Symmetric Indefinite Linear Systems

LA_SYTRF / LA_HETRF
Real, complex, and complex Hermitian versions.

SUBROUTINE LA_SYTRF( UPLO, N, A, LDA, & 


IPIV, WORK, LWORK, INFO ) 


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


INTEGER, INTENT(IN) :: LDA, LWORK, N 


INTEGER, INTENT(OUT) :: INFO, IPIV(*) 

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

type(wp), INTENT(OUT) :: WORK( LWORK ) 


where 

type ::= REAL $\mid$ COMPLEX 

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

LA_SYTRF / LA_HETRF compute the factorization of a real symmetric / complex symmetric / complex Hermitian matrix $A$ using the Bunch-Kaufman diagonal pivoting method.
References: See  [1] and [9,21,20].
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LA_SYTRS / LA_HETRS
Real, complex, and complex Hermitian versions.

SUBROUTINE LA_SYTRS( UPLO, N, NRHS, A, & 


LDA, IPIV, B, LDB, INFO ) 


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


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


INTEGER, INTENT(OUT) :: INFO 


INTEGER , INTENT(IN) :: IPIV(*) 

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

type(wp), INTENT(INOUT) :: rhs 


where 

type ::= REAL $\mid$ COMPLEX 

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

rhs  ::= B(LDB,*) $\mid$ B(*)

LA_SYTRS / LA_HETRS solve a system of linear equations $AX = B$ with a real symmetric / complex symmetric / complex Hermitian matrix $A$ using the factorization computed by LA_SYTRF / LA_HETRF, respectively.
References: See  [1] and [9,20].
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LA_SYCON / LA_HECON
Real version.

SUBROUTINE LA_SYCON( UPLO, N, A, LDA, & 


IPIV, ANORM, RCOND, WORK, IWORK, & 


INFO ) 


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


INTEGER, INTENT(IN) :: LDA, N 


INTEGER, INTENT(OUT) :: INFO, IWORK(*) 


REAL(wp), INTENT(IN) :: ANORM 


REAL(wp), INTENT(OUT) :: RCOND 


INTEGER, INTENT(IN) :: IPIV(*) 


REAL(wp), INTENT(IN) :: A( LDA,*) 


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


where 

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

Complex and complex Hermitian versions.

 SUBROUTINE LA_SYCON / LA_HECON( UPLO, & 


N, A, LDA, IPIV, ANORM, RCOND, WORK, & 


INFO ) 


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


INTEGER, INTENT(IN) :: LDA, N 


INTEGER, INTENT(OUT) :: INFO 


REAL(wp), INTENT(IN) :: ANORM 


REAL(wp), INTENT(OUT) :: RCOND 


INTEGER, INTENT(IN) :: IPIV(*) 


COMPLEX(wp), INTENT(IN) :: A( LDA,*) 


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


where 

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

LA_SYCON / LA_HECON estimates the reciprocal of the condition number of a real symmetric / complex symmetric / complex Hermitian matrix $A$ using the factorization computed by LA_SYTRF / LA_HETRF, respectively.
References: See  [1] and [9,21,20].
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LA_SYRFS / LA_HERFS
Real version.

SUBROUTINE LA_SYRFS( UPLO, N, NRHS, A, & 


LDA, AF, LDAF, IPIV, B, LDB, X, LDX, & 


FERR, BERR, WORK, IWORK, INFO ) 


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


INTEGER, INTENT(IN) :: LDA, LDAF, LDB, & 


LDX, N, NRHS 


INTEGER, INTENT(OUT) :: INFO, IWORK(*) 


INTEGER, INTENT(IN) :: IPIV(*) 


REAL(wp), INTENT(OUT) :: err 


REAL(wp), INTENT(IN) ::  A( LDA,*), & 


AF( LDAF,*), rhs 


REAL(wp), INTENT(INOUT) :: sol 


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


where 

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

rhs  ::= B(LDB,*) $\mid$ B(*) 

sol  ::= X(LDX,*) $\mid$ X(*) 

err  ::= FERR(*), BERR(*) $\mid$ FERR, BERR

Complex and complex Hermitian versions.

