numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/EIG/cchkdmd.f90 | 25781B | -rw-r--r-- |
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! This is a test program for checking the implementations of ! the implementations of the following subroutines ! ! CGEDMD, for computation of the ! Dynamic Mode Decomposition (DMD) ! CGEDMDQ, for computation of a ! QR factorization based compressed DMD ! ! Developed and supported by: ! =========================== ! Developed and coded by Zlatko Drmac, Faculty of Science, ! University of Zagreb; drmac@math.hr ! In cooperation with ! AIMdyn Inc., Santa Barbara, CA. ! ======================================================== ! How to run the code (compiler, link info) ! ======================================================== ! Compile as FORTRAN 90 (or later) and link with BLAS and ! LAPACK libraries. ! NOTE: The code is developed and tested on top of the ! Intel MKL library (versions 2022.0.3 and 2022.2.0), ! using the Intel Fortran compiler. ! ! For developers of the C++ implementation ! ======================================================== ! See the LAPACK++ and Template Numerical Toolkit (TNT) ! ! Note on a development of the GPU HP implementation ! ======================================================== ! Work in progress. See CUDA, MAGMA, SLATE. ! NOTE: The four SVD subroutines used in this code are ! included as a part of R&D and for the completeness. ! This was also an opportunity to test those SVD codes. ! If the scaling option is used all four are essentially ! equally good. For implementations on HP platforms, ! one can use whichever SVD is available. !............................................................ !............................................................ !............................................................ ! PROGRAM DMD_TEST use iso_fortran_env IMPLICIT NONE integer, parameter :: WP = real32 !............................................................ REAL(KIND=WP), PARAMETER :: ONE = 1.0_WP REAL(KIND=WP), PARAMETER :: ZERO = 0.0_WP COMPLEX(KIND=WP), PARAMETER :: CONE = ( 1.0_WP, 0.0_WP ) COMPLEX(KIND=WP), PARAMETER :: CZERO = ( 0.0_WP, 0.0_WP ) !............................................................ REAL(KIND=WP), ALLOCATABLE, DIMENSION(:) :: RES, & RES1, RESEX, SINGVX, SINGVQX, WORK INTEGER , ALLOCATABLE, DIMENSION(:) :: IWORK REAL(KIND=WP) :: WDUMMY(2) INTEGER :: IDUMMY(4), ISEED(4) REAL(KIND=WP) :: ANORM, COND, CONDL, CONDR, EPS, & TOL, TOL2, SVDIFF, TMP, TMP_AU, & TMP_FQR, TMP_REZ, TMP_REZQ, TMP_XW, & TMP_EX !............................................................ COMPLEX(KIND=WP) :: CMAX INTEGER :: LCWORK COMPLEX(KIND=WP), ALLOCATABLE, DIMENSION(:,:) :: A, AC, & AU, F, F0, F1, S, W, & X, X0, Y, Y0, Y1, Z, Z1 COMPLEX(KIND=WP), ALLOCATABLE, DIMENSION(:) :: CDA, CDR, & CDL, CEIGS, CEIGSA, CWORK COMPLEX(KIND=WP) :: CDUMMY(22), CDUM2X2(2,2) !............................................................ INTEGER :: K, KQ, LDF, LDS, LDA, LDAU, LDW, LDX, LDY, & LDZ, LIWORK, LWORK, M, N, LLOOP, NRNK INTEGER :: i, iJOBREF, iJOBZ, iSCALE, INFO, j, & NFAIL, NFAIL_AU, NFAIL_F_QR, NFAIL_REZ, & NFAIL_REZQ, NFAIL_SVDIFF, NFAIL_TOTAL, NFAILQ_TOTAL, & NFAIL_Z_XV, MODE, MODEL, MODER, WHTSVD INTEGER :: iNRNK, iWHTSVD, K_traj, LWMINOPT CHARACTER :: GRADE, JOBREF, JOBZ, PIVTNG, RSIGN, & SCALE, RESIDS, WANTQ, WANTR LOGICAL :: TEST_QRDMD !..... external subroutines (BLAS and LAPACK) EXTERNAL CAXPY, CGEEV, CGEMM, CGEMV, CLASCL !.....external subroutines DMD package ! subroutines under test EXTERNAL CGEDMD, CGEDMDQ !..... external functions (BLAS and LAPACK) EXTERNAL SCNRM2, SLAMCH REAL(KIND=WP) :: SCNRM2, SLAMCH EXTERNAL CLANGE REAL(KIND=WP) :: CLANGE EXTERNAL ICAMAX INTEGER ICAMAX EXTERNAL LSAME LOGICAL LSAME INTRINSIC ABS, INT, MIN, MAX, SIGN !............................................................ WRITE(*,*) 'COMPLEX CODE TESTING' ! The test is always in pairs : ( CGEDMD and CGEDMDQ) ! because the test includes comparing the results (in pairs). !..................................................................................... ! This code by default performs tests on CGEDMDQ ! Since the QR factorizations based algorithm is designed for ! single trajectory data, only single trajectory tests will ! be performed with xGEDMDQ. WANTQ = 'Q' WANTR = 'R' !................................................................................. EPS = SLAMCH( 'P' ) ! machine precision WP ! Global counters of failures of some particular tests NFAIL = 0 NFAIL_REZ = 0 NFAIL_REZQ = 0 NFAIL_Z_XV = 0 NFAIL_F_QR = 0 NFAIL_AU = 0 NFAIL_SVDIFF = 0 NFAIL_TOTAL = 0 NFAILQ_TOTAL = 0 DO LLOOP = 1, 4 WRITE(*,*) 'L Loop Index = ', LLOOP ! Set the dimensions of the problem ... READ(*,*) M WRITE(*,*) 'M = ', M ! ... and the number of snapshots. READ(*,*) N WRITE(*,*) 'N = ', N ! Test the dimensions IF ( ( MIN(M,N) == 0 ) .OR. ( M < N ) ) THEN WRITE(*,*) 'Bad dimensions. Required: M >= N > 0.' STOP END IF !............. ! The seed inside the LLOOP so that each pass can be reproduced easily. ISEED(1) = 4 ISEED(2) = 3 ISEED(3) = 2 ISEED(4) = 1 LDA = M LDF = M LDX = M LDY = M LDW = N LDZ = M LDAU = M LDS = N TMP_XW = ZERO TMP_AU = ZERO TMP_REZ = ZERO TMP_REZQ = ZERO SVDIFF = ZERO TMP_EX = ZERO ALLOCATE( A(LDA,M) ) ALLOCATE( AC(LDA,M) ) ALLOCATE( F(LDF,N+1) ) ALLOCATE( F0(LDF,N+1) ) ALLOCATE( F1(LDF,N+1) ) ALLOCATE( X(LDX,N) ) ALLOCATE( X0(LDX,N) ) ALLOCATE( Y(LDY,N+1) ) ALLOCATE( Y0(LDY,N+1) ) ALLOCATE( Y1(LDY,N+1) ) ALLOCATE( AU(LDAU,N) ) ALLOCATE( W(LDW,N) ) ALLOCATE( S(LDS,N) ) ALLOCATE( Z(LDZ,N) ) ALLOCATE( Z1(LDZ,N) ) ALLOCATE( RES(N) ) ALLOCATE( RES1(N) ) ALLOCATE( RESEX(N) ) ALLOCATE( CEIGS(N) ) ALLOCATE( SINGVX(N) ) ALLOCATE( SINGVQX(N) ) TOL = 10*M*EPS TOL2 = 10*M*N*EPS !............. DO K_traj = 1, 2 ! Number of intial conditions in the simulation/trajectories (1 or 2) COND = 1.0D4 CMAX = (1.0D1,1.0D1) RSIGN = 'F' GRADE = 'N' MODEL = 6 CONDL = 1.0D1 MODER = 6 CONDR = 1.0D1 PIVTNG = 'N' ! Loop over all parameter MODE values for CLATMR (+-1,..,+-6) DO MODE = 1, 6 ALLOCATE( IWORK(2*M) ) ALLOCATE( CDA(M) ) ALLOCATE( CDL(M) ) ALLOCATE( CDR(M) ) CALL CLATMR( M, M, 'N', ISEED, 'N', CDA, MODE, COND, & CMAX, RSIGN, GRADE, CDL, MODEL, CONDL, & CDR, MODER, CONDR, PIVTNG, IWORK, M, M, & ZERO, -ONE, 'N', A, LDA, IWORK(M+1), INFO ) DEALLOCATE( CDR ) DEALLOCATE( CDL ) DEALLOCATE( CDA ) DEALLOCATE( IWORK ) LCWORK = MAX(1,2*M) ALLOCATE( CEIGSA(M) ) ALLOCATE( CWORK(LCWORK) ) ALLOCATE( WORK(2*M) ) AC(1:M,1:M) = A(1:M,1:M) CALL CGEEV( 'N','N', M, AC, LDA, CEIGSA, CDUM2X2, 2, & CDUM2X2, 2, CWORK, LCWORK, WORK, INFO ) ! LAPACK CALL DEALLOCATE(WORK) DEALLOCATE(CWORK) TMP = ABS(CEIGSA(ICAMAX(M, CEIGSA, 1))) ! The spectral radius of A ! Scale the matrix A to have unit spectral radius. CALL CLASCL( 'G',0, 0, TMP, ONE, M, M, & A, LDA, INFO ) CALL CLASCL( 'G',0, 0, TMP, ONE, M, 1, & CEIGSA, M, INFO ) ANORM = CLANGE( 'F', M, M, A, LDA, WDUMMY ) IF ( K_traj == 2 ) THEN ! generate data as two trajectories ! with two inital conditions CALL CLARNV(2, ISEED, M, F(1,1) ) DO i = 1, N/2 CALL CGEMV( 'N', M, M, CONE, A, LDA, F(1,i), 1, & CZERO, F(1,i+1), 1 ) END DO X0(1:M,1:N/2) = F(1:M,1:N/2) Y0(1:M,1:N/2) = F(1:M,2:N/2+1) CALL CLARNV(2, ISEED, M, F(1,1) ) DO i = 1, N-N/2 CALL CGEMV( 'N', M, M, CONE, A, LDA, F(1,i), 1, & CZERO, F(1,i+1), 1 ) END DO X0(1:M,N/2+1:N) = F(1:M,1:N-N/2) Y0(1:M,N/2+1:N) = F(1:M,2:N-N/2+1) ELSE CALL CLARNV(2, ISEED, M, F(1,1) ) DO i = 1, N CALL CGEMV( 'N', M, M, CONE, A, M, F(1,i), 1, & CZERO, F(1,i+1), 1 ) END DO F0(1:M,1:N+1) = F(1:M,1:N+1) X0(1:M,1:N) = F0(1:M,1:N) Y0(1:M,1:N) = F0(1:M,2:N+1) END IF DEALLOCATE( CEIGSA ) !........................................................................ DO iJOBZ = 1, 4 SELECT CASE ( iJOBZ ) CASE(1) JOBZ = 'V' RESIDS = 'R' CASE(2) JOBZ = 'V' RESIDS = 'N' CASE(3) JOBZ = 'F' RESIDS = 'N' CASE(4) JOBZ = 'N' RESIDS = 'N' END SELECT DO iJOBREF = 1, 3 SELECT CASE ( iJOBREF ) CASE(1) JOBREF = 'R' CASE(2) JOBREF = 'E' CASE(3) JOBREF = 'N' END SELECT DO iSCALE = 1, 4 SELECT CASE ( iSCALE ) CASE(1) SCALE = 'S' CASE(2) SCALE = 'C' CASE(3) SCALE = 'Y' CASE(4) SCALE = 'N' END SELECT DO iNRNK = -1, -2, -1 NRNK = iNRNK DO iWHTSVD = 1, 3 ! Check all four options to compute the POD basis ! via the SVD. WHTSVD = iWHTSVD DO LWMINOPT = 1, 2 ! Workspace query for the minimal (1) and for the optimal ! (2) workspace lengths determined by workspace query. ! CGEDMD is always tested and its results are also used for ! comparisons with CGEDMDQ. X(1:M,1:N) = X0(1:M,1:N) Y(1:M,1:N) = Y0(1:M,1:N) CALL