*> \brief \b CPTTRF
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CPTTRF( N, D, E, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, N
* ..
* .. Array Arguments ..
* REAL D( * )
* COMPLEX E( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> 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.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexPTcomputational
*
* =====================================================================
SUBROUTINE CPTTRF( N, D, E, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, N
* ..
* .. Array Arguments ..
REAL D( * )
COMPLEX E( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, I4
REAL EII, EIR, F, G
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC AIMAG, CMPLX, MOD, REAL
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
CALL XERBLA( 'CPTTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Compute the L*D*L**H (or U**H *D*U) factorization of A.
*
I4 = MOD( N-1, 4 )
DO 10 I = 1, I4
IF( D( I ).LE.ZERO ) THEN
INFO = I
GO TO 20
END IF
EIR = REAL( E( I ) )
EII = AIMAG( E( I ) )
F = EIR / D( I )
G = EII / D( I )
E( I ) = CMPLX( F, G )
D( I+1 ) = D( I+1 ) - F*EIR - G*EII
10 CONTINUE
*
DO 110 I = I4+1, N - 4, 4
*
* Drop out of the loop if d(i) <= 0: the matrix is not positive
* definite.
*
IF( D( I ).LE.ZERO ) THEN
INFO = I
GO TO 20
END IF
*
* Solve for e(i) and d(i+1).
*
EIR = REAL( E( I ) )
EII = AIMAG( E( I ) )
F = EIR / D( I )
G = EII / D( I )
E( I ) = CMPLX( F, G )
D( I+1 ) = D( I+1 ) - F*EIR - G*EII
*
IF( D( I+1 ).LE.ZERO ) THEN
INFO = I+1
GO TO 20
END IF
*
* Solve for e(i+1) and d(i+2).
*
EIR = REAL( E( I+1 ) )
EII = AIMAG( E( I+1 ) )
F = EIR / D( I+1 )
G = EII / D( I+1 )
E( I+1 ) = CMPLX( F, G )
D( I+2 ) = D( I+2 ) - F*EIR - G*EII
*
IF( D( I+2 ).LE.ZERO ) THEN
INFO = I+2
GO TO 20
END IF
*
* Solve for e(i+2) and d(i+3).
*
EIR = REAL( E( I+2 ) )
EII = AIMAG( E( I+2 ) )
F = EIR / D( I+2 )
G = EII / D( I+2 )
E( I+2 ) = CMPLX( F, G )
D( I+3 ) = D( I+3 ) - F*EIR - G*EII
*
IF( D( I+3 ).LE.ZERO ) THEN
INFO = I+3
GO TO 20
END IF
*
* Solve for e(i+3) and d(i+4).
*
EIR = REAL( E( I+3 ) )
EII = AIMAG( E( I+3 ) )
F = EIR / D( I+3 )
G = EII / D( I+3 )
E( I+3 ) = CMPLX( F, G )
D( I+4 ) = D( I+4 ) - F*EIR - G*EII
110 CONTINUE
*
* Check d(n) for positive definiteness.
*
IF( D( N ).LE.ZERO )
$ INFO = N
*
20 CONTINUE
RETURN
*
* End of CPTTRF
*
END