 SUBROUTINE LA_SYRFS / LA_HERFS( UPLO, & 


N, NRHS, A, LDA, AF, LDAF, IPIV, B, & 


LDB, X, LDX, FERR, BERR, WORK, & 


RWORK, INFO ) 


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


INTEGER, INTENT(IN) :: LDA, LDAF, LDB, & 


LDX, N, NRHS 


INTEGER, INTENT(OUT) :: INFO 


INTEGER, INTENT(IN) :: IPIV(*) 


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


COMPLEX(wp), INTENT(IN) ::  A( LDA,*), & 


AF( LDAF,*), rhs 


COMPLEX(wp), INTENT(INOUT) :: sol 


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


where 

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

rhs  ::= B(LDB,*) $\mid$ B(*) 

sol  ::= X(LDX,*) $\mid$ X(*) 

err  ::= FERR(*), BERR(*) $\mid$ FERR, BERR

LA_SYRFS / LA_HERFS improve the computed solution to a system of linear equations when the coefficient matrix is real symmetric / complex symmetric / complex Hermitian indefinite, and provides error bounds and backward error estimates for the solution.
References: See  [1] and [9,21,20].
-----------------------------------

LA_SYTRI / LA_HETRI
Real, complex, and complex Hermitian versions.

SUBROUTINE LA_SYTRI /LA_HETRI( UPLO, & 


N, A, LDA, IPIV, WORK, INFO ) 


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


INTEGER, INTENT(IN) :: LDA, N 


INTEGER, INTENT(OUT) :: INFO 


INTEGER, INTENT(IN) :: IPIV(*) 

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

type(wp), INTENT(OUT) :: WORK(*) 


where 

type ::= REAL $\mid$ COMPLEX 

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

LA_SYTRI / LA_HETRI compute the inverse of real symmetric, complex symmetric / complex Hermitian indefinite matrix $A$ using the factorization computed by LA_SYTRF / LA_HETRF respectively.
References: See  [1] and [9,20].
-----------------------------------

LA_SPTRF / LA_HPTRF
Real, complex, and complex Hermitian versions.

SUBROUTINE LA_SPTRF /LA_HPTRF( UPLO, & 


N, AP, IPIV, INFO ) 


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


INTEGER, INTENT(IN) :: N 


INTEGER, INTENT(OUT) :: INFO, IPIV(*) 

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


where 

type ::= REAL $\mid$ COMPLEX 

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

LA_SPTRF and LA_HPTRF compute the factorization of a real symmetric / complex symmetric / complex Hermitian indefinite matrix $A$ stored in packed format using the Bunch-Kaufman diagonal pivoting method.
References: See  [1] and [9,21,20].
-----------------------------------

LA_SPTRS / LA_HPTRS
Real, complex, and complex Hermitian versions.

SUBROUTINE LA_SPTRS /LA_HPTRS( UPLO, & 


N, NRHS, AP, IPIV, B, LDB, INFO ) 


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


INTEGER, INTENT(IN) :: LDB, N, NRHS 


INTEGER, INTENT(OUT) :: INFO 


INTEGER, INTENT(IN) :: IPIV(*) 

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

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


where 

type ::= REAL $\mid$ COMPLEX 

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

rhs  ::= B(LDB,*) $\mid$ B(*)

LA_SPTRS / LA_HPTRS solve a system of linear equations $AX = B$ with a real symmetric / complex symmetric / complex Hermitian matrix $A$ stored in packed format using the factorization computed by LA_SPTRF / LA_HPTRF respectively.
References: See  [1] and [9,20].
-----------------------------------

LA_SPCON / LA_HPCON
Real version.