CGEDMD( SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, & M, N, X, LDX, Y, LDY, NRNK, TOL, & K, CEIGS, Z, LDZ, RES, & AU, LDAU, W, LDW, S, LDS, & CDUMMY, -1, WDUMMY, -1, IDUMMY, -1, INFO ) IF ( (INFO .EQ. 2) .OR. ( INFO .EQ. 3 ) & .OR. ( INFO < 0 ) ) THEN WRITE(*,*) 'Call to CGEDMD workspace query failed. & &Check the calling sequence and the code.' WRITE(*,*) 'The error code is ', INFO WRITE(*,*) 'The input parameters were ', & SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, & M, N, LDX, LDY, NRNK, TOL, LDZ, LDAU, LDW, LDS STOP ELSE !WRITE(*,*) '... done. Workspace length computed.' END IF LCWORK = INT(CDUMMY(LWMINOPT)) ALLOCATE(CWORK(LCWORK)) LIWORK = IDUMMY(1) ALLOCATE(IWORK(LIWORK)) LWORK = INT(WDUMMY(1)) ALLOCATE(WORK(LWORK)) CALL CGEDMD( SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, & M, N, X, LDX, Y, LDY, NRNK, TOL, & K, CEIGS, Z, LDZ, RES, & AU, LDAU, W, LDW, S, LDS, & CWORK, LCWORK, WORK, LWORK, IWORK, LIWORK, INFO ) IF ( INFO /= 0 ) THEN WRITE(*,*) 'Call to CGEDMD failed. & &Check the calling sequence and the code.' WRITE(*,*) 'The error code is ', INFO WRITE(*,*) 'The input parameters were ',& SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, & M, N, LDX, LDY, NRNK, TOL STOP END IF SINGVX(1:N) = WORK(1:N) !...... CGEDMD check point IF ( LSAME(JOBZ,'V') ) THEN ! Check that Z = X*W, on return from CGEDMD ! This checks that the returned eigenvectors in Z are ! the product of the SVD'POD basis returned in X ! and the eigenvectors of the Rayleigh quotient ! returned in W CALL CGEMM( 'N', 'N', M, K, K, CONE, X, LDX, W, LDW, & CZERO, Z1, LDZ ) TMP = ZERO DO i = 1, K CALL CAXPY( M, -CONE, Z(1,i), 1, Z1(1,i), 1) TMP = MAX(TMP, SCNRM2( M, Z1(1,i), 1 ) ) END DO TMP_XW = MAX(TMP_XW, TMP ) IF ( TMP_XW <= TOL ) THEN !WRITE(*,*) ' :) .... OK .........CGEDMD PASSED.' ELSE NFAIL_Z_XV = NFAIL_Z_XV + 1 WRITE(*,*) ':( .................CGEDMD FAILED!', & 'Check the code for implementation errors.' WRITE(*,*) 'The input parameters were ',& SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, & M, N, LDX, LDY, NRNK, TOL END IF END IF !...... CGEDMD check point IF ( LSAME(JOBREF,'R') ) THEN ! The matrix A*U is returned for computing refined Ritz vectors. ! Check that A*U is computed correctly using the formula ! A*U = Y * V * inv(SIGMA). This depends on the ! accuracy in the computed singular values and vectors of X. ! See the paper for an error analysis. ! Note that the left singular vectors of the input matrix X ! are returned in the array X. CALL CGEMM( 'N', 'N', M, K, M, CONE, A, LDA, X, LDX, & CZERO, Z1, LDZ ) TMP = ZERO DO i = 1, K CALL CAXPY( M, -CONE, AU(1,i), 1, Z1(1,i), 1) TMP = MAX( TMP, SCNRM2( M, Z1(1,i),1 ) * & SINGVX(K)/(ANORM*SINGVX(1)) ) END DO TMP_AU = MAX( TMP_AU, TMP ) IF ( TMP <= TOL2 ) THEN !WRITE(*,*) ':) .... OK .........CGEDMD PASSED.' ELSE NFAIL_AU = NFAIL_AU + 1 WRITE(*,*) ':( .................CGEDMD