*********************************************************************** ----------------------------------- MACHINE-SPECIFIC INSTALLATION HINTS: ----------------------------------- Entries are listed in ALPHABETICAL ORDER by the computer name. +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ TEMPLATE FOR THE ENTRIES: + +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ================================================================== + Computer name, version of OS, and version of fortran compiler used + ================================================================== + + Compiler/options: + + BLAS: + + Test status: + + Notes: + + ----- Date reported: + + ================================================================== + +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ---------------------- KNOWN TESTING FAILURES: ---------------------- The only known testing failures are in condition number estimation routines in the generalized nonsymmetric eigenproblem testing. Specifically in sgd.out, dgd.out, cgd.out and zgd.out. The cause for the failures of some test cases is that the mathematical algorithm used for estimating the condition numbers could over- or under-estimate the true values in a certain factor in some rare cases. Further details can be found in LAPACK Working Note 87. The failures noted below were reported to us and are still under investigation. Please contact us (lapack@cs.utk.edu) if you feel that an entry is out-of-date or incorrect. Please NOTE that no claim is made as to the accuracy of the installation information for specific computers; in some cases, no attempts were made at verification. ====================================================================== Apple Mac G4 OS: PPC RedHat Linux 6.0 (kernel 2.2.15) g77 (version egcs-2.91.66) LAPACK, version 3.0 + update FORTRAN = g77 OPTS = -fno-f2c -O3 DRVOPTS = $(OPTS) NOOPT = LOADER = g77 LOADOPTS = ARCH = ar ARCHFLAGS= cr RANLIB = ranlib Notes: (1)Do not use -funroll-all-loops option! Test status: Expected failures in sgd.out and cgd.out; Minor failures of SPB and SLS in stest.out and ctest.out; ----- Date reported: March, 2000 ======================================================================= CRAY C90, Unicos 9.0 with Programming Environment 3.0 LAPACK: VERSION 3.0 FORTRAN = f90 OPTS = -O3 DRVOPTS = $(OPTS) NOOPT = -g LOADER = f90 LOADOPTS = BLAS: /lib/libsci.a except for SNRM2 and SCNRM2 (use Fortran versions) Notes: 1. The Cray compilers implement a complex divide without scaling. To run the complex linear equation tests on the T3D, I had to modify SLABAD to take the square root of overflow and underflow. I ran the eigenvalue tests with the default version of SLABAD. 2. I also needed the Fortran SNRM2 when running the real linear equation tests on a CRAY C90. 3. Set ILAENV=0 for ISPEC=10 and ISPEC=11 in LAPACK/SRC/ilaenv.f, as well as the specialized versions of ILAENV in TESTING/LIN/, TESTING/EIG/, TIMING/LIN/, and TIMING/EIG/. Test status: Expected failures in sgd.out and cgd.out; Failure in ssg.in (under investigation); ------- ssg.out ------- SSG: NB = 3, NBMIN = 2, NX = 1 SDRVSG: SSYGVX(V,AU) returned INFO= 1. N= 3, JTYPE= 10, ISEED=( 458, 2510, 3431, 397) SSG -- Real Symmetric Generalized eigenvalue problem Matrix types (see xDRVSG for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense or Banded Symmetric Matrices: 8=Evenly spaced eigenvals. 15=Matrix with small random entries. 9=Geometrically spaced eigenvals. 16=Evenly spaced eigenvals, KA=1, KB=1. 10=Clustered eigenvalues. 17=Evenly spaced eigenvals, KA=2, KB=1. 11=Large, evenly spaced eigenvals. 18=Evenly spaced eigenvals, KA=2, KB=2. 12=Small, evenly spaced eigenvals. 19=Evenly spaced eigenvals, KA=3, KB=1. 13=Matrix with random O(1) entries. 20=Evenly spaced eigenvals, KA=3, KB=2. 14=Matrix with large random entries. 21=Evenly spaced eigenvals, KA=3, KB=3. Tests performed: ( For each pair (A,B), where A is of the given type and B is a random well-conditioned matrix. D is diagonal, and Z is orthogonal. ) 1 = SSYGV, with ITYPE=1 and UPLO='U': | A Z - B Z D | / ( |A| |Z| n ulp ) 2 = SSPGV, with ITYPE=1 and UPLO='U': | A Z - B Z D | / ( |A| |Z| n ulp ) 3 = SSBGV, with ITYPE=1 and UPLO='U': | A Z - B Z D | / ( |A| |Z| n ulp ) 4 = SSYGV, with ITYPE=1 and UPLO='L': | A Z - B Z D | / ( |A| |Z| n ulp ) 5 = SSPGV, with ITYPE=1 and UPLO='L': | A Z - B Z D | / ( |A| |Z| n ulp ) 6 = SSBGV, with ITYPE=1 and UPLO='L': | A Z - B Z D | / ( |A| |Z| n ulp ) 7 = SSYGV, with ITYPE=2 and UPLO='U': | A B Z - Z D | / ( |A| |Z| n ulp ) 8 = SSPGV, with ITYPE=2 and UPLO='U': | A B Z - Z D | / ( |A| |Z| n ulp ) 9 = SSPGV, with ITYPE=2 and UPLO='L': | A B Z - Z D | / ( |A| |Z| n ulp ) 10 = SSPGV, with ITYPE=2 and UPLO='L': | A B Z - Z D | / ( |A| |Z| n ulp ) 11 = SSYGV, with ITYPE=3 and UPLO='U': | B A Z - Z D | / ( |A| |Z| n ulp ) 12 = SSPGV, with ITYPE=3 and UPLO='U': | B A Z - Z D | / ( |A| |Z| n ulp ) 13 = SSYGV, with ITYPE=3 and UPLO='L': | B A Z - Z D | / ( |A| |Z| n ulp ) 14 = SSPGV, with ITYPE=3 and UPLO='L': | B A Z - Z D | / ( |A| |Z| n ulp ) Matrix order= 3, type=10, seed= 458,2510,3431, 397, result 53 is 3.518E+13 SSG: 1 out of 10288 tests failed to pass the threshold ----- Date reported: April, 1999 ======================================================================= ======================================================================= DCG ALPHA LX164 OS: Alpha RedHat Linux 6.0 (kernel 