NAME

hegst - {he,sy}gst: reduction to standard form

SYNOPSIS

Functions

subroutine chegst (itype, uplo, n, a, lda, b, ldb, info)
CHEGST subroutine dsygst (itype, uplo, n, a, lda, b, ldb, info)
DSYGST subroutine ssygst (itype, uplo, n, a, lda, b, ldb, info)
SSYGST subroutine zhegst (itype, uplo, n, a, lda, b, ldb, info)
ZHEGST

Detailed Description

Function Documentation

subroutine chegst (integer itype, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer info)

CHEGST

Purpose:



 CHEGST reduces a complex Hermitian-definite generalized


 eigenproblem to standard form.


 If ITYPE = 1, the problem is A*x = lambda*B*x,


 and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)


 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**H or L**H*A*L.


 B must have been previously factorized as U**H*U or L*L**H by CPOTRF.

Parameters

ITYPE



          ITYPE is INTEGER


          = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);


          = 2 or 3: compute U*A*U**H or L**H*A*L.

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored and B is factored as


                  U**H*U;


          = 'L':  Lower triangle of A is stored and B is factored as


                  L*L**H.



          N is INTEGER


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



          A is COMPLEX array, dimension (LDA,N)


          On entry, the Hermitian 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



          LDA is INTEGER


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



          B is COMPLEX array, dimension (LDB,N)


          The triangular factor from the Cholesky factorization of B,


          as returned by CPOTRF.


          B is modified by the routine but restored on exit.

LDB



          LDB is INTEGER


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

INFO



          INFO is INTEGER


          = 0:  successful exit


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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file chegst.f.

subroutine dsygst (integer itype, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DSYGST

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.

Parameters

ITYPE



          ITYPE is 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



          UPLO is 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 is INTEGER


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



          A is 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



          LDA is INTEGER


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



          B is DOUBLE PRECISION array, dimension (LDB,N)


          The triangular factor from the Cholesky factorization of B,


          as returned by DPOTRF.

LDB



          LDB is INTEGER


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

INFO



          INFO is INTEGER


          = 0:  successful exit


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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 126 of file dsygst.f.

subroutine ssygst (integer itype, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)

SSYGST

Purpose:



 SSYGST 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 SPOTRF.

Parameters

ITYPE



          ITYPE is 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



          UPLO is 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 is INTEGER


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



          A is REAL 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



          LDA is INTEGER


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



          B is REAL array, dimension (LDB,N)


          The triangular factor from the Cholesky factorization of B,


          as returned by SPOTRF.

LDB



          LDB is INTEGER


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

INFO



          INFO is INTEGER


          = 0:  successful exit


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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 126 of file ssygst.f.

subroutine zhegst (integer itype, character uplo, integer n, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, integer info)

ZHEGST

Purpose:



 ZHEGST reduces a complex Hermitian-definite generalized


 eigenproblem to standard form.


 If ITYPE = 1, the problem is A*x = lambda*B*x,


 and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)


 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**H or L**H*A*L.


 B must have been previously factorized as U**H*U or L*L**H by ZPOTRF.

Parameters

ITYPE



          ITYPE is INTEGER


          = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);


          = 2 or 3: compute U*A*U**H or L**H*A*L.

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored and B is factored as


                  U**H*U;


          = 'L':  Lower triangle of A is stored and B is factored as


                  L*L**H.



          N is INTEGER


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



          A is COMPLEX*16 array, dimension (LDA,N)


          On entry, the Hermitian 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



          LDA is INTEGER


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



          B is COMPLEX*16 array, dimension (LDB,N)


          The triangular factor from the Cholesky factorization of B,


          as returned by ZPOTRF.


          B is modified by the routine but restored on exit.

LDB



          LDB is INTEGER


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

INFO



          INFO is INTEGER


          = 0:  successful exit


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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file zhegst.f.

Author

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