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diff --git a/SRC/cstegr.f b/SRC/cstegr.f new file mode 100644 index 00000000..ff3ff3f6 --- /dev/null +++ b/SRC/cstegr.f @@ -0,0 +1,180 @@ + SUBROUTINE CSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, + $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, + $ LIWORK, INFO ) + + IMPLICIT NONE +* +* +* -- LAPACK computational routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, RANGE + INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N + REAL ABSTOL, VL, VU +* .. +* .. Array Arguments .. + INTEGER ISUPPZ( * ), IWORK( * ) + REAL D( * ), E( * ), W( * ), WORK( * ) + COMPLEX Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +* CSTEGR computes selected eigenvalues and, optionally, eigenvectors +* of a real symmetric tridiagonal matrix T. Any such unreduced matrix has +* a well defined set of pairwise different real eigenvalues, the corresponding +* real eigenvectors are pairwise orthogonal. +* +* The spectrum may be computed either completely or partially by specifying +* either an interval (VL,VU] or a range of indices IL:IU for the desired +* eigenvalues. +* +* CSTEGR is a compatability wrapper around the improved CSTEMR routine. +* See SSTEMR for further details. +* +* One important change is that the ABSTOL parameter no longer provides any +* benefit and hence is no longer used. +* +* Note : CSTEGR and CSTEMR work only on machines which follow +* IEEE-754 floating-point standard in their handling of infinities and +* NaNs. Normal execution may create these exceptiona values and hence +* may abort due to a floating point exception in environments which +* do not conform to the IEEE-754 standard. +* +* Arguments +* ========= +* +* JOBZ (input) CHARACTER*1 +* = 'N': Compute eigenvalues only; +* = 'V': Compute eigenvalues and eigenvectors. +* +* RANGE (input) CHARACTER*1 +* = 'A': all eigenvalues will be found. +* = 'V': all eigenvalues in the half-open interval (VL,VU] +* will be found. +* = 'I': the IL-th through IU-th eigenvalues will be found. +* +* 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 +* T. On exit, D is overwritten. +* +* E (input/output) REAL array, dimension (N) +* On entry, the (N-1) subdiagonal elements of the tridiagonal +* matrix T in elements 1 to N-1 of E. E(N) need not be set on +* input, but is used internally as workspace. +* On exit, E is overwritten. +* +* VL (input) REAL +* VU (input) REAL +* If RANGE='V', the lower and upper bounds of the interval to +* be searched for eigenvalues. VL < VU. +* Not referenced if RANGE = 'A' or 'I'. +* +* IL (input) INTEGER +* IU (input) INTEGER +* If RANGE='I', the indices (in ascending order) of the +* smallest and largest eigenvalues to be returned. +* 1 <= IL <= IU <= N, if N > 0. +* Not referenced if RANGE = 'A' or 'V'. +* +* ABSTOL (input) REAL +* Unused. Was the absolute error tolerance for the +* eigenvalues/eigenvectors in previous versions. +* +* M (output) INTEGER +* The total number of eigenvalues found. 0 <= M <= N. +* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. +* +* W (output) REAL array, dimension (N) +* The first M elements contain the selected eigenvalues in +* ascending order. +* +* Z (output) COMPLEX array, dimension (LDZ, max(1,M) ) +* If JOBZ = 'V', and if INFO = 0, then the first M columns of Z +* contain the orthonormal eigenvectors of the matrix T +* corresponding to the selected eigenvalues, with the i-th +* column of Z holding the eigenvector associated with W(i). +* If JOBZ = 'N', then Z is not referenced. +* Note: the user must ensure that at least max(1,M) columns are +* supplied in the array Z; if RANGE = 'V', the exact value of M +* is not known in advance and an upper bound must be used. +* Supplying N columns is always safe. +* +* LDZ (input) INTEGER +* The leading dimension of the array Z. LDZ >= 1, and if +* JOBZ = 'V', then LDZ >= max(1,N). +* +* ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) ) +* The support of the eigenvectors in Z, i.e., the indices +* indicating the nonzero elements in Z. The i-th computed eigenvector +* is nonzero only in elements ISUPPZ( 2*i-1 ) through +* ISUPPZ( 2*i ). This is relevant in the case when the matrix +* is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. +* +* WORK (workspace/output) REAL array, dimension (LWORK) +* On exit, if INFO = 0, WORK(1) returns the optimal +* (and minimal) LWORK. +* +* LWORK (input) INTEGER +* The dimension of the array WORK. LWORK >= max(1,18*N) +* if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* IWORK (workspace/output) INTEGER array, dimension (LIWORK) +* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. +* +* LIWORK (input) INTEGER +* The dimension of the array IWORK. LIWORK >= max(1,10*N) +* if the eigenvectors are desired, and LIWORK >= max(1,8*N) +* if only the eigenvalues are to be computed. +* If LIWORK = -1, then a workspace query is assumed; the +* routine only calculates the optimal size of the IWORK array, +* returns this value as the first entry of the IWORK array, and +* no error message related to LIWORK is issued by XERBLA. +* +* INFO (output) INTEGER +* On exit, INFO +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: if INFO = 1X, internal error in SLARRE, +* if INFO = 2X, internal error in CLARRV. +* Here, the digit X = ABS( IINFO ) < 10, where IINFO is +* the nonzero error code returned by SLARRE or +* CLARRV, respectively. +* +* Further Details +* =============== +* +* Based on contributions by +* Inderjit Dhillon, IBM Almaden, USA +* Osni Marques, LBNL/NERSC, USA +* Christof Voemel, LBNL/NERSC, USA +* +* ===================================================================== +* +* .. Local Scalars .. + LOGICAL TRYRAC +* .. +* .. External Subroutines .. + EXTERNAL CSTEMR +* .. +* .. Executable Statements .. + INFO = 0 + TRYRAC = .FALSE. + + CALL CSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, + $ M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK, + $ IWORK, LIWORK, INFO ) +* +* End of CSTEGR +* + END |