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|
!!$BSD Software License
!!$
!!$Pertains to ARPACK and P_ARPACK
!!$
!!$Copyright (c) 1996-2008 Rice University.
!!$Developed by D.C. Sorensen, R.B. Lehoucq, C. Yang, and K. Maschhoff.
!!$All rights reserved.
!!$
!!$Redistribution and use in source and binary forms, with or without
!!$modification, are permitted provided that the following conditions are
!!$met:
!!$
!!$- Redistributions of source code must retain the above copyright
!!$ notice, this list of conditions and the following disclaimer.
!!$
!!$- Redistributions in binary form must reproduce the above copyright
!!$ notice, this list of conditions and the following disclaimer listed
!!$ in this license in the documentation and/or other materials
!!$ provided with the distribution.
!!$
!!$- Neither the name of the copyright holders nor the names of its
!!$ contributors may be used to endorse or promote products derived from
!!$ this software without specific prior written permission.
!!$
!!$THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
!!$"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
!!$LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
!!$A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
!!$OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
!!$SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
!!$LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
!!$DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
!!$THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
!!$(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
!!$OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
!!$
#include "fdebug.h"
module snapsvd_module
use vector_tools
implicit none
contains
subroutine snapsvd(m,n,snapmatrix,nsvd_total,nsvd,usv,svdval)
!
! This code shows how to use ARPACK to find a few of the
! largest singular values(sigma) and corresponding right singular
! vectors (v) for the the matrix A by solving the symmetric problem:
!
! (A'*A)*v = sigma*v
!
! where A is an m by n real matrix.
!
! This code may be easily modified to estimate the 2-norm
! condition number largest(sigma)/smallest(sigma) by setting
! which = 'BE' below. This will ask for a few of the smallest
! and a few of the largest singular values simultaneously.
! The condition number could then be estimated by taking
! the ratio of the largest and smallest singular values.
!
! This formulation is appropriate when m .ge. n.
! Reverse the roles of A and A' in the case that m .le. n.
!
! The main points illustrated here are
!
! 1) How to declare sufficient memory to find NEV
! largest singular values of A .
!
! 2) Illustration of the reverse communication interface
! needed to utilize the top level ARPACK routine DSAUPD
! that computes the quantities needed to construct
! the desired singular values and vectors(if requested).
!
! 3) How to extract the desired singular values and vectors
! using the ARPACK routine DSEUPD.
!
! 4) How to construct the left singular vectors U from the
! right singular vectors V to obtain the decomposition
!
! A*V = U*S
!
! where S = diag(sigma_1, sigma_2, ..., sigma_k).
!
! The only thing that must be supplied in order to use this
! routine on your problem is to change the array dimensions
! appropriately, to specify WHICH singular values you want to
! compute and to supply a the matrix-vector products
!
! w <- Ax
! y <- A'w
!
! in place of the calls to AV( ) and ATV( ) respectively below.
!
! Further documentation is available in the header of DSAUPD
! which may be found in the SRC directory.
!
! This codes implements
!
!\Example-1
! ... Suppose we want to solve A'A*v = sigma*v in regular mode,
! where A is derived from the simplest finite difference
! discretization of the 2-dimensional kernel K(s,t)dt where
!
! K(s,t) = s(t-1) if 0 .le. s .le. t .le. 1,
! t(s-1) if 0 .le. t .lt. s .le. 1.
!
! See subroutines AV and ATV for details.
! ... OP = A'*A and B = I.
! ... Assume "call av (n,x,y)" computes y = A*x
! ... Assume "call atv (n,y,w)" computes w = A'*y
! ... Assume exact shifts are used
! ...
!
!\BeginLib
!
!\Routines called:
! dsaupd ARPACK reverse communication interface routine.
! dseupd ARPACK routine that returns Ritz values and (optionally)
! Ritz vectors.
! dnrm2 Level 1 BLAS that computes the norm of a vector.
! daxpy Level 1 BLAS that computes y <- alpha*x+y.
! dscal Level 1 BLAS thst computes x <- x*alpha.
! dcopy Level 1 BLAS thst computes y <- x.
!
!-----------------------------------------------------------------------
!
