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man pages->IRIX man pages -> complib/IMTQL2 (3)
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### Contents

```
_IMTQL2(3F)							   _IMTQL2(3F)

```

### NAME[Toc][Back]

```     IMTQL2, SIMTQL2  -	 EISPACK routine.  This	subroutine finds the
eigenvalues and eigenvectors of a SYMMETRIC TRIDIAGONAL matrix by the
implicit QL method.  The eigenvectors of a	FULL SYMMETRIC matrix can also
be	found if  TRED2	 has been used to reduce this full matrix to
tridiagonal form.

```

### SYNOPSYS[Toc][Back]

```	  subroutine  imtql2(nm, n, d, e, z, ierr)
integer	   nm, n, ierr
double precision d(n), e(n), z(nm,n)

subroutine simtql2(nm, n, d, e, z, ierr)
integer	   nm, n, ierr
real		   d(n), e(n), z(nm,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.

D contains	the diagonal elements of the input matrix.

E contains	the subdiagonal	elements of the	input matrix in	its last N-1
positions.	 E(1) is arbitrary.

Z contains	the transformation matrix produced in the reduction by	TRED2,
if	performed.  If the eigenvectors	of the tridiagonal matrix are desired,
Z must contain the	identity matrix.  On OUTPUT

D contains	the eigenvalues	in ASCENDING order.  If	an error exit is made,
the eigenvalues are correct but UNORDERED for indices 1,2,...,IERR-1.

E has been	destroyed.

Z contains	orthonormal eigenvectors of the	symmetric tridiagonal (or
full) matrix.  If an error	exit is	made, Z	contains the eigenvectors
associated	with the stored	eigenvalues.

IERR is set to ZERO       for normal return, J	     if	the J-th
eigenvalue	has not	been
determined after 30 iterations.	 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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