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NAG[f08fec] NAG[nag_dsytrd] - Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form
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Calling Sequence
f08fec(uplo, a, d, e, tau, 'n'=n, 'fail'=fail)
nag_dsytrd(. . .)
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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a - 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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If  , the upper triangular part of  must be stored and the elements of the array below the diagonal are not referenced.
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If  , the lower triangular part of  must be stored and the elements of the array above the diagonal are not referenced.
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On exit: a is overwritten by the tridiagonal matrix  and details of the orthogonal matrix  as specified by uplo.
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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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tau - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array tau must be at least  .
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On exit: further details of the orthogonal matrix  .
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'n'=n - integer; (optional)
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Default value: the dimension of the array a.
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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_dsytrd (f08fec) reduces a real symmetric matrix to tridiagonal form.
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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:  .
"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  .
To form the orthogonal matrix  nag_dsytrd (f08fec) may be followed by a call to f08ffc (nag_dorgtr):
nag_dorgtr (uplo,a,tau,'n'=n)
To apply  to an  by  real matrix  nag_dsytrd (f08fec) may be followed by a call to f08fgc (nag_dormtr). For example,
nag_dormtr ("Nag_LeftSide",uplo,"Nag_NoTrans",a,tau,c,'m'=n,'n'=p)
forms the matrix product  .
The complex analogue of this function is f08fsc (nag_zhetrd).
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Examples
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uplo := "Nag_Lower":
n := 4:
a := Matrix([[2.07, 0, 0, 0], [3.87, -0.21, 0, 0], [4.2, 1.87, 1.15, 0], [-1.15, 0.63, 2.06, -1.81]], datatype=float[8]):
d := Vector(4, datatype=float[8]):
e := Vector(3, datatype=float[8]):
tau := Vector(3, datatype=float[8]):
NAG:-f08fec(uplo, a, d, e, tau, 'n' = n):
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