! %------------------------------------------------------%
! | Storage Declarations: |
! | |
! | It is assumed that A is M by N with M .ge. N. |
! | |
! | The maximum dimensions for all arrays are |
! | set here to accommodate a problem size of |
! | M .le. MAXM and N .le. MAXN |
! | |
! | The NEV right singular vectors will be computed in |
! | the N by NCV array V. |
! | |
! | The NEV left singular vectors will be computed in |
! | the M by NEV array U. |
! | |
! | NEV is the number of singular values requested. |
! | See specifications for ARPACK usage below. |
! | |
! | NCV is the largest number of basis vectors that will |
! | be used in the Implicitly Restarted Arnoldi |
! | Process. Work per major iteration is |
! | proportional to N*NCV*NCV. |
! | |
! | You must set: |
! | |
! | MAXM: Maximum number of rows of the A allowed. |
! | MAXN: Maximum number of columns of the A allowed. |
! | MAXNEV: Maximum NEV allowed |
! | MAXNCV: Maximum NCV allowed |
! %------------------------------------------------------%
!
use FLDebug
!include 'paramnew.h'
integer maxm, maxn, maxnev, maxncv, ldv, ldu, m, n, i
integer ndigit,logfil, msgets, msaitr, msapps, msaupd, msaup2, mseigt, mseupd
! parameter (maxm = istate,maxn=nrsnapshots,maxnev=nrsnapshots-1, &
! maxncv=nrsnapshots, ldu = maxm, ldv=maxn )
! %--------------%
! | Local Arrays |
! %--------------%
!
!real v(ldv,maxncv), u(ldu, maxnev), &
! workl(maxncv*(maxncv+8)), workd(3*maxn), &
! s(maxncv,2), resid(maxn), ax(maxm)
!logical select(maxncv)
integer iparam(11), ipntr(11)
REAL, ALLOCATABLE, DIMENSION(:,:):: v,u,s
REAL, ALLOCATABLE, DIMENSION(:):: workl,workd,resid,ax
logical, ALLOCATABLE, DIMENSION(:):: select
!
! %---------------%
! | Local Scalars |
! %---------------%
!
character bmat*1, which*2
integer ido, nev, ncv, lworkl, info, ierr, &
j, ishfts, maxitr, mode1, nconv
logical rvec
real toll, sigma, temp
!
! %------------%
! | Parameters |
! %------------%
!
real one, zero
parameter (one = 1.0D+0, zero = 0.0D+0)
!ccccc declare input
real snapmatrix(m,n)
integer nsvd,nsvd_total
!cccccccc declare output
real usv(m,nsvd),svdval(nsvd) ! left svd, svdval
!
!
! %-----------------------------%
! | BLAS & LAPACK routines used |
! %-----------------------------%
!
real dnrm2
!
! %-------------%
! | local |
! %-------------%
REAL TOTAL_E,PARTIAL_E,PERCENT_E
! external dnrm2, daxpy, dcopy, dscal
!
! %-----------------------%
! | Executable Statements |
! %-----------------------%
!
! %-------------------------------------------------%
! | The following include statement and assignments |
! | initiate trace output from the internal |
! | actions of ARPACK. See debug.doc in the |
! | DOCUMENTS directory for usage. Initially, the |
! | most useful information will be a breakdown of |
! | time spent in the various stages of computation |
! | given by setting msaupd = 1. |
! %-------------------------------------------------%
!
! include 'debug1.h'
#ifdef HAVE_LIBARPACK
maxm = m
maxn=n
maxnev=n-1
maxncv=n
ldu = maxm
ldv=maxn
ALLOCATE(v(ldv,maxncv))
ALLOCATE(u(ldu,maxnev))
ALLOCATE(s(maxncv,2))
ALLOCATE(workl(maxncv*(maxncv+8)))
ALLOCATE(workd(3*maxn))
ALLOCATE(resid(maxn))
ALLOCATE(ax(maxm))
ALLOCATE(select(maxncv))
ewrite(3,*) 'in snapsvd.F'
ewrite(3,*) M,maxm
! maxm=m
! ldu = maxm
ndigit = -3
logfil = 6
msgets = 0
msaitr = 0
msapps = 0
msaupd = 1
msaup2 = 0
mseigt = 0
mseupd = 0
!
! %-------------------------------------------------%
! | The following sets dimensions for this problem. |
! %-------------------------------------------------%
!
