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Diffstat (limited to 'SRC/ssbev.f')
| -rw-r--r-- | SRC/ssbev.f | 205 |
1 files changed, 205 insertions, 0 deletions
diff --git a/SRC/ssbev.f b/SRC/ssbev.f new file mode 100644 index 00000000..064b2dce --- /dev/null +++ b/SRC/ssbev.f @@ -0,0 +1,205 @@ + SUBROUTINE SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, + $ INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley 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 |