Add tests for the DMD functions (Reference-LAPACK PR 736)
This commit is contained in:
Martin Kroeker
GitHub
parent
e3039fa7f6
commit
a53a79e059
|
|
@ -64,6 +64,8 @@ SEIGTST = schkee.o \
|
||||||
sort03.o ssbt21.o ssgt01.o sslect.o sspt21.o sstt21.o \
|
sort03.o ssbt21.o ssgt01.o sslect.o sspt21.o sstt21.o \
|
||||||
sstt22.o ssyl01.o ssyt21.o ssyt22.o
|
sstt22.o ssyl01.o ssyt21.o ssyt22.o
|
||||||
|
|
||||||
|
SDMDEIGTST = schkdmd.o
|
||||||
|
|
||||||
CEIGTST = cchkee.o \
|
CEIGTST = cchkee.o \
|
||||||
cbdt01.o cbdt02.o cbdt03.o cbdt05.o \
|
cbdt01.o cbdt02.o cbdt03.o cbdt05.o \
|
||||||
cchkbb.o cchkbd.o cchkbk.o cchkbl.o cchkec.o \
|
cchkbb.o cchkbd.o cchkbk.o cchkbl.o cchkec.o \
|
||||||
|
|
@ -81,6 +83,8 @@ CEIGTST = cchkee.o \
|
||||||
csgt01.o cslect.o csyl01.o\
|
csgt01.o cslect.o csyl01.o\
|
||||||
cstt21.o cstt22.o cunt01.o cunt03.o
|
cstt21.o cstt22.o cunt01.o cunt03.o
|
||||||
|
|
||||||
|
CDMDEIGTST = cchkdmd.o
|
||||||
|
|
||||||
DZIGTST = dlafts.o dlahd2.o dlasum.o dlatb9.o dstech.o dstect.o \
|
DZIGTST = dlafts.o dlahd2.o dlasum.o dlatb9.o dstech.o dstect.o \
|
||||||
dsvdch.o dsvdct.o dsxt1.o
|
dsvdch.o dsvdct.o dsxt1.o
|
||||||
|
|
||||||
|
|
@ -101,6 +105,8 @@ DEIGTST = dchkee.o \
|
||||||
dort03.o dsbt21.o dsgt01.o dslect.o dspt21.o dstt21.o \
|
dort03.o dsbt21.o dsgt01.o dslect.o dspt21.o dstt21.o \
|
||||||
dstt22.o dsyl01.o dsyt21.o dsyt22.o
|
dstt22.o dsyl01.o dsyt21.o dsyt22.o
|
||||||
|
|
||||||
|
DDMDEIGTST = dchkdmd.o
|
||||||
|
|
||||||
ZEIGTST = zchkee.o \
|
ZEIGTST = zchkee.o \
|
||||||
zbdt01.o zbdt02.o zbdt03.o zbdt05.o \
|
zbdt01.o zbdt02.o zbdt03.o zbdt05.o \
|
||||||
zchkbb.o zchkbd.o zchkbk.o zchkbl.o zchkec.o \
|
zchkbb.o zchkbd.o zchkbk.o zchkbl.o zchkec.o \
|
||||||
|
|
@ -118,27 +124,45 @@ ZEIGTST = zchkee.o \
|
||||||
zsgt01.o zslect.o zsyl01.o\
|
zsgt01.o zslect.o zsyl01.o\
|
||||||
zstt21.o zstt22.o zunt01.o zunt03.o
|
zstt21.o zstt22.o zunt01.o zunt03.o
|
||||||
|
|
||||||
|
ZDMDEIGTST = zchkdmd.o
|
||||||
|
|
||||||
.PHONY: all
|
.PHONY: all
|
||||||
all: single complex double complex16
|
all: single complex double complex16
|
||||||
|
|
||||||
.PHONY: single complex double complex16
|
.PHONY: single complex double complex16
|
||||||
single: xeigtsts
|
single: xeigtsts xdmdeigtsts
|
||||||
complex: xeigtstc
|
complex: xeigtstc xdmdeigtstc
|
||||||
double: xeigtstd
|
double: xeigtstd xdmdeigtstd
|
||||||
complex16: xeigtstz
|
complex16: xeigtstz xdmdeigtstz
|
||||||
|
|
||||||
xeigtsts: $(SEIGTST) $(SCIGTST) $(AEIGTST) $(TMGLIB) ../$(LAPACKLIB) $(BLASLIB)
|
xdmdeigtsts: $(SDMDEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
|
||||||
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
||||||
|
|
||||||
xeigtstc: $(CEIGTST) $(SCIGTST) $(AEIGTST) $(TMGLIB) ../$(LAPACKLIB) $(BLASLIB)
|
xdmdeigtstc: $(CDMDEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
|
||||||
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
||||||
|
|
||||||
xeigtstd: $(DEIGTST) $(DZIGTST) $(AEIGTST) $(TMGLIB) ../$(LAPACKLIB) $(BLASLIB)
|
xdmdeigtstd: $(DDMDEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
|
||||||
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
||||||
|
|
||||||
xeigtstz: $(ZEIGTST) $(DZIGTST) $(AEIGTST) $(TMGLIB) ../$(LAPACKLIB) $(BLASLIB)
|
xdmdeigtstz: $(ZDMDEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
|
||||||
$(LOADER) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
||||||
|
|
||||||
|
xeigtsts: $(SEIGTST) $(SCIGTST) $(AEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
|
||||||
|
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
||||||
|
|
||||||
|
xeigtstc: $(CEIGTST) $(SCIGTST) $(AEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
|
||||||
|
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
||||||
|
|
||||||
|
xeigtstd: $(DEIGTST) $(DZIGTST) $(AEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
|
||||||
|
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
||||||
|
|
||||||
|
xeigtstz: $(ZEIGTST) $(DZIGTST) $(AEIGTST) $(TMGLIB) $(LAPACKLIB) $(BLASLIB)
|
||||||
|
$(FC) $(FFLAGS) $(LDFLAGS) -o $@ $^
|
||||||
|
|
||||||
|
$(SDMDEIGTST): $(FRC)
|
||||||
|
$(CDMDEIGTST): $(FRC)
|
||||||
|
$(DDMDEIGTST): $(FRC)
|
||||||
|
$(ZDMDEIGTST): $(FRC)
|
||||||
$(AEIGTST): $(FRC)
|
$(AEIGTST): $(FRC)
|
||||||
$(SCIGTST): $(FRC)
|
$(SCIGTST): $(FRC)
|
||||||
$(DZIGTST): $(FRC)
|
$(DZIGTST): $(FRC)
|
||||||
|
|
@ -155,7 +179,7 @@ clean: cleanobj cleanexe
|
||||||
cleanobj:
|
cleanobj:
|
||||||
rm -f *.o
|
rm -f *.o
|
||||||
cleanexe:
|
cleanexe:
|
||||||
rm -f xeigtst*
|
rm -f xeigtst* xdmdeigtst*
|
||||||
|
|
||||||
schkee.o: schkee.F
|
schkee.o: schkee.F
|
||||||
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
||||||
|
|
@ -165,3 +189,11 @@ cchkee.o: cchkee.F
|
||||||
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
||||||
zchkee.o: zchkee.F
|
zchkee.o: zchkee.F
|
||||||
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
||||||
|
schkdmd.o: schkdmd.f90
|
||||||
|
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
||||||
|
cchkdmd.o: cchkdmd.f90
|
||||||
|
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
||||||
|
dchkdmd.o: dchkdmd.f90
|
||||||
|
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
||||||
|
zchkdmd.o: zchkdmd.f90
|
||||||
|
$(FC) $(FFLAGS_DRV) -c -o $@ $<
|
||||||
|
|
|
||||||
|
|
@ -0,0 +1,721 @@
|
||||||
|
! 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
|
||||||
|
|
@ -0,0 +1,813 @@
|
||||||
|
! This is a test program for checking the implementations of
|
||||||
|
! the implementations of the following subroutines
|
||||||
|
!
|
||||||
|
! DGEDMD for computation of the
|
||||||
|
! Dynamic Mode Decomposition (DMD)
|
||||||
|
! DGEDMDQ 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.
|
||||||
|
!... .........................................................
|
||||||
|
! NOTE:
|
||||||
|
! When using the Intel MKL 2022.0.3 the subroutine xGESVDQ
|
||||||
|
! (optionally used in xGEDMD) may cause access violation
|
||||||
|
! error for x = S, D, C, Z, but only if called with the
|
||||||
|
! work space query. (At least in our Windows 10 MSVS 2019.)
|
||||||
|
! The problem can be mitigated by downloading the source
|
||||||
|
! code of xGESVDQ from the LAPACK repository and use it
|
||||||
|
! localy instead of the one in the MKL. This seems to
|
||||||
|
! indicate that the problem is indeed in the MKL.
|
||||||
|
! This problem did not appear whith Intel MKL 2022.2.0.
|
||||||
|
!
|
||||||
|
! NOTE:
|
||||||
|
! xGESDD seems to have a problem with workspace. In some
|
||||||
|
! cases the length of the optimal workspace is returned
|
||||||
|
! smaller than the minimal workspace, as specified in the
|
||||||
|
! code. As a precaution, all optimal workspaces are
|
||||||
|
! set as MAX(minimal, optimal).
|
||||||
|
! Latest implementations of complex xGESDD have different
|
||||||
|
! length of the real worksapce. We use max value over
|
||||||
|
! two versions.
|
||||||
|
!............................................................
|
||||||
|
!............................................................
|
||||||
|
!
|
||||||
|
PROGRAM DMD_TEST
|
||||||
|
use iso_fortran_env, only: real64
|
||||||
|
IMPLICIT NONE
|
||||||
|
integer, parameter :: WP = real64
|
||||||
|
|
||||||
|
!............................................................
|
||||||
|
REAL(KIND=WP), PARAMETER :: ONE = 1.0_WP
|
||||||
|
REAL(KIND=WP), PARAMETER :: ZERO = 0.0_WP
|
||||||
|
!............................................................
|
||||||
|
REAL(KIND=WP), ALLOCATABLE, DIMENSION(:,:) :: &
|
||||||
|
A, AC, EIGA, LAMBDA, LAMBDAQ, F, F1, F2,&
|
||||||
|
Z, Z1, S, AU, W, VA, X, X0, Y, Y0, Y1
|
||||||
|
REAL(KIND=WP), ALLOCATABLE, DIMENSION(:) :: &
|
||||||
|
DA, DL, DR, REIG, REIGA, REIGQ, IEIG, &
|
||||||
|
IEIGA, IEIGQ, RES, RES1, RESEX, SINGVX,&
|
||||||
|
SINGVQX, WORK
|
||||||
|
INTEGER , ALLOCATABLE, DIMENSION(:) :: IWORK
|
||||||
|
REAL(KIND=WP) :: AB(2,2), WDUMMY(2)
|
||||||
|
INTEGER :: IDUMMY(2), ISEED(4), RJOBDATA(8)
|
||||||
|
REAL(KIND=WP) :: ANORM, COND, CONDL, CONDR, DMAX, EPS, &
|
||||||
|
TOL, TOL2, SVDIFF, TMP, TMP_AU, &
|
||||||
|
TMP_FQR, TMP_REZ, TMP_REZQ, TMP_ZXW, &
|
||||||
|
TMP_EX, XNORM, YNORM
|
||||||
|
!............................................................
|
||||||
|
INTEGER :: K, KQ, LDF, LDS, LDA, LDAU, LDW, LDX, LDY, &
|
||||||
|
LDZ, LIWORK, LWORK, M, N, L, LLOOP, NRNK
|
||||||
|
INTEGER :: i, iJOBREF, iJOBZ, iSCALE, INFO, j, KDIFF, &
|
||||||
|
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(LEN=1) GRADE, JOBREF, JOBZ, PIVTNG, RSIGN, &
|
||||||
|
SCALE, RESIDS, WANTQ, WANTR
|
||||||
|
|
||||||
|
LOGICAL TEST_QRDMD
|
||||||
|
!..... external subroutines (BLAS and LAPACK)
|
||||||
|
EXTERNAL DAXPY, DGEEV, DGEMM, DGEMV, DLACPY, DLASCL
|
||||||
|
EXTERNAL DLARNV, DLATMR
|
||||||
|
!.....external subroutines DMD package, part 1
|
||||||
|
! subroutines under test
|
||||||
|
EXTERNAL DGEDMD, DGEDMDQ
|
||||||
|
|
||||||
|
!..... external functions (BLAS and LAPACK)
|
||||||
|
EXTERNAL DLAMCH, DLANGE, DNRM2
|
||||||
|
REAL(KIND=WP) :: DLAMCH, DLANGE, DNRM2
|
||||||
|
EXTERNAL LSAME
|
||||||
|
LOGICAL LSAME
|
||||||
|
|
||||||
|
INTRINSIC ABS, INT, MIN, MAX
|
||||||
|
!............................................................
