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NAG[g05qbc] NAG[nag_rngs_corr_matrix] - Computes a random correlation matrix
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Calling Sequence
g05qbc(d, c, igen, iseed, 'n'=n, 'eps'=eps, 'fail'=fail)
nag_rngs_corr_matrix(. . .)
Parameters
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d - Vector(1..n, datatype=float[8]);
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![d[i] >= 0.](/support/helpjp/helpview.aspx?si=9865/file08524/math32.png) , for  ;
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![sum(d[i], i = 1 .. n) = n](/support/helpjp/helpview.aspx?si=9865/file08524/math37.png) to within eps.
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c - Matrix(1..dim1, 1..n, datatype=float[8], order=order);
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Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
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On exit: a random correlation matrix,  , of dimension  .
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iseed - Vector(1.. , datatype=integer[kernelopts('wordsize')/8]);
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On entry: contains values which define the current state of the selected generator.
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On exit: contains updated values defining the new state of the selected generator.
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'n'=n - integer; (optional)
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On entry:  , the dimension of the correlation matrix to be generated.
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Constraint:  . .
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'eps'=eps - float; (optional)
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On entry:  , the maximum acceptable error in the diagonal elements.
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Constraint:  (see Chapter x02). .
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Suggested value:  . (default:  )
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_rngs_corr_matrix (g05qbc) generates a random correlation matrix with given eigenvalues.
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Error Indicators and Warnings
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"NE_ALLOC_FAIL"
Dynamic memory allocation failed.
"NE_BAD_PARAM"
On entry, argument  had an illegal value.
"NE_DIAG_ELEMENTS"
The error in a diagonal element is greater than eps. The value of eps should be increased. Otherwise the program could be rerun with a different value used for the seed of the random number generator, see g05kbc (nag_rngs_init_repeatable) or g05kcc (nag_rngs_init_nonrepeatable).
"NE_EIGVAL_SUM"
On entry, the eigenvalues do not sum to n.
"NE_INT"
On entry,  . Constraint:  .
"NE_INTERNAL_ERROR"
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.
"NE_NEGATIVE_EIGVAL"
On entry, an eigenvalue is negative.
"NE_REAL"
On entry,  :  .
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Accuracy
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The maximum error in a diagonal element is given by eps.
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Further Comments
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The time taken by nag_rngs_corr_matrix (g05qbc) is approximately proportional to  .
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Examples
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>
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n := 3:
eps := 0.0001:
igen := 1:
d := Vector([0.7, 0.9, 1.4], datatype=float[8]):
c := Matrix(3, 3, datatype=float[8]):
iseed := Vector([1762543, 9324783, 423446, 742355], datatype=integer[kernelopts('wordsize')/8]):
NAG:-g05qbc(d, c, igen, iseed, 'n' = n, 'eps' = eps):
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