SSPGV computes all the eigenvalues and, optionally, the eigenvectors


 of a real generalized symmetric-definite eigenproblem, of the form


 A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.


 Here A and B are assumed to be symmetric, stored in packed format,


 and B is also positive definite.

ITYPE

          ITYPE is INTEGER


          Specifies the problem type to be solved:


          = 1:  A*x = (lambda)*B*x


          = 2:  A*B*x = (lambda)*x


          = 3:  B*A*x = (lambda)*x

JOBZ

          JOBZ is CHARACTER*1


          = 'N':  Compute eigenvalues only;


          = 'V':  Compute eigenvalues and eigenvectors.

UPLO

          UPLO is CHARACTER*1


          = 'U':  Upper triangles of A and B are stored;


          = 'L':  Lower triangles of A and B are stored.

N

          N is INTEGER


          The order of the matrices A and B.  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, the contents of AP are destroyed.

BP

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


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


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


          is stored in the array BP as follows:


          if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;


          if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.


          On exit, the triangular factor U or L from the Cholesky


          factorization B = U**T*U or B = L*L**T, in the same storage


          format as B.

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 matrix Z of


          eigenvectors.  The eigenvectors are normalized as follows:


          if ITYPE = 1 or 2, Z**T*B*Z = I;


          if ITYPE = 3, Z**T*inv(B)*Z = 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 (3*N)

INFO

          INFO is INTEGER


          = 0:  successful exit


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


          > 0:  SPPTRF or SSPEV returned an error code:


             <= N:  if INFO = i, SSPEV failed to converge;


                    i off-diagonal elements of an intermediate


                    tridiagonal form did not converge to zero.


             > N:   if INFO = n + i, for 1 <= i <= n, then the leading


                    minor of order i of B is not positive definite.


                    The factorization of B could not be completed and


                    no eigenvalues or eigenvectors were computed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

June 2017