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NAG[f08hec] NAG[nag_dsbtrd] - Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form
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Calling Sequence
f08hec(vect, uplo, kd, ab, d, e, q, 'n'=n, 'fail'=fail)
nag_dsbtrd(. . .)
Parameters
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uplo - String;
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On entry: indicates whether the upper or lower triangular part of  is stored.
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 The upper triangular part of  is stored.
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 The lower triangular part of  is stored.
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Constraint:   "Nag_Upper" or "Nag_Lower". .
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kd - integer;
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Constraint:  . .
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ab - Matrix(1..dim1, 1..dim2, 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:  is overwritten.
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d - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array d must be at least  .
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On exit: the diagonal elements of the tridiagonal matrix  .
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e - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array e must be at least  .
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On exit: the off-diagonal elements of the tridiagonal matrix  .
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q - Matrix(1..dim1, 1..dim2, 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 entry: if  , q must contain the matrix formed in a previous stage of the reduction (for example, the reduction of a banded symmetric-definite generalized eigenproblem); otherwise q need not be set.
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If  , q is not referenced.
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'n'=n - integer; (optional)
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Default value: the dimension of the array ab.
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On entry:  , the order of the matrix  .
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Constraint:  . .
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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_dsbtrd (f08hec) reduces a real symmetric band matrix to tridiagonal form.
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Description
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nag_dsbtrd (f08hec) reduces a symmetric band matrix  to symmetric tridiagonal form  by an orthogonal similarity transformation:
The orthogonal matrix  is determined as a product of Givens rotation matrices, and may be formed explicitly by the function if required.
The function uses a vectorizable form of the reduction, due to Kaufman (1984).
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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_INT"
On entry,  . Constraint:  .
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.
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Further Comments
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The total number of floating-point operations is approximately  if  with  additional operations if  .
The complex analogue of this function is f08hsc (nag_zhbtrd).
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Examples
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vect := "Nag_FormQ":
uplo := "Nag_Lower":
n := 4:
kd := 2:
ab := Matrix([[0, 0, 4.99, 0], [0.04, 1.05, 0.22, -0.79], [-2.31, 1.04, -1.3, -0.43]], datatype=float[8], order='C_order'):
d := Vector(4, datatype=float[8]):
e := Vector(3, datatype=float[8]):
q := Matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], datatype=float[8], order='C_order'):
NAG:-f08hec(vect, uplo, kd, ab, d, e, q, 'n' = n):
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