|
||||||
|
|
||||||
|
! The test is always in pairs : ( DGEDMD and DGEDMDQ )
|
||||||
|
! because the test includes comparing the results (in pairs).
|
||||||
|
!.....................................................................................
|
||||||
|
TEST_QRDMD = .TRUE. ! This code by default performs tests on DGEDMDQ
|
||||||
|
! 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 = DLAMCH( 'P' ) ! machine precision DP
|
||||||
|
|
||||||
|
! 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
|
||||||
|
KDIFF = 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 ...
|
||||||
|
WRITE(*,*) 'M = '
|
||||||
|
READ(*,*) M
|
||||||
|
WRITE(*,*) M
|
||||||
|
! ... and the number of snapshots.
|
||||||
|
WRITE(*,*) 'N = '
|
||||||
|
READ(*,*) N
|
||||||
|
WRITE(*,*) 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 = MAX(M,N+1)
|
||||||
|
LDY = MAX(M,N+1)
|
||||||
|
LDW = N
|
||||||
|
LDZ = M
|
||||||
|
LDAU = MAX(M,N+1)
|
||||||
|
LDS = N
|
||||||
|
|
||||||
|
TMP_ZXW = ZERO
|
||||||
|
TMP_AU = ZERO
|
||||||
|
TMP_REZ = ZERO
|
||||||
|
TMP_REZQ = ZERO
|
||||||
|
SVDIFF = ZERO
|
||||||
|
TMP_EX = ZERO
|
||||||
|
|
||||||
|
!
|
||||||
|
! Test the subroutines on real data snapshots. All
|
||||||
|
! computation is done in real arithmetic, even when
|
||||||
|
! Koopman eigenvalues and modes are real.
|
||||||
|
!
|
||||||
|
! Allocate memory space
|
||||||
|
ALLOCATE( A(LDA,M) )
|
||||||
|
ALLOCATE( AC(LDA,M) )
|
||||||
|
ALLOCATE( DA(M) )
|
||||||
|
ALLOCATE( DL(M) )
|
||||||
|
ALLOCATE( F(LDF,N+1) )
|
||||||
|
ALLOCATE( F1(LDF,N+1) )
|
||||||
|
ALLOCATE( F2(LDF,N+1) )
|
||||||
|
ALLOCATE( X(LDX,N) )
|
||||||
|
ALLOCATE( X0(LDX,N) )
|
||||||
|
ALLOCATE( SINGVX(N) )
|
||||||
|
ALLOCATE( SINGVQX(N) )
|
||||||
|
ALLOCATE( Y(LDY,N+1) )
|
||||||
|
ALLOCATE( Y0(LDY,N+1) )
|
||||||
|
ALLOCATE( Y1(M,N+1) )
|
||||||
|
ALLOCATE( Z(LDZ,N) )
|
||||||
|
ALLOCATE( Z1(LDZ,N) )
|
||||||
|
ALLOCATE( RES(N) )
|
||||||
|
ALLOCATE( RES1(N) )
|
||||||
|
ALLOCATE( RESEX(N) )
|
||||||
|
ALLOCATE( REIG(N) )
|
||||||
|
ALLOCATE( IEIG(N) )
|
||||||
|
ALLOCATE( REIGQ(N) )
|
||||||
|
ALLOCATE( IEIGQ(N) )
|
||||||
|
ALLOCATE( REIGA(M) )
|
||||||
|
ALLOCATE( IEIGA(M) )
|
||||||
|
ALLOCATE( VA(LDA,M) )
|
||||||
|
ALLOCATE( LAMBDA(N,2) )
|
||||||
|
ALLOCATE( LAMBDAQ(N,2) )
|
||||||
|
ALLOCATE( EIGA(M,2) )
|
||||||
|
ALLOCATE( W(LDW,N) )
|
||||||
|
ALLOCATE( AU(LDAU,N) )
|
||||||
|
ALLOCATE( S(N,N) )
|
||||||
|
|
||||||
|
TOL = M*EPS
|
||||||
|
! This mimics O(M*N)*EPS bound for accumulated roundoff error.
|
||||||
|
! The factor 10 is somewhat arbitrary.
|
||||||
|
TOL2 = 10*M*N*EPS
|
||||||
|
|
||||||
|
!.............
|
||||||
|
|
||||||
|
DO K_TRAJ = 1, 2
|
||||||
|
! Number of intial conditions in the simulation/trajectories (1 or 2)
|
||||||
|
|
||||||
|
COND = 1.0D8
|
||||||
|
DMAX = 1.0D2
|
||||||
|
RSIGN = 'F'
|
||||||
|
GRADE = 'N'
|
||||||
|
MODEL = 6
|
||||||
|
CONDL = 1.0D2
|
||||||
|
MODER = 6
|
||||||
|
CONDR = 1.0D2
|
||||||
|
PIVTNG = 'N'
|
||||||
|
|
||||||
|
! Loop over all parameter MODE values for ZLATMR (+1,..,+6)
|
||||||
|
DO MODE = 1, 6
|
||||||
|
|
||||||
|
ALLOCATE( IWORK(2*M) )
|
||||||
|
ALLOCATE(DR(N))
|
||||||
|
CALL DLATMR( M, M, 'S', ISEED, 'N', DA, MODE, COND, &
|
||||||
|
DMAX, RSIGN, GRADE, DL, MODEL, CONDL, &
|
||||||
|
DR, MODER, CONDR, PIVTNG, IWORK, M, M, &
|
||||||
|
ZERO, -ONE, 'N', A, LDA, IWORK(M+1), INFO )
|
||||||
|
DEALLOCATE(IWORK)
|
||||||
|
DEALLOCATE(DR)
|
||||||
|
|
||||||
|
LWORK = 4*M+1
|
||||||
|
ALLOCATE(WORK(LWORK))
|
||||||
|
AC = A
|
||||||
|
CALL DGEEV( 'N','V', M, AC, M, REIGA, IEIGA, VA, M, &
|
||||||
|
VA, M, WORK, LWORK, INFO ) ! LAPACK CALL
|
||||||
|
DEALLOCATE(WORK)
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, M
|
||||||
|
EIGA(i,1) = REIGA(i)
|
||||||
|
EIGA(i,2) = IEIGA(i)
|
||||||
|
TMP = MAX( TMP, SQRT(REIGA(i)**2+IEIGA(i)**2))
|
||||||
|
END DO
|
||||||
|
|
||||||
|
! Scale A to have the desirable spectral radius.
|
||||||
|
CALL DLASCL( 'G', 0, 0, TMP, ONE, M, M, A, M, INFO )
|
||||||
|
CALL DLASCL( 'G', 0, 0, TMP, ONE, M, 2, EIGA, M, INFO )
|
||||||
|
|
||||||
|
! Compute the norm of A
|
||||||
|
ANORM = DLANGE( 'F', N, N, A, M, WDUMMY )
|
||||||
|
|
||||||
|
IF ( K_TRAJ == 2 ) THEN
|
||||||
|
! generate data with two inital conditions
|
||||||
|
CALL DLARNV(2, ISEED, M, F1(1,1) )
|
||||||
|
F1(1:M,1) = 1.0E-10*F1(1:M,1)
|
||||||
|
DO i = 1, N/2
|
||||||
|
CALL DGEMV( 'N', M, M, ONE, A, M, F1(1,i), 1, ZERO, &
|
||||||
|
F1(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
X0(1:M,1:N/2) = F1(1:M,1:N/2)
|
||||||
|
Y0(1:M,1:N/2) = F1(1:M,2:N/2+1)
|
||||||
|
|
||||||
|
CALL DLARNV(2, ISEED, M, F1(1,1) )
|
||||||
|
DO i = 1, N-N/2
|
||||||
|
CALL DGEMV( 'N', M, M, ONE, A, M, F1(1,i), 1, ZERO, &
|
||||||
|
F1(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
X0(1:M,N/2+1:N) = F1(1:M,1:N-N/2)
|
||||||
|
Y0(1:M,N/2+1:N) = F1(1:M,2:N-N/2+1)
|
||||||
|
ELSE
|
||||||
|
CALL DLARNV(2, ISEED, M, F(1,1) )
|
||||||
|
DO i = 1, N
|
||||||
|
CALL DGEMV( 'N', M, M, ONE, A, M, F(1,i), 1, ZERO, &
|
||||||
|
F(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
X0(1:M,1:N) = F(1:M,1:N)
|
||||||
|
Y0(1:M,1:N) = F(1:M,2:N+1)
|
||||||
|
END IF
|
||||||
|
|
||||||
|
XNORM = DLANGE( 'F', M, N, X0, LDX, WDUMMY )
|
||||||
|
YNORM = DLANGE( 'F', M, N, Y0, LDX, WDUMMY )
|
||||||
|
!............................................................
|
||||||
|
|
||||||
|
DO iJOBZ = 1, 4
|
||||||
|
|
||||||
|
SELECT CASE ( iJOBZ )
|
||||||
|
CASE(1)
|
||||||
|
JOBZ = 'V' ! Ritz vectors will be computed
|
||||||
|
RESIDS = 'R' ! Residuals will be computed
|
||||||
|
CASE(2)
|
||||||
|
JOBZ = 'V'
|
||||||
|
RESIDS = 'N'
|
||||||
|
CASE(3)
|
||||||
|
JOBZ = 'F' ! Ritz vectors in factored form
|
||||||
|
RESIDS = 'N'
|
||||||
|
CASE(4)
|
||||||
|
JOBZ = 'N'
|
||||||
|
RESIDS = 'N'
|
||||||
|
END SELECT
|
||||||
|
|
||||||
|
DO iJOBREF = 1, 3
|
||||||
|
|
||||||
|
SELECT CASE ( iJOBREF )
|
||||||
|
CASE(1)
|
||||||
|
JOBREF = 'R' ! Data for refined Ritz vectors
|
||||||
|
CASE(2)
|
||||||
|
JOBREF = 'E' ! Exact DMD vectors
|
||||||
|
CASE(3)
|
||||||
|
JOBREF = 'N'
|
||||||
|
END SELECT
|
||||||
|
|
||||||
|
DO iSCALE = 1, 4
|
||||||
|
|
||||||
|
SELECT CASE ( iSCALE )
|
||||||
|
CASE(1)
|
||||||
|
SCALE = 'S' ! X data normalized
|
||||||
|
CASE(2)
|
||||||
|
SCALE = 'C' ! X normalized, consist. check
|
||||||
|
CASE(3)
|
||||||
|
SCALE = 'Y' ! Y data normalized
|
||||||
|
CASE(4)
|
||||||
|
SCALE = 'N'
|
||||||
|
END SELECT
|
||||||
|
|
||||||
|
DO iNRNK = -1, -2, -1
|
||||||
|
! Two truncation strategies. The "-2" case for R&D
|
||||||
|
! purposes only - it uses possibly low accuracy small
|
||||||
|
! singular values, in which case the formulas used in
|
||||||
|
! the DMD are highly sensitive.
|
||||||
|
NRNK = iNRNK
|
||||||
|
|
||||||
|
DO iWHTSVD = 1, 4
|
||||||
|
! 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.
