!>
!> CHPEVD computes all the eigenvalues and, optionally, eigenvectors of
!> a complex Hermitian matrix A in packed storage.  If eigenvectors are
!> desired, it uses a divide and conquer algorithm.
!>
!> 

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 COMPLEX array, dimension (N*(N+1)/2)
!>          On entry, the upper or lower triangle of the Hermitian 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 COMPLEX 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 COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of array WORK.
!>          If N <= 1,               LWORK must be at least 1.
!>          If JOBZ = 'N' and N > 1, LWORK must be at least N.
!>          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the required 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 (MAX(1,LRWORK))
!>          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
!> 

LRWORK

!>          LRWORK is INTEGER
!>          The dimension of 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 required 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 required LIWORK.
!> 

LIWORK

!>          LIWORK is INTEGER
!>          The dimension of 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, 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, the algorithm failed to converge; i
!>                off-diagonal elements of an intermediate tridiagonal
!>                form did not converge to zero.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!> DSPEVD 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.
!>
!> 

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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!> 

Z

!>          Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!> 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.
!>
!> 

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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!> ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
!> a complex Hermitian matrix A in packed storage.  If eigenvectors are
!> desired, it uses a divide and conquer algorithm.
!>
!> 

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 COMPLEX*16 array, dimension (N*(N+1)/2)
!>          On entry, the upper or lower triangle of the Hermitian 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 DOUBLE PRECISION array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!> 

Z

!>          Z is COMPLEX*16 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 COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of array WORK.
!>          If N <= 1,               LWORK must be at least 1.
!>          If JOBZ = 'N' and N > 1, LWORK must be at least N.
!>          If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the required 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 DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
!>          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
!> 

LRWORK

!>          LRWORK is INTEGER
!>          The dimension of 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 required 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 required LIWORK.
!> 

LIWORK

!>          LIWORK is INTEGER
!>          The dimension of 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, 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, the algorithm failed to converge; i
!>                off-diagonal elements of an intermediate tridiagonal
!>                form did not converge to zero.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.