! if (n .ne. nrsnapshots) then
! write(*,*) 'dimension error in svd routine',n,nrsnapshots
! stop
! end if
!
! %------------------------------------------------%
! | Specifications for ARPACK usage are set |
! | below: |
! | |
! | 1) NEV = 4 asks for 4 singular values to be |
! | computed. |
! | |
! | 2) NCV = 20 sets the length of the Arnoldi |
! | factorization |
! | |
! | 3) This is a standard problem |
! | (indicated by bmat = 'I') |
! | |
! | 4) Ask for the NEV singular values of |
! | largest magnitude |
! | (indicated by which = 'LM') |
! | See documentation in DSAUPD for the |
! | other options SM, BE. |
! | |
! | Note: NEV and NCV must satisfy the following |
! | conditions: |
! | NEV <= MAXNEV, |
! | NEV + 1 <= NCV <= MAXNCV |
! %------------------------------------------------%
!
nev = nsvd_total
ncv = n
bmat = 'I'
which = 'LM'
!
if ( n .gt. maxn ) then
ewrite(3,*) ' ERROR with _SVD: N is greater than MAXN '
go to 9000
else if ( m .gt. maxm ) then
ewrite(3,*) ' ERROR with _SVD: M is greater than MAXM ',M,MAXM
go to 9000
else if ( nev .gt. maxnev ) then
ewrite(3,*) ' ERROR with _SVD: NEV is greater than MAXNEV '
go to 9000
else if ( ncv .gt. maxncv ) then
ewrite(3,*) ' ERROR with _SVD: NCV is greater than MAXNCV '
go to 9000
end if
!
! %-----------------------------------------------------%
! | Specification of stopping rules and initial |
! | conditions before calling DSAUPD |
! | |
! | abs(sigmaC - sigmaT) < TOL*abs(sigmaC) |
! | computed true |
! | |
! | If TOL .le. 0, then TOL <- macheps |
! | (machine precision) is used. |
! | |
! | IDO is the REVERSE COMMUNICATION parameter |
! | used to specify actions to be taken on return |
! | from DSAUPD. (See usage below.) |
! | |
! | It MUST initially be set to 0 before the first |
! | call to DSAUPD. |
! | |
! | INFO on entry specifies starting vector information |
! | and on return indicates error codes |
! | |
! | Initially, setting INFO=0 indicates that a |
! | random starting vector is requested to |
! | start the ARNOLDI iteration. Setting INFO to |
! | a nonzero value on the initial call is used |
! | if you want to specify your own starting |
! | vector (This vector must be placed in RESID.) |
! | |
! | The work array WORKL is used in DSAUPD as |
! | workspace. Its dimension LWORKL is set as |
! | illustrated below. |
! %-----------------------------------------------------%
!
lworkl = ncv*(ncv+8)
toll = 0.0d-3 ! 1.d-3
info = 0
ido = 0
!
! %---------------------------------------------------%
! | Specification of Algorithm Mode: |
! | |
! | This program uses the exact shift strategy |
! | (indicated by setting IPARAM(1) = 1.) |
! | IPARAM(3) specifies the maximum number of Arnoldi |
! | iterations allowed. Mode 1 of DSAUPD is used |
! | (IPARAM(7) = 1). All these options can be changed |
! | by the user. For details see the documentation in |
! | DSAUPD. |
! %---------------------------------------------------%
!
ishfts = 1
maxitr = n
mode1 = 1
!
iparam(1) = ishfts
!
iparam(3) = maxitr
!
iparam(7) = mode1
!
! %------------------------------------------------%
! | M A I N L O O P (Reverse communication loop) |
! %------------------------------------------------%
!
10 continue
!
! %---------------------------------------------%
! | Repeatedly call the routine DSAUPD and take |
! | actions indicated by parameter IDO until |
! | either convergence is indicated or maxitr |
! | has been exceeded. |
! %---------------------------------------------%
!
#ifdef DOUBLEP
call dsaupd ( ido, bmat, n, which, nev, toll, resid, &
ncv, v, ldv, iparam, ipntr, workd, workl, &
lworkl, info )
#else
call ssaupd ( ido, bmat, n, which, nev, toll, resid, &
ncv, v, ldv, iparam, ipntr, workd, workl, &
lworkl, info )
#endif
!
if (ido .eq. -1 .or. ido .eq. 1) then
!