|
||||||
|
|
||||||
|
X(1:M,1:N) = X0(1:M,1:N)
|
||||||
|
Y(1:M,1:N) = Y0(1:M,1:N)
|
||||||
|
|
||||||
|
! DGEDMD: Workspace query and workspace allocation
|
||||||
|
CALL DGEDMD( SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, M, &
|
||||||
|
N, X, LDX, Y, LDY, NRNK, TOL, K, REIG, IEIG, Z, &
|
||||||
|
LDZ, RES, AU, LDAU, W, LDW, S, LDS, WDUMMY, -1, &
|
||||||
|
IDUMMY, -1, INFO )
|
||||||
|
|
||||||
|
LIWORK = IDUMMY(1)
|
||||||
|
ALLOCATE( IWORK(LIWORK) )
|
||||||
|
LWORK = INT(WDUMMY(LWMINOPT))
|
||||||
|
ALLOCATE( WORK(LWORK) )
|
||||||
|
|
||||||
|
! DGEDMD test: CALL DGEDMD
|
||||||
|
CALL DGEDMD( SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, M, &
|
||||||
|
N, X, LDX, Y, LDY, NRNK, TOL, K, REIG, IEIG, Z, &
|
||||||
|
LDZ, RES, AU, LDAU, W, LDW, S, LDS, WORK, LWORK,&
|
||||||
|
IWORK, LIWORK, INFO )
|
||||||
|
|
||||||
|
SINGVX(1:N) = WORK(1:N)
|
||||||
|
|
||||||
|
!...... DGEDMD check point
|
||||||
|
IF ( LSAME(JOBZ,'V') ) THEN
|
||||||
|
! Check that Z = X*W, on return from DGEDMD
|
||||||
|
! This checks that the returned aigenvectors in Z are
|
||||||
|
! the product of the SVD'POD basis returned in X
|
||||||
|
! and the eigenvectors of the rayleigh quotient
|
||||||
|
! returned in W
|
||||||
|
CALL DGEMM( 'N', 'N', M, K, K, ONE, X, LDX, W, LDW, &
|
||||||
|
ZERO, Z1, LDZ )
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, K
|
||||||
|
CALL DAXPY( M, -ONE, Z(1,i), 1, Z1(1,i), 1)
|
||||||
|
TMP = MAX(TMP, DNRM2( M, Z1(1,i), 1 ) )
|
||||||
|
END DO
|
||||||
|
TMP_ZXW = MAX(TMP_ZXW, TMP )
|
||||||
|
|
||||||
|
IF ( TMP_ZXW > 10*M*EPS ) THEN
|
||||||
|
NFAIL_Z_XV = NFAIL_Z_XV + 1
|
||||||
|
WRITE(*,*) ':( .................DGEDMD 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
|
||||||
|
|
||||||
|
!...... DGEDMD 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 DGEMM( 'N', 'N', M, K, M, ONE, A, LDA, X, LDX, &
|
||||||
|
ZERO, Z1, LDZ )
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, K
|
||||||
|
CALL DAXPY( M, -ONE, AU(1,i), 1, Z1(1,i), 1)
|
||||||
|
TMP = MAX( TMP, DNRM2( M, Z1(1,i),1 ) * &
|
||||||
|
SINGVX(K)/(ANORM*SINGVX(1)) )
|
||||||
|
END DO
|
||||||
|
TMP_AU = MAX( TMP_AU, TMP )
|
||||||
|
|
||||||
|
IF ( TMP > TOL2 ) THEN
|
||||||
|
NFAIL_AU = NFAIL_AU + 1
|
||||||
|
WRITE(*,*) ':( .................DGEDMD 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
|
||||||
|
|
||||||
|
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 DGEMM( 'N', 'N', M, K, M, ONE, A, LDA, AU, LDAU, ZERO, Y1, M )
|
||||||
|
i=1
|
||||||
|
DO WHILE ( i <= K )
|
||||||
|
IF ( IEIG(i) == ZERO ) THEN
|
||||||
|
! have a real eigenvalue with real eigenvector
|
||||||
|
CALL DAXPY( M, -REIG(i), AU(1,i), 1, Y1(1,i), 1 )
|
||||||
|
RESEX(i) = DNRM2( M, Y1(1,i), 1) / DNRM2(M,AU(1,i),1)
|
||||||
|
i = i + 1
|
||||||
|
ELSE
|
||||||
|
! Have a complex conjugate pair
|
||||||
|
! REIG(i) +- sqrt(-1)*IMEIG(i).
|
||||||
|
! Since all computation is done in real
|
||||||
|
! arithmetic, the formula for the residual
|
||||||
|
! is recast for real representation of the
|
||||||
|
! complex conjugate eigenpair. See the
|
||||||
|
! description of RES.
|
||||||
|
AB(1,1) = REIG(i)
|
||||||
|
AB(2,1) = -IEIG(i)
|
||||||
|
AB(1,2) = IEIG(i)
|
||||||
|
AB(2,2) = REIG(i)
|
||||||
|
CALL DGEMM( 'N', 'N', M, 2, 2, -ONE, AU(1,i), &
|
||||||
|
M, AB, 2, ONE, Y1(1,i), M )
|
||||||
|
RESEX(i) = DLANGE( 'F', M, 2, Y1(1,i), M, &
|
||||||
|
WORK )/ DLANGE( 'F', M, 2, AU(1,i), M, &
|
||||||
|
WORK )
|
||||||
|
RESEX(i+1) = RESEX(i)
|
||||||
|
i = i + 2
|
||||||
|
END IF
|
||||||
|
END DO
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!...... DGEDMD check point
|
||||||
|
IF ( LSAME(RESIDS, 'R') ) THEN
|
||||||
|
! Compare the residuals returned by DGEDMD with the
|
||||||
|
! explicitly computed residuals using the matrix A.
|
||||||
|
! Compute explicitly Y1 = A*Z
|
||||||
|
CALL DGEMM( 'N', 'N', M, K, M, ONE, A, LDA, Z, LDZ, ZERO, Y1, M )
|
||||||
|
! ... 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 DGEDMD,)
|
||||||
|
i = 1
|
||||||
|
DO WHILE ( i <= K )
|
||||||
|
IF ( IEIG(i) == ZERO ) THEN
|
||||||
|
! have a real eigenvalue with real eigenvector
|
||||||
|
CALL DAXPY( M, -REIG(i), Z(1,i), 1, Y1(1,i), 1 )
|
||||||
|
RES1(i) = DNRM2( M, Y1(1,i), 1)
|
||||||
|
i = i + 1
|
||||||
|
ELSE
|
||||||
|
! Have a complex conjugate pair
|
||||||
|
! REIG(i) +- sqrt(-1)*IMEIG(i).
|
||||||
|
! Since all computation is done in real
|
||||||
|
! arithmetic, the formula for the residual
|
||||||
|
! is recast for real representation of the
|
||||||
|
! complex conjugate eigenpair. See the
|
||||||
|
! description of RES.
|
||||||
|
AB(1,1) = REIG(i)
|
||||||
|
AB(2,1) = -IEIG(i)
|
||||||
|
AB(1,2) = IEIG(i)
|
||||||
|
AB(2,2) = REIG(i)
|
||||||
|
CALL DGEMM( 'N', 'N', M, 2, 2, -ONE, Z(1,i), &
|
||||||
|
M, AB, 2, ONE, Y1(1,i), M )
|
||||||
|
RES1(i) = DLANGE( 'F', M, 2, Y1(1,i), M, &
|
||||||
|
WORK )
|
||||||
|
RES1(i+1) = RES1(i)
|
||||||
|
i = i + 2
|
||||||
|
END IF
|
||||||
|
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
|
||||||
|
NFAIL_REZ = NFAIL_REZ + 1
|
||||||
|
WRITE(*,*) ':( ..................DGEDMD 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
|
||||||
|
|
||||||
|
!..... store the results for inspection
|
||||||
|
DO i = 1, K
|
||||||
|
LAMBDA(i,1) = REIG(i)
|
||||||
|
LAMBDA(i,2) = IEIG(i)
|
||||||
|
END DO
|
||||||
|
|
||||||
|
DEALLOCATE(IWORK)
|
||||||
|
DEALLOCATE(WORK)
|
||||||
|
|
||||||
|
!======================================================================
|
||||||
|
! Now test the DGEDMDQ
|
||||||
|
!======================================================================
|
||||||
|
IF ( TEST_QRDMD .AND. (K_TRAJ == 1) ) THEN
|
||||||
|
RJOBDATA(2) = 1
|
||||||
|
F1 = F
|
||||||
|
|
||||||
|
! DGEDMDQ test: Workspace query and workspace allocation
|
||||||
|
CALL DGEDMDQ( SCALE, JOBZ, RESIDS, WANTQ, WANTR, &
|
||||||
|
JOBREF, WHTSVD, M, N+1, F1, LDF, X, LDX, Y, &
|
||||||
|
LDY, NRNK, TOL, KQ, REIGQ, IEIGQ, Z, LDZ, &
|
||||||
|
RES, AU, LDAU, W, LDW, S, LDS, WDUMMY, &
|
||||||
|
-1, IDUMMY, -1, INFO )
|
||||||
|
LIWORK = IDUMMY(1)
|
||||||
|
ALLOCATE( IWORK(LIWORK) )
|
||||||
|
LWORK = INT(WDUMMY(LWMINOPT))
|
||||||
|
ALLOCATE(WORK(LWORK))
|
||||||
|
! DGEDMDQ test: CALL DGEDMDQ
|
||||||
|
CALL DGEDMDQ( SCALE, JOBZ, RESIDS, WANTQ, WANTR, &
|
||||||
|
JOBREF, WHTSVD, M, N+1, F1, LDF, X, LDX, Y, &
|
||||||
|
LDY, NRNK, TOL, KQ, REIGQ, IEIGQ, Z, LDZ, &
|
||||||
|
RES, AU, LDAU, W, LDW, S, LDS, &
|
||||||
|
WORK, LWORK, IWORK, LIWORK, INFO )
|
||||||
|
|
||||||
|
SINGVQX(1:KQ) = WORK(MIN(M,N+1)+1: MIN(M,N+1)+KQ)
|
||||||
|
|
||||||
|
!..... DGEDMDQ check point
|
||||||
|
IF ( KQ /= K ) THEN
|
||||||
|
KDIFF = KDIFF+1
|
||||||
|
END IF
|
||||||
|
|
||||||
|
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 > M*N*EPS ) THEN
|
||||||
|
WRITE(*,*) 'FAILED! Something was wrong with the run.'
|
||||||
|
NFAIL_SVDIFF = NFAIL_SVDIFF + 1
|
||||||
|
DO j =1, 3
|
||||||
|
write(*,*) j, SINGVX(j), SINGVQX(j)
|
||||||
|
read(*,*)
|
||||||
|
END DO
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!..... DGEDMDQ 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.
|
||||||
|
F2 = F
|
||||||
|
CALL DGEMM( 'N', 'N', M, N+1, MIN(M,N+1), -ONE, F1, &
|
||||||
|
LDF, Y, LDY, ONE, F2, LDF )
|
||||||
|
TMP_FQR = DLANGE( 'F', M, N+1, F2, LDF, WORK ) / &
|
||||||
|
DLANGE( 'F', M, N+1, F, LDF, WORK )
|
||||||
|
IF ( TMP_FQR > TOL2 ) THEN
|
||||||
|
WRITE(*,*) 'FAILED! Something was wrong with the run.'
|
||||||
|
NFAIL_F_QR = NFAIL_F_QR + 1
|
||||||
|
END IF
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!..... DGEDMDQ check point
|
||||||
|
IF ( LSAME(RESIDS, 'R') ) THEN
|
||||||
|
! Compare the residuals returned by DGEDMDQ with the
|
||||||
|
! explicitly computed residuals using the matrix A.
|
||||||
|
! Compute explicitly Y1 = A*Z
|
||||||
|
CALL DGEMM( 'N', 'N', M, KQ, M, ONE, A, M, Z, M, ZERO, Y1, M )
|
||||||
|
! ... 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 DGEDMDQ)
|
||||||
|
i = 1
|
||||||
|
DO WHILE ( i <= KQ )
|
||||||
|
IF ( IEIGQ(i) == ZERO ) THEN
|
||||||
|
! have a real eigenvalue with real eigenvector
|
||||||
|
CALL DAXPY( M, -REIGQ(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) = DNRM2( M, Y1(1,i), 1)
|
||||||
|
i = i + 1
|
||||||
|
ELSE
|
||||||
|
! Have a complex conjugate pair
|
||||||
|
! REIG(i) +- sqrt(-1)*IMEIG(i).
|
||||||
|
! Since all computation is done in real
|
||||||
|
! arithmetic, the formula for the residual
|
||||||
|
! is recast for real representation of the
|
||||||
|
! complex conjugate eigenpair. See the
|
||||||
|
! description of RES.
|
||||||
|
AB(1,1) = REIGQ(i)
|
||||||
|
AB(2,1) = -IEIGQ(i)
|
||||||
|
AB(1,2) = IEIGQ(i)
|
||||||
|
AB(2,2) = REIGQ(i)
|
||||||
|
CALL DGEMM( 'N', 'N', M, 2, 2, -ONE, Z(1,i), &
|
||||||
|
M, AB, 2, ONE, Y1(1,i), M ) ! BLAS CALL
|
||||||
|
! Y(1:M,i:i+1) = Y(1:M,i:i+1) - Z(1:M,i:i+1) * AB ! INTRINSIC
|
||||||
|
RES1(i) = DLANGE( 'F', M, 2, Y1(1,i), M, &
|
||||||
|
WORK ) ! LAPACK CALL
|
||||||
|
RES1(i+1) = RES1(i)
|
||||||
|
i = i + 2
|
||||||
|
END IF
|
||||||
|
END DO
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, KQ
|
||||||
|
TMP = MAX( TMP, ABS(RES(i) - RES1(i)) * &
|
||||||
|
SINGVQX(K)/(ANORM*SINGVQX(1)) )
|
||||||
|
END DO
|
||||||
|
TMP_REZQ = MAX( TMP_REZQ, TMP )
|
||||||
|
IF ( TMP > TOL2 ) THEN
|
||||||
|
NFAIL_REZQ = NFAIL_REZQ + 1
|
||||||
|
WRITE(*,*) '................ DGEDMDQ FAILED!', &
|
||||||
|
'Check the code for implementation errors.'
