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diff --git a/SRC/cheevd.f b/SRC/cheevd.f new file mode 100644 index 00000000..79490a6e --- /dev/null +++ b/SRC/cheevd.f @@ -0,0 +1,305 @@ + SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, 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, LDA, LIWORK, LRWORK, LWORK, N +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + REAL RWORK( * ), W( * ) + COMPLEX A( LDA, * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* CHEEVD computes all eigenvalues and, optionally, eigenvectors of a +* complex Hermitian 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. +* +* A (input/output) COMPLEX array, dimension (LDA, N) +* On entry, the Hermitian matrix A. If UPLO = 'U', the +* leading N-by-N upper triangular part of A contains the +* upper triangular part of the matrix A. If UPLO = 'L', +* the leading N-by-N lower triangular part of A contains +* the lower triangular part of the matrix A. +* On exit, if JOBZ = 'V', then if INFO = 0, A contains the +* orthonormal eigenvectors of the matrix A. +* If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') +* or the upper triangle (if UPLO='U') of A, including the +* diagonal, is destroyed. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,N). +* +* W (output) REAL array, dimension (N) +* If INFO = 0, the eigenvalues in ascending order. +* +* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The length 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 + 1. +* If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + 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 the 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 the array IWORK. +* If N <= 1, LIWORK must be at least 1. +* If JOBZ = 'N' and 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 and JOBZ = 'N', then the algorithm failed +* to converge; i off-diagonal elements of an intermediate +* tridiagonal form did not converge to zero; +* if INFO = i and JOBZ = 'V', then the algorithm failed +* to compute an eigenvalue while working on the submatrix +* lying in rows and columns INFO/(N+1) through +* mod(INFO,N+1). +* +* Further Details +* =============== +* +* Based on contributions by +* Jeff Rutter, Computer Science Division, University of California +* at Berkeley, USA +* +* Modified description of INFO. Sven, 16 Feb 05. +* ===================================================================== +* +* .. Parameters .. + REAL ZERO, ONE + PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) + COMPLEX CONE + PARAMETER ( CONE = ( 1.0E0, 0.0E0 ) ) +* .. +* .. Local Scalars .. + LOGICAL LOWER, LQUERY, WANTZ + INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2, + $ INDWRK, ISCALE, LIOPT, LIWMIN, LLRWK, LLWORK, + $ LLWRK2, LOPT, LROPT, LRWMIN, LWMIN + REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, + $ SMLNUM +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + REAL CLANHE, SLAMCH + EXTERNAL ILAENV, LSAME, CLANHE, SLAMCH +* .. +* .. External Subroutines .. + EXTERNAL CHETRD, CLACPY, CLASCL, CSTEDC, CUNMTR, SSCAL, + $ SSTERF, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, SQRT +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + LOWER = LSAME( UPLO, 'L' ) + LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) +* + 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( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + END IF +* + IF( INFO.EQ.0 ) THEN + IF( N.LE.1 ) THEN + LWMIN = 1 + LRWMIN = 1 + LIWMIN = 1 + LOPT = LWMIN + LROPT = LRWMIN + LIOPT = LIWMIN + ELSE + IF( WANTZ ) THEN + LWMIN = 2*N + N*N + LRWMIN = 1 + 5*N + 2*N**2 + LIWMIN = 3 + 5*N + ELSE + LWMIN = N + 1 + LRWMIN = N + LIWMIN = 1 + END IF + LOPT = MAX( LWMIN, N + + $ ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 ) ) + LROPT = LRWMIN + LIOPT = LIWMIN + END IF + WORK( 1 ) = LOPT + RWORK( 1 ) = LROPT + IWORK( 1 ) = LIOPT +* + IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -8 + ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN + INFO = -10 + ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN + INFO = -12 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CHEEVD', -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 ) = A( 1, 1 ) + IF( WANTZ ) + $ A( 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 = CLANHE( 'M', UPLO, N, A, LDA, 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 ) + $ CALL CLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) +* +* Call CHETRD to reduce Hermitian matrix to tridiagonal form. +* + INDE = 1 + INDTAU = 1 + INDWRK = INDTAU + N + INDRWK = INDE + N + INDWK2 = INDWRK + N*N + LLWORK = LWORK - INDWRK + 1 + LLWRK2 = LWORK - INDWK2 + 1 + LLRWK = LRWORK - INDRWK + 1 + CALL CHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ), + $ WORK( INDWRK ), LLWORK, IINFO ) +* +* For eigenvalues only, call SSTERF. For eigenvectors, first call +* CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the +* tridiagonal matrix, then call CUNMTR to multiply it to the +* Householder transformations represented as Householder vectors in +* A. +* + IF( .NOT.WANTZ ) THEN + CALL SSTERF( N, W, RWORK( INDE ), INFO ) + ELSE + CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK( INDWRK ), N, + $ WORK( INDWK2 ), LLWRK2, RWORK( INDRWK ), LLRWK, + $ IWORK, LIWORK, INFO ) + CALL CUNMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), + $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) + CALL CLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) + 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 ) = LOPT + RWORK( 1 ) = LROPT + IWORK( 1 ) = LIOPT +* + RETURN +* +* End of CHEEVD +* + END |