! %---------------------------------------%
! | Perform matrix vector multiplications |
! | w <--- A*x (av()) |
! | y <--- A'*w (atv()) |
! | The user should supply his/her own |
! | matrix vector multiplication routines |
! | here that takes workd(ipntr(1)) as |
! | the input, and returns the result in |
! | workd(ipntr(2)). |
! %---------------------------------------%
!
call av (m,n,snapmatrix,workd(ipntr(1)),ax)
call atv (m,n,snapmatrix,ax,workd(ipntr(2)))
!
! %-----------------------------------------%
! | L O O P B A C K to call DSAUPD again. |
! %-----------------------------------------%
!
go to 10
!
end if
!
! %----------------------------------------%
! | Either we have convergence or there is |
! | an error. |
! %----------------------------------------%
!
if ( info .lt. 0 ) then
!
! %--------------------------%
! | Error message. Check the |
! | documentation in DSAUPD. |
! %--------------------------%
!
ewrite(3,*) ' '
ewrite(3,*) ' Error with _saupd, info = ', info
ewrite(3,*) ' Check documentation in _saupd '
ewrite(3,*) ' '
!
else
!
! %--------------------------------------------%
! | No fatal errors occurred. |
! | Post-Process using DSEUPD. |
! | |
! | Computed singular values may be extracted. |
! | |
! | Singular vectors may also be computed now |
! | if desired. (indicated by rvec = .true.) |
! | |
! | The routine DSEUPD now called to do this |
! | post processing |
! %--------------------------------------------%
!
rvec = .true.
!
#ifdef DOUBLEP
call dseupd ( rvec, 'All', select, s, v, ldv, sigma, &
bmat, n, which, nev, toll, resid, ncv, v, ldv, &
iparam, ipntr, workd, workl, lworkl, ierr )
#else
call sseupd ( rvec, 'All', select, s, v, ldv, sigma, &
bmat, n, which, nev, toll, resid, ncv, v, ldv, &
iparam, ipntr, workd, workl, lworkl, ierr )
#endif
!
! %-----------------------------------------------%
! | Singular values are returned in the first |
! | column of the two dimensional array S |
! | and the corresponding right singular vectors |
! | are returned in the first NEV columns of the |
! | two dimensional array V as requested here. |
! %-----------------------------------------------%
!
ewrite(3,*) ipntr(7)
ewrite(3,*) ipntr(7)+ncv
ewrite(3,*) (workl(ipntr(7)+ncv+j-1),j=1,ncv)
TOTAL_E=0.0
DO J=1,NCV
IF(workl(ipntr(7)+ncv+j-1).ge.0.0) THEN
TOTAL_E=TOTAL_E+sqrt(workl(ipntr(7)+ncv+j-1))
ENDIF
ENDDO
if ( ierr .ne. 0) then
!
! %------------------------------------%
! | Error condition: |
! | Check the documentation of DSEUPD. |
! %------------------------------------%
!
ewrite(3,*) ' '
ewrite(3,*) ' Error with _seupd, info = ', ierr
ewrite(3,*) ' Check the documentation of _seupd. '
ewrite(3,*) ' '
!
else
!
nconv = iparam(5)
ewrite(3,*) 'nconv',nconv
PARTIAL_E=0.0
do 20 j=1, nconv
s(j,1) = sqrt(s(j,1))
if(j.le.nsvd) then
PARTIAL_E=PARTIAL_E+s(j,1)
endif
!
! %-----------------------------%
! | Compute the left singular |
! | vectors from the formula |
! | |
! | u = Av/sigma |
! | |
! | u should have norm 1 so |
! | divide by norm(Av) instead. |
! %-----------------------------%
!
call av(m, n, snapmatrix, v(1,j), ax)
u(:,j)=ax
!call dcopy(m, ax, 1, u(1,j), 1)
temp = one/norm2(u(:,j))
!temp = one/dnrm2(m, u(1,j), 1)
u(:,j)=u(:,j)*temp
!call dscal(m, temp, u(1,j), 1)
!
! %---------------------------%
! | |
! | Compute the residual norm |
! | |
! | || A*v - sigma*u || |
! | |
! | for the NCONV accurately |
! | computed singular values |
! | and vectors. (iparam(5) |
! | indicates how many are |
! | accurate to the requested |
! | tolerance). |
! | Store the result in 2nd |
! | column of array S. |
! %---------------------------%
!
