sspevd.f −

**Functions/Subroutines**

subroutine **sspevd** (JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)

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

**subroutine sspevd (characterJOBZ, characterUPLO, integerN, real, dimension( * )AP, real, dimension( * )W, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)
SSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices**

**Purpose:**

SSPEVD computes all the eigenvalues and, optionally, eigenvectors

of a real symmetric matrix A in packed storage. 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.

*UPLO*

UPLO is CHARACTER*1

= ’U’: Upper triangle of A is stored;

= ’L’: Lower triangle of A is stored.

*N*

N is INTEGER

The order of the matrix A. N >= 0.

*AP*

AP is REAL array, dimension (N*(N+1)/2)

On entry, the upper or lower triangle of the symmetric matrix

A, packed columnwise in a linear array. The j-th column of A

is stored in the array AP as follows:

if UPLO = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;

if UPLO = ’L’, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated during the

reduction to tridiagonal form. If UPLO = ’U’, the diagonal

and first superdiagonal of the tridiagonal matrix T overwrite

the corresponding elements of A, and if UPLO = ’L’, the

diagonal and first subdiagonal of T overwrite the

corresponding elements of A.

*W*

W is REAL array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

*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 W(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 (MAX(1,LWORK))

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

*LWORK*

LWORK is INTEGER

The dimension of the array WORK.

If N <= 1, LWORK must be at least 1.

If JOBZ = ’N’ and N > 1, LWORK must be at least 2*N.

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

1 + 6*N + N**2.

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

only calculates the required 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 required LIWORK.

*LIWORK*

LIWORK is INTEGER

The dimension of the array IWORK.

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

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

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

routine only calculates the required 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 an intermediate tridiagonal

form 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 178 of file sspevd.f.

Generated automatically by Doxygen for LAPACK from the source code.