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author | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
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committer | jason <jason@8a072113-8704-0410-8d35-dd094bca7971> | 2008-10-28 01:38:50 +0000 |
commit | baba851215b44ac3b60b9248eb02bcce7eb76247 (patch) | |
tree | 8c0f5c006875532a30d4409f5e94b0f310ff00a7 /SRC/chbevd.f | |
download | lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.gz lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.tar.bz2 lapack-baba851215b44ac3b60b9248eb02bcce7eb76247.zip |
Move LAPACK trunk into position.
Diffstat (limited to 'SRC/chbevd.f')
-rw-r--r-- | SRC/chbevd.f | 302 |
1 files changed, 302 insertions, 0 deletions
diff --git a/SRC/chbevd.f b/SRC/chbevd.f new file mode 100644 index 00000000..e37bdd0f --- /dev/null +++ b/SRC/chbevd.f @@ -0,0 +1,302 @@ + SUBROUTINE CHBEVD( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, + $ LWORK, RWORK, LRWORK, IWORK, LIWORK, 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, LIWORK, LRWORK, LWORK, N +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + REAL RWORK( * ), W( * ) + COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* CHBEVD computes all the eigenvalues and, optionally, eigenvectors of +* a complex Hermitian band matrix A. If eigenvectors are desired, it +* uses a divide and conquer algorithm. +* +* The divide and conquer algorithm makes very mild assumptions about +* floating point arithmetic. It will work on machines with a guard +* digit in add/subtract, or on those binary machines without guard +* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or +* Cray-2. It could conceivably fail on hexadecimal or decimal machines +* without guard digits, but we know of none. +* +* 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) COMPLEX array, dimension (LDAB, N) +* On entry, the upper or lower triangle of the Hermitian 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) COMPLEX 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/output) COMPLEX array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The dimension of the array WORK. +* If N <= 1, LWORK must be at least 1. +* If JOBZ = 'N' and N > 1, LWORK must be at least N. +* If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal sizes of the WORK, RWORK and +* IWORK arrays, returns these values as the first entries of +* the WORK, RWORK and IWORK arrays, and no error message +* related to LWORK or LRWORK or LIWORK is issued by XERBLA. +* +* RWORK (workspace/output) REAL array, +* dimension (LRWORK) +* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. +* +* LRWORK (input) INTEGER +* The dimension of array RWORK. +* If N <= 1, LRWORK must be at least 1. +* If JOBZ = 'N' and N > 1, LRWORK must be at least N. +* If JOBZ = 'V' and N > 1, LRWORK must be at least +* 1 + 5*N + 2*N**2. +* +* If LRWORK = -1, then a workspace query is assumed; the +* routine only calculates the optimal sizes of the WORK, RWORK +* and IWORK arrays, returns these values as the first entries +* of the WORK, RWORK and IWORK arrays, and no error message +* related to LWORK or LRWORK or LIWORK is issued by XERBLA. +* +* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) +* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. +* +* LIWORK (input) INTEGER +* The dimension of array IWORK. +* If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. +* If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N . +* +* If LIWORK = -1, then a workspace query is assumed; the +* routine only calculates the optimal sizes of the WORK, RWORK +* and IWORK arrays, returns these values as the first entries +* of the WORK, RWORK and IWORK arrays, and no error message +* related to LWORK or LRWORK or LIWORK is issued by XERBLA. +* +* 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 ) + COMPLEX CZERO, CONE + PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ), + $ CONE = ( 1.0E0, 0.0E0 ) ) +* .. +* .. Local Scalars .. + LOGICAL LOWER, LQUERY, WANTZ + INTEGER IINFO, IMAX, INDE, INDWK2, INDWRK, ISCALE, + $ LIWMIN, LLRWK, LLWK2, LRWMIN, LWMIN + REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, + $ SMLNUM +* .. +* .. External Functions .. + LOGICAL LSAME + REAL CLANHB, SLAMCH + EXTERNAL LSAME, CLANHB, SLAMCH +* .. +* .. External Subroutines .. + EXTERNAL CGEMM, CHBTRD, CLACPY, CLASCL, CSTEDC, SSCAL, + $ SSTERF, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC SQRT +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + LOWER = LSAME( UPLO, 'L' ) + LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 .OR. LRWORK.EQ.-1 ) +* + INFO = 0 + IF( N.LE.1 ) THEN + LWMIN = 1 + LRWMIN = 1 + LIWMIN = 1 + ELSE + IF( WANTZ ) THEN + LWMIN = 2*N**2 + LRWMIN = 1 + 5*N + 2*N**2 + LIWMIN = 3 + 5*N + ELSE + LWMIN = N + LRWMIN = N + LIWMIN = 1 + END IF + END IF + 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.EQ.0 ) THEN + WORK( 1 ) = LWMIN + RWORK( 1 ) = LRWMIN + IWORK( 1 ) = LIWMIN +* + IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -11 + ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN + INFO = -13 + ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN + INFO = -15 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CHBEVD', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( N.EQ.1 ) THEN + W( 1 ) = AB( 1, 1 ) + IF( WANTZ ) + $ Z( 1, 1 ) = CONE + 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 = CLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK ) + 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 CLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO ) + ELSE + CALL CLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO ) + END IF + END IF +* +* Call CHBTRD to reduce Hermitian band matrix to tridiagonal form. +* + INDE = 1 + INDWRK = INDE + N + INDWK2 = 1 + N*N + LLWK2 = LWORK - INDWK2 + 1 + LLRWK = LRWORK - INDWRK + 1 + CALL CHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z, + $ LDZ, WORK, IINFO ) +* +* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEDC. +* + IF( .NOT.WANTZ ) THEN + CALL SSTERF( N, W, RWORK( INDE ), INFO ) + ELSE + CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ), + $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK, + $ INFO ) + CALL CGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO, + $ WORK( INDWK2 ), N ) + CALL CLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ ) + 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 +* + WORK( 1 ) = LWMIN + RWORK( 1 ) = LRWMIN + IWORK( 1 ) = LIWMIN + RETURN +* +* End of CHBEVD +* + END |