Computational Routines for the Generalized Symmetric Definite Eigenproblem

LA_SYGST / LA_HEGST
Real and complex versions.

SUBROUTINE LA_SYGST / LA_HEGST( ITYPE, & 


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


CHARACTER(LEN=1), INTENT(IN) :: UPLO 


INTEGER, INTENT(IN) :: ITYPE, LDA, LDB, N 


INTEGER, INTENT(OUT) :: INFO 

type(wp), INTENT(IN) :: B(LDB,*) 

type(wp), INTENT(INOUT) :: A(LDA,*) 


where 

type ::= REAL $\mid$ COMPLEX 

wp   ::= KIND(1.0) $\mid$ KIND(1.0D0)

LA_SYGST / LA_HEGST reduces a real symmetric / complex Hermitian definite generalized eigenproblem to standard form.

References: See  [1] and [9,20].
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LA_SPGST / LA_HPGST
Real and complex versions.

SUBROUTINE LA_SPGST / LA_HPGST( ITYPE, & 


UPLO, N, AP, BP, INFO ) 


CHARACTER(LEN=1), INTENT(IN) :: UPLO 


INTEGER, INTENT(IN) :: ITYPE, N 


INTEGER, INTENT(OUT) :: INFO 

type(wp), INTENT(IN) :: BP(*) 

type(wp), INTENT(INOUT) :: AP(*) 


where 

type ::= REAL $\mid$ COMPLEX 

wp   ::= KIND(1.0) $\mid$ KIND(1.0D0)

LA_SPGST / LA_HPGST reduces a real symmetric / complex Hermitian definite generalized eigenproblem to standard form, using packed storage.

References: See  [1] and [9,20].
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LA_PBSTF
Real and complex versions.

SUBROUTINE LA_PBSTF( UPLO, N, KD, AB, & 


LDAB, INFO ) 


CHARACTER(LEN=1), INTENT(IN) :: UPLO 


INTEGER, INTENT(IN) :: KD, LDAB, N 


INTEGER, INTENT(OUT) :: INFO 

type(wp), INTENT(INOUT) :: AB(LDAB,*) 


where 

type ::= REAL $\mid$ COMPLEX 

wp   ::= KIND(1.0) $\mid$ KIND(1.0D0)

LA_PBSTF computes a split Cholesky factorization of a real symmetric / complex Hermitian positive definite band matrix $A$.
References: See  [1] and [9,20].
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LA_SBGST / LA_HBGST
Real version.

SUBROUTINE LA_SBGST( VECT, UPLO, N, & 


KA, KB, AB, LDAB, BB, LDBB, X, LDX, & 


WORK, INFO ) 


CHARACTER(LEN=1), INTENT(IN) :: UPLO, & 


VECT 


INTEGER, INTENT(IN) :: KA, KB, LDAB, & 


LDBB, LDX, N 


INTEGER, INTENT(OUT) :: INFO 


REAL(wp), INTENT(IN) :: BB(LDBB,*) 


REAL(wp), INTENT(INOUT) :: AB(LDAB,*) 


REAL(wp), INTENT(OUT) :: WORK(*), X(LDX,*) 


where 

wp   ::= KIND(1.0) $\mid$ KIND(1.0D0)

Complex version.

 SUBROUTINE LA_HBGST( VECT, UPLO, N, & 


KA, KB, AB, LDAB, BB, LDBB, X, LDX, & 


WORK, RWORK, INFO ) 


CHARACTER(LEN=1), INTENT(IN) :: UPLO, & 


VECT 


INTEGER, INTENT(IN) :: KA, KB, LDAB, & 


LDBB, LDX, N 


INTEGER, INTENT(OUT) :: INFO 


REAL(wp), INTENT(OUT) :: RWORK(*) 


COMPLEX(wp), INTENT(IN) :: BB(LDBB,*) 


COMPLEX(wp), INTENT(INOUT) :: AB(LDAB,*) 


COMPLEX(wp), INTENT(OUT) :: WORK(*), & 


X(LDX,*) 


where 

wp   ::= KIND(1.0) $\mid$ KIND(1.0D0)

LA_SBGST / LA_HBGST reduces a real symmetric / complex Hermitian definite banded generalized eigenproblem $A x = \lambda B x$ to standard form $C y = \lambda y$, such that $C$ has the same bandwidth as $A$.
References: See  [1] and [9,20].
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