FAILED!', & 'Check the code for implementation errors.' WRITE(*,*) 'The input parameters were ',& SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, & M, N, LDX, LDY, NRNK, TOL2 END IF ELSEIF ( LSAME(JOBREF,'E') ) THEN ! The unscaled vectors of the Exact DMD are computed. ! This option is included for the sake of completeness, ! for users who prefer the Exact DMD vectors. The ! returned vectors are in the real form, in the same way ! as the Ritz vectors. Here we just save the vectors ! and test them separately using a Matlab script. CALL CGEMM( 'N', 'N', M, K, M, CONE, A, LDA, AU, LDAU, CZERO, Y1, LDY ) DO i=1, K CALL CAXPY( M, -CEIGS(i), AU(1,i), 1, Y1(1,i), 1 ) RESEX(i) = SCNRM2( M, Y1(1,i), 1) / SCNRM2(M,AU(1,i),1) END DO END IF !...... CGEDMD check point IF ( LSAME(RESIDS, 'R') ) THEN ! Compare the residuals returned by CGEDMD with the ! explicitly computed residuals using the matrix A. ! Compute explicitly Y1 = A*Z CALL CGEMM( 'N', 'N', M, K, M, CONE, A, LDA, Z, LDZ, CZERO, Y1, LDY ) ! ... and then A*Z(:,i) - LAMBDA(i)*Z(:,i), using the real forms ! of the invariant subspaces that correspond to complex conjugate ! pairs of eigencalues. (See the description of Z in CGEDMD,) DO i=1, K ! have a real eigenvalue with real eigenvector CALL CAXPY( M, -CEIGS(i), Z(1,i), 1, Y1(1,i), 1 ) RES1(i) = SCNRM2( M, Y1(1,i), 1) END DO TMP = ZERO DO i = 1, K TMP = MAX( TMP, ABS(RES(i) - RES1(i)) * & SINGVX(K)/(ANORM*SINGVX(1)) ) END DO TMP_REZ = MAX( TMP_REZ, TMP ) IF ( TMP <= TOL2 ) THEN !WRITE(*,*) ':) .... OK ..........CGEDMD PASSED.' ELSE NFAIL_REZ = NFAIL_REZ + 1 WRITE(*,*) ':( ..................CGEDMD FAILED!', & 'Check the code for implementation errors.' WRITE(*,*) 'The input parameters were ',& SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, & M, N, LDX, LDY, NRNK, TOL END IF IF ( LSAME(JOBREF,'E') ) THEN TMP = ZERO DO i = 1, K TMP = MAX( TMP, ABS(RES1(i) - RESEX(i))/(RES1(i)+RESEX(i)) ) END DO TMP_EX = MAX(TMP_EX,TMP) END IF END IF DEALLOCATE(CWORK) DEALLOCATE(WORK) DEALLOCATE(IWORK) !....................................................................................................... IF ( K_traj == 1 ) THEN F(1:M,1:N+1) = F0(1:M,1:N+1) CALL CGEDMDQ( SCALE, JOBZ, RESIDS, WANTQ, WANTR, JOBREF, & WHTSVD, M, N+1, F, LDF, X, LDX, Y, LDY, & NRNK, TOL, K, CEIGS, Z, LDZ, RES, AU, & LDAU, W, LDW, S, LDS, CDUMMY, -1, & WDUMMY, -1, IDUMMY, -1, INFO ) LCWORK = INT(CDUMMY(LWMINOPT)) ALLOCATE(CWORK(LCWORK)) LIWORK = IDUMMY(1) ALLOCATE(IWORK(LIWORK)) LWORK = INT(WDUMMY(1)) ALLOCATE(WORK(LWORK)) CALL CGEDMDQ( SCALE, JOBZ, RESIDS, WANTQ, WANTR, JOBREF, & WHTSVD, M, N+1, F, LDF, X, LDX, Y, LDY, & NRNK, TOL, KQ, CEIGS, Z, LDZ, RES, AU, & LDAU, W, LDW, S, LDS, CWORK, LCWORK, & WORK, LWORK, IWORK, LIWORK, INFO ) IF ( INFO /= 0 ) THEN WRITE(*,*) 'Call to CGEDMDQ failed. & &Check the calling sequence