|
||||||
|
STOP
|
||||||
|
END IF
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
DO i = 1, KQ
|
||||||
|
LAMBDAQ(i,1) = REIGQ(i)
|
||||||
|
LAMBDAQ(i,2) = IEIGQ(i)
|
||||||
|
END DO
|
||||||
|
|
||||||
|
DEALLOCATE(WORK)
|
||||||
|
DEALLOCATE(IWORK)
|
||||||
|
END IF ! TEST_QRDMD
|
||||||
|
!======================================================================
|
||||||
|
|
||||||
|
END DO ! LWMINOPT
|
||||||
|
!write(*,*) 'LWMINOPT loop completed'
|
||||||
|
END DO ! WHTSVD LOOP
|
||||||
|
!write(*,*) 'WHTSVD loop completed'
|
||||||
|
END DO ! NRNK LOOP
|
||||||
|
!write(*,*) 'NRNK loop completed'
|
||||||
|
END DO ! SCALE LOOP
|
||||||
|
!write(*,*) 'SCALE loop completed'
|
||||||
|
END DO ! JOBF LOOP
|
||||||
|
!write(*,*) 'JOBREF loop completed'
|
||||||
|
END DO ! JOBZ LOOP
|
||||||
|
!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(DA)
|
||||||
|
DEALLOCATE(DL)
|
||||||
|
DEALLOCATE(F)
|
||||||
|
DEALLOCATE(F1)
|
||||||
|
DEALLOCATE(F2)
|
||||||
|
DEALLOCATE(X)
|
||||||
|
DEALLOCATE(X0)
|
||||||
|
DEALLOCATE(SINGVX)
|
||||||
|
DEALLOCATE(SINGVQX)
|
||||||
|
DEALLOCATE(Y)
|
||||||
|
DEALLOCATE(Y0)
|
||||||
|
DEALLOCATE(Y1)
|
||||||
|
DEALLOCATE(Z)
|
||||||
|
DEALLOCATE(Z1)
|
||||||
|
DEALLOCATE(RES)
|
||||||
|
DEALLOCATE(RES1)
|
||||||
|
DEALLOCATE(RESEX)
|
||||||
|
DEALLOCATE(REIG)
|
||||||
|
DEALLOCATE(IEIG)
|
||||||
|
DEALLOCATE(REIGQ)
|
||||||
|
DEALLOCATE(IEIGQ)
|
||||||
|
DEALLOCATE(REIGA)
|
||||||
|
DEALLOCATE(IEIGA)
|
||||||
|
DEALLOCATE(VA)
|
||||||
|
DEALLOCATE(LAMBDA)
|
||||||
|
DEALLOCATE(LAMBDAQ)
|
||||||
|
DEALLOCATE(EIGA)
|
||||||
|
DEALLOCATE(W)
|
||||||
|
DEALLOCATE(AU)
|
||||||
|
DEALLOCATE(S)
|
||||||
|
|
||||||
|
!............................................................
|
||||||
|
! Generate random M-by-M matrix A. Use DLATMR from
|
||||||
|
END DO ! LLOOP
|
||||||
|
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*) ' Test summary for DGEDMD :'
|
||||||
|
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_ZXW
|
||||||
|
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(*,*) '>>>> DGEDMD :: ALL TESTS PASSED.'
|
||||||
|
ELSE
|
||||||
|
WRITE(*,*) NFAIL_TOTAL, 'FAILURES!'
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>> DGEDMD :: TESTS FAILED. CHECK THE IMPLEMENTATION.'
|
||||||
|
END IF
|
||||||
|
|
||||||
|
IF ( TEST_QRDMD ) THEN
|
||||||
|
WRITE(*,*)
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*) ' Test summary for DGEDMDQ :'
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*)
|
||||||
|
|
||||||
|
IF ( NFAIL_SVDIFF == 0 ) THEN
|
||||||
|
WRITE(*,*) '>>>> DGEDMD and DGEDMDQ computed singular &
|
||||||
|
&values test PASSED.'
|
||||||
|
ELSE
|
||||||
|
WRITE(*,*) 'DGEDMD and DGEDMDQ 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(*,*) '>>>>>>> DGEDMDQ :: ALL TESTS PASSED.'
|
||||||
|
ELSE
|
||||||
|
WRITE(*,*) NFAILQ_TOTAL, 'FAILURES!'
|
||||||
|
WRITE(*,*) '>>>>>>> DGEDMDQ :: TESTS FAILED. CHECK THE IMPLEMENTATION.'
|
||||||
|
END IF
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
WRITE(*,*)
|
||||||
|
WRITE(*,*) 'Test completed.'
|
||||||
|
STOP
|
||||||
|
END
|
||||||
|
|
@ -0,0 +1,792 @@
|
||||||
|
! This is a test program for checking the implementations of
|
||||||
|
! the implementations of the following subroutines
|
||||||
|
!
|
||||||
|
! SGEDMD for computation of the
|
||||||
|
! Dynamic Mode Decomposition (DMD)
|
||||||
|
! SGEDMDQ 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.
|
||||||
|
!... .........................................................
|
||||||
|
! NOTE:
|
||||||
|
! When using the Intel MKL 2022.0.3 the subroutine xGESVDQ
|
||||||
|
! (optionally used in xGEDMD) may cause access violation
|
||||||
|
! error for x = S, D, C, Z, but only if called with the
|
||||||
|
! work space query. (At least in our Windows 10 MSVS 2019.)
|
||||||
|
! The problem can be mitigated by downloading the source
|
||||||
|
! code of xGESVDQ from the LAPACK repository and use it
|
||||||
|
! localy instead of the one in the MKL. This seems to
|
||||||
|
! indicate that the problem is indeed in the MKL.
|
||||||
|
! This problem did not appear whith Intel MKL 2022.2.0.
|
||||||
|
!
|
||||||
|
! NOTE:
|
||||||
|
! xGESDD seems to have a problem with workspace. In some
|
||||||
|
! cases the length of the optimal workspace is returned
|
||||||
|
! smaller than the minimal workspace, as specified in the
|
||||||
|
! code. As a precaution, all optimal workspaces are
|
||||||
|
! set as MAX(minimal, optimal).
|
||||||
|
! Latest implementations of complex xGESDD have different
|
||||||
|
! length of the real worksapce. We use max value over
|
||||||
|
! two versions.
|
||||||
|
!............................................................
|
||||||
|
!............................................................
|
||||||
|
!
|
||||||
|
PROGRAM DMD_TEST
|
||||||
|
use iso_fortran_env, only: real32
|
||||||
|
IMPLICIT NONE
|
||||||
|
integer, parameter :: WP = real32
|
||||||
|
|
||||||
|
!............................................................
|
||||||
|
REAL(KIND=WP), PARAMETER :: ONE = 1.0_WP
|
||||||
|
REAL(KIND=WP), PARAMETER :: ZERO = 0.0_WP
|
||||||
|
!............................................................
|
||||||
|
REAL(KIND=WP), ALLOCATABLE, DIMENSION(:,:) :: &
|
||||||
|
A, AC, EIGA, LAMBDA, LAMBDAQ, F, F1, F2,&
|
||||||
|
Z, Z1, S, AU, W, VA, X, X0, Y, Y0, Y1
|
||||||
|
REAL(KIND=WP), ALLOCATABLE, DIMENSION(:) :: &
|
||||||
|
DA, DL, DR, REIG, REIGA, REIGQ, IEIG, &
|
||||||
|
IEIGA, IEIGQ, RES, RES1, RESEX, SINGVX,&
|
||||||
|
SINGVQX, WORK
|
||||||
|
INTEGER , ALLOCATABLE, DIMENSION(:) :: IWORK
|
||||||
|
REAL(KIND=WP) :: AB(2,2), WDUMMY(2)
|
||||||
|
INTEGER :: IDUMMY(2), ISEED(4), RJOBDATA(8)
|
||||||
|
REAL(KIND=WP) :: ANORM, COND, CONDL, CONDR, DMAX, EPS, &
|
||||||
|
TOL, TOL2, SVDIFF, TMP, TMP_AU, &
|
||||||
|
TMP_FQR, TMP_REZ, TMP_REZQ, TMP_ZXW, &
|
||||||
|
TMP_EX, XNORM, YNORM
|
||||||
|
!............................................................
|
||||||
|
INTEGER :: K, KQ, LDF, LDS, LDA, LDAU, LDW, LDX, LDY, &
|
||||||
|
LDZ, LIWORK, LWORK, M, N, L, LLOOP, NRNK
|
||||||
|
INTEGER :: i, iJOBREF, iJOBZ, iSCALE, INFO, KDIFF, &
|
||||||
|
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(LEN=1) GRADE, JOBREF, JOBZ, PIVTNG, RSIGN, &
|
||||||
|
SCALE, RESIDS, WANTQ, WANTR
|
||||||
|
|
||||||
|
LOGICAL TEST_QRDMD
|
||||||
|
!..... external subroutines (BLAS and LAPACK)
|
||||||
|
EXTERNAL SAXPY, SGEEV, SGEMM, SGEMV, SLACPY, SLASCL
|
||||||
|
EXTERNAL SLARNV, SLATMR
|
||||||
|
!.....external subroutines DMD package, part 1
|
||||||
|
! subroutines under test
|
||||||
|
EXTERNAL SGEDMD, SGEDMDQ
|
||||||
|
|
||||||
|
!..... external functions (BLAS and LAPACK)
|
||||||
|
EXTERNAL SLAMCH, SLANGE, SNRM2
|
||||||
|
REAL(KIND=WP) :: SLAMCH, SLANGE, SNRM2
|
||||||
|
EXTERNAL LSAME
|
||||||
|
LOGICAL LSAME
|
||||||
|
|
||||||
|
INTRINSIC ABS, INT, MIN, MAX
|
||||||
|
!............................................................
|
||||||
|
|
||||||
|
! The test is always in pairs : ( SGEDMD and SGEDMDQ )
|
||||||
|
! because the test includes comparing the results (in pairs).
|
||||||
|
!.....................................................................................
|
||||||
|
TEST_QRDMD = .TRUE. ! This code by default performs tests on SGEDMDQ
|
||||||
|
! 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 SP
|
||||||
|
|
||||||
|
! 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
|
||||||
|
KDIFF = 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 ...
|
||||||
|
WRITE(*,*) 'M = '
|
||||||
|
READ(*,*) M
|
||||||
|
WRITE(*,*) M
|
||||||
|
! ... and the number of snapshots.
|
||||||
|
WRITE(*,*) 'N = '
|
||||||
|
READ(*,*) N
|
||||||
|
WRITE(*,*) 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 = MAX(M,N+1)
|
||||||
|
LDY = MAX(M,N+1)
|
||||||
|
LDW = N
|
||||||
|
LDZ = M
|
||||||
|
LDAU = MAX(M,N+1)
|
||||||
|
LDS = N
|
||||||
|
|
||||||
|
TMP_ZXW = ZERO
|
||||||
|
TMP_AU = ZERO
|
||||||
|
TMP_REZ = ZERO
|
||||||
|
TMP_REZQ = ZERO
|
||||||
|
SVDIFF = ZERO
|
||||||
|
TMP_EX = ZERO
|
||||||
|
|
||||||
|
!
|
||||||
|
! Test the subroutines on real data snapshots. All
|
||||||
|
! computation is done in real arithmetic, even when
|
||||||
|
! Koopman eigenvalues and modes are real.
|
||||||
|
!
|
||||||
|
! Allocate memory space
|
||||||
|
ALLOCATE( A(LDA,M) )
|
||||||
|
ALLOCATE( AC(LDA,M) )
|
||||||
|
ALLOCATE( DA(M) )
|
||||||
|
ALLOCATE( DL(M) )
|
||||||
|
ALLOCATE( F(LDF,N+1) )
|
||||||
|
ALLOCATE( F1(LDF,N+1) )
|
||||||
|
ALLOCATE( F2(LDF,N+1) )
|
||||||
|
ALLOCATE( X(LDX,N) )
|
||||||
|
ALLOCATE( X0(LDX,N) )
|
||||||
|
ALLOCATE( SINGVX(N) )
|
||||||
|
ALLOCATE( SINGVQX(N) )
|
||||||
|
ALLOCATE( Y(LDY,N+1) )
|
||||||
|
ALLOCATE( Y0(LDY,N+1) )
|
||||||
|
ALLOCATE( Y1(M,N+1) )
|
||||||
|
ALLOCATE( Z(LDZ,N) )
|
||||||
|
ALLOCATE( Z1(LDZ,N) )
|
||||||
|
ALLOCATE( RES(N) )
|
||||||
|
ALLOCATE( RES1(N) )
|
||||||
|
ALLOCATE( RESEX(N) )
|
||||||
|
ALLOCATE( REIG(N) )
|
||||||
|
ALLOCATE( IEIG(N) )
|
||||||
|
ALLOCATE( REIGQ(N) )
|
||||||
|
ALLOCATE( IEIGQ(N) )
|
||||||
|
ALLOCATE( REIGA(M) )
|
||||||
|
ALLOCATE( IEIGA(M) )
|
||||||
|
ALLOCATE( VA(LDA,M) )
|
||||||
|
ALLOCATE( LAMBDA(N,2) )
|
||||||
|
ALLOCATE( LAMBDAQ(N,2) )
|
||||||
|
ALLOCATE( EIGA(M,2) )
|
||||||
|
ALLOCATE( W(LDW,N) )
|
||||||
|
ALLOCATE( AU(LDAU,N) )
|
||||||
|
ALLOCATE( S(N,N) )
|
||||||
|
|
||||||
|
TOL = M*EPS
|
||||||
|
! This mimics O(M*N)*EPS bound for accumulated roundoff error.