2.2.5-16) g77 (version egcs-2.91.66) LAPACK, version 3.0 + update FORTRAN = g77 OPTS = -funroll-all-loops -fno-f2c -O3 DRVOPTS = $(OPTS) NOOPT = LOADER = g77 LOADOPTS = ARCH = ar ARCHFLAGS= cr RANLIB = ranlib Notes: (1)Set ILAENV=0 for ISPEC=10 and ISPEC=11 in LAPACK/SRC/ilaenv.f, as well as the specialized versions of ILAENV in TESTING/LIN/, TESTING/EIG/, TIMING/LIN/, and TIMING/EIG/. Test status: Expected failures in sgd.out and cgd.out; Minor failures of SPB and SLS in stest.out and ctest.out; Failure in csvd.out and minor failure in zsep.out; Failure in cgbak.out (under investigation, optimization?); --------- cgbak.out --------- .. test output of CGGBAK .. value of largest test error = 0.796E+04 example number where CGGBAL info is not 0 = 0 example number where CGGBAK(L) info is not 0 = 0 example number where CGGBAK(R) info is not 0 = 0 example number having largest error = 5 number of examples where info is not 0 = 0 total number of examples tested = 10 End of tests Total time used = 0.01 seconds ----- Date reported: March, 2000 ======================================================================= ======================================================================= DEC 3000-500 ALPHA OS: OSF1 V4.0 (Rev. 1091) COMPILER: F90 LAPACK, version 3.0 + update FORTRAN = f77 OPTS = -O4 -fpe1 DRVOPTS = $(OPTS) NOOPT = LOADER = f77 LOADOPTS = ARCH = ar ARCHFLAGS= cr RANLIB = ranlib BLASLIB = -ldxml Test status: Expected failures in sgd.out and cgd.out; Minor failures of SPB and SLS in stest.out and ctest.out; Minor failures in ssep.out/csep.out and ssvd.out/csvd.out; Failure in cgbak.out (under investigation, optimization?); If (-O5 -fpe1 level of optimization) is used, failures in STP,DTP,CTP, and ZTP tests in _test.out; --------- cgbak.out --------- .. test output of CGGBAK .. value of largest test error = 0.796E+04 example number where CGGBAL info is not 0 = 0 example number where CGGBAK(L) info is not 0 = 0 example number where CGGBAK(R) info is not 0 = 0 example number having largest error = 5 number of examples where info is not 0 = 0 total number of examples tested = 10 End of tests Total time used = 0.01 seconds ----- Date reported: November, 1999 ======================================================================= ======================================================================= Hewlett Packard HP 9000 Model 735 OS: HP-UX A.09.05 F77, HP-UX Release 10.0 LAPACK, version 3.0 FORTRAN = f77 OPTS = +O4 +U77 DRVOPTS = $(OPTS) -K NOOPT = +U77 LOADER = f77 LOADOPTS = -Aa +U77 ARCH = ar ARCHFLAGS= cr RANLIB = echo BLASLIB = -lblas (HP BLAS) Test status: As yet, Unable to run xeigtst_ tests due to swap space problem Notes: 1. Due to unscaled complex divide, you must set LAPACK/SRC/slabad.f and dlabad.f to take the square root of SMLNUM and BIGNUM as for the Cray. 2. LAPACK/INSTALL/testieee test failed for NaN arithmetic. Set ILAENV=0 for ISPEC=10 and ISPEC=11 in ilaenv.f. ----- Date reported: April, 1999 ======================================================================= ======================================================================= IBM RS/6000 Power3 OS: AIX VERSION 4.3.3 COMPILER: XL FORTRAN Compiler Version 6.1.0.0 LAPACK, version 3.0 + UPDATE FORTRAN = xlf OPTS = -O3 -qarch=pwr3 -qmaxmem=-1 DRVOPTS = $(OPTS) NOOPT = LOADER = xlf LOADOPTS = ARCH = ar ARCHFLAGS= cr RANLIB = ranlib BLASLIB = -lessl BLAS: (ESSL version 3.1.1.0) Notes: (1) use XLF-supplied routine ETIME_ for second.f and dsecnd.f (2) Remove all optimization for SRC/cgtrfs.f (xlf -qarch=pwr3) SRC/zgtrfs.f TESTING/LIN/cgtt05.f TESTING/LIN/zgtt05.f Example error message: "cgtrfs.f", 1500-008 (S) COMPILER LIMIT EXCEEDED in cgtrfs: Program too complicated to be compiled. Compilation ended. Reduce the complexity of the program and recompile, or lower the level of optimization and recompile. Test status: Expected failures in _gd.out; RMAX failures in sec.out/dec.out; Failure in zgbak.out (under investigation, optimization?); Failure in ssvd.out/dsvd.out/zsvd.out (under investigation); Minors failure in ssep.out and snep.out; Failures in csep.out/zsep.out (under investigation). -------- dec.out ------- Tests of the Nonsymmetric eigenproblem condition estimation routines DLALN2, DLASY2, DLANV2, DLAEXC, DTRSYL, DTREXC, DTRSNA, DTRSEN, DLAQTR Relative machine precision (EPS) = .222045D-15 Safe minimum (SFMIN) = .222507-307 Routines pass computational tests if test ratio is less than 20.00 DEC routines passed the tests of the error exits ( 35 tests done) Error in DLANV2: RMAX = .117D+16 LMAX = 16067 NINFO= 0 KNT= 20736 Error in DLAEXC: RMAX = .808D+15 LMAX = 11125 NINFO= 148 0 KNT= 42258 Error in DTREXC: RMAX = .686D+15 LMAX = 14 NINFO= 0 0 0 KNT= 14 Error in DTRSEN: RMAX = .728D+05 .152D+01 .152D+01 LMAX = 76 68 68 NINFO= 0 0 0 KNT= 78 End of tests Total time used = 6.65 seconds -------- zgbak.out --------- .. test output of ZGGBAK .. value of largest test error = .796D+04 example number where ZGGBAL info is not 0 = 0 example number where ZGGBAK(L) info is not 0 = 0 example number where ZGGBAK(R) info is not 0 = 0 example number having largest error = 5 number of examples where info is not 0 = 0 total number of examples tested = 10 End of tests Total time used = .02 seconds -------- ssvd.out -------- SVD: NB = 1, NBMIN = 2, NX = 1, NRHS = 2 SCHKBD: SBDSDC(vects) returned INFO= 1. M= 30, N= 40, JTYPE= 12, ISEED=( 2195, 634, 3653, 1853) SBD -- Real Singular Value Decomposition