SUBROUTINE CPTTRF( N, D, E, INFO ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, N * .. * .. Array Arguments .. REAL D( * ) COMPLEX E( * ) * .. * * Purpose * ======= * * CPTTRF 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) 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' factorization of A. * * E (input/output) 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' 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 .. 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' (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 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