SUBROUTINE ZPTTRF( N, D, E, INFO )
*
* -- LAPACK routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * )
COMPLEX*16 E( * )
* ..
*
* Purpose
* =======
*
* ZPTTRF computes the L*D*L' factorization of a complex Hermitian
* positive definite tridiagonal matrix A. The factorization may also
* be regarded as having the form A = U'*D*U.
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* D (input/output) 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' factorization of A.
*
* E (input/output) 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' factorization of A.
* E can also be regarded as the superdiagonal of the unit
* bidiagonal factor U from the U'*D*U factorization of A.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -k, the k-th argument had an illegal value
* > 0: if INFO = k, the leading minor of order k is not
* positive definite; if k < N, the factorization could not
* be completed, while if k = N, the factorization was
* completed, but D(N) <= 0.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, I4
DOUBLE PRECISION EII, EIR, F, G
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, DIMAG, MOD
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
CALL XERBLA( 'ZPTTRF', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Compute the L*D*L' (or U'*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 30
END IF
EIR = DBLE( E( I ) )
EII = DIMAG( E( I ) )
F = EIR / D( I )
G = EII / D( I )
E( I ) = DCMPLX( F, G )
D( I+1 ) = D( I+1 ) - F*EIR - G*EII
10 CONTINUE
*
DO 20 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 30
END IF
*
* Solve for e(i) and d(i+1).
*
EIR = DBLE( E( I ) )
EII = DIMAG( E( I ) )
F = EIR / D( I )
G = EII / D( I )
E( I ) = DCMPLX( F, G )
D( I+1 ) = D( I+1 ) - F*EIR - G*EII
*
IF( D( I+1 ).LE.ZERO ) THEN
INFO = I + 1
GO TO 30
END IF
*
* Solve for e(i+1) and d(i+2).
*
EIR = DBLE( E( I+1 ) )
EII = DIMAG( E( I+1 ) )
F = EIR / D( I+1 )
G = EII / D( I+1 )
E( I+1 ) = DCMPLX( F, G )
D( I+2 ) = D( I+2 ) - F*EIR - G*EII
*
IF( D( I+2 ).LE.ZERO ) THEN
INFO = I + 2
GO TO 30
END IF
*
* Solve for e(i+2) and d(i+3).
*
EIR = DBLE( E( I+2 ) )
EII = DIMAG( E( I+2 ) )
F = EIR / D( I+2 )
G = EII / D( I+2 )
E( I+2 ) = DCMPLX( F, G )
D( I+3 ) = D( I+3 ) - F*EIR - G*EII
*
IF( D( I+3 ).LE.ZERO ) THEN
INFO = I + 3
GO TO 30
END IF
*
* Solve for e(i+3) and d(i+4).
*
EIR = DBLE( E( I+3 ) )
EII = DIMAG( E( I+3 ) )
F = EIR / D( I+3 )
G = EII / D( I+3 )
E( I+3 ) = DCMPLX( F, G )
D( I+4 ) = D( I+4 ) - F*EIR - G*EII
20 CONTINUE
*
* Check d(n) for positive definiteness.
*
IF( D( N ).LE.ZERO )
$ INFO = N
*
30 CONTINUE
RETURN
*
* End of ZPTTRF
*
END