!call daxpy(m, -s(j,1), u(1,j), 1, ax, 1)
ax=ax-s(j,1)*u(:,j)
s(j,2) = norm2(ax)
!s(j,2) = dnrm2(m, ax, 1)
!
20 end do
PERCENT_E = 100.0*PARTIAL_E/TOTAL_E
ewrite(3,*) PARTIAL_E,TOTAL_E
EWRITE(3,*) 'The energry captured(%)',PERCENT_E
!
! %-------------------------------%
! | Display computed residuals |
! %-------------------------------%
#ifdef DOUBLEP
call dmout(6, nconv, 2, s, maxncv, -6, &
'Singular values and direct residuals')
#else
call smout(6, nconv, 2, s, maxncv, -6, &
'Singular values and direct residuals')
#endif
end if
!
! %------------------------------------------%
! | Print additional convergence information |
! %------------------------------------------%
!
if ( info .eq. 1) then
ewrite(3,*) ' '
ewrite(3,*) ' Maximum number of iterations reached.'
ewrite(3,*) ' '
else if ( info .eq. 3) then
ewrite(3,*) ' '
ewrite(3,*) ' No shifts could be applied during implicit', &
' Arnoldi update, try increasing NCV.'
ewrite(3,*) ' '
end if
!
ewrite(3,*) ' '
ewrite(3,*) ' _SVD '
ewrite(3,*) ' ==== '
ewrite(3,*) ' '
ewrite(3,*) ' Size of the matrix is ', n
ewrite(3,*) ' The number of Ritz values requested is ', nev
ewrite(3,*) ' The number of Arnoldi vectors generated', &
' (NCV) is ', ncv
ewrite(3,*) ' What portion of the spectrum: ', which
ewrite(3,*) ' The number of converged Ritz values is ', &
nconv
ewrite(3,*) ' The number of Implicit Arnoldi update', &
' iterations taken is ', iparam(3)
ewrite(3,*) ' The number of OP*x is ', iparam(9)
ewrite(3,*) ' The convergence criterion is ', toll
ewrite(3,*) ' '
!
end if
!
! %-------------------------%
! | Done with program dsvd. |
! %-------------------------%
!
9000 continue
if (nconv .ne. nsvd_total) then
write(*,*) 'convergence error in svd computation'
stop
end if
do j = nsvd,1,-1
svdval(nconv+1-j)= s(j,1) ! decreasing order
enddo
do j = nsvd,1,-1
do i=1,m
usv(i,nconv+1-j) = u(i,j)
enddo
enddo
ewrite(3,*) 'the end of snapsvd'
1000 format (1X, E24.16, 1X, E24.16)
2000 format (100(1X,E24.16))
DEALLOCATE(v)
DEALLOCATE(u)
DEALLOCATE(s)
DEALLOCATE(workl)
DEALLOCATE(workd)
DEALLOCATE(resid)
DEALLOCATE(ax)
DEALLOCATE(select)
#else
FLExit("No ARPACK support, recompile with ARPACK - cannot run reduced model.")
#endif
return
end subroutine snapsvd
!*******************H1***********************
subroutine snapsvd_H1(m,n,epsilon,snapmatrix,snapmatrix_dx,snapmatrix_dy,snapmatrix_dz,nsvd_total,nsvd,usv,svdval,D3)
!
! This code shows how to use ARPACK to find a few of the
! largest singular values(sigma) and corresponding right singular
! vectors (v) for the the matrix A by solving the symmetric problem:
!
! (A'*A)*v = sigma*v
!
! where A is an m by n real matrix.
!
! This code may be easily modified to estimate the 2-norm
! condition number largest(sigma)/smallest(sigma) by setting
! which = 'BE' below. This will ask for a few of the smallest
! and a few of the largest singular values simultaneously.
! The condition number could then be estimated by taking
! the ratio of the largest and smallest singular values.
!
! This formulation is appropriate when m .ge. n.
! Reverse the roles of A and A' in the case that m .le. n.
!
! The main points illustrated here are
!
! 1) How to declare sufficient memory to find NEV
! largest singular values of A .
!
! 2) Illustration of the reverse communication interface
! needed to utilize the top level ARPACK routine DSAUPD
! that computes the quantities needed to construct
! the desired singular values and vectors(if requested).