Matrix types (see xCHKBD for details): Diagonal matrices: 1: Zero 5: Clustered entries 2: Identity 6: Large, evenly spaced entries 3: Evenly spaced entries 7: Small, evenly spaced entries 4: Geometrically spaced entries General matrices: 8: Evenly spaced sing. vals. 12: Small, evenly spaced sing vals 9: Geometrically spaced sing vals 13: Random, O(1) entries 10: Clustered sing. vals. 14: Random, scaled near overflow 11: Large, evenly spaced sing vals 15: Random, scaled near underflow Test ratios: (B: bidiagonal, S: diagonal, Q, P, U, and V: orthogonal X: m x nrhs, Y = Q' X, and Z = U' Y) 1: norm( A - Q B P' ) / ( norm(A) max(m,n) ulp ) 2: norm( I - Q' Q ) / ( m ulp ) 3: norm( I - P' P ) / ( n ulp ) 4: norm( B - U S V' ) / ( norm(B) min(m,n) ulp ) 5: norm( Y - U Z ) / ( norm(Z) max(min(m,n),k) ulp ) 6: norm( I - U' U ) / ( min(m,n) ulp ) 7: norm( I - V' V ) / ( min(m,n) ulp ) 8: Test ordering of S (0 if nondecreasing, 1/ulp otherwise) 9: norm( S - S2 ) / ( norm(S) ulp ), where S2 is computed without computing U and V' 10: Sturm sequence test (0 if sing. vals of B within THRESH of S) 11: norm( A - (QU) S (V' P') ) / ( norm(A) max(m,n) ulp ) 12: norm( X - (QU) Z ) / ( |X| max(M,k) ulp ) 13: norm( I - (QU)'(QU) ) / ( M ulp ) 14: norm( I - (V' P') (P V) ) / ( N ulp ) M= 30, N= 40, type 12, seed=2195, 634,3653,1853, test(15)= .8389E+07 SBD: 1 out of 5510 tests failed to pass the threshold *** Error code from SCHKBD = 1 -------- csep.out -------- SEP: NB = 3, NBMIN = 2, NX = 9 All tests for CST passed the threshold ( 3276 tests run) CST -- Complex Hermitian eigenvalue problem Matrix types (see xDRVST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Hermitian Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. Tests performed: See cdrvst.f Matrix order= 20, type= 9, seed=1494,3156,1807,2209, result 47 is 1.006E+04 Matrix order= 20, type= 9, seed=1494,3156,1807,2209, result 101 is 114.52 CST drivers: 2 out of 11664 tests failed to pass the threshold -------- zsep.out -------- SEP: NB = 3, NBMIN = 2, NX = 9 All tests for ZST passed the threshold ( 3276 tests run) ZST -- Complex Hermitian eigenvalue problem Matrix types (see xDRVST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Hermitian Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. Tests performed: See cdrvst.f Matrix order= 5, type=10, seed= 791,4087,1614,3401, result 46 is NaNQ Matrix order= 5, type=10, seed= 791,4087,1614,3401, result 47 is 4.504D+15 Matrix order= 5, type=10, seed= 791,4087,1614,3401, result 48 is NaNQ ZST drivers: 3 out of 11664 tests failed to pass the threshold ----- Date reported: November, 1999 ======================================================================= ======================================================================= IBM RISC/6000 model 550 OS: AIX VERSION 4.1 COMPILER: XL FORTRAN Compiler Version 4.1 LAPACK, version 3.0 FORTRAN = xlf OPTS = -O3 -qmaxmem=-1 (except -O2 for LAPACK/SRC/cgelsx.f ) (except -O2 for LAPACK/TESTING/LIN/zchktp.f ) (except -O2 for LAPACK/TIMING/EIG/deispack.f and LAPACK/TIMING/EIG/zeispack.f ) DRVOPTS = $(OPTS) NOOPT = LOADER = xlf LOADOPTS = ARCH = ar ARCHFLAGS= cr RANLIB = ranlib BLASLIB = -lessl BLAS: (ESSL version 2.2.2.2) Notes: (1) use XLF-supplied routine ETIME_ for second.f and dsecnd.f Test status: Expected failures in _gd.out; Failure in dsvd.out (under investigation); Failures in dsep.out and zsep.out (under investigation). -------- dsvd.out -------- SVD: NB = 1, NBMIN = 2, NX = 1, NRHS = 2 DCHKBD: DBDSDC(vects) returned INFO= 1. M= 30, N= 40, JTYPE= 12, ISEED=( 2195, 634, 3653, 1853) DBD -- Real Singular Value Decomposition Matrix types (see xCHKBD for details): Diagonal matrices: 1: Zero 5: Clustered entries 2: Identity 6: Large, evenly spaced entries 3: Evenly spaced entries 7: Small, evenly spaced entries 4: Geometrically spaced entries General matrices: 8: Evenly spaced sing. vals. 12: Small, evenly spaced sing vals 9: Geometrically spaced sing vals 13: Random, O(1) entries 10: Clustered sing. vals. 14: Random, scaled near overflow 11: Large, evenly spaced sing vals 15: Random, scaled near underflow Test ratios: (B: bidiagonal, S: diagonal, Q, P, U, and V: orthogonal X: m x nrhs, Y = Q' X, and Z = U' Y) 1: norm( A - Q B P' ) / ( norm(A) max(m,n) ulp ) 2: norm( I - Q' Q ) / ( m ulp ) 3: norm( I - P' P ) / ( n ulp ) 4: norm( B - U S V' ) / ( norm(B) min(m,n) ulp ) 5: norm( Y - U Z ) / ( norm(Z) max(min(m,n),k) ulp ) 6: norm( I - U' U ) / ( min(m,n) ulp ) 7: norm( I - V' V ) / ( min(m,n) ulp ) 8: Test ordering of S (0 if nondecreasing, 1/ulp otherwise) 9: norm( S - S2 ) / ( norm(S) ulp ), where S2 is computed without computing U and V' 10: Sturm sequence test (0 if sing. vals of B within THRESH of S) 11: norm( A - (QU) S (V' P') ) / ( norm(A) max(m,n) ulp ) 12: norm( X - (QU) Z ) / ( |X| max(M,k) ulp ) 13: norm( I - (QU)'(QU) ) / ( M ulp ) 14: norm( I - (V' P') (P V) ) / ( N ulp ) M= 30, N= 40, type 12, seed=2195, 634,3653,1853, test(15)= .4504E+16 DBD: 1 out of 5510 tests failed to pass the threshold *** Error code from DCHKBD = 1 -------- dsep.out -------- SEP: NB = 3, NBMIN = 2, NX = 5 DST -- Real Symmetric eigenvalue problem Matrix types (see DCHKST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Symmetric Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. 