and the code.' WRITE(*,*) 'The error code is ', INFO WRITE(*,*) 'The input parameters were ',& SCALE, JOBZ, RESIDS, WANTQ, WANTR, WHTSVD, & M, N, LDX, LDY, NRNK, TOL STOP END IF SINGVQX(1:N) =WORK(1:N) !..... ZGEDMDQ check point TMP = ZERO DO i = 1, MIN(K, KQ) TMP = MAX(TMP, ABS(SINGVX(i)-SINGVQX(i)) / & SINGVX(1) ) END DO SVDIFF = MAX( SVDIFF, TMP ) IF ( TMP > TOL2 ) THEN WRITE(*,*) 'FAILED! Something was wrong with the run.' NFAIL_SVDIFF = NFAIL_SVDIFF + 1 END IF !..... CGEDMDQ check point !..... CGEDMDQ check point IF ( LSAME(WANTQ,'Q') .AND. LSAME(WANTR,'R') ) THEN ! Check that the QR factors are computed and returned ! as requested. The residual ||F-Q*R||_F / ||F||_F ! is compared to M*N*EPS. F1(1:M,1:N+1) = F0(1:M,1:N+1) CALL CGEMM( 'N', 'N', M, N+1, MIN(M,N+1), -CONE, F, & LDF, Y, LDY, CONE, F1, LDF ) TMP_FQR = CLANGE( 'F', M, N+1, F1, LDF, WORK ) / & CLANGE( 'F', M, N+1, F0, LDF, WORK ) IF ( TMP_FQR <= TOL2 ) THEN !WRITE(*,*) ':) CGEDMDQ ........ PASSED.' ELSE WRITE(*,*) ':( CGEDMDQ ........ FAILED.' NFAIL_F_QR = NFAIL_F_QR + 1 END IF END IF !..... ZGEDMDQ checkpoint !..... ZGEDMDQ checkpoint IF ( LSAME(RESIDS, 'R') ) THEN ! Compare the residuals returned by ZGEDMDQ with the ! explicitly computed residuals using the matrix A. ! Compute explicitly Y1 = A*Z CALL CGEMM( 'N', 'N', M, KQ, M, CONE, A, LDA, Z, LDZ, CZERO, Y1, LDY ) ! ... and then A*Z(:,i) - LAMBDA(i)*Z(:,i), using the real forms ! of the invariant subspaces that correspond to complex conjugate ! pairs of eigencalues. (See the description of Z in ZGEDMDQ) DO i = 1, KQ ! have a real eigenvalue with real eigenvector CALL CAXPY( M, -CEIGS(i), Z(1,i), 1, Y1(1,i), 1 ) ! Y(1:M,i) = Y(1:M,i) - REIG(i)*Z(1:M,i) RES1(i) = SCNRM2( M, Y1(1,i), 1) END DO TMP = ZERO DO i = 1, KQ TMP = MAX( TMP, ABS(RES(i) - RES1(i)) * & SINGVQX(KQ)/(ANORM*SINGVQX(1)) ) END DO TMP_REZQ = MAX( TMP_REZQ, TMP ) IF ( TMP <= TOL2 ) THEN !WRITE(*,*) '.... OK ........ CGEDMDQ PASSED.' ELSE NFAIL_REZQ = NFAIL_REZQ + 1 WRITE(*,*) '................ CGEDMDQ FAILED!', & 'Check the code for implementation errors.' END IF END IF DEALLOCATE(CWORK) DEALLOCATE(WORK) DEALLOCATE(IWORK) END IF END DO ! LWMINOPT !write(*,*) 'LWMINOPT loop completed' END DO ! iWHTSVD !write(*,*) 'WHTSVD loop completed' END DO ! iNRNK -2:-1 !write(*,*) 'NRNK loop completed' END DO ! iSCALE 1:4 !write(*,*) 'SCALE loop completed' END DO !write(*,*) 'JOBREF loop completed' END DO ! iJOBZ !write(*,*) 'JOBZ loop completed' END DO ! MODE -6:6 !write(*,*) 'MODE loop completed' END DO ! 