!
! 3) How to extract the desired singular values and vectors
! using the ARPACK routine DSEUPD.
!
! 4) How to construct the left singular vectors U from the
! right singular vectors V to obtain the decomposition
!
! A*V = U*S
!
! where S = diag(sigma_1, sigma_2, ..., sigma_k).
!
! The only thing that must be supplied in order to use this
! routine on your problem is to change the array dimensions
! appropriately, to specify WHICH singular values you want to
! compute and to supply a the matrix-vector products
!
! w <- Ax
! y <- A'w
!
! in place of the calls to AV( ) and ATV( ) respectively below.
!
! Further documentation is available in the header of DSAUPD
! which may be found in the SRC directory.
!
! This codes implements
!
!\Example-1
! ... Suppose we want to solve A'A*v = sigma*v in regular mode,
! where A is derived from the simplest finite difference
! discretization of the 2-dimensional kernel K(s,t)dt where
!
! K(s,t) = s(t-1) if 0 .le. s .le. t .le. 1,
! t(s-1) if 0 .le. t .lt. s .le. 1.
!
! See subroutines AV and ATV for details.
! ... OP = A'*A and B = I.
! ... Assume "call av (n,x,y)" computes y = A*x
! ... Assume "call atv (n,y,w)" computes w = A'*y
! ... Assume exact shifts are used
! ...
!
!\BeginLib
!
!\Routines called:
! dsaupd ARPACK reverse communication interface routine.
! dseupd ARPACK routine that returns Ritz values and (optionally)
! Ritz vectors.
! dnrm2 Level 1 BLAS that computes the norm of a vector.
! daxpy Level 1 BLAS that computes y <- alpha*x+y.
! dscal Level 1 BLAS thst computes x <- x*alpha.
! dcopy Level 1 BLAS thst computes y <- x.
!
!-----------------------------------------------------------------------
!
! %------------------------------------------------------%
! | Storage Declarations: |
! | |
! | It is assumed that A is M by N with M .ge. N. |
! | |
! | The maximum dimensions for all arrays are |
! | set here to accommodate a problem size of |
! | M .le. MAXM and N .le. MAXN |
! | |
! | The NEV right singular vectors will be computed in |
! | the N by NCV array V. |
! | |
! | The NEV left singular vectors will be computed in |
! | the M by NEV array U. |
! | |
! | NEV is the number of singular values requested. |
! | See specifications for ARPACK usage below. |
! | |
! | NCV is the largest number of basis vectors that will |
! | be used in the Implicitly Restarted Arnoldi |
! | Process. Work per major iteration is |
! | proportional to N*NCV*NCV. |
! | |
! | You must set: |
! | |
! | MAXM: Maximum number of rows of the A allowed. |
! | MAXN: Maximum number of columns of the A allowed. |
! | MAXNEV: Maximum NEV allowed |
! | MAXNCV: Maximum NCV allowed |
! %------------------------------------------------------%
!
use FLDebug
!IMPLICIT NONE
!include 'paramnew.h'
integer maxm, maxn, maxnev, maxncv, ldv, ldu,m,n,i
integer ndigit,logfil, msgets, msaitr, msapps, msaupd, msaup2, mseigt, mseupd
! parameter (maxm = istate,maxn=nrsnapshots,maxnev=nrsnapshots-1, &
! maxncv=nrsnapshots, ldu = maxm, ldv=maxn )
! %--------------%
! | Local Arrays |
! %--------------%
!
!real v(ldv,maxncv), u(ldu, maxnev), &
! workl(maxncv*(maxncv+8)), workd(3*maxn), &
! s(maxncv,2), resid(maxn), ax(maxm)
!logical select(maxncv)
integer iparam(11), ipntr(11)
REAL, ALLOCATABLE, DIMENSION(:,:):: v,u,s
REAL, ALLOCATABLE, DIMENSION(:):: workl,workd,resid,ax
REAL, ALLOCATABLE, DIMENSION(:):: ay,ay_dx,ay_dy,ay_dz
logical, ALLOCATABLE, DIMENSION(:):: select
logical ::D3
!
! %---------------%
! | Local Scalars |
! %---------------%
!
character bmat*1, which*2
integer ido, nev, ncv, lworkl, info, ierr, &
j, ishfts, maxitr, mode1, nconv
logical rvec
real toll, sigma, temp
!