16=Positive definite, evenly spaced eigenvalues 17=Positive definite, geometrically spaced eigenvlaues 18=Positive definite, clustered eigenvalues 19=Positive definite, small evenly spaced eigenvalues 20=Positive definite, large evenly spaced eigenvalues 21=Diagonally dominant tridiagonal, geometrically spaced eigenvalues Test performed: see DCHKST for details. N= 40, seed=1451, 418,3916,1509, type 9, test(35)= .335E+12 N= 40, seed=1451, 418,3916,1509, type 9, test(36)= .269E+15 DST: 2 out of 4662 tests failed to pass the threshold All tests for DST drivers passed the threshold ( 14256 tests run) -------- zsep.out -------- SEP: NB = 3, NBMIN = 2, NX = 0 ZST -- Complex Hermitian eigenvalue problem Matrix types (see ZCHKST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Hermitian Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. 16=Positive definite, evenly spaced eigenvalues 17=Positive definite, geometrically spaced eigenvlaues 18=Positive definite, clustered eigenvalues 19=Positive definite, small evenly spaced eigenvalues 20=Positive definite, large evenly spaced eigenvalues 21=Diagonally dominant tridiagonal, geometrically spaced eigenvalues Test performed: see ZCHKST for details. Matrix order= 40, type= 9, seed= 419, 892, 345,2089, result 35 is 2.756D+12 Matrix order= 40, type= 9, seed= 419, 892, 345,2089, result 36 is 3.073D+14 ZST: 2 out of 4662 tests failed to pass the threshold All tests for ZST drivers passed the threshold ( 11664 tests run) ----- Date reported: April, 1999 ======================================================================= ======================================================================= Intel Pentium 120MHz (IBM Thinkpad 760E) Linux 2.0.34 g77 (version egcs-2.91.60) LAPACK, version 3.0 FORTRAN = g77 OPTS = -g DRVOPTS = $(OPTS) NOOPT = -g LOADER = g77 LOADOPTS = -g ARCH = ar ARCHFLAGS= cr RANLIB = ranlib BLASLIB = Fortran 77 BLAS Test status: Expected failures in _gd.out; Two failures in ded.out (DES, DSX); One failure in dgg.out (DGG); ------- ded.out ------- DGEES passed the tests of the error exits ( 6 tests done) DDRVES: DGEES1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) DES -- Real Schur Form Decomposition Driver Matrix types (see DDRVES for details): Special Matrices: 1=Zero matrix. 5=Diagonal: geometr. spaced entries. 2=Identity matrix. 6=Diagonal: clustered entries. 3=Transposed Jordan block. 7=Diagonal: large, evenly spaced. 4=Diagonal: evenly spaced entries. 8=Diagonal: small, evenly spaced. Dense, Non-Symmetric Matrices: 9=Well-cond., evenly spaced eigenvals. 14=Ill-cond., geomet. spaced eigenals. 10=Well-cond., geom. spaced eigenvals. 15=Ill-conditioned, clustered e.vals. 11=Well-conditioned, clustered e.vals. 16=Ill-cond., random complex 12=Well-cond., random complex 17=Ill-cond., large rand. complx 13=Ill-conditioned, evenly spaced. 18=Ill-cond., small rand. complx 19=Matrix with random O(1) entries. 21=Matrix with small random entries. 20=Matrix with large random entries. Tests performed with test threshold = 20.00 ( A denotes A on input and T denotes A on output) 1 = 0 if T in Schur form (no sort), 1/ulp otherwise 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort) 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort), 1/ulp otherwise 5 = 0 if T same no matter if VS computed (no sort), 1/ulp otherwise 6 = 0 if WR, WI same no matter if VS computed (no sort), 1/ulp otherwise 7 = 0 if T in Schur form (sort), 1/ulp otherwise 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort) 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort), 1/ulp otherwise 11 = 0 if T same no matter if VS computed (sort), 1/ulp otherwise 12 = 0 if WR, WI same no matter if VS computed (sort), 1/ulp otherwise 13 = 0 if sorting succesful, 1/ulp otherwise N= 5, IWK= 2, seed= 100,2082, 33, 613, type 17, test( 7)= 0.450E+16 DES: 1 out of 3270 tests failed to pass the threshold *** Error code from DGEES = 6 ... DGEESX passed the tests of the error exits ( 7 tests done) DGET24: DGEESX1 returned INFO= 6. N= 5, JTYPE= 17, ISEED=( 100, 2082, 33, 613) DSX -- Real Schur Form Decomposition Expert Driver Matrix types (see DDRVSX for details): Special Matrices: 1=Zero matrix. 5=Diagonal: geometr. spaced entries. 2=Identity matrix. 6=Diagonal: clustered entries. 3=Transposed Jordan block. 7=Diagonal: large, evenly spaced. 4=Diagonal: evenly spaced entries. 8=Diagonal: small, evenly spaced. Dense, Non-Symmetric Matrices: 9=Well-cond., evenly spaced eigenvals. 14=Ill-cond., geomet. spaced eigenals. 10=Well-cond., geom. spaced eigenvals. 15=Ill-conditioned, clustered e.vals. 11=Well-conditioned, clustered e.vals. 16=Ill-cond., random complex 12=Well-cond., random complex 17=Ill-cond., large rand. complx 13=Ill-conditioned, evenly spaced. 18=Ill-cond., small rand. complx 19=Matrix with random O(1) entries. 21=Matrix with small random entries. 