Miscellaneous (original) (raw)

This vignette is adapted from the official Armadillo documentation.

Constants

The reference for these constants are National Institute of Standards and Technology (1994) and Wolfram Research (2009).

| Expression | Description | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ----------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------- | ------------------------------------------------------ | | --------------- | ------------------------------------------ | | ------------ | --------------------------------------------------------- | | ----------------- | ------------------------------------------- | | --------------- | ------------------------------------------ | | ---------------- | --------------------------------- | | --------------- | -------------------------------------------------------- | | --------------- | -------------------------------------------------- | | --------------- | ------------------------------------------------------- | | ----------------- | --------------------------------------------------------- | | --------------- | --------------------------------------------- | | datum::tau | The ratio of any circle’s circumference to its radius ($\tau \approx 6.28319$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::pi | The ratio of any circle’s circumference to its diameter ($\pi \approx 3.14159$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::inf | Infinity ($\infty$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::nan | Not a number | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::eps | Machine dependent epsilon ($\epsilon \approx 2.2204 \times 10^{-16}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::e | Base of the natural logarithm ($e \approx 2.71828$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::sqrt2 | Square root of two ($\sqrt{2} \approx 1.41421$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::log_min | Type and machine dependent log of minimum non-zero value | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::log_max | Type and machine dependent log of maximum value | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::euler | Euler-Mascheroni constant ($\gamma \approx 0.577216$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::gratio | Golden ratio ($ $) | | `datum::m_u` | Atomic mass constant in kilograms ($m_u ^{-27} $) | | `datum::N_A` | Avogadro constant ($N_A ^{23} ^{-1}$) | | `datum::k` | Boltzmann constant in joules per kelvin ($k ^{-23} $) | | `datum::k_evk` | Boltzmann constant in eV/K ($k ^{-5} $) | | `datum::a_0` | Bohr radius in meters ($a_0 ^{-11} $) | | `datum::mu_B` | Bohr magneton ($_B ^{-24} $) | | `datum::Z_0` | Characteristic impedance of vacuum in ohms ($Z_0 $) | | `datum::G_0` | Conductance quantum in siemens ($G_0 ^{-5} $) | | `datum::k_e` | Coulomb's constant in meters per farad ($k_e ^9 $) | | `datum::eps_0` | Electric constant in farads per meter ($_0 ^{-12} $) | | `datum::m_e` | Electron mass in kilograms ($m_e ^{-31} $) | | datum::eV | Electron volt in joules ($1 \text{ eV} \approx 1.60218 \times 10^{-19} \text{J}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::ec | Elementary charge in coulombs ($e \approx 1.60218 \times 10^{-19} \text{C}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::F | Faraday constant in coulombs ($F \approx 9.64853 \times 10^4 \text{C/mol}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::alpha | Fine-structure constant ($\alpha \approx 7.29735 \times 10^{-3}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::alpha_inv | Inverse fine-structure constant ($\alpha^{-1} \approx 137.036$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::K_J | Josephson constant ($K_J \approx 4.83598 \times 10^{14} \text{Hz/V}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::mu_0 | Magnetic constant in henries per meter ($\mu_0 \approx 1.25664 \times 10^{-6} \text{H/m}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::phi_0 | Magnetic flux quantum in webers ($\phi_0 \approx 2.06783 \times 10^{-15} \text{Wb}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::R | Molar gas constant in joules per mole kelvin ($R \approx 8.31446 \text{ J/mol K}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::G | Newtonian constant of gravitation in newton square meters per kilogram squared ($G \approx 6.67430 \times 10^{-11} \text{m}^3 \text{kg}^{-1} \text{s}^{-2}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::h | Planck constant in joule seconds ($h \approx 6.62607 \times 10^{-34} \text{J s}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::h_bar | Reduced Planck constant in joule seconds ($\hbar \approx 1.05457 \times 10^{-34} \text{J s}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::m_p | Proton mass in kilograms ($m_p \approx 1.67262 \times 10^{-27} \text{kg}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::R_inf | Rydberg constant in reciprocal meters ($R_\infty \approx 1.09737 \times 10^7 \text{m}^{-1}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::c_0 | Speed of light in vacuum in meters per second ($c_0 \approx 2.99792 \times 10^8 \text{m/s}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::sigma | Stefan-Boltzmann constant ($\sigma \approx 5.67037 \times 10^{-8} \text{W} \text{m}^{-2} \text{K}^{-4}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::R_k | von Klitzing constant in ohms ($R_k \approx 25,812.807 \Omega$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | datum::b | Wien wavelength displacement law constant ($b \approx 2.89777 \times 10^{-3} \text{m K}$) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

The constants are stored in the Datum<type> class, where type is either float or double. For convenience, Datum<double> is typedefed as datum, and Datum<float> is typedefed as fdatum.

Caveats:

datum::nan is not equal to anything, even itself.
To check whether a scalar x is finite, use std::isfinite(x).

These caveats mean that

double x = datum::pi;
double y = datum::nan;

bool is_nan_y = (y == datum::nan); // false

// this block will lead to an arithmetic error
if (is_nan_y == false) {
  return x + y; // pi + nan
}

Wall clock

The wall_clock class is a simple timer class for measuring the number of elapsed seconds. An instance of the class has two member functions:

.tic(): start the timer
.toc(): return the number of seconds since the last call to .tic()

Examples

[[cpp11::register]] list tictoc1_(const int& n) {
  mat m1(n, n, fill::randu);

  wall_clock timer;
  timer.tic();

  mat m2 = inv(m1);

  double n = timer.toc(); // time to invert m1

  writable::list res(2);

  res[0] = n
  res[1] = as_doubles_matrix(m2);

  return res;
}

Random number generator

The random number generator (RNG) is based on the Mersenne Twister algorithm. The RNG is thread-safe, and each thread has its own RNG state.

Usage:

set_seed(integer);
set_seed_random();

The set_seed() function sets the RNG seed to the specified value.

The set_seed_random() function sets the RNG seed to a value drawn from std::random_device (if the reported entropy is not zero), or /dev/urandom for Linux and macOS, or based on the current time (on systems without /dev/urandom).

Caveat:

When using a multi-threading framework (such as OpenMP) and the underlying system supports the thread_local storage specifier, the above functions change the seed only within the thread they are running on.

To change the seeds on all OpenMP threads to the same value, adapt the following code:

#pragma omp parallel
{
  set_seed(123);
  // some computation
}

To change the seeds on all OpenMP threads to unique values, adapt the following code:

std::atomic<std::size_t> counter(0);

#pragma omp parallel
{
  set_seed(123 + counter++);
  // some computation
}

Unsigned and signed integers

The uword class is a typedef for an unsigned integer type. It is used for matrix indices as well as all internal counters and loops.

The sword class is a typedef for a signed integer type.

The minimum width of both uword and sword is either 32 or 64 bits:

The default width is 32 bits on 32-bit platforms.
The default width is 64 bits on 64-bit platforms.
The default width is 32 bits when using Armadillo in the R environment on either 32-bit or 64-bit platforms.

The width can also be forcefully set to 64 bits by enabling ARMA_64BIT_WORD by editing armadillo/config.hpp.

Short forms for complex data types

The cx_double class is a convenience short form (typedef) for the complex element type std::complex<double>.

The cx_float class is a convenience short form (typedef) for the complex element type std::complex<float>.

Example:

[[cpp11::register]] list cx_double_example_() {
  cx_double z(3.4, 5.6);
  return as_complex(z);
}