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NAG[f08gsc] NAG[nag_zhptrd] - Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage
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Calling Sequence
f08gsc(uplo, n, ap, d, e, tau, 'fail'=fail)
nag_zhptrd(. . .)
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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n - integer;
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On entry:  , the order of the matrix  .
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Constraint:  . .
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ap - Vector(1..dim, datatype=complex[8]);
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Note: the dimension, dim, of the array ap must be at least  .
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On entry: the Hermitian matrix  , packed by rows or columns. The storage of elements ![a[i*j]](/support/helpjp/helpview.aspx?si=10417/file08248/math71.png) depends on the storage order and uplo arguments as follows:
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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=complex[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 unitary matrix  .
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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_zhptrd (f08gsc) reduces a complex Hermitian matrix to tridiagonal form, using packed storage.
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Error Indicators and Warnings
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"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 real floating-point operations is approximately  .
To form the unitary matrix  nag_zhptrd (f08gsc) may be followed by a call to f08gtc (nag_zupgtr):
nag_zupgtr (uplo,ap,tau,q,'n'=n)
To apply  to an  by  complex matrix  nag_zhptrd (f08gsc) may be followed by a call to f08guc (nag_zupmtr). For example,
nag_zupmtr ("Nag_LeftSide",uplo,"Nag_NoTrans",ap,tau,c,'m'=n,'n'=p)
forms the matrix product  .
The real analogue of this function is f08gec (nag_dsptrd).
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Examples
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uplo := "Nag_Upper":
n := 4:
ap := Vector([-2.28 +0*I, 1.78 -2.03*I, 2.26 +0.1*I, -0.12 +2.53*I, -1.12 +0*I, 0.01 +0.43*I, -1.07 +0.86*I, -0.37 +0*I, 2.31 -0.92*I, -0.73 +0*I], datatype=complex[8], order='C_order'):
d := Vector(4, datatype=float[8]):
e := Vector(3, datatype=float[8]):
tau := Vector(3, datatype=complex[8]):
NAG:-f08gsc(uplo, n, ap, d, e, tau):
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