20=Matrix with large random entries. Tests performed with test threshold = 20.00 ( A denotes A on input and T denotes A on output) 1 = 0 if T in Schur form (no sort), 1/ulp otherwise 2 = | A - VS T transpose(VS) | / ( n |A| ulp ) (no sort) 3 = | I - VS transpose(VS) | / ( n ulp ) (no sort) 4 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (no sort), 1/ulp otherwise 5 = 0 if T same no matter if VS computed (no sort), 1/ulp otherwise 6 = 0 if WR, WI same no matter if VS computed (no sort), 1/ulp otherwise 7 = 0 if T in Schur form (sort), 1/ulp otherwise 8 = | A - VS T transpose(VS) | / ( n |A| ulp ) (sort) 9 = | I - VS transpose(VS) | / ( n ulp ) (sort) 10 = 0 if WR+sqrt(-1)*WI are eigenvalues of T (sort), 1/ulp otherwise 11 = 0 if T same no matter what else computed (sort), 1/ulp otherwise 12 = 0 if WR, WI same no matter what else computed (sort), 1/ulp otherwise 13 = 0 if sorting succesful, 1/ulp otherwise 14 = 0 if RCONDE same no matter what else computed, 1/ulp otherwise 15 = 0 if RCONDv same no matter what else computed, 1/ulp otherwise 16 = | RCONDE - RCONDE(precomputed) | / cond(RCONDE), 17 = | RCONDV - RCONDV(precomputed) | / cond(RCONDV), N= 5, IWK= 2, seed= 100,2082, 33, 613, type 17, test( 7)= 0.450E+16 DSX: 1 out of 3500 tests failed to pass the threshold ------- dgg.out ------- DGG: NB = 2, NBMIN = 2, NS = 4, MAXB = 2, NBCOL = 2 DCHKGG: DHGEQZ(E) returned INFO= 9. N= 16, JTYPE= 18, ISEED=( 740, 2515, 3243, 3753) DGG -- Real Generalized eigenvalue problem Matrix types (see DCHKGG for details): Special Matrices: (J'=transposed Jordan block) 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J',J') 6=(diag(J',I), diag(I,J')) Diagonal Matrices: ( D=diag(0,1,2,...) ) 7=(D,I) 9=(large*D, small*I) 11=(large*I, small*D) 13=(large*D, large*I) 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) 14=(small*D, small*I) 15=(D, reversed D) Matrices Rotated by Random Orthogonal Matrices U, V: 16=Transposed Jordan Blocks 19=geometric alpha, beta=0,1 17=arithm. alpha&beta 20=arithmetic alpha, beta=0,1 18=clustered alpha, beta=0,1 21=random alpha, beta=0,1 Large & Small Matrices: 22=(large, small) 23=(small,large) 24=(small,small) 25=(large,large) 26=random O(1) matrices. Tests performed: (H is Hessenberg, S is Schur, B, T, P are triangular, U, V, Q, and Z are orthogonal, l and r are the appropriate left and right eigenvectors, resp., a is alpha, b is beta, and ' means transpose.) 1 = | A - U H V' | / ( |A| n ulp ) 2 = | B - U T V' | / ( |B| n ulp ) 3 = | I - UU' | / ( n ulp ) 4 = | I - VV' | / ( n ulp ) 5 = | H - Q S Z' | / ( |H| n ulp ) 6 = | T - Q P Z' | / ( |T| n ulp ) 7 = | I - QQ' | / ( n ulp ) 8 = | I - ZZ' | / ( n ulp ) 9 = max | ( b S - a P )' l | / const. 10 = max | ( b H - a T )' l | / const. 11= max | ( b S - a P ) r | / const. 12 = max | ( b H - a T ) r | / const. Matrix order= 16, type=18, seed= 740,2515,3243,3753, result 5 is 4.504E+15 DGG: 1 out of 2177 tests failed to pass the threshold *** Error code from DCHKGG = 9 All tests for DGG drivers passed the threshold ( 1274 tests run) ----- Date reported: May, 1999 ======================================================================= ======================================================================= Intel Pentium II 300MHz RedHat Linux 2.2.5-15 g77 (version egcs-2.91.66) LAPACK, version 3.0 + UPDATE FORTRAN = g77 OPTS = -funroll-all-loops -fno-f2c -O3 DRVOPTS = $(OPTS) NOOPT = LOADER = g77 LOADOPTS = $(OPTS) ARCH = ar ARCHFLAGS= cr RANLIB = ranlib BLASLIB = Fortran 77 BLAS Test status: Expected failures in _gd.out; Failure in cgbak.out (under investigation); Failures in ssep.out/csep.out (under investigation); --------- cgbak.out --------- .. test output of CGGBAK .. value of largest test error = 0.796E+04 example number where CGGBAL info is not 0 = 0 example number where CGGBAK(L) info is not 0 = 0 example number where CGGBAK(R) info is not 0 = 0 example number having largest error = 5 number of examples where info is not 0 = 0 total number of examples tested = 10 End of tests Total time used = 0.04 seconds -------- ssep.out -------- SEP: NB = 3, NBMIN = 2, NX = 9 SST -- Real Symmetric eigenvalue problem Matrix types (see SCHKST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Symmetric Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. 16=Positive definite, evenly spaced eigenvalues 17=Positive definite, geometrically spaced eigenvlaues 18=Positive definite, clustered eigenvalues 19=Positive definite, small evenly spaced eigenvalues 20=Positive definite, large evenly spaced eigenvalues 21=Diagonally dominant tridiagonal, geometrically spaced eigenvalues Test performed: see SCHKST for details. N= 20, seed= 443,2933, 429,1581, type 9, test(35)= 0.224E+05 N= 20, seed= 443,2933, 429,1581, type 9, test(36)= 0.207E+07 SST: 2 out of 4662 tests failed to pass the threshold -------- csep.out -------- SEP: NB = 3, NBMIN = 2, NX = 9 CST -- Complex Hermitian eigenvalue problem Matrix types (see CCHKST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Hermitian Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. 16=Positive definite, evenly spaced eigenvalues 17=Positive definite, geometrically spaced eigenvlaues 18=Positive definite, clustered eigenvalues 19=Positive definite, small evenly spaced eigenvalues 20=Positive definite, large evenly spaced eigenvalues 21=Diagonally dominant tridiagonal, geometrically spaced eigenvalues Test performed: see CCHKST for details. Matrix order= 20, type= 9, seed=1052,3651,3662,3633, result 35 is 88.19 Matrix order= 20, type= 9, seed=1052,3651,3662,3633, result 36 is 2616.94 CST: 2 out of 4662 tests failed to pass the threshold CST -- Complex Hermitian eigenvalue problem Matrix types (see xDRVST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Hermitian Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. Tests performed: See cdrvst.f Matrix order= 20, type= 9, seed=1494,3156,1807,2209, result 46 is 8.389E+06 Matrix order= 20, type= 9, seed=1494,3156,1807,2209, result 47 is 8.389E+06 CST drivers: 2 out of 11664 tests failed to pass the threshold ----- Date reported: November, 1999 ======================================================================= ======================================================================= Intel PentiumII PC OS: Linux (SuSE 6.1) COMPILER: Portland Group pgf77, version 3.0 COMPILER OPTIONS: -tp p6 -pc 64 -mp -O2 -Munroll BLAS: Optimized BLAS for PentiumII/Pro, obtained from http://www.cs.utk.edu/~ghenry/distrib/ LAPACK, version 3.0 Test status: Expected failures in _gd.out; ----- Date reported: October, 1999 ======================================================================= ======================================================================= Intel Pentium PPro OS: Windows NT 4.0 COMPILER: Watcom Fortran 77/32 Compiler Version 11.0 LAPACK, version 3.0 FORTRAN = wfc386 OPTS = -EXP -NOER -NOR DRVOPTS = -EXP -NOER -NOR NOOPT = -EXP -NOER -NOR LOADER = wlink LOADOPTS = ARCH = wlib ARCHFLAGS= -b -fa RANLIB = echo BLASLIB = ..\..\blas_win32.lib (Fortran 77 reference implementation) Notes: (1) separate LAPACK distribution file: http://www.netlib.org/lapack/lapack-pc-wfc.zip (2) use CLOCK() for second.f and dsecnd.f (3) Set ILAENV=0 for ISPEC=10 and ISPEC=11 in lapack\src\ilaenv.f, as well as the specialized versions of ILAENV in testing\lin\, testing\eig\, timing\lin\, and timing\eig\. Test status: Expected failures in _gd.out; ----- Date reported: August, 1999 ======================================================================= ======================================================================= Intel Pentium PPro OS: Windows NT 4.0 COMPILER: Digital Fortran LAPACK, version 3.0 + UPDATES FORTRAN = df OPTS = -optimize:2 DRVOPTS = $(OPTS) NOOPT = -optimize:0 LOADER = $(FORTRAN) LOADOPTS = ARCH = lib ARCHFLAGS= -out: RANLIB = echo BLASLIB = ..\..\blas_win32.lib (Fortran 77 reference implementation) Notes: (1) separate LAPACK distribution file: http://www.netlib.org/lapack/lapack-pc-df.zip (2) use SECNDS() for second.f and dsecnd.f (3) Set ILAENV=0 for ISPEC=10 and ISPEC=11 in lapack\src\ilaenv.f, as well as the specialized versions of ILAENV in testing\lin\, testing\eig\, timing\lin\, and timing\eig\. Test status: Expected failures in _gd.out; ----- Date reported: August, 1999 ======================================================================= ======================================================================= SGI Indigo, IRIX Release 6.5, IP28, f77, MIPSpro version 7.2.1 LAPACK, version 3.0 FORTRAN = f77 OPTS = -O3 -64 -mips4 -r10000 -OPT:IEEE_NaN_inf=ON DRVOPTS = $(OPTS) -static NOOPT = -64 -mips4 -r10000 -OPT:IEEE_NaN_inf=ON LOADER = f77 LOADOPTS = -O3 -64 -mips4 -r10000 -OPT:IEEE_NaN_inf=ON ARCH = ar ARCHFLAGS= cr RANLIB = echo BLASLIB = -lblas BLAS: -lblas (bug in SDOT, so must link with Fortran 77 SDOT) Notes: (1) Set SHELL = /sbin/sh in make.inc. (2) Compiler options -trapuv and -OPT:IEEE_NaN_inf=ON cannot be used together. Test status: Expected failures in _gd.out; Failures in stest.out, ssep.out and zsep.out. --------- stest.out --------- SLS: Least squares driver routines Matrix types (1-3: full rank, 4-6: rank deficient): 1 and 4. Normal scaling 2 and 5. Scaled near overflow 3 and 6. Scaled near underflow Test ratios: (1-2: SGELS, 3-6: SGELSX, 7-10: SGELSY, 11-14: SGELSS, 15-18: SGELSD) 1: norm( B - A * X ) / ( max(M,N) * norm(A) * norm(X) * EPS ) 2: norm( (A*X-B)' *A ) / ( max(M,N,NRHS) * norm(A) * norm(B) * EPS ) if TRANS='N' and M.GE.N or TRANS='T' and M.LT.N, otherwise check if X is in the row space of A or A' (overdetermined case) 3: norm(svd(A)-svd(R)) / ( min(M,N) * norm(svd(R)) * EPS ) 4: norm( B - A * X ) / ( max(M,N) * norm(A) * norm(X) * EPS ) 5: norm( (A*X-B)' *A ) / ( max(M,N,NRHS) * norm(A) * norm(B) * EPS ) 6: Check if X is in the row space of A or A' 7-10: same as 3-6 11-14: same as 3-6 15-18: same as 3-6 Messages: TRANS='N', M= 16, N= 1, NRHS= 15, NB= 20, type 3, test( 1)= 91.327 TRANS='T', M= 16, N= 2, NRHS= 15, NB= 3, type 3, test( 1)= 47.908 SLS drivers: 2 out of 65268 tests failed to pass the threshold -------- ssep.out -------- SST -- Real Symmetric eigenvalue problem Matrix types (see xDRVST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Symmetric Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. Tests performed: See sdrvst.f Matrix order= 40, type= 9, seed= 905, 436,1903, 257, result 71 is 4.204E+05 SST drivers: 1 out of 14256 tests failed to pass the threshold -------- zsep.out -------- ZST -- Complex Hermitian eigenvalue problem Matrix types (see ZCHKST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Hermitian Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. 16=Positive definite, evenly spaced eigenvalues 17=Positive definite, geometrically spaced eigenvlaues 18=Positive definite, clustered eigenvalues 19=Positive definite, small evenly spaced eigenvalues 20=Positive definite, large evenly spaced eigenvalues 21=Diagonally dominant tridiagonal, geometrically spaced eigenvalues Test performed: see ZCHKST for details. Matrix order= 40, type= 9, seed= 869,2319,1455, 761, result 35 is 9.007D+15 Matrix order= 40, type= 9, seed= 869,2319,1455, 761, result 36 is 9.007D+15 ZST: 2 out of 4662 tests failed to pass the threshold ----- Date reported: April, 1999 ======================================================================= ======================================================================= SGI Octane, IRIX Release 6.5, R12000 IP30, f77, MIPSpro version 7.3.0 LAPACK, version 3.0 + update FORTRAN = f77 OPTS = -g -DEBUG:subscript_check=ON -OPT:IEEE_NaN_inf=ON DRVOPTS = $(OPTS) -static -TENV:large_GOT:ON NOOPT = -g -DEBUG:subscript_check=ON -OPT:IEEE_NaN_inf=ON LOADER = f77 LOADOPTS = -g -DEBUG:subscript_check=ON -OPT:IEEE_NaN_inf=ON ARCH = ar ARCHFLAGS= cr RANLIB = echo BLASLIB = -lblas Notes: (1) Set SHELL = /sbin/sh in make.inc. (2) Compiler options -trapuv and -OPT:IEEE_NaN_inf=ON cannot be used together. And it seems that optimization also disables -OPT:IEEE_NaN_inf=ON, as the LAPACK/INSTALL/tstieee test fails if both are used. Test status: Expected failures in _gd.out; Minor failures (SPB and SLS) in stest.out; Minor failures in ssvd.out; Failures in ssep.out (under investigation); Failure in cgbak.out (under investigation); --------- stest.out --------- SPB: Symmetric positive definite band matrices Matrix types: 1. Random, CNDNUM = 2 5. Random, CNDNUM = sqrt(0.1/EPS) *2. First row and column zero 6. Random, CNDNUM = 0.1/EPS *3. Last row and column zero 7. Scaled near underflow *4. Middle row and column zero 8. Scaled near overflow (* - tests error exits from SPBTRF, no test ratios are computed) Test ratios: 1: norm( U' * U - A ) / ( N * norm(A) * EPS ), or norm( L * L' - A ) / ( N * norm(A) * EPS ) 2: norm( B - A * X ) / ( norm(A) * norm(X) * EPS ) 3: norm( X - XACT ) / ( norm(XACT) * CNDNUM * EPS ) 4: norm( X - XACT ) / ( norm(XACT) * CNDNUM * EPS ), refined 5: norm( X - XACT ) / ( norm(XACT) * (error bound) ) 6: (backward error) / EPS 7: RCOND * CNDNUM - 1.0 Messages: UPLO='L', N= 50, KD= 37, NRHS= 15, type 7, test( 3) = 39.913 SPB: 1 out of 3458 tests failed to pass the threshold SLS: Least squares driver routines Matrix types (1-3: full rank, 4-6: rank deficient): 1 and 4. Normal scaling 2 and 5. Scaled near overflow 3 and 6. Scaled near underflow Test ratios: (1-2: SGELS, 3-6: SGELSX, 7-10: SGELSY, 11-14: SGELSS, 15-18: SGELSD) 1: norm( B - A * X ) / ( max(M,N) * norm(A) * norm(X) * EPS ) 2: norm( (A*X-B)' *A ) / ( max(M,N,NRHS) * norm(A) * norm(B) * EPS ) if TRANS='N' and M.GE.N or TRANS='T' and M.LT.N, otherwise check if X is in the row space of A or A' (overdetermined case) 3: norm(svd(A)-svd(R)) / ( min(M,N) * norm(svd(R)) * EPS ) 4: norm( B - A * X ) / ( max(M,N) * norm(A) * norm(X) * EPS ) 5: norm( (A*X-B)' *A ) / ( max(M,N,NRHS) * norm(A) * norm(B) * EPS ) 6: Check if X is in the row space of A or A' 7-10: same as 3-6 11-14: same as 3-6 15-18: same as 3-6 Messages: TRANS='T', M= 50, N= 1, NRHS= 2, NB= 3, type 3, test( 1)= 139.96 TRANS='T', M= 50, N= 1, NRHS= 15, NB= 3, type 3, test( 1)= 1235.6 TRANS='T', M= 50, N= 1, NRHS= 15, NB= 3, type 3, test( 1)= 91.860 SLS drivers: 3 out of 65268 tests failed to pass the threshold -------- ssep.out -------- SEP: NB = 3, NBMIN = 2, NX = 9 SST -- Real Symmetric eigenvalue problem Matrix types (see SCHKST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Symmetric Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. 16=Positive definite, evenly spaced eigenvalues 17=Positive definite, geometrically spaced eigenvlaues 18=Positive definite, clustered eigenvalues 19=Positive definite, small evenly spaced eigenvalues 20=Positive definite, large evenly spaced eigenvalues 21=Diagonally dominant tridiagonal, geometrically spaced eigenvalues Test performed: see SCHKST for details. N= 20, seed= 443,2933, 429,1581, type 9, test(35)= 0.681E+04 N= 20, seed= 443,2933, 429,1581, type 9, test(36)= 0.195E+07 SST: 2 out of 4662 tests failed to pass the threshold SST -- Real Symmetric eigenvalue problem Matrix types (see xDRVST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Symmetric Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. Tests performed: See sdrvst.f Matrix order= 20, type= 9, seed=3966,3411,3597,2265, result 71 is 104.82 Matrix order= 20, type= 9, seed=3966,3411,3597,2265, result 72 is 61.70 SST drivers: 2 out of 14256 tests failed to pass the threshold --------- cgbak.out --------- .. test output of CGGBAK .. value of largest test error = 0.796E+04 example number where CGGBAL info is not 0 = 0 example number where CGGBAK(L) info is not 0 = 0 example number where CGGBAK(R) info is not 0 = 0 example number having largest error = 5 number of examples where info is not 0 = 0 total number of examples tested = 10 End of tests Total time used = 0.01 seconds ----- Date reported: December, 1999 ======================================================================= ======================================================================= SGI O2K, IRIX Release 6.5, R12000 IP27, f77, MIPSpro version 7.2.1.2 LAPACK, version 3.0 FORTRAN = f77 OPTS = -O3 -64 -mips4 -r10000 -OPT:IEEE_NaN_inf=ON DRVOPTS = $(OPTS) -static NOOPT = -64 -mips4 -r10000 -OPT:IEEE_NaN_inf=ON LOADER = f77 LOADOPTS = -O3 -64 -mips4 -r10000 -OPT:IEEE_NaN_inf=ON ARCH = ar ARCHFLAGS= cr RANLIB = echo BLASLIB = -lblas Notes: (1) Set SHELL = /sbin/sh in make.inc. (2) Compiler options -trapuv and -OPT:IEEE_NaN_inf=ON cannot be used together. Test status: Expected failures in _gd.out; Minor failures in stest.out; --------- stest.out --------- SLS: Least squares driver routines Matrix types (1-3: full rank, 4-6: rank deficient): 1 and 4. Normal scaling 2 and 5. Scaled near overflow 3 and 6. Scaled near underflow Test ratios: (1-2: SGELS, 3-6: SGELSX, 7-10: SGELSY, 11-14: SGELSS, 15-18: SGELSD) 1: norm( B - A * X ) / ( max(M,N) * norm(A) * norm(X) * EPS ) 2: norm( (A*X-B)' *A ) / ( max(M,N,NRHS) * norm(A) * norm(B) * EPS ) if TRANS='N' and M.GE.N or TRANS='T' and M.LT.N, otherwise check if X is in the row