Language Reference |
HADAMARD Function |
The HADAMARD function returns a Hadamard matrix. The arguments to the HADAMARD function are as follows:
specifies the order of the Hadamard matrix. You can specify that n is 1, 2, or a multiple of 4. Furthermore, n must satisfy at least one of the following conditions:
n
n – 1 is prime
(n is prime and n
n for some positives integers and , and satisfies one of the preceding conditions
When any other n is specified, the HADAMARD function returns a zero.
specifies the row number to return. When i is not specified or i is negative, the full Hadamard matrix is returned.
The HADAMARD function returns a Hadamard matrix, which is an matrix that consists entirely of the values 1 and –1. The columns of a Hadamard matrix are all orthogonal. Hadamard matrices are frequently used to make orthogonal array experimental designs for two-level factors. For example, the following statements create a Hadamard matrix:
h = hadamard(12); print h[format=2.];
The output is shown in Figure 23.122. The first column is an intercept and the next 11 columns form an orthogonal array experimental design for 11 two-level factors in 12 runs, .
h | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 |
1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 |
1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 |
1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 |
1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | 1 |
1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 |
1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 |
1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 |
1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | 1 |
1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 |
1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | 1 |
To request the seventeenth row of a Hadamard matrix of order 448, use the following statement:
h17 = hadamard(448, 17);
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