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pttrf(3) LAPACK pttrf(3)

NAME

pttrf - pttrf: triangular factor

SYNOPSIS

Functions


subroutine cpttrf (n, d, e, info)
CPTTRF subroutine dpttrf (n, d, e, info)
DPTTRF subroutine spttrf (n, d, e, info)
SPTTRF subroutine zpttrf (n, d, e, info)
ZPTTRF

Detailed Description

Function Documentation

subroutine cpttrf (integer n, real, dimension( * ) d, complex, dimension( * ) e, integer info)

CPTTRF

Purpose:

!>
!> CPTTRF computes the L*D*L**H factorization of a complex Hermitian
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**H *D*U.
!>

Parameters

N 

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

D

!>          D is REAL array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal matrix
!>          A.  On exit, the n diagonal elements of the diagonal matrix
!>          D from the L*D*L**H factorization of A.
!>

E

!>          E is COMPLEX array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix A.  On exit, the (n-1) subdiagonal elements of the
!>          unit bidiagonal factor L from the L*D*L**H factorization of A.
!>          E can also be regarded as the superdiagonal of the unit
!>          bidiagonal factor U from the U**H *D*U factorization of A.
!>

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>          > 0: if INFO = k, the leading principal minor of order k
!>               is not positive; if k < N, the factorization could not
!>               be completed, while if k = N, the factorization was
!>               completed, but D(N) <= 0.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dpttrf (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer info)

DPTTRF

Purpose:

!>
!> DPTTRF computes the L*D*L**T factorization of a real symmetric
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**T*D*U.
!>

Parameters

N 

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal matrix
!>          A.  On exit, the n diagonal elements of the diagonal matrix
!>          D from the L*D*L**T factorization of A.
!>

E

!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix A.  On exit, the (n-1) subdiagonal elements of the
!>          unit bidiagonal factor L from the L*D*L**T factorization of A.
!>          E can also be regarded as the superdiagonal of the unit
!>          bidiagonal factor U from the U**T*D*U factorization of A.
!>

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>          > 0: if INFO = k, the leading principal minor of order k
!>               is not positive; if k < N, the factorization could not
!>               be completed, while if k = N, the factorization was
!>               completed, but D(N) <= 0.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine spttrf (integer n, real, dimension( * ) d, real, dimension( * ) e, integer info)

SPTTRF

Purpose:

!>
!> SPTTRF computes the L*D*L**T factorization of a real symmetric
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**T*D*U.
!>

Parameters

N 

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

D

!>          D is REAL array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal matrix
!>          A.  On exit, the n diagonal elements of the diagonal matrix
!>          D from the L*D*L**T factorization of A.
!>

E

!>          E is REAL array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix A.  On exit, the (n-1) subdiagonal elements of the
!>          unit bidiagonal factor L from the L*D*L**T factorization of A.
!>          E can also be regarded as the superdiagonal of the unit
!>          bidiagonal factor U from the U**T*D*U factorization of A.
!>

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>          > 0: if INFO = k, the leading principal minor of order k
!>               is not positive; if k < N, the factorization could not
!>               be completed, while if k = N, the factorization was
!>               completed, but D(N) <= 0.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zpttrf (integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e, integer info)

ZPTTRF

Purpose:

!>
!> ZPTTRF computes the L*D*L**H factorization of a complex Hermitian
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**H *D*U.
!>

Parameters

N 

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          On entry, the n diagonal elements of the tridiagonal matrix
!>          A.  On exit, the n diagonal elements of the diagonal matrix
!>          D from the L*D*L**H factorization of A.
!>

E

!>          E is COMPLEX*16 array, dimension (N-1)
!>          On entry, the (n-1) subdiagonal elements of the tridiagonal
!>          matrix A.  On exit, the (n-1) subdiagonal elements of the
!>          unit bidiagonal factor L from the L*D*L**H factorization of A.
!>          E can also be regarded as the superdiagonal of the unit
!>          bidiagonal factor U from the U**H *D*U factorization of A.
!>

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>          > 0: if INFO = k, the leading principal minor of order k
!>               is not positive; if k < N, the factorization could not
!>               be completed, while if k = N, the factorization was
!>               completed, but D(N) <= 0.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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