*> \brief \b ZPTTRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZPTTRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZPTTRF( N, D, E, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ) * COMPLEX*16 E( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> 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. *> \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 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. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> 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. *> \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 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. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16PTcomputational * * ===================================================================== SUBROUTINE ZPTTRF( 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 .. DOUBLE PRECISION D( * ) COMPLEX*16 E( * ) * .. * * ===================================================================== * * .. 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**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 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