numeric. The expected period of $f(x)$
tolerance	Passed on to waldo::compare(). If non-null, ignores small floating point differences
...	Additional arguments passed into waldo::compare()

Details

Tests that $f(x+T) = f(x)$

See Also

Other function properties: expect_idempotent(), expect_involutory(), expect_n_idempotent(), expect_n_involutory()

Examples

expect_periodic(cos, c(0, 1, 2), 2*pi)
expect_periodic(cos, c(0, 1, 2), 4*pi)
expect_periodic(cos, c(pi/2), pi)

---

Do you expect a matrix to be positive semidefinite?

Description

Do you expect a matrix to be positive semidefinite?

Usage

expect_psd(matrix, tolerance = testthat::testthat_tolerance())

Arguments

matrix	matrix. The matrix you are checking to be PSD.
tolerance	numeric. The tolerance for symmetry checks and eigenvalues. Defaults to testthat's default tolerance.

Details

In addition to checking whether the matrix is symmetric, it also checks if the eigenvalues of matrix are all positive. Equivalent to checking if $x^TAx \ge 0$.

See Also

Other matrix properties: expect_diagonal(), expect_orthogonal(), expect_spd(), expect_symmetric()

Examples

# Matrix with zero eigenvalue (PSD, but not strictly PD)
mat_psd <- matrix(c(1, 1, 1, 1), nrow = 2)
expect_psd(mat_psd)

# Indefinite matrix fails PSD
mat_bad <- matrix(c(1, 2, 2, 1), nrow = 2)
testthat::expect_failure(expect_psd(mat_bad))

---

Do you expect a matrix to be symmetric positive definite?

Description

Do you expect a matrix to be symmetric positive definite?

Usage

expect_spd(matrix, tolerance = testthat::testthat_tolerance())

Arguments

matrix	matrix. The matrix you are checking to be SPD.
tolerance	numeric. The tolerance for symmetry checks and eigenvalues. Defaults to testthat's default tolerance.

Details

In addition to checking whether the matrix is symmetric, it also checks if the eigenvalues of matrix are all strictly positive. Equivalent to checking if $x^TAx > 0$.

See Also

Other matrix properties: expect_diagonal(), expect_orthogonal(), expect_psd(), expect_symmetric()

Examples

mat_spd <- matrix(c(2, -1, -1, 2), nrow = 2) # spd
mat_not_spd <- matrix(c(1, 2, 2, 1), nrow = 2) # symmetric, but not positive definite

expect_spd(mat_spd)
testthat::expect_failure(expect_spd(mat_not_spd))

---

Do you expect a matrix to be symmetric?

Description

Do you expect a matrix to be symmetric?

Usage

expect_symmetric(matrix, tolerance = testthat::testthat_tolerance())

Arguments

matrix	matrix. The matrix you are checking for symmetry.
tolerance	numeric. The tolerance of difference between compared entries. Defaults to testthat's default tolerance

Details

Checks whether $A_{ij} = A_{ji}$ for all i, j. As soon as an infringement is found, it breaks early.

See Also

Other matrix properties: expect_diagonal(), expect_orthogonal(), expect_psd(), expect_spd()

Examples

mat1 <- matrix(c(7, 4, 4, 5), nrow = 2, ncol = 2) # symmetric
mat2 <- matrix(c(4, 1, 3, 9), nrow = 2, ncol = 2) # not symmetric

expect_symmetric(mat1)
testthat::expect_failure(expect_symmetric(mat2))

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