---
name: "dsygst"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dsygst/3lapack"
---

# dsygst(3lapack)

reduces a real symmetric-definite generalized eigenproblem to standard form

## NAME

DSYGST - reduces a real symmetric-definite generalized eigenproblem to standard form

## SYNOPSIS

- SUBROUTINE DSYGST(

  ITYPE, UPLO, N, A, LDA, B, LDB, INFO )

- CHARACTER

  UPLO

- INTEGER

  INFO, ITYPE, LDA, LDB, N

- DOUBLE

  PRECISION A( LDA, \* ), B( LDB, \* )

## PURPOSE

DSYGST reduces a real symmetric-definite generalized eigenproblem to standard form. 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 DPOTRF.

## 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\*1

  \= '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) INTEGER

  The order of the matrices A and B.  N \>= 0.

- A (input/output) DOUBLE PRECISION array, dimension (LDA,N)

  On entry, the symmetric matrix A.  If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced.  If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the transformed matrix, stored in the same format as A.

- LDA (input) INTEGER

  The leading dimension of the array A.  LDA \>= max(1,N).

- B (input) DOUBLE PRECISION array, dimension (LDB,N)

  The triangular factor from the Cholesky factorization of B, as returned by DPOTRF.

- LDB (input) INTEGER

  The leading dimension of the array B.  LDB \>= max(1,N).

- INFO (output) INTEGER

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