|
||||||
|
! The factor 10 is somewhat arbitrary.
|
||||||
|
TOL2 = 10*M*N*EPS
|
||||||
|
|
||||||
|
!.............
|
||||||
|
|
||||||
|
DO K_TRAJ = 1, 2
|
||||||
|
! Number of intial conditions in the simulation/trajectories (1 or 2)
|
||||||
|
|
||||||
|
COND = 1.0D8
|
||||||
|
DMAX = 1.0D2
|
||||||
|
RSIGN = 'F'
|
||||||
|
GRADE = 'N'
|
||||||
|
MODEL = 6
|
||||||
|
CONDL = 1.0D2
|
||||||
|
MODER = 6
|
||||||
|
CONDR = 1.0D2
|
||||||
|
PIVTNG = 'N'
|
||||||
|
|
||||||
|
! Loop over all parameter MODE values for ZLATMR (+1,..,+6)
|
||||||
|
DO MODE = 1, 6
|
||||||
|
|
||||||
|
ALLOCATE( IWORK(2*M) )
|
||||||
|
ALLOCATE(DR(N))
|
||||||
|
CALL SLATMR( M, M, 'S', ISEED, 'N', DA, MODE, COND, &
|
||||||
|
DMAX, RSIGN, GRADE, DL, MODEL, CONDL, &
|
||||||
|
DR, MODER, CONDR, PIVTNG, IWORK, M, M, &
|
||||||
|
ZERO, -ONE, 'N', A, LDA, IWORK(M+1), INFO )
|
||||||
|
DEALLOCATE(IWORK)
|
||||||
|
DEALLOCATE(DR)
|
||||||
|
|
||||||
|
LWORK = 4*M+1
|
||||||
|
ALLOCATE(WORK(LWORK))
|
||||||
|
AC = A
|
||||||
|
CALL SGEEV( 'N','V', M, AC, M, REIGA, IEIGA, VA, M, &
|
||||||
|
VA, M, WORK, LWORK, INFO ) ! LAPACK CALL
|
||||||
|
DEALLOCATE(WORK)
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, M
|
||||||
|
EIGA(i,1) = REIGA(i)
|
||||||
|
EIGA(i,2) = IEIGA(i)
|
||||||
|
TMP = MAX( TMP, SQRT(REIGA(i)**2+IEIGA(i)**2))
|
||||||
|
END DO
|
||||||
|
|
||||||
|
! Scale A to have the desirable spectral radius.
|
||||||
|
CALL SLASCL( 'G', 0, 0, TMP, ONE, M, M, A, M, INFO )
|
||||||
|
CALL SLASCL( 'G', 0, 0, TMP, ONE, M, 2, EIGA, M, INFO )
|
||||||
|
|
||||||
|
! Compute the norm of A
|
||||||
|
ANORM = SLANGE( 'F', N, N, A, M, WDUMMY )
|
||||||
|
|
||||||
|
IF ( K_TRAJ == 2 ) THEN
|
||||||
|
! generate data with two inital conditions
|
||||||
|
CALL SLARNV(2, ISEED, M, F1(1,1) )
|
||||||
|
F1(1:M,1) = 1.0E-10*F1(1:M,1)
|
||||||
|
DO i = 1, N/2
|
||||||
|
CALL SGEMV( 'N', M, M, ONE, A, M, F1(1,i), 1, ZERO, &
|
||||||
|
F1(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
X0(1:M,1:N/2) = F1(1:M,1:N/2)
|
||||||
|
Y0(1:M,1:N/2) = F1(1:M,2:N/2+1)
|
||||||
|
|
||||||
|
CALL SLARNV(2, ISEED, M, F1(1,1) )
|
||||||
|
DO i = 1, N-N/2
|
||||||
|
CALL SGEMV( 'N', M, M, ONE, A, M, F1(1,i), 1, ZERO, &
|
||||||
|
F1(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
X0(1:M,N/2+1:N) = F1(1:M,1:N-N/2)
|
||||||
|
Y0(1:M,N/2+1:N) = F1(1:M,2:N-N/2+1)
|
||||||
|
ELSE
|
||||||
|
! single trajectory
|
||||||
|
CALL SLARNV(2, ISEED, M, F(1,1) )
|
||||||
|
DO i = 1, N
|
||||||
|
CALL SGEMV( 'N', M, M, ONE, A, M, F(1,i), 1, ZERO, &
|
||||||
|
F(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
X0(1:M,1:N) = F(1:M,1:N)
|
||||||
|
Y0(1:M,1:N) = F(1:M,2:N+1)
|
||||||
|
END IF
|
||||||
|
|
||||||
|
XNORM = SLANGE( 'F', M, N, X0, LDX, WDUMMY )
|
||||||
|
YNORM = SLANGE( 'F', M, N, Y0, LDX, WDUMMY )
|
||||||
|
!............................................................
|
||||||
|
|
||||||
|
DO iJOBZ = 1, 4
|
||||||
|
|
||||||
|
SELECT CASE ( iJOBZ )
|
||||||
|
CASE(1)
|
||||||
|
JOBZ = 'V' ! Ritz vectors will be computed
|
||||||
|
RESIDS = 'R' ! Residuals will be computed
|
||||||
|
CASE(2)
|
||||||
|
JOBZ = 'V'
|
||||||
|
RESIDS = 'N'
|
||||||
|
CASE(3)
|
||||||
|
JOBZ = 'F' ! Ritz vectors in factored form
|
||||||
|
RESIDS = 'N'
|
||||||
|
CASE(4)
|
||||||
|
JOBZ = 'N'
|
||||||
|
RESIDS = 'N'
|
||||||
|
END SELECT
|
||||||
|
|
||||||
|
DO iJOBREF = 1, 3
|
||||||
|
|
||||||
|
SELECT CASE ( iJOBREF )
|
||||||
|
CASE(1)
|
||||||
|
JOBREF = 'R' ! Data for refined Ritz vectors
|
||||||
|
CASE(2)
|
||||||
|
JOBREF = 'E' ! Exact DMD vectors
|
||||||
|
CASE(3)
|
||||||
|
JOBREF = 'N'
|
||||||
|
END SELECT
|
||||||
|
|
||||||
|
DO iSCALE = 1, 4
|
||||||
|
|
||||||
|
SELECT CASE ( iSCALE )
|
||||||
|
CASE(1)
|
||||||
|
SCALE = 'S' ! X data normalized
|
||||||
|
CASE(2)
|
||||||
|
SCALE = 'C' ! X normalized, consist. check
|
||||||
|
CASE(3)
|
||||||
|
SCALE = 'Y' ! Y data normalized
|
||||||
|
CASE(4)
|
||||||
|
SCALE = 'N'
|
||||||
|
END SELECT
|
||||||
|
|
||||||
|
DO iNRNK = -1, -2, -1
|
||||||
|
! Two truncation strategies. The "-2" case for R&D
|
||||||
|
! purposes only - it uses possibly low accuracy small
|
||||||
|
! singular values, in which case the formulas used in
|
||||||
|
! the DMD are highly sensitive.
|
||||||
|
NRNK = iNRNK
|
||||||
|
|
||||||
|
DO iWHTSVD = 1, 4
|
||||||
|
! 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.
|
||||||
|
|
||||||
|
X(1:M,1:N) = X0(1:M,1:N)
|
||||||
|
Y(1:M,1:N) = Y0(1:M,1:N)
|
||||||
|
|
||||||
|
! SGEDMD: Workspace query and workspace allocation
|
||||||
|
CALL SGEDMD( SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, M, &
|
||||||
|
N, X, LDX, Y, LDY, NRNK, TOL, K, REIG, IEIG, Z, &
|
||||||
|
LDZ, RES, AU, LDAU, W, LDW, S, LDS, WDUMMY, -1, &
|
||||||
|
IDUMMY, -1, INFO )
|
||||||
|
|
||||||
|
LIWORK = IDUMMY(1)
|
||||||
|
ALLOCATE( IWORK(LIWORK) )
|
||||||
|
LWORK = INT(WDUMMY(LWMINOPT))
|
||||||
|
ALLOCATE( WORK(LWORK) )
|
||||||
|
|
||||||
|
! SGEDMD test: CALL SGEDMD
|
||||||
|
CALL SGEDMD( SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, M, &
|
||||||
|
N, X, LDX, Y, LDY, NRNK, TOL, K, REIG, IEIG, Z, &
|
||||||
|
LDZ, RES, AU, LDAU, W, LDW, S, LDS, WORK, LWORK,&
|
||||||
|
IWORK, LIWORK, INFO )
|
||||||
|
|
||||||
|
SINGVX(1:N) = WORK(1:N)
|
||||||
|
|
||||||
|
!...... SGEDMD check point
|
||||||
|
IF ( LSAME(JOBZ,'V') ) THEN
|
||||||
|
! Check that Z = X*W, on return from SGEDMD
|
||||||
|
! This checks that the returned aigenvectors in Z are
|
||||||
|
! the product of the SVD'POD basis returned in X
|
||||||
|
! and the eigenvectors of the rayleigh quotient
|
||||||
|
! returned in W
|
||||||
|
CALL SGEMM( 'N', 'N', M, K, K, ONE, X, LDX, W, LDW, &
|
||||||
|
ZERO, Z1, LDZ )
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, K
|
||||||
|
CALL SAXPY( M, -ONE, Z(1,i), 1, Z1(1,i), 1)
|
||||||
|
TMP = MAX(TMP, SNRM2( M, Z1(1,i), 1 ) )
|
||||||
|
END DO
|
||||||
|
TMP_ZXW = MAX(TMP_ZXW, TMP )
|
||||||
|
|
||||||
|
IF ( TMP_ZXW > 10*M*EPS ) THEN
|
||||||
|
NFAIL_Z_XV = NFAIL_Z_XV + 1
|
||||||
|
END IF
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!...... SGEDMD 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 SGEMM( 'N', 'N', M, K, M, ONE, A, LDA, X, LDX, &
|
||||||
|
ZERO, Z1, LDZ )
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, K
|
||||||
|
CALL SAXPY( M, -ONE, AU(1,i), 1, Z1(1,i), 1)
|
||||||
|
TMP = MAX( TMP, SNRM2( M, Z1(1,i),1 ) * &
|
||||||
|
SINGVX(K)/(ANORM*SINGVX(1)) )
|
||||||
|
END DO
|
||||||
|
TMP_AU = MAX( TMP_AU, TMP )
|
||||||
|
|
||||||
|
IF ( TMP > TOL2 ) THEN
|
||||||
|
NFAIL_AU = NFAIL_AU + 1
|
||||||
|
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 SGEMM( 'N', 'N', M, K, M, ONE, A, LDA, AU, LDAU, ZERO, Y1, M )
|
||||||
|
i=1
|
||||||
|
DO WHILE ( i <= K )
|
||||||
|
IF ( IEIG(i) == ZERO ) THEN
|
||||||
|
! have a real eigenvalue with real eigenvector
|
||||||
|
CALL SAXPY( M, -REIG(i), AU(1,i), 1, Y1(1,i), 1 )
|
||||||
|
RESEX(i) = SNRM2( M, Y1(1,i), 1) / SNRM2(M,AU(1,i),1)
|
||||||
|
i = i + 1
|
||||||
|
ELSE
|
||||||
|
! Have a complex conjugate pair
|
||||||
|
! REIG(i) +- sqrt(-1)*IMEIG(i).
|
||||||
|
! Since all computation is done in real
|
||||||
|
! arithmetic, the formula for the residual
|
||||||
|
! is recast for real representation of the
|
||||||
|
! complex conjugate eigenpair. See the
|
||||||
|
! description of RES.
|
||||||
|
AB(1,1) = REIG(i)
|
||||||
|
AB(2,1) = -IEIG(i)
|
||||||
|
AB(1,2) = IEIG(i)
|
||||||
|
AB(2,2) = REIG(i)
|
||||||
|
CALL SGEMM( 'N', 'N', M, 2, 2, -ONE, AU(1,i), &
|
||||||
|
M, AB, 2, ONE, Y1(1,i), M )
|
||||||
|
RESEX(i) = SLANGE( 'F', M, 2, Y1(1,i), M, &
|
||||||
|
WORK )/ SLANGE( 'F', M, 2, AU(1,i), M, &
|
||||||
|
WORK )
|
||||||
|
RESEX(i+1) = RESEX(i)
|
||||||
|
i = i + 2
|
||||||
|
END IF
|
||||||
|
END DO
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!...... SGEDMD check point
|
||||||
|
IF ( LSAME(RESIDS, 'R') ) THEN
|
||||||
|
! Compare the residuals returned by SGEDMD with the
|
||||||
|
! explicitly computed residuals using the matrix A.
