SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, 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 .. CHARACTER COMPZ INTEGER INFO, LDZ, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) * .. * * Purpose * ======= * * DPTEQR computes all eigenvalues and, optionally, eigenvectors of a * symmetric positive definite tridiagonal matrix by first factoring the * matrix using DPTTRF, and then calling DBDSQR to compute the singular * values of the bidiagonal factor. * * This routine computes the eigenvalues of the positive definite * tridiagonal matrix to high relative accuracy. This means that if the * eigenvalues range over many orders of magnitude in size, then the * small eigenvalues and corresponding eigenvectors will be computed * more accurately than, for example, with the standard QR method. * * The eigenvectors of a full or band symmetric positive definite matrix * can also be found if DSYTRD, DSPTRD, or DSBTRD has been used to * reduce this matrix to tridiagonal form. (The reduction to tridiagonal * form, however, may preclude the possibility of obtaining high * relative accuracy in the small eigenvalues of the original matrix, if * these eigenvalues range over many orders of magnitude.) * * Arguments * ========= * * COMPZ (input) CHARACTER*1 * = 'N': Compute eigenvalues only. * = 'V': Compute eigenvectors of original symmetric * matrix also. Array Z contains the orthogonal * matrix used to reduce the original matrix to * tridiagonal form. * = 'I': Compute eigenvectors of tridiagonal matrix also. * * N (input) INTEGER * The order of the matrix. N >= 0. * * D (input/output) DOUBLE PRECISION array, dimension (N) * On entry, the n diagonal elements of the tridiagonal * matrix. * On normal exit, D contains the eigenvalues, in descending * order. * * E (input/output) DOUBLE PRECISION array, dimension (N-1) * On entry, the (n-1) subdiagonal elements of the tridiagonal * matrix. * On exit, E has been destroyed. * * Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N) * On entry, if COMPZ = 'V', the orthogonal matrix used in the * reduction to tridiagonal form. * On exit, if COMPZ = 'V', the orthonormal eigenvectors of the * original symmetric matrix; * if COMPZ = 'I', the orthonormal eigenvectors of the * tridiagonal matrix. * If INFO > 0 on exit, Z contains the eigenvectors associated * with only the stored eigenvalues. * If COMPZ = 'N', then Z is not referenced. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= 1, and if * COMPZ = 'V' or 'I', LDZ >= max(1,N). * * WORK (workspace) DOUBLE PRECISION array, dimension (4*N) * * INFO (output) INTEGER * = 0: successful exit. * < 0: if INFO = -i, the i-th argument had an illegal value. * > 0: if INFO = i, and i is: * <= N the Cholesky factorization of the matrix could * not be performed because the i-th principal minor * was not positive definite. * > N the SVD algorithm failed to converge; * if INFO = N+i, i off-diagonal elements of the * bidiagonal factor did not converge to zero. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DBDSQR, DLASET, DPTTRF, XERBLA * .. * .. Local Arrays .. DOUBLE PRECISION C( 1, 1 ), VT( 1, 1 ) * .. * .. Local Scalars .. INTEGER I, ICOMPZ, NRU * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( LSAME( COMPZ, 'N' ) ) THEN ICOMPZ = 0 ELSE IF( LSAME( COMPZ, 'V' ) ) THEN ICOMPZ = 1 ELSE IF( LSAME( COMPZ, 'I' ) ) THEN ICOMPZ = 2 ELSE ICOMPZ = -1 END IF IF( ICOMPZ.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, \$ N ) ) ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DPTEQR', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * IF( N.EQ.1 ) THEN IF( ICOMPZ.GT.0 ) \$ Z( 1, 1 ) = ONE RETURN END IF IF( ICOMPZ.EQ.2 ) \$ CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ ) * * Call DPTTRF to factor the matrix. * CALL DPTTRF( N, D, E, INFO ) IF( INFO.NE.0 ) \$ RETURN DO 10 I = 1, N D( I ) = SQRT( D( I ) ) 10 CONTINUE DO 20 I = 1, N - 1 E( I ) = E( I )*D( I ) 20 CONTINUE * * Call DBDSQR to compute the singular values/vectors of the * bidiagonal factor. * IF( ICOMPZ.GT.0 ) THEN NRU = N ELSE NRU = 0 END IF CALL DBDSQR( 'Lower', N, 0, NRU, 0, D, E, VT, 1, Z, LDZ, C, 1, \$ WORK, INFO ) * * Square the singular values. * IF( INFO.EQ.0 ) THEN DO 30 I = 1, N D( I ) = D( I )*D( I ) 30 CONTINUE ELSE INFO = N + INFO END IF * RETURN * * End of DPTEQR * END