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Diffstat (limited to 'SRC/sstevd.f')
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diff --git a/SRC/sstevd.f b/SRC/sstevd.f new file mode 100644 index 00000000..045ec9d9 --- /dev/null +++ b/SRC/sstevd.f @@ -0,0 +1,219 @@ + SUBROUTINE SSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, 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 + INTEGER INFO, LDZ, LIWORK, LWORK, N +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + REAL D( * ), E( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* SSTEVD computes all eigenvalues and, optionally, eigenvectors of a +* real symmetric tridiagonal matrix. 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. +* +* N (input) INTEGER +* The order of the matrix. N >= 0. +* +* D (input/output) REAL array, dimension (N) +* On entry, the n diagonal elements of the tridiagonal matrix +* A. +* On exit, if INFO = 0, the eigenvalues in ascending order. +* +* E (input/output) REAL array, dimension (N-1) +* On entry, the (n-1) subdiagonal elements of the tridiagonal +* matrix A, stored in elements 1 to N-1 of E. +* On exit, the contents of E are destroyed. +* +* 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 D(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) REAL array, +* dimension (LWORK) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The dimension of the array WORK. +* If JOBZ = 'N' or N <= 1 then LWORK must be at least 1. +* If JOBZ = 'V' and N > 1 then LWORK must be at least +* ( 1 + 4*N + N**2 ). +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal sizes of the WORK and IWORK +* arrays, returns these values as the first entries of the WORK +* and IWORK arrays, and no error message related to LWORK 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 JOBZ = 'N' or N <= 1 then LIWORK must be at least 1. +* If JOBZ = 'V' and N > 1 then 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 and +* IWORK arrays, returns these values as the first entries of +* the WORK and IWORK arrays, and no error message related to +* LWORK 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 E did not converge to zero. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO, ONE + PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY, WANTZ + INTEGER ISCALE, LIWMIN, LWMIN + REAL BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM, + $ TNRM +* .. +* .. External Functions .. + LOGICAL LSAME + REAL SLAMCH, SLANST + EXTERNAL LSAME, SLAMCH, SLANST +* .. +* .. External Subroutines .. + EXTERNAL SSCAL, SSTEDC, SSTERF, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC SQRT +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) +* + INFO = 0 + LIWMIN = 1 + LWMIN = 1 + IF( N.GT.1 .AND. WANTZ ) THEN + LWMIN = 1 + 4*N + N**2 + LIWMIN = 3 + 5*N + END IF +* + IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN + INFO = -6 + END IF +* + IF( INFO.EQ.0 ) THEN + WORK( 1 ) = LWMIN + IWORK( 1 ) = LIWMIN +* + IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -8 + ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN + INFO = -10 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'SSTEVD', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( N.EQ.1 ) THEN + 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. +* + ISCALE = 0 + TNRM = SLANST( 'M', N, D, E ) + IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN + ISCALE = 1 + SIGMA = RMIN / TNRM + ELSE IF( TNRM.GT.RMAX ) THEN + ISCALE = 1 + SIGMA = RMAX / TNRM + END IF + IF( ISCALE.EQ.1 ) THEN + CALL SSCAL( N, SIGMA, D, 1 ) + CALL SSCAL( N-1, SIGMA, E( 1 ), 1 ) + END IF +* +* For eigenvalues only, call SSTERF. For eigenvalues and +* eigenvectors, call SSTEDC. +* + IF( .NOT.WANTZ ) THEN + CALL SSTERF( N, D, E, INFO ) + ELSE + CALL SSTEDC( 'I', N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, + $ INFO ) + END IF +* +* If matrix was scaled, then rescale eigenvalues appropriately. +* + IF( ISCALE.EQ.1 ) + $ CALL SSCAL( N, ONE / SIGMA, D, 1 ) +* + WORK( 1 ) = LWMIN + IWORK( 1 ) = LIWMIN +* + RETURN +* +* End of SSTEVD +* + END |