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man pages->IRIX man pages -> complib/HTRID3 (3)
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### Contents

```
_HTRID3(3F)							   _HTRID3(3F)

```

### NAME[Toc][Back]

```     HTRID3, SHTRID3  -	 EISPACK routine.  This	subroutine reduces a COMPLEX
HERMITIAN matrix, stored as a single square array,	to a real symmetric
tridiagonal matrix	using unitary similarity transformations.

```

### SYNOPSYS[Toc][Back]

```	  subroutine  htrid3(nm, n, a, d, e, e2, tau)
integer	   nm, n
double precision a(nm,n), d(n), e(n),	e2(n), tau(2,n)

subroutine shtrid3(nm, n, a, d, e, e2, tau)
integer	   nm, n
real		   a(nm,n), d(n), e(n),	e2(n), tau(2,n)

```

### DESCRIPTION[Toc][Back]

```     On	INPUT

NM	must be	set to the row dimension of two-dimensional array parameters
as	declared in the	calling	program	dimension statement.

N is the order of the matrix.

A contains	the lower triangle of the complex hermitian input matrix.  The
real parts	of the matrix elements are stored in the full lower triangle
of	A, and the imaginary parts are stored in the transposed	positions of
the strict	upper triangle of A.  No storage is required for the zero
imaginary parts of	the diagonal elements.	On OUTPUT

A contains	information about the unitary transformations used in the
reduction.

D contains	the diagonal elements of the the tridiagonal matrix.

E contains	the subdiagonal	elements of the	tridiagonal matrix in its last
N-1 positions.  E(1) is set to zero.

E2	contains the squares of	the corresponding elements of E. E2 may
coincide with E if	the squares are	not needed.

TAU contains further information about the	transformations. Calls
PYTHAG(A,B) for sqrt(A**2 + B**2).	 Questions and comments	should be
directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL
LABORATORY

PPPPaaaaggggeeee 1111```
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