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# dspgst

```
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      UPLO

INTEGER        INFO, ITYPE, N

DOUBLE         PRECISION AP( * ), BP( * )

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 DPPTRF.

ARGUMENTS
ITYPE   (input) INTEGER
= 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) CHARACTER
= 'U':  Upper triangle of A is stored and B is fac-
tored as U**T*U; = 'L':  Lower triangle of A is
stored and B is factored as L*L**T.

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

(N*(N+1)/2)
AP      (input/output) DOUBLE PRECISION array, dimension
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 factoriza-
tion of B, stored in the same format as A, as
returned by DPPTRF.

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