SUBROUTINE LA_SPCON( UPLO, N, AP, IPIV, & 


ANORM, RCOND, WORK, IWORK, INFO ) 


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


INTEGER, INTENT(IN) :: N 


INTEGER, INTENT(OUT) :: INFO, IWORK(*) 


REAL(wp), INTENT(IN) :: ANORM 


REAL(wp), INTENT(OUT) :: RCOND 


INTEGER, INTENT(IN) :: IPIV( * ) 


REAL(wp), INTENT(IN) :: AP(*) 


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


where 

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

Complex and complex Hermitian versions.

SUBROUTINE LA_SPCON /LA_HPCON( UPLO, & 


N, AP, IPIV, ANORM, RCOND, WORK, & 


INFO ) 


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


INTEGER, INTENT(IN) :: N 


INTEGER, INTENT(OUT) :: INFO 


REAL(wp), INTENT(IN) :: ANORM 


REAL(wp), INTENT(OUT) :: RCOND 


INTEGER, INTENT(IN) :: IPIV( * ) 


COMPLEX(wp), INTENT(IN) :: AP(*) 


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


where 

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

LA_SPCON / LA_HPCON estimates the reciprocal of the condition number of real symmetric / complex symmetric / complex Hermitian indefinite packed matrix $A$ using the factorization computed by LA_SPTRF / LA_HPTRF respectively.
References: See  [1] and [9,20,21].
-----------------------------------

LA_SPRFS / LA_HPRFS
Real version.

SUBROUTINE LA_SPRFS( UPLO, N, NRHS, & 


AP, AFP, IPIV, B, LDB, X, LDX, FERR, & 


BERR, WORK, IWORK, INFO ) 


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


INTEGER, INTENT(IN) :: LDB, LDX, N, NRHS 


INTEGER, INTENT(OUT) :: INFO, IWORK(*) 


INTEGER, INTENT(IN) :: IPIV(*) 


REAL(wp), INTENT(OUT) :: err 


REAL(wp), INTENT(IN) :: AFP(*), AP(*), rhs 


REAL(wp), INTENT(INOUT) :: sol 


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


where 

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

rhs  ::= B(LDB,*) $\mid$ B(*) 

sol  ::= X(LDX,*) $\mid$ X(*) 

err  ::= FERR(*), BERR(*) $\mid$ FERR, BERR

Complex and complex Hermitian versions.

SUBROUTINE LA_SPRFS /LA_HPRFS( UPLO, & 


N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, & 


FERR, BERR, WORK, RWORK, INFO ) 


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


INTEGER, INTENT(IN) :: LDB, LDX, N, NRHS 


INTEGER, INTENT(OUT) :: INFO 


INTEGER, INTENT(IN) :: IPIV(*) 


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


COMPLEX(wp), INTENT(IN) :: AFP(*), AP(*), & 

rhs 


COMPLEX(wp), INTENT(INOUT) :: sol 


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


where 

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

rhs  ::= B(LDB,*) $\mid$ B(*) 

sol  ::= X(LDX,*) $\mid$ X(*) 

err  ::= FERR(*), BERR(*) $\mid$ FERR, BERR

LA_SPRFS / LA_HPRFS improve the computed solution to a system of linear equations when the coefficient matrix is a real symmetric / complex symmetric / complex Hermitian, indefinite and packed, and provides error bounds and backward error estimates for the solution.
References: See  [1] and [9,21,20].
-----------------------------------

LA_SPTRI / LA_HPTRI
Real, complex, and complex Hermitian versions.

SUBROUTINE LA_SYTRI /LA_HETRI( UPLO, & 


N, AP, IPIV, WORK, INFO ) 


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


INTEGER, INTENT(IN) :: N 


INTEGER, INTENT(OUT) :: INFO 


INTEGER, INTENT(IN) :: IPIV(*) 

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

type(wp), INTENT(OUT) :: WORK(*) 


where 

type ::= REAL $\mid$ COMPLEX 

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

LA_SPTRI / LA_HPTRI compute the inverse of a real symmetric / complex symmetric / complex Hermitian, indefinite matrix $A$ in packed storage using the factorization computed by LA_SPTRF / LA_HPTRF respectively.
References: See  [1] and [9,20].
-----------------------------------