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.

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.

December 2016