space of A or A' (overdetermined case) 3: norm(svd(A)-svd(R)) / ( min(M,N) * norm(svd(R)) * EPS ) 4: norm( B - A * X ) / ( max(M,N) * norm(A) * norm(X) * EPS ) 5: norm( (A*X-B)' *A ) / ( max(M,N,NRHS) * norm(A) * norm(B) * EPS ) 6: Check if X is in the row space of A or A' 7-10: same as 3-6 11-14: same as 3-6 15-18: same as 3-6 Messages: TRANS='N', M= 16, N= 1, NRHS= 15, NB= 20, type 3, test( 1)= 91.243 TRANS='T', M= 16, N= 2, NRHS= 15, NB= 3, type 3, test( 1)= 47.768 SLS drivers: 2 out of 65268 tests failed to pass the threshold ----- Date reported: May, 1999 ======================================================================= ======================================================================= SUN Ultra-2, Solaris 2.7, f77 (SC 5.0) LAPACK, version 3.0 + patches from release_notes.html FORTRAN = f77 OPTS = -f -dalign -native -xO5 -xarch=v8plusa DRVOPTS = $(OPTS) NOOPT = -f LOADER = f77 LOADOPTS = -f -dalign -native -xO5 -xarch=v8plusa ARCH = ar ARCHFLAGS= cr RANLIB = echo BLASLIB = -xlic_lib=sunperf BLAS: Sun Performance Library BLAS Notes: (1) If using "f90" instead of "f77", I strangely need to add "-lF77" to link line in LAPACK/TESTING/LIN/Makefile and LAPACK/TESTING/EIG/Makefile, or else the link fails with missing Fortran77 I/0 routines. Similarly for makefiles in LAPACK/TIMING. (2) If using "f90" instead of "f77" compiler, you MUST additionally supply "-ftrap=%none". The defaults for IEEE arithmetic using "f77" and "f90" are not the same! The f90 default is -ftrap=common. (Note that the default with f77 is -ftrap=%none.) See "man f90" for full details. Test status: Expected failures in _gd.out; Failure in dsvd.out and zsvd.out; One minor failure in zsep.out; -------- dsvd.out -------- DBD -- Real Singular Value Decomposition Matrix types (see xCHKBD for details): Diagonal matrices: 1: Zero 5: Clustered entries 2: Identity 6: Large, evenly spaced entries 3: Evenly spaced entries 7: Small, evenly spaced entries 4: Geometrically spaced entries General matrices: 8: Evenly spaced sing. vals. 12: Small, evenly spaced sing vals 9: Geometrically spaced sing vals 13: Random, O(1) entries 10: Clustered sing. vals. 14: Random, scaled near overflow 11: Large, evenly spaced sing vals 15: Random, scaled near underflow Test ratios: (B: bidiagonal, S: diagonal, Q, P, U, and V: orthogonal X: m x nrhs, Y = Q' X, and Z = U' Y) 1: norm( A - Q B P' ) / ( norm(A) max(m,n) ulp ) 2: norm( I - Q' Q ) / ( m ulp ) 3: norm( I - P' P ) / ( n ulp ) 4: norm( B - U S V' ) / ( norm(B) min(m,n) ulp ) 5: norm( Y - U Z ) / ( norm(Z) max(min(m,n),k) ulp ) 6: norm( I - U' U ) / ( min(m,n) ulp ) 7: norm( I - V' V ) / ( min(m,n) ulp ) 8: Test ordering of S (0 if nondecreasing, 1/ulp otherwise) 9: norm( S - S2 ) / ( norm(S) ulp ), where S2 is computed without computing U and V' 10: Sturm sequence test (0 if sing. vals of B within THRESH of S) 11: norm( A - (QU) S (V' P') ) / ( norm(A) max(m,n) ulp ) 12: norm( X - (QU) Z ) / ( |X| max(M,k) ulp ) 13: norm( I - (QU)'(QU) ) / ( M ulp ) 14: norm( I - (V' P') (P V) ) / ( N ulp ) M= 40, N= 30, type 16, seed=3445,2073,3188, 129, test( 9)= 0.4502E+16 DBD: 1 out of 5510 tests failed to pass the threshold ----- Date reported: April, 2000 ======================================================================= ======================================================================= SUN Ultra-2, Solaris 2.5.1, f77 (SC 5.0) LAPACK, version 3.0 FORTRAN = f77 OPTS = -u -f -dalign -native -xO5 -xarch=v8plusa DRVOPTS = $(OPTS) NOOPT = -u -f LOADER = f77 LOADOPTS = -f -dalign -native -xO5 -xarch=v8plusa ARCH = ar ARCHFLAGS= cr RANLIB = echo BLASLIB = -xlic_lib=sunperf BLAS: Sun Performance Library BLAS Test status: Expected failures in _gd.out; Two failures in ssep.out, one minor failure in zsep.out; IEEE warning exceptions of "Division by Zero" and "Invalid Operation" in ssep.out, dsep.out, csep.out, and zsep.out, as a result of ILAENV IEEECK test; -------- ssep.out -------- SEP: NB = 3, NBMIN = 2, NX = 0 All tests for SST passed the threshold ( 4662 tests run) SST -- Real Symmetric eigenvalue problem Matrix types (see xDRVST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Symmetric Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. Tests performed: See sdrvst.f Matrix order= 20, type= 9, seed=2570,2010,1676,1489, result 124 is 1.577E+05 Matrix order= 20, type= 9, seed=2570,2010,1676,1489, result 125 is 6.605E+05 SST drivers: 2 out of 14256 tests failed to pass the threshold -------- zsep.out -------- SEP: NB = 3, NBMIN = 2, NX = 9 All tests for ZST passed the threshold ( 4662 tests run) ZST -- Complex Hermitian eigenvalue problem Matrix types (see xDRVST for details): Special Matrices: 1=Zero matrix. 5=Diagonal: clustered entries. 2=Identity matrix. 6=Diagonal: large, evenly spaced. 3=Diagonal: evenly spaced entries. 7=Diagonal: small, evenly spaced. 4=Diagonal: geometr. spaced entries. Dense Hermitian Matrices: 8=Evenly spaced eigenvals. 12=Small, evenly spaced eigenvals. 9=Geometrically spaced eigenvals. 13=Matrix with random O(1) entries. 10=Clustered eigenvalues. 14=Matrix with large random entries. 11=Large, evenly spaced eigenvals. 15=Matrix with small random entries. Tests performed: See cdrvst.f Matrix order= 20, type=10, seed=3336, 516, 978,2569, result 71 is 59.27 ZST drivers: 1 out of 11664 tests failed to pass the threshold ---- Date reported: April, 1999 ======================================================================