SUBROUTINE DPTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley 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