CHEEVD computes all eigenvalues and, optionally, eigenvectors of a


 complex Hermitian matrix A.  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.

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.

A

          A is COMPLEX array, dimension (LDA, N)


          On entry, the Hermitian matrix A.  If UPLO = 'U', the


          leading N-by-N upper triangular part of A contains the


          upper triangular part of the matrix A.  If UPLO = 'L',


          the leading N-by-N lower triangular part of A contains


          the lower triangular part of the matrix A.


          On exit, if JOBZ = 'V', then if INFO = 0, A contains the


          orthonormal eigenvectors of the matrix A.


          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')


          or the upper triangle (if UPLO='U') of A, including the


          diagonal, is destroyed.

LDA

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

W

          W is REAL array, dimension (N)


          If INFO = 0, the eigenvalues in ascending order.

WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))


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

LWORK

          LWORK is INTEGER


          The length of the array WORK.


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


          If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.


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


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


          only calculates the optimal sizes of the WORK, RWORK and


          IWORK arrays, returns these values as the first entries of


          the WORK, RWORK and IWORK arrays, and no error message


          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

          RWORK is REAL array,


                                         dimension (LRWORK)


          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

          LRWORK is INTEGER


          The dimension of the array RWORK.


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


          If JOBZ  = 'N' and N > 1, LRWORK must be at least N.


          If JOBZ  = 'V' and N > 1, LRWORK must be at least


                         1 + 5*N + 2*N**2.


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


          routine only calculates the optimal sizes of the WORK, RWORK


          and IWORK arrays, returns these values as the first entries


          of the WORK, RWORK and IWORK arrays, and no error message


          related to LWORK or LRWORK 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 N <= 1,                LIWORK must be at least 1.


          If JOBZ  = 'N' and 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 optimal sizes of the WORK, RWORK


          and IWORK arrays, returns these values as the first entries


          of the WORK, RWORK and IWORK arrays, and no error message


          related to LWORK or LRWORK 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 and JOBZ = 'N', then the algorithm failed


                to converge; i off-diagonal elements of an intermediate


                tridiagonal form did not converge to zero;


                if INFO = i and JOBZ = 'V', then the algorithm failed


                to compute an eigenvalue while working on the submatrix


                lying in rows and columns INFO/(N+1) through


                mod(INFO,N+1).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011

Modified description of INFO. Sven, 16 Feb 05.

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA