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Vectorize matrix matlab code#

The set of probabilities is stored in a transition matrix P, where entry (i, j) is the transition probability from state i to state j. The sum of the transition probabilities out of any node is, by definition, 1. The nodes of the digraph represent the states, and the directed edge weight between two states a and b represents the probability (called the transition probability from a to b) that the system will move to state b in the next time period, given that it is currently in state a. The following Maple techniques are highlighted:Ī Markov Chain is a weighted digraph representing a discrete-time system that can be in any number of discrete states. This worksheet demonstrates the use of Maple to investigate Markov-chain models. Each complete pass through the nind matrix fills one row of the output array.Computing the Steady-State Vector of a Markov Chain

Moving columnwise through mind, each element is paired with the elements of nind as above.

The result fills the first row of the output array. MATLAB moves through the nind matrix in a columnwise fashion, so mind(1,1) goes with nind(1,1), then nind(2,1), and so on.

The first element of mind, the row index, is paired with each element of nind.

Each element of the row index array, mind, is paired with each element of the column index array, nind, using the following procedure: Step 4 uses array indexing to create the output array. Where n_cols is the desired number of columns in the resulting matrix.

Step 3 uses a MATLAB vectorization trick to replicate a single column of data through any number of columns. The nind variable contains the integers from 1 through the column size of A. mind contains the integers from 1 through the row size of A. Step 1, above, obtains the row and column sizes of the input array. % Step 3 Creates index matrices from vectors above % Step 2 Generate vectors of indices from 1 to row/column size Repmat uses vectorization to create the indices that place elements in the output array.

Repmat creates an output array that contains the elements of array A, replicated and "tiled" in an M-by- N arrangement. It accepts three input arguments: an array A, a row dimension M, and a column dimension N. Repmat is an example of a function that takes advantage of vectorization.

Vectorize matrix matlab code#

Test this on your system by creating M-file scripts that contain the code shown, then using the tic and toc functions to time the M-files. The second example executes much faster than the first and is the way MATLAB is meant to be used. Here is one way to compute the sine of 1001 values ranging from 0 to 10.Ī vectorized version of the same code is: You may be able to speed up your program by just as much using the MATLAB JIT Accelerator instead of vectorizing. Vectorization means converting for and while loops to equivalent vector or matrix operations.īefore taking the time to vectorize your code, read the section on Performance Acceleration. You can often speed up your M-file code by using vectorizing algorithms that take advantage of this design. MATLAB is a matrix language, which means it is designed for vector and matrix operations. Maximizing MATLAB Performance (Programming and Data Types) Programming and Data Types