SUBROUTINE SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, \$ INFO ) * * -- LAPACK driver 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 JOBZ, UPLO INTEGER INFO, KD, LDAB, LDZ, N * .. * .. Array Arguments .. REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * Purpose * ======= * * SSBEV computes all the eigenvalues and, optionally, eigenvectors of * a real symmetric band matrix A. * * Arguments * ========= * * JOBZ (input) CHARACTER*1 * = 'N': Compute eigenvalues only; * = 'V': Compute eigenvalues and eigenvectors. * * UPLO (input) CHARACTER*1 * = 'U': Upper triangle of A is stored; * = 'L': Lower triangle of A is stored. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * KD (input) INTEGER * The number of superdiagonals of the matrix A if UPLO = 'U', * or the number of subdiagonals if UPLO = 'L'. KD >= 0. * * AB (input/output) REAL array, dimension (LDAB, N) * On entry, the upper or lower triangle of the symmetric band * matrix A, stored in the first KD+1 rows of the array. The * j-th column of A is stored in the j-th column of the array AB * as follows: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). * * On exit, AB is overwritten by values generated during the * reduction to tridiagonal form. If UPLO = 'U', the first * superdiagonal and the diagonal of the tridiagonal matrix T * are returned in rows KD and KD+1 of AB, and if UPLO = 'L', * the diagonal and first subdiagonal of T are returned in the * first two rows of AB. * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KD + 1. * * W (output) REAL array, dimension (N) * If INFO = 0, the eigenvalues in ascending order. * * Z (output) REAL array, dimension (LDZ, N) * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal * eigenvectors of the matrix A, with the i-th column of Z * holding the eigenvector associated with W(i). * If JOBZ = 'N', then Z is not referenced. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= 1, and if * JOBZ = 'V', LDZ >= max(1,N). * * WORK (workspace) REAL array, dimension (max(1,3*N-2)) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: if INFO = i, the algorithm failed to converge; i * off-diagonal elements of an intermediate tridiagonal * form did not converge to zero. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. LOGICAL LOWER, WANTZ INTEGER IINFO, IMAX, INDE, INDWRK, ISCALE REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, \$ SMLNUM * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANSB EXTERNAL LSAME, SLAMCH, SLANSB * .. * .. External Subroutines .. EXTERNAL SLASCL, SSBTRD, SSCAL, SSTEQR, SSTERF, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LOWER = LSAME( UPLO, 'L' ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( KD.LT.0 ) THEN INFO = -4 ELSE IF( LDAB.LT.KD+1 ) THEN INFO = -6 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -9 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SSBEV ', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * IF( N.EQ.1 ) THEN IF( LOWER ) THEN W( 1 ) = AB( 1, 1 ) ELSE W( 1 ) = AB( KD+1, 1 ) END IF IF( WANTZ ) \$ Z( 1, 1 ) = ONE RETURN END IF * * Get machine constants. * SAFMIN = SLAMCH( 'Safe minimum' ) EPS = SLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = SLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK ) ISCALE = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) THEN IF( LOWER ) THEN CALL SLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO ) ELSE CALL SLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO ) END IF END IF * * Call SSBTRD to reduce symmetric band matrix to tridiagonal form. * INDE = 1 INDWRK = INDE + N CALL SSBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, WORK( INDE ), Z, LDZ, \$ WORK( INDWRK ), IINFO ) * * For eigenvalues only, call SSTERF. For eigenvectors, call SSTEQR. * IF( .NOT.WANTZ ) THEN CALL SSTERF( N, W, WORK( INDE ), INFO ) ELSE CALL SSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ), \$ INFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = N ELSE IMAX = INFO - 1 END IF CALL SSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * RETURN * * End of SSBEV * END