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NAME
     sspgv - compute all the  eigenvalues  and,  optionally,  the
     eigenvectors of a real generalized symmetric-definite eigen-
     problem, of the form A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or
     B*A*x=(lambda)*x

SYNOPSIS
     SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W,  Z,  LDZ,
               WORK, INFO )

     CHARACTER JOBZ, UPLO

     INTEGER INFO, ITYPE, LDZ, N

     REAL AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * )



     #include <sunperf.h>

     void sspgv(int itype, char jobz, char  uplo,  int  n,  float
               *sap, float *bp, float *w, float *sz, int ldz, int
               *info) ;

PURPOSE
     SSPGV computes all  the  eigenvalues  and,  optionally,  the
     eigenvectors of a real generalized symmetric-definite eigen-
     problem, 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.


ARGUMENTS
     ITYPE     (input) 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      (input) CHARACTER*1
               = 'N':  Compute eigenvalues only;
               = 'V':  Compute eigenvalues and eigenvectors.

     UPLO      (input) CHARACTER*1
               = 'U':  Upper triangles of A and B are stored;
               = 'L':  Lower triangles of A and B are stored.

     N         (input) INTEGER
               The order of the matrices A and B.  N >= 0.

     AP        (input/output) 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        (input/output) REAL array, dimension (N*(N+1)/2)
               On entry, the upper or lower triangle of the  sym-
               metric  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         (output) REAL array, dimension (N)
               If INFO = 0, the eigenvalues in ascending order.

     Z         (output) 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       (input) INTEGER
               The leading dimension of the array Z.  LDZ  >=  1,
               and if JOBZ = 'V', LDZ >= max(1,N).

     WORK      (workspace) REAL array, dimension (3*N)

     INFO      (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  SPPTRF or SSPEV returned an error code:
               <= N:  if INFO = i, SSPEV failed  to  converge;  i
               off-diagonal elements of an intermediate tridiago-
               nal 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.

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