|
||||||
|
! Compute explicitly Y1 = A*Z
|
||||||
|
CALL SGEMM( 'N', 'N', M, K, M, ONE, A, LDA, Z, LDZ, ZERO, Y1, M )
|
||||||
|
! ... 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 SGEDMD,)
|
||||||
|
i = 1
|
||||||
|
DO WHILE ( i <= K )
|
||||||
|
IF ( IEIG(i) == ZERO ) THEN
|
||||||
|
! have a real eigenvalue with real eigenvector
|
||||||
|
CALL SAXPY( M, -REIG(i), Z(1,i), 1, Y1(1,i), 1 )
|
||||||
|
RES1(i) = SNRM2( M, Y1(1,i), 1)
|
||||||
|
i = i + 1
|
||||||
|
ELSE
|
||||||
|
! Have a complex conjugate pair
|
||||||
|
! REIG(i) +- sqrt(-1)*IMEIG(i).
|
||||||
|
! Since all computation is done in real
|
||||||
|
! arithmetic, the formula for the residual
|
||||||
|
! is recast for real representation of the
|
||||||
|
! complex conjugate eigenpair. See the
|
||||||
|
! description of RES.
|
||||||
|
AB(1,1) = REIG(i)
|
||||||
|
AB(2,1) = -IEIG(i)
|
||||||
|
AB(1,2) = IEIG(i)
|
||||||
|
AB(2,2) = REIG(i)
|
||||||
|
CALL SGEMM( 'N', 'N', M, 2, 2, -ONE, Z(1,i), &
|
||||||
|
M, AB, 2, ONE, Y1(1,i), M )
|
||||||
|
RES1(i) = SLANGE( 'F', M, 2, Y1(1,i), M, &
|
||||||
|
WORK )
|
||||||
|
RES1(i+1) = RES1(i)
|
||||||
|
i = i + 2
|
||||||
|
END IF
|
||||||
|
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
|
||||||
|
NFAIL_REZ = NFAIL_REZ + 1
|
||||||
|
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
|
||||||
|
|
||||||
|
! ... store the results for inspection
|
||||||
|
DO i = 1, K
|
||||||
|
LAMBDA(i,1) = REIG(i)
|
||||||
|
LAMBDA(i,2) = IEIG(i)
|
||||||
|
END DO
|
||||||
|
|
||||||
|
DEALLOCATE(IWORK)
|
||||||
|
DEALLOCATE(WORK)
|
||||||
|
|
||||||
|
!======================================================================
|
||||||
|
! Now test the SGEDMDQ, if requested.
|
||||||
|
!======================================================================
|
||||||
|
IF ( TEST_QRDMD .AND. (K_TRAJ == 1) ) THEN
|
||||||
|
RJOBDATA(2) = 1
|
||||||
|
F1 = F
|
||||||
|
|
||||||
|
! SGEDMDQ test: Workspace query and workspace allocation
|
||||||
|
CALL SGEDMDQ( SCALE, JOBZ, RESIDS, WANTQ, WANTR, &
|
||||||
|
JOBREF, WHTSVD, M, N+1, F1, LDF, X, LDX, Y, &
|
||||||
|
LDY, NRNK, TOL, KQ, REIGQ, IEIGQ, Z, LDZ, &
|
||||||
|
RES, AU, LDAU, W, LDW, S, LDS, WDUMMY, &
|
||||||
|
-1, IDUMMY, -1, INFO )
|
||||||
|
LIWORK = IDUMMY(1)
|
||||||
|
ALLOCATE( IWORK(LIWORK) )
|
||||||
|
LWORK = INT(WDUMMY(LWMINOPT))
|
||||||
|
ALLOCATE(WORK(LWORK))
|
||||||
|
|
||||||
|
! SGEDMDQ test: CALL SGEDMDQ
|
||||||
|
CALL SGEDMDQ( SCALE, JOBZ, RESIDS, WANTQ, WANTR, &
|
||||||
|
JOBREF, WHTSVD, M, N+1, F1, LDF, X, LDX, Y, &
|
||||||
|
LDY, NRNK, TOL, KQ, REIGQ, IEIGQ, Z, LDZ, &
|
||||||
|
RES, AU, LDAU, W, LDW, S, LDS, &
|
||||||
|
WORK, LWORK, IWORK, LIWORK, INFO )
|
||||||
|
|
||||||
|
SINGVQX(1:KQ) = WORK(MIN(M,N+1)+1: MIN(M,N+1)+KQ)
|
||||||
|
|
||||||
|
!..... SGEDMDQ check point
|
||||||
|
IF ( KQ /= K ) THEN
|
||||||
|
KDIFF = KDIFF+1
|
||||||
|
END IF
|
||||||
|
|
||||||
|
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 > M*N*EPS ) THEN
|
||||||
|
NFAIL_SVDIFF = NFAIL_SVDIFF + 1
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!..... SGEDMDQ 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.
|
||||||
|
F2 = F
|
||||||
|
CALL SGEMM( 'N', 'N', M, N+1, MIN(M,N+1), -ONE, F1, &
|
||||||
|
LDF, Y, LDY, ONE, F2, LDF )
|
||||||
|
TMP_FQR = SLANGE( 'F', M, N+1, F2, LDF, WORK ) / &
|
||||||
|
SLANGE( 'F', M, N+1, F, LDF, WORK )
|
||||||
|
IF ( TMP_FQR > TOL2 ) THEN
|
||||||
|
NFAIL_F_QR = NFAIL_F_QR + 1
|
||||||
|
END IF
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!..... SGEDMDQ checkpoint
|
||||||
|
IF ( LSAME(RESIDS, 'R') ) THEN
|
||||||
|
! Compare the residuals returned by SGEDMDQ with the
|
||||||
|
! explicitly computed residuals using the matrix A.
|
||||||
|
! Compute explicitly Y1 = A*Z
|
||||||
|
CALL SGEMM( 'N', 'N', M, KQ, M, ONE, A, M, Z, M, ZERO, Y1, M )
|
||||||
|
! ... 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 SGEDMDQ)
|
||||||
|
i = 1
|
||||||
|
DO WHILE ( i <= KQ )
|
||||||
|
IF ( IEIGQ(i) == ZERO ) THEN
|
||||||
|
! have a real eigenvalue with real eigenvector
|
||||||
|
CALL SAXPY( M, -REIGQ(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) = SNRM2( M, Y1(1,i), 1)
|
||||||
|
i = i + 1
|
||||||
|
ELSE
|
||||||
|
! Have a complex conjugate pair
|
||||||
|
! REIG(i) +- sqrt(-1)*IMEIG(i).
|
||||||
|
! Since all computation is done in real
|
||||||
|
! arithmetic, the formula for the residual
|
||||||
|
! is recast for real representation of the
|
||||||
|
! complex conjugate eigenpair. See the
|
||||||
|
! description of RES.
|
||||||
|
AB(1,1) = REIGQ(i)
|
||||||
|
AB(2,1) = -IEIGQ(i)
|
||||||
|
AB(1,2) = IEIGQ(i)
|
||||||
|
AB(2,2) = REIGQ(i)
|
||||||
|
CALL SGEMM( 'N', 'N', M, 2, 2, -ONE, Z(1,i), &
|
||||||
|
M, AB, 2, ONE, Y1(1,i), M ) ! BLAS CALL
|
||||||
|
! Y(1:M,i:i+1) = Y(1:M,i:i+1) - Z(1:M,i:i+1) * AB ! INTRINSIC
|
||||||
|
RES1(i) = SLANGE( 'F', M, 2, Y1(1,i), M, &
|
||||||
|
WORK ) ! LAPACK CALL
|
||||||
|
RES1(i+1) = RES1(i)
|
||||||
|
i = i + 2
|
||||||
|
END IF
|
||||||
|
END DO
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, KQ
|
||||||
|
TMP = MAX( TMP, ABS(RES(i) - RES1(i)) * &
|
||||||
|
SINGVQX(K)/(ANORM*SINGVQX(1)) )
|
||||||
|
END DO
|
||||||
|
TMP_REZQ = MAX( TMP_REZQ, TMP )
|
||||||
|
IF ( TMP > TOL2 ) THEN
|
||||||
|
NFAIL_REZQ = NFAIL_REZQ + 1
|
||||||
|
END IF
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
DO i = 1, KQ
|
||||||
|
LAMBDAQ(i,1) = REIGQ(i)
|
||||||
|
LAMBDAQ(i,2) = IEIGQ(i)
|
||||||
|
END DO
|
||||||
|
|
||||||
|
DEALLOCATE(WORK)
|
||||||
|
DEALLOCATE(IWORK)
|
||||||
|
END IF ! TEST_QRDMD
|
||||||
|
!======================================================================
|
||||||
|
|
||||||
|
END DO ! LWMINOPT
|
||||||
|
!write(*,*) 'LWMINOPT loop completed'
|
||||||
|
END DO ! WHTSVD LOOP
|
||||||
|
!write(*,*) 'WHTSVD loop completed'
|
||||||
|
END DO ! NRNK LOOP
|
||||||
|
!write(*,*) 'NRNK loop completed'
|
||||||
|
END DO ! SCALE LOOP
|
||||||
|
!write(*,*) 'SCALE loop completed'
|
||||||
|
END DO ! JOBF LOOP
|
||||||
|
!write(*,*) 'JOBREF loop completed'
|
||||||
|
END DO ! JOBZ LOOP
|
||||||
|
!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(DA)
|
||||||
|
DEALLOCATE(DL)
|
||||||
|
DEALLOCATE(F)
|
||||||
|
DEALLOCATE(F1)
|
||||||
|
DEALLOCATE(F2)
|
||||||
|
DEALLOCATE(X)
|
||||||
|
DEALLOCATE(X0)
|
||||||
|
DEALLOCATE(SINGVX)
|
||||||
|
DEALLOCATE(SINGVQX)
|
||||||
|
DEALLOCATE(Y)
|
||||||
|
DEALLOCATE(Y0)
|
||||||
|
DEALLOCATE(Y1)
|
||||||
|
DEALLOCATE(Z)
|
||||||
|
DEALLOCATE(Z1)
|
||||||
|
DEALLOCATE(RES)
|
||||||
|
DEALLOCATE(RES1)
|
||||||
|
DEALLOCATE(RESEX)
|
||||||
|
DEALLOCATE(REIG)
|
||||||
|
DEALLOCATE(IEIG)
|
||||||
|
DEALLOCATE(REIGQ)
|
||||||
|
DEALLOCATE(IEIGQ)
|
||||||
|
DEALLOCATE(REIGA)
|
||||||
|
DEALLOCATE(IEIGA)
|
||||||
|
DEALLOCATE(VA)
|
||||||
|
DEALLOCATE(LAMBDA)
|
||||||
|
DEALLOCATE(LAMBDAQ)
|
||||||
|
DEALLOCATE(EIGA)
|
||||||
|
DEALLOCATE(W)
|
||||||
|
DEALLOCATE(AU)
|
||||||
|
DEALLOCATE(S)
|
||||||
|
|
||||||
|
!............................................................
|
||||||
|
! Generate random M-by-M matrix A. Use DLATMR from
|
||||||
|
END DO ! LLOOP
|
||||||
|
|
||||||
|
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*) ' Test summary for SGEDMD :'
|
||||||
|
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_ZXW
|
||||||
|
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(*,*) '>>>> SGEDMD :: ALL TESTS PASSED.'
|
||||||
|
ELSE
|
||||||
|
WRITE(*,*) NFAIL_TOTAL, 'FAILURES!'