1 or 2 trajectories !write(*,*) 'trajectories loop completed' DEALLOCATE( A ) DEALLOCATE( AC ) DEALLOCATE( Z ) DEALLOCATE( F ) DEALLOCATE( F0 ) DEALLOCATE( F1 ) DEALLOCATE( X ) DEALLOCATE( X0 ) DEALLOCATE( Y ) DEALLOCATE( Y0 ) DEALLOCATE( Y1 ) DEALLOCATE( AU ) DEALLOCATE( W ) DEALLOCATE( S ) DEALLOCATE( Z1 ) DEALLOCATE( RES ) DEALLOCATE( RES1 ) DEALLOCATE( RESEX ) DEALLOCATE( CEIGS ) DEALLOCATE( SINGVX ) DEALLOCATE( SINGVQX ) END DO ! LLOOP WRITE(*,*) WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>' WRITE(*,*) ' Test summary for CGEDMD :' WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>' WRITE(*,*) IF ( NFAIL_Z_XV == 0 ) THEN WRITE(*,*) '>>>> Z - U*V test PASSED.' ELSE WRITE(*,*) 'Z - U*V test FAILED ', NFAIL_Z_XV, ' time(s)' WRITE(*,*) 'Max error ||Z-U*V||_F was ', TMP_XW NFAIL_TOTAL = NFAIL_TOTAL + NFAIL_z_XV END IF IF ( NFAIL_AU == 0 ) THEN WRITE(*,*) '>>>> A*U test PASSED. ' ELSE WRITE(*,*) 'A*U test FAILED ', NFAIL_AU, ' time(s)' WRITE(*,*) 'Max A*U test adjusted error measure was ', TMP_AU WRITE(*,*) 'It should be up to O(M*N) times EPS, EPS = ', EPS NFAIL_TOTAL = NFAIL_TOTAL + NFAIL_AU END IF IF ( NFAIL_REZ == 0 ) THEN WRITE(*,*) '>>>> Rezidual computation test PASSED.' ELSE WRITE(*,*) 'Rezidual computation test FAILED ', NFAIL_REZ, 'time(s)' WRITE(*,*) 'Max residual computing test adjusted error measure was ', TMP_REZ WRITE(*,*) 'It should be up to O(M*N) times EPS, EPS = ', EPS NFAIL_TOTAL = NFAIL_TOTAL + NFAIL_REZ END IF IF ( NFAIL_TOTAL == 0 ) THEN WRITE(*,*) '>>>> CGEDMD :: ALL TESTS PASSED.' ELSE WRITE(*,*) NFAIL_TOTAL, 'FAILURES!' WRITE(*,*) '>>>>>>>>>>>>>> CGEDMD :: TESTS FAILED. CHECK THE IMPLEMENTATION.' END IF WRITE(*,*) WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>' WRITE(*,*) ' Test summary for CGEDMDQ :' WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>' WRITE(*,*) IF ( NFAIL_SVDIFF == 0 ) THEN WRITE(*,*) '>>>> CGEDMD and CGEDMDQ computed singular & &values test PASSED.' ELSE WRITE(*,*) 'ZGEDMD and ZGEDMDQ discrepancies in & &the singular values unacceptable ', & NFAIL_SVDIFF, ' times. Test FAILED.' WRITE(*,*) 'The maximal discrepancy in the singular values (relative to the norm) was ', SVDIFF WRITE(*,*) 'It should be up to O(M*N) times EPS, EPS = ', EPS NFAILQ_TOTAL = NFAILQ_TOTAL + NFAIL_SVDIFF END IF IF ( NFAIL_F_QR == 0 ) THEN WRITE(*,*) '>>>> F - Q*R test PASSED.' ELSE WRITE(*,*) 'F - Q*R test FAILED ', NFAIL_F_QR, ' time(s)' WRITE(*,*) 'The largest relative residual was ', TMP_FQR WRITE(*,*) 'It should be up to O(M*N) times EPS, EPS = ', EPS NFAILQ_TOTAL = NFAILQ_TOTAL + NFAIL_F_QR END IF IF ( NFAIL_REZQ == 0 ) THEN WRITE(*,*) '>>>> Rezidual computation test PASSED.' ELSE WRITE(*,*) 'Rezidual computation test FAILED ', NFAIL_REZQ, 'time(s)' WRITE(*,*) 'Max residual computing test adjusted error measure was ', TMP_REZQ WRITE(*,*) 'It should be up to O(M*N) times EPS, EPS = ', EPS NFAILQ_TOTAL = NFAILQ_TOTAL + NFAIL_REZQ END IF IF ( NFAILQ_TOTAL == 0 ) THEN WRITE(*,*) '>>>>>>> CGEDMDQ :: ALL TESTS PASSED.' ELSE WRITE(*,*) NFAILQ_TOTAL, 'FAILURES!' WRITE(*,*) '>>>>>>> CGEDMDQ :: TESTS FAILED. CHECK THE IMPLEMENTATION.' END IF WRITE(*,*) WRITE(*,*) 'Test completed.' STOP END