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What is the random number generation capabilities in Armadillo, including available distributions and the methods for generating random matrices and vectors.

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Armadillo provides random number generation capabilities through its built-in functions. It supports various distributions, including uniform, normal (Gaussian), and exponential.

Uniform distribution is available via randu() for continuous values and randi() for discrete integers. Normal distribution can be generated using randn(). Exponential distribution is accessible with exprnd() function.

For generating random matrices and vectors, Armadillo offers simple syntax. Use arma::mat or arma::vec followed by the desired size and distribution function. For example:

1. Uniform matrix: arma::mat A = arma::randu(rows, cols);
2. Normal vector: arma::vec B = arma::randn(size);

Additionally, you can set seeds to control reproducibility of random numbers using arma_rng::set_seed(seed_value) or arma_rng::set_seed_random() for a truly random seed based on system time.

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