! %------------%
! | Parameters |
! %------------%
!
real one, zero
parameter (one = 1.0D+0, zero = 0.0D+0)
!ccccc declare input
real snapmatrix(m,n)
real snapmatrix_dx(m,n),snapmatrix_dy(m,n),snapmatrix_dz(m,n)
real epsilon
integer nsvd,nsvd_total
!cccccccc declare output
real usv(m,nsvd),svdval(nsvd) ! left svd, svdval
!
!
! %-----------------------------%
! | BLAS & LAPACK routines used |
! %-----------------------------%
!
real dnrm2
!
! %-------------%
! | local |
! %-------------%
REAL TOTAL_E,PARTIAL_E,PERCENT_E
! external dnrm2, daxpy, dcopy, dscal
!
! %-----------------------%
! | Executable Statements |
! %-----------------------%
!
! %-------------------------------------------------%
! | The following include statement and assignments |
! | initiate trace output from the internal |
! | actions of ARPACK. See debug.doc in the |
! | DOCUMENTS directory for usage. Initially, the |
! | most useful information will be a breakdown of |
! | time spent in the various stages of computation |
! | given by setting msaupd = 1. |
! %-------------------------------------------------%
!
! include 'debug1.h'
#ifdef HAVE_LIBARPACK
maxm = m
maxn=n
maxnev=n
maxncv=n
ldu = maxm
ldv=maxn
ALLOCATE(v(ldv,maxncv))
ALLOCATE(u(ldu, maxnev))
ALLOCATE(s(maxncv,2))
ALLOCATE(workl(maxncv*(maxncv+8)))
ALLOCATE(workd(3*maxn))
ALLOCATE(resid(maxn))
ALLOCATE(ax(maxm))
ALLOCATE(select(maxncv))
ALLOCATE(ay(maxn))
ALLOCATE(ay_dx(maxn))
ALLOCATE(ay_dy(maxn))
ALLOCATE(ay_dz(maxn))
ewrite(3,*) 'in snapsvd.F'
ewrite(3,*) M,maxm
! maxm=m
! ldu = maxm
ndigit = -3
logfil = 6
msgets = 0
msaitr = 0
msapps = 0
msaupd = 1
msaup2 = 0
mseigt = 0
mseupd = 0
ay=0.0
ay_dx=0.0
ay_dy=0.0
ay_dz=0.0
!
! %-------------------------------------------------%
! | The following sets dimensions for this problem. |
! %-------------------------------------------------%
!
! if (n .ne. nrsnapshots) then
! write(*,*) 'dimension error in svd routine',n,nrsnapshots
! stop
! end if
!
! %------------------------------------------------%
! | Specifications for ARPACK usage are set |
! | below: |
! | |
! | 1) NEV = 4 asks for 4 singular values to be |
! | computed. |
! | |
! | 2) NCV = 20 sets the length of the Arnoldi |
! | factorization |
! | |
! | 3) This is a standard problem |
! | (indicated by bmat = 'I') |
! | |
! | 4) Ask for the NEV singular values of |
! | largest magnitude |
! | (indicated by which = 'LM') |
! | See documentation in DSAUPD for the |
! | other options SM, BE. |
! | |
! | Note: NEV and NCV must satisfy the following |
! | conditions: |
! | NEV <= MAXNEV, |
! | NEV + 1 <= NCV <= MAXNCV |
! %------------------------------------------------%
!
nev = nsvd_total
ncv = n
bmat = 'I'
which = 'LM'
!
if ( n .gt. maxn ) then
ewrite(3,*) ' ERROR with _SVD: N is greater than MAXN '
go to 9000
else if ( m .gt. maxm ) then
ewrite(3,*) ' ERROR with _SVD: M is greater than MAXM ',M,MAXM
go to 9000
else if ( nev .gt. maxnev ) then
ewrite(3,*) ' ERROR with _SVD: NEV is greater than MAXNEV '
go to 9000
else if ( ncv .gt. maxncv ) then
ewrite(3,*) ' ERROR with _SVD: NCV is greater than MAXNCV '
go to 9000
end if
!
! %-----------------------------------------------------%
! | Specification of stopping rules and initial |
! | conditions before calling DSAUPD |
! | |