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Port of Reference-LAPACK PR OpenMathLib#1424. DSTEBR and SSTEBR compute all eigenvalues of a real symmetric tridiagonal matrix with a values-only divide-and-conquer method. Only the first and last boundary rows of each local eigenvector block are propagated across merge levels, so no *LAEDA-style full-block store/replay is needed. The workspace is O(N): LWORK >= MAX(16*N, 2*N + SMLSIZ**2 + 2*SMLSIZ - 2) and LIWORK >= 7*N for N > SMLSIZ; blocks with N <= SMLSIZ fall back to *STERF. DSTEBR and SSTEBR are new routines and do not change the behavior of *STEDC or *STERF. New public routines: DSTEBR, SSTEBR. Private helpers: *LAED0_BR, *LAED4_BR, *LAED7_BR/*LAED8_BR, *LAED9_BR. LAPACKE gains LAPACKE_dstebr, LAPACKE_sstebr and their _work variants. DCHKST and SCHKST gain test (38), varying SMLSIZ to exercise merges.
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Thanks - adding new LAPACK routines here entails producing C versions of them for the Androids and Fortran haters that walk among us. I plan to import the latest LAPACK changes soon |
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Description
Adds two new public routines,
DSTEBRandSSTEBR, that compute alleigenvalues of a real symmetric tridiagonal matrix with a values-only
divide-and-conquer method. This is a port of the routines accepted in
Reference-LAPACK PR #1424.
Only the first and last boundary rows of each local eigenvector block are
propagated across merge levels, instead of storing complete secular
eigenvector blocks for
*LAEDA-style replay. The workspace is therefore O(N):LWORK >= MAX(16*N, 2*N + SMLSIZ**2 + 2*SMLSIZ - 2),LIWORK >= 7*NforN > SMLSIZN <= SMLSIZfall back to*STERFDSTEBR/SSTEBRare new routines and do not change the behavior of*STEDCor
*STERF.New files
lapack-netlib/SRC/dstebr.f,sstebr.flapack-netlib/SRC/dlaed0_br.f/slaed0_br.f(also define*LAED0_MERGE_PAIR,*STEQR_BOUNDARY_BR)lapack-netlib/SRC/dlaed4_br.f/slaed4_br.flapack-netlib/SRC/dlaed7_br.f/slaed7_br.f(also define*LAED8_BR)lapack-netlib/SRC/dlaed9_br.f/slaed9_br.flapack-netlib/LAPACKE/src/lapacke_dstebr.c,lapacke_dstebr_work.c,lapacke_sstebr.c,lapacke_sstebr_work.cUpdated files
lapack-netlib/SRC/Makefile,lapack-netlib/SRC/CMakeLists.txt,cmake/lapack.cmakelapack-netlib/TESTING/EIG/dchkst.f,schkst.f: test (38),| D1 - D5 | / ( |D1| ulp )with D1 from*STEQR('V'), varying SMLSIZover 2, 8, 25 so merges run even with the small sizes in
sep.inlapack-netlib/LAPACKE/include/lapack.h,lapacke.h,LAPACKE/src/Makefile,LAPACKE/src/CMakeLists.txtexports/gensymbol: exportdstebr/sstebrand the LAPACKE wrappersTesting
DSTERFandDSTEDC('N'): 0 failures.SSTERF: max difference 1.8e-6.LAPACKE_dstebr/LAPACKE_sstebrcalled from C: values match.-fimplicit-none -fcheck=alland with-fdefault-integer-8 -Werror=conversion.Compatibility
No existing public interface changes, and no change to
*STEDCor*STERFbehavior.