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>> SGEDMD :: TESTS FAILED. CHECK THE IMPLEMENTATION.'
|
||||||
|
END IF
|
||||||
|
|
||||||
|
IF ( TEST_QRDMD ) THEN
|
||||||
|
WRITE(*,*)
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*) ' Test summary for SGEDMDQ :'
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*)
|
||||||
|
|
||||||
|
IF ( NFAIL_SVDIFF == 0 ) THEN
|
||||||
|
WRITE(*,*) '>>>> SGEDMD and SGEDMDQ computed singular &
|
||||||
|
&values test PASSED.'
|
||||||
|
ELSE
|
||||||
|
WRITE(*,*) 'SGEDMD and SGEDMDQ 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(*,*) '>>>>>>> SGEDMDQ :: ALL TESTS PASSED.'
|
||||||
|
ELSE
|
||||||
|
WRITE(*,*) NFAILQ_TOTAL, 'FAILURES!'
|
||||||
|
WRITE(*,*) '>>>>>>> SGEDMDQ :: TESTS FAILED. CHECK THE IMPLEMENTATION.'
|
||||||
|
END IF
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
WRITE(*,*)
|
||||||
|
WRITE(*,*) 'Test completed.'
|
||||||
|
STOP
|
||||||
|
END
|
||||||
|
|
@ -0,0 +1,745 @@
|
||||||
|
! This is a test program for checking the implementations of
|
||||||
|
! the implementations of the following subroutines
|
||||||
|
!
|
||||||
|
! ZGEDMD, for computation of the
|
||||||
|
! Dynamic Mode Decomposition (DMD)
|
||||||
|
! ZGEDMDQ, 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, only: real64
|
||||||
|
IMPLICIT NONE
|
||||||
|
integer, parameter :: WP = real64
|
||||||
|
|
||||||
|
!............................................................
|
||||||
|
REAL(KIND=WP), PARAMETER :: ONE = 1.0_WP
|
||||||
|
REAL(KIND=WP), PARAMETER :: ZERO = 0.0_WP
|
||||||
|
|
||||||
|
COMPLEX(KIND=WP), PARAMETER :: ZONE = ( 1.0_WP, 0.0_WP )
|
||||||
|
COMPLEX(KIND=WP), PARAMETER :: ZZERO = ( 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_ZXW, &
|
||||||
|
TMP_EX
|
||||||
|
|
||||||
|
!............................................................
|
||||||
|
COMPLEX(KIND=WP) :: ZMAX
|
||||||
|
INTEGER :: LZWORK
|
||||||
|
COMPLEX(KIND=WP), ALLOCATABLE, DIMENSION(:,:) :: ZA, ZAC, &
|
||||||
|
ZAU, ZF, ZF0, ZF1, ZS, ZW, &
|
||||||
|
ZX, ZX0, ZY, ZY0, ZY1, ZZ, ZZ1
|
||||||
|
COMPLEX(KIND=WP), ALLOCATABLE, DIMENSION(:) :: ZDA, ZDR, &
|
||||||
|
ZDL, ZEIGS, ZEIGSA, ZWORK
|
||||||
|
COMPLEX(KIND=WP) :: ZDUMMY(22), ZDUM2X2(2,2)
|
||||||
|
!............................................................
|
||||||
|
INTEGER :: K, KQ, LDF, LDS, LDA, LDAU, LDW, LDX, LDY, &
|
||||||
|
LDZ, LIWORK, LWORK, M, N, LLOOP, NRNK, NRNKsp
|
||||||
|
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, &
|
||||||
|
WHTSVDsp
|
||||||
|
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 DAXPY, DGEEV, DGEMM, DGEMV, DLACPY, DLASCL
|
||||||
|
EXTERNAL ZGEEV, ZGEMV, ZLASCL
|
||||||
|
EXTERNAL ZLARNV, ZLATMR
|
||||||
|
EXTERNAL ZAXPY, ZGEMM
|
||||||
|
!.....external subroutines DMD package, part 1
|
||||||
|
! subroutines under test
|
||||||
|
EXTERNAL ZGEDMD, ZGEDMDQ
|
||||||
|
!.....external functions (BLAS and LAPACK)
|
||||||
|
EXTERNAL DLAMCH, DZNRM2
|
||||||
|
REAL(KIND=WP) :: DLAMCH, DZNRM2
|
||||||
|
REAL(KIND=WP) :: ZLANGE
|
||||||
|
EXTERNAL IZAMAX
|
||||||
|
INTEGER IZAMAX
|
||||||
|
EXTERNAL LSAME
|
||||||
|
LOGICAL LSAME
|
||||||
|
|
||||||
|
INTRINSIC ABS, INT, MIN, MAX, SIGN
|
||||||
|
!............................................................
|
||||||
|
|
||||||
|
! The test is always in pairs : ( ZGEDMD and ZGEDMDQ )
|
||||||
|
! because the test includes comparing the results (in pairs).
|
||||||
|
!.....................................................................................
|
||||||
|
TEST_QRDMD = .TRUE. ! This code by default performs tests on ZGEDMDQ
|
||||||
|
! 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 = DLAMCH( 'P' ) ! machine precision DP
|
||||||
|
|
||||||
|
! 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 ...
|
||||||
|
WRITE(*,*) 'M = '
|
||||||
|
READ(*,*) M
|
||||||
|
WRITE(*,*) M
|
||||||
|
! ... and the number of snapshots.
|
||||||
|
WRITE(*,*) 'N = '
|
||||||
|
READ(*,*) N
|
||||||
|
WRITE(*,*) 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_ZXW = ZERO
|
||||||
|
TMP_AU = ZERO
|
||||||
|
TMP_REZ = ZERO
|
||||||
|
TMP_REZQ = ZERO
|
||||||
|
SVDIFF = ZERO
|
||||||
|
TMP_EX = ZERO
|
||||||
|
|
||||||
|
ALLOCATE( ZA(LDA,M) )
|
||||||
|
ALLOCATE( ZAC(LDA,M) )
|
||||||
|
ALLOCATE( ZF(LDF,N+1) )
|
||||||
|
ALLOCATE( ZF0(LDF,N+1) )
|
||||||
|
ALLOCATE( ZF1(LDF,N+1) )
|
||||||
|
ALLOCATE( ZX(LDX,N) )
|
||||||
|
ALLOCATE( ZX0(LDX,N) )
|
||||||
|
ALLOCATE( ZY(LDY,N+1) )
|
||||||
|
ALLOCATE( ZY0(LDY,N+1) )
|
||||||
|
ALLOCATE( ZY1(LDY,N+1) )
|
||||||
|
ALLOCATE( ZAU(LDAU,N) )
|
||||||
|
ALLOCATE( ZW(LDW,N) )
|
||||||
|
ALLOCATE( ZS(LDS,N) )
|
||||||
|
ALLOCATE( ZZ(LDZ,N) )
|
||||||
|
ALLOCATE( ZZ1(LDZ,N) )
|
||||||
|
ALLOCATE( RES(N) )
|
||||||
|
ALLOCATE( RES1(N) )
|
||||||
|
ALLOCATE( RESEX(N) )
|
||||||
|
ALLOCATE( ZEIGS(N) )
|
||||||
|
ALLOCATE( SINGVX(N) )
|
||||||
|
ALLOCATE( SINGVQX(N) )
|
||||||
|
|
||||||
|
TOL = M*EPS
|
||||||
|
! This mimics O(M*N)*EPS bound for accumulated roundoff error.
|
||||||
|
! The factor 10 is somewhat arbitrary.
|
||||||
|
TOL2 = 10*M*N*EPS
|
||||||
|
|
||||||
|
!.............
|
||||||
|
|
||||||
|
DO K_TRAJ = 1, 2
|
||||||
|
! Number of intial conditions in the simulation/trajectories (1 or 2)
|
||||||
|
|
||||||
|
COND = 1.0D4
|
||||||
|
ZMAX = (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 ZLATMR (+1,..,+6)
|
||||||
|
DO MODE = 1, 6
|
||||||
|
|
||||||
|
ALLOCATE( IWORK(2*M) )
|
||||||
|
ALLOCATE( ZDA(M) )
|
||||||
|
ALLOCATE( ZDL(M) )
|
||||||
|
ALLOCATE( ZDR(M) )
|
||||||
|
|
||||||
|
CALL ZLATMR( M, M, 'N', ISEED, 'N', ZDA, MODE, COND, &
|
||||||
|
ZMAX, RSIGN, GRADE, ZDL, MODEL, CONDL, &
|
||||||
|
ZDR, MODER, CONDR, PIVTNG, IWORK, M, M, &
|
||||||
|
ZERO, -ONE, 'N', ZA, LDA, IWORK(M+1), INFO )
|
||||||
|
DEALLOCATE( ZDR )
|
||||||
|
DEALLOCATE( ZDL )
|
||||||
|
DEALLOCATE( ZDA )
|
||||||
|
DEALLOCATE( IWORK )
|
||||||
|
|
||||||
|
LZWORK = MAX(1,2*M)
|
||||||
|
ALLOCATE( ZEIGSA(M) )
|
||||||
|
ALLOCATE( ZWORK(LZWORK) )
|
||||||
|
ALLOCATE( WORK(2*M) )
|
||||||
|
ZAC(1:M,1:M) = ZA(1:M,1:M)
|
||||||
|
CALL ZGEEV( 'N','N', M, ZAC, LDA, ZEIGSA, ZDUM2X2, 2, &
|
||||||
|
ZDUM2X2, 2, ZWORK, LZWORK, WORK, INFO ) ! LAPACK CALL
|
||||||
|
DEALLOCATE(WORK)
|
||||||
|
DEALLOCATE(ZWORK)
|
||||||
|
|
||||||
|
TMP = ABS(ZEIGSA(IZAMAX(M, ZEIGSA, 1))) ! The spectral radius of ZA
|
||||||
|
! Scale the matrix ZA to have unit spectral radius.
|
||||||
|
CALL ZLASCL( 'G',0, 0, TMP, ONE, M, M, &
|
||||||
|
ZA, LDA, INFO )
|
||||||
|
CALL ZLASCL( 'G',0, 0, TMP, ONE, M, 1, &
|
||||||
|
ZEIGSA, M, INFO )
|
||||||
|
ANORM = ZLANGE( 'F', M, M, ZA, LDA, WDUMMY )
|
||||||
|
|
||||||
|
IF ( K_TRAJ == 2 ) THEN
|
||||||
|
! generate data as two trajectories
|
||||||
|
! with two inital conditions
|
||||||
|
CALL ZLARNV(2, ISEED, M, ZF(1,1) )
|
||||||
|
DO i = 1, N/2
|
||||||
|
CALL ZGEMV( 'N', M, M, ZONE, ZA, LDA, ZF(1,i), 1, &
|
||||||
|
ZZERO, ZF(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
ZX0(1:M,1:N/2) = ZF(1:M,1:N/2)
|
||||||
|
ZY0(1:M,1:N/2) = ZF(1:M,2:N/2+1)
|
||||||
|
|
||||||
|
CALL ZLARNV(2, ISEED, M, ZF(1,1) )
|
||||||
|
DO i = 1, N-N/2
|
||||||
|
CALL ZGEMV( 'N', M, M, ZONE, ZA, LDA, ZF(1,i), 1, &
|
||||||
|
ZZERO, ZF(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
ZX0(1:M,N/2+1:N) = ZF(1:M,1:N-N/2)
|
||||||
|
ZY0(1:M,N/2+1:N) = ZF(1:M,2:N-N/2+1)
|
||||||
|
ELSE
|
||||||
|
CALL ZLARNV(2, ISEED, M, ZF(1,1) )
|
||||||
|
DO i = 1, N
|
||||||
|
CALL ZGEMV( 'N', M, M, ZONE, ZA, M, ZF(1,i), 1, &
|
||||||
|
ZZERO, ZF(1,i+1), 1 )
|
||||||
|
END DO
|
||||||
|
ZF0(1:M,1:N+1) = ZF(1:M,1:N+1)
|
||||||
|
ZX0(1:M,1:N) = ZF0(1:M,1:N)
|
||||||
|
ZY0(1:M,1:N) = ZF0(1:M,2:N+1)
|
||||||
|
END IF
|
||||||
|
|
||||||
|
DEALLOCATE( ZEIGSA )
|
||||||
|
!........................................................................
|
||||||
|
|
||||||
|
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
|
||||||
|
NRNKsp = iNRNK
|
||||||
|
|
||||||
|
DO iWHTSVD = 1, 3
|
||||||
|
! Check all four options to compute the POD basis
|
||||||
|
! via the SVD.
|
||||||
|
WHTSVD = iWHTSVD
|
||||||
|
WHTSVDsp = iWHTSVD
|
||||||
|
|
||||||
|
DO LWMINOPT = 1, 2
|
||||||
|
! Workspace query for the minimal (1) and for the optimal
|
||||||
|
! (2) workspace lengths determined by workspace query.
|
||||||
|
|
||||||
|
! ZGEDMD is always tested and its results are also used for
|
||||||
|
! comparisons with ZGEDMDQ.
