sstevd.f −

**Functions/Subroutines**

subroutine **sstevd** (JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)

SSTEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

**subroutine sstevd (characterJOBZ, integerN, real, dimension( * )D, real, dimension( * )E, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)
SSTEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices**

**Purpose:**

SSTEVD computes all eigenvalues and, optionally, eigenvectors of a

real symmetric tridiagonal matrix. If eigenvectors are desired, it

uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assumptions about

floating point arithmetic. It will work on machines with a guard

digit in add/subtract, or on those binary machines without guard

digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or

Cray-2. It could conceivably fail on hexadecimal or decimal machines

without guard digits, but we know of none.

**Parameters:**

*JOBZ*

JOBZ is CHARACTER*1

= ’N’: Compute eigenvalues only;

= ’V’: Compute eigenvalues and eigenvectors.

*N*

N is INTEGER

The order of the matrix. N >= 0.

*D*

D is REAL array, dimension (N)

On entry, the n diagonal elements of the tridiagonal matrix

A.

On exit, if INFO = 0, the eigenvalues in ascending order.

*E*

E is REAL array, dimension (N-1)

On entry, the (n-1) subdiagonal elements of the tridiagonal

matrix A, stored in elements 1 to N-1 of E.

On exit, the contents of E are destroyed.

*Z*

Z is REAL array, dimension (LDZ, N)

If JOBZ = ’V’, then if INFO = 0, Z contains the orthonormal

eigenvectors of the matrix A, with the i-th column of Z

holding the eigenvector associated with D(i).

If JOBZ = ’N’, then Z is not referenced.

*LDZ*

LDZ is INTEGER

The leading dimension of the array Z. LDZ >= 1, and if

JOBZ = ’V’, LDZ >= max(1,N).

*WORK*

WORK is REAL array,

dimension (LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*

LWORK is INTEGER

The dimension of the array WORK.

If JOBZ = ’N’ or N <= 1 then LWORK must be at least 1.

If JOBZ = ’V’ and N > 1 then LWORK must be at least

( 1 + 4*N + N**2 ).

If LWORK = -1, then a workspace query is assumed; the routine

only calculates the optimal sizes of the WORK and IWORK

arrays, returns these values as the first entries of the WORK

and IWORK arrays, and no error message related to LWORK or

LIWORK is issued by XERBLA.

*IWORK*

IWORK is INTEGER array, dimension (MAX(1,LIWORK))

On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

*LIWORK*

LIWORK is INTEGER

The dimension of the array IWORK.

If JOBZ = ’N’ or N <= 1 then LIWORK must be at least 1.

If JOBZ = ’V’ and N > 1 then LIWORK must be at least 3+5*N.

If LIWORK = -1, then a workspace query is assumed; the

routine only calculates the optimal sizes of the WORK and

IWORK arrays, returns these values as the first entries of

the WORK and IWORK arrays, and no error message related to

LWORK or LIWORK is issued by XERBLA.

*INFO*

INFO is INTEGER

= 0: successful exit

< 0: if INFO = -i, the i-th argument had an illegal value

> 0: if INFO = i, the algorithm failed to converge; i

off-diagonal elements of E did not converge to zero.

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 163 of file sstevd.f.

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