Contents


NAME

     dspgst - reduce a real symmetric-definite generalized eigen-
     problem to standard form, using packed storage

SYNOPSIS

     SUBROUTINE DSPGST(ITYPE, UPLO, N, AP, BP, INFO)

     CHARACTER * 1 UPLO
     INTEGER ITYPE, N, INFO
     DOUBLE PRECISION AP(*), BP(*)

     SUBROUTINE DSPGST_64(ITYPE, UPLO, N, AP, BP, INFO)

     CHARACTER * 1 UPLO
     INTEGER*8 ITYPE, N, INFO
     DOUBLE PRECISION AP(*), BP(*)

  F95 INTERFACE
     SUBROUTINE SPGST(ITYPE, UPLO, [N], AP, BP, [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER :: ITYPE, N, INFO
     REAL(8), DIMENSION(:) :: AP, BP

     SUBROUTINE SPGST_64(ITYPE, UPLO, [N], AP, BP, [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER(8) :: ITYPE, N, INFO
     REAL(8), DIMENSION(:) :: AP, BP

  C INTERFACE
     #include <sunperf.h>

     void dspgst(int itype, char uplo, int n, double *ap,  double
               *bp, int *info);

     void dspgst_64(long itype, char uplo, long  n,  double  *ap,
               double *bp, long *info);

PURPOSE

     dspgst reduces a real symmetric-definite generalized  eigen-
     problem to standard form, using packed storage.

     If ITYPE = 1, the problem is A*x = lambda*B*x,
     and   A   is   overwritten    by    inv(U**T)*A*inv(U)    or
     inv(L)*A*inv(L**T)
     If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
     B*A*x = lambda*x,  and  A  is  overwritten  by  U*A*U**T  or
     L**T*A*L.

     B must have been previously factorized as U**T*U  or  L*L**T
     by SPPTRF.

ARGUMENTS

     ITYPE (input)
               =     1:     compute     inv(U**T)*A*inv(U)     or
               inv(L)*A*inv(L**T);
               = 2 or 3: compute U*A*U**T or L**T*A*L.

     UPLO (input)
               = 'U':  Upper triangle of A is  stored  and  B  is
               factored as U**T*U; = 'L':  Lower triangle of A is
               stored and B is factored as L*L**T.

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

     AP (input/output)
               Double precision array, dimension  (N*(N+1)/2)  On
               entry,  the  upper  or  lower triangle of the sym-
               metric 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)*(2n-j)/2) = A(i,j) for j<=i<=n.

               On exit, if INFO  =  0,  the  transformed  matrix,
               stored in the same format as A.

     BP (input)
               Double precision array, dimension (N*(N+1)/2)  The
               triangular  factor from the Cholesky factorization
               of B, stored in the same format as A, as  returned
               by SPPTRF.

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value