|
||||||
|
|
||||||
|
ZX(1:M,1:N) = ZX0(1:M,1:N)
|
||||||
|
ZY(1:M,1:N) = ZY0(1:M,1:N)
|
||||||
|
|
||||||
|
CALL ZGEDMD( SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, &
|
||||||
|
M, N, ZX, LDX, ZY, LDY, NRNK, TOL, &
|
||||||
|
K, ZEIGS, ZZ, LDZ, RES, ZAU, LDAU, &
|
||||||
|
ZW, LDW, ZS, LDS, ZDUMMY, -1, &
|
||||||
|
WDUMMY, -1, IDUMMY, -1, INFO )
|
||||||
|
IF ( (INFO .EQ. 2) .OR. ( INFO .EQ. 3 ) &
|
||||||
|
.OR. ( INFO < 0 ) ) THEN
|
||||||
|
WRITE(*,*) 'Call to ZGEDMD 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
|
||||||
|
END IF
|
||||||
|
|
||||||
|
LZWORK = INT(ZDUMMY(LWMINOPT))
|
||||||
|
LWORK = INT(WDUMMY(1))
|
||||||
|
LIWORK = IDUMMY(1)
|
||||||
|
|
||||||
|
ALLOCATE(ZWORK(LZWORK))
|
||||||
|
ALLOCATE( WORK(LWORK))
|
||||||
|
ALLOCATE(IWORK(LIWORK))
|
||||||
|
|
||||||
|
CALL ZGEDMD( SCALE, JOBZ, RESIDS, JOBREF, WHTSVD, &
|
||||||
|
M, N, ZX, LDX, ZY, LDY, NRNK, TOL, &
|
||||||
|
K, ZEIGS, ZZ, LDZ, RES, ZAU, LDAU, &
|
||||||
|
ZW, LDW, ZS, LDS, ZWORK, LZWORK, &
|
||||||
|
WORK, LWORK, IWORK, LIWORK, INFO )
|
||||||
|
|
||||||
|
IF ( INFO /= 0 ) THEN
|
||||||
|
WRITE(*,*) 'Call to ZGEDMD 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)
|
||||||
|
|
||||||
|
!...... ZGEDMD check point
|
||||||
|
IF ( LSAME(JOBZ,'V') ) THEN
|
||||||
|
! Check that Z = X*W, on return from ZGEDMD
|
||||||
|
! 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 ZGEMM( 'N', 'N', M, K, K, ZONE, ZX, LDX, ZW, LDW, &
|
||||||
|
ZZERO, ZZ1, LDZ )
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, K
|
||||||
|
CALL ZAXPY( M, -ZONE, ZZ(1,i), 1, ZZ1(1,i), 1)
|
||||||
|
TMP = MAX(TMP, DZNRM2( M, ZZ1(1,i), 1 ) )
|
||||||
|
END DO
|
||||||
|
TMP_ZXW = MAX(TMP_ZXW, TMP )
|
||||||
|
IF ( TMP_ZXW <= 10*M*EPS ) THEN
|
||||||
|
!WRITE(*,*) ' :) .... OK .........ZGEDMD PASSED.'
|
||||||
|
ELSE
|
||||||
|
NFAIL_Z_XV = NFAIL_Z_XV + 1
|
||||||
|
WRITE(*,*) ':( .................ZGEDMD 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
|
||||||
|
|
||||||
|
|
||||||
|
!...... ZGEDMD 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 ZGEMM( 'N', 'N', M, K, M, ZONE, ZA, LDA, ZX, LDX, &
|
||||||
|
ZZERO, ZZ1, LDZ )
|
||||||
|
TMP = ZERO
|
||||||
|
DO i = 1, K
|
||||||
|
CALL ZAXPY( M, -ZONE, ZAU(1,i), 1, ZZ1(1,i), 1)
|
||||||
|
TMP = MAX( TMP, DZNRM2( M, ZZ1(1,i),1 ) * &
|
||||||
|
SINGVX(K)/(ANORM*SINGVX(1)) )
|
||||||
|
END DO
|
||||||
|
TMP_AU = MAX( TMP_AU, TMP )
|
||||||
|
IF ( TMP <= TOL2 ) THEN
|
||||||
|
!WRITE(*,*) ':) .... OK .........ZGEDMD PASSED.'
|
||||||
|
ELSE
|
||||||
|
NFAIL_AU = NFAIL_AU + 1
|
||||||
|
WRITE(*,*) ':( .................ZGEDMD 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
|
||||||
|
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 ZGEMM( 'N', 'N', M, K, M, ZONE, ZA, LDA, ZAU, LDAU, ZZERO, ZY1, LDY )
|
||||||
|
|
||||||
|
DO i=1, K
|
||||||
|
! have a real eigenvalue with real eigenvector
|
||||||
|
CALL ZAXPY( M, -ZEIGS(i), ZAU(1,i), 1, ZY1(1,i), 1 )
|
||||||
|
RESEX(i) = DZNRM2( M, ZY1(1,i), 1) / DZNRM2(M,ZAU(1,i),1)
|
||||||
|
END DO
|
||||||
|
END IF
|
||||||
|
!...... ZGEDMD check point
|
||||||
|
|
||||||
|
IF ( LSAME(RESIDS, 'R') ) THEN
|
||||||
|
! Compare the residuals returned by ZGEDMD with the
|
||||||
|
! explicitly computed residuals using the matrix A.
|
||||||
|
! Compute explicitly Y1 = A*Z
|
||||||
|
CALL ZGEMM( 'N', 'N', M, K, M, ZONE, ZA, LDA, ZZ, LDZ, ZZERO, ZY1, 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 ZGEDMD,)
|
||||||
|
|
||||||
|
DO i=1, K
|
||||||
|
! have a real eigenvalue with real eigenvector
|
||||||
|
CALL ZAXPY( M, -ZEIGS(i), ZZ(1,i), 1, ZY1(1,i), 1 )
|
||||||
|
RES1(i) = DZNRM2( M, ZY1(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 ..........ZGEDMD PASSED.'
|
||||||
|
ELSE
|
||||||
|
NFAIL_REZ = NFAIL_REZ + 1
|
||||||
|
WRITE(*,*) ':( ..................ZGEDMD 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(ZWORK)
|
||||||
|
DEALLOCATE(WORK)
|
||||||
|
DEALLOCATE(IWORK)
|
||||||
|
|
||||||
|
IF ( TEST_QRDMD .AND. (K_TRAJ == 1) ) THEN
|
||||||
|
|
||||||
|
ZF(1:M,1:N+1) = ZF0(1:M,1:N+1)
|
||||||
|
|
||||||
|
CALL ZGEDMDQ( SCALE, JOBZ, RESIDS, WANTQ, WANTR, JOBREF, &
|
||||||
|
WHTSVD, M, N+1, ZF, LDF, ZX, LDX, ZY, LDY, &
|
||||||
|
NRNK, TOL, K, ZEIGS, ZZ, LDZ, RES, ZAU, &
|
||||||
|
LDAU, ZW, LDW, ZS, LDS, ZDUMMY, -1, &
|
||||||
|
WDUMMY, -1, IDUMMY, -1, INFO )
|
||||||
|
|
||||||
|
LZWORK = INT(ZDUMMY(LWMINOPT))
|
||||||
|
ALLOCATE( ZWORK(LZWORK) )
|
||||||
|
LIWORK = IDUMMY(1)
|
||||||
|
ALLOCATE(IWORK(LIWORK))
|
||||||
|
LWORK = INT(WDUMMY(1))
|
||||||
|
ALLOCATE(WORK(LWORK))
|
||||||
|
|
||||||
|
CALL ZGEDMDQ( SCALE, JOBZ, RESIDS, WANTQ, WANTR, JOBREF, &
|
||||||
|
WHTSVD, M, N+1, ZF, LDF, ZX, LDX, ZY, LDY, &
|
||||||
|
NRNK, TOL, KQ, ZEIGS, ZZ, LDZ, RES, ZAU, &
|
||||||
|
LDAU, ZW, LDW, ZS, LDS, ZWORK, LZWORK, &
|
||||||
|
WORK, LWORK, IWORK, LIWORK, INFO )
|
||||||
|
|
||||||
|
IF ( INFO /= 0 ) THEN
|
||||||
|
WRITE(*,*) 'Call to ZGEDMDQ 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
|
||||||
|
|
||||||
|
IF ( 1 == 0 ) THEN
|
||||||
|
! Comparison of ZGEDMD and ZGEDMDQ singular values disabled
|
||||||
|
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 > M*N*EPS ) THEN
|
||||||
|
WRITE(*,*) 'FAILED! Something was wrong with the run.'
|
||||||
|
NFAIL_SVDIFF = NFAIL_SVDIFF + 1
|
||||||
|
DO j =1, 3
|
||||||
|
write(*,*) j, SINGVX(j), SINGVQX(j)
|
||||||
|
read(*,*)
|
||||||
|
END DO
|
||||||
|
|
||||||
|
END IF
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!..... ZGEDMDQ 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.
|
||||||
|
ZF1(1:M,1:N+1) = ZF0(1:M,1:N+1)
|
||||||
|
CALL ZGEMM( 'N', 'N', M, N+1, MIN(M,N+1), -ZONE, ZF, &
|
||||||
|
LDF, ZY, LDY, ZONE, ZF1, LDF )
|
||||||
|
TMP_FQR = ZLANGE( 'F', M, N+1, ZF1, LDF, WORK ) / &
|
||||||
|
ZLANGE( 'F', M, N+1, ZF0, LDF, WORK )
|
||||||
|
IF ( TMP_FQR > TOL2 ) THEN
|
||||||
|
WRITE(*,*) 'FAILED! Something was wrong with the run.'
|
||||||
|
NFAIL_F_QR = NFAIL_F_QR + 1
|
||||||
|
ELSE
|
||||||
|
!WRITE(*,*) '........ PASSED.'
|
||||||
|
END IF
|
||||||
|
END IF
|
||||||
|
|
||||||
|
!..... ZGEDMDQ check point
|
||||||
|
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 ZGEMM( 'N', 'N', M, KQ, M, ZONE, ZA, LDA, ZZ, LDZ, ZZERO, ZY1, 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 ZAXPY( M, -ZEIGS(i), ZZ(1,i), 1, ZY1(1,i), 1 )
|
||||||
|
! Y(1:M,i) = Y(1:M,i) - REIG(i)*Z(1:M,i)
|
||||||
|
RES1(i) = DZNRM2( M, ZY1(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 ........ ZGEDMDQ PASSED.'
|
||||||
|
ELSE
|
||||||
|
NFAIL_REZQ = NFAIL_REZQ + 1
|
||||||
|
WRITE(*,*) '................ ZGEDMDQ FAILED!', &
|
||||||
|
'Check the code for implementation errors.'
|
||||||
|
STOP
|
||||||
|
END IF
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
DEALLOCATE( ZWORK )
|
||||||
|
DEALLOCATE( WORK )
|
||||||
|
DEALLOCATE( IWORK )
|
||||||
|
|
||||||
|
END IF ! ZGEDMDQ
|
||||||
|
|
||||||
|
!.......................................................................................................
|
||||||
|
|
||||||
|
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( ZA )
|
||||||
|
DEALLOCATE( ZAC )
|
||||||
|
DEALLOCATE( ZZ )
|
||||||
|
DEALLOCATE( ZF )
|
||||||
|
DEALLOCATE( ZF0 )
|
||||||
|
DEALLOCATE( ZF1 )
|
||||||
|
DEALLOCATE( ZX )
|
||||||
|
DEALLOCATE( ZX0 )
|
||||||
|
DEALLOCATE( ZY )
|
||||||
|
DEALLOCATE( ZY0 )
|
||||||
|
DEALLOCATE( ZY1 )
|
||||||
|
DEALLOCATE( ZAU )
|
||||||
|
DEALLOCATE( ZW )
|
||||||
|
DEALLOCATE( ZS )
|
||||||
|
DEALLOCATE( ZZ1 )
|
||||||
|
DEALLOCATE( RES )
|
||||||
|
DEALLOCATE( RES1 )
|
||||||
|
DEALLOCATE( RESEX )
|
||||||
|
DEALLOCATE( ZEIGS )
|
||||||
|
DEALLOCATE( SINGVX )
|
||||||
|
DEALLOCATE( SINGVQX )
|
||||||
|
|
||||||
|
END DO ! LLOOP
|
||||||
|
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*) ' Test summary for ZGEDMD :'
|
||||||
|
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_ZXW
|
||||||
|
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(*,*) '>>>> ZGEDMD :: ALL TESTS PASSED.'
|
||||||
|
ELSE
|
||||||
|
WRITE(*,*) NFAIL_TOTAL, 'FAILURES!'
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>> ZGEDMD :: TESTS FAILED. CHECK THE IMPLEMENTATION.'
|
||||||
|
END IF
|
||||||
|
|
||||||
|
IF ( TEST_QRDMD ) THEN
|
||||||
|
WRITE(*,*)
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*) ' Test summary for ZGEDMDQ :'
|
||||||
|
WRITE(*,*) '>>>>>>>>>>>>>>>>>>>>>>>>>>'
|
||||||
|
WRITE(*,*)
|
||||||
|
|
||||||
|
IF ( NFAIL_SVDIFF == 0 ) THEN
|
||||||
|
WRITE(*,*) '>>>> ZGEDMD and ZGEDMDQ 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(*,*) '>>>>>>> ZGEDMDQ :: ALL TESTS PASSED.'
|
||||||
|
ELSE
|
||||||
|
WRITE(*,*) NFAILQ_TOTAL, 'FAILURES!'
|
||||||
|
WRITE(*,*) '>>>>>>> ZGEDMDQ :: TESTS FAILED. CHECK THE IMPLEMENTATION.'
|
||||||
|
END IF
|
||||||
|
|
||||||
|
END IF
|
||||||
|
|
||||||
|
WRITE(*,*)
|
||||||
|
WRITE(*,*) 'Test completed.'
|
||||||
|
STOP
|
||||||
|
END
|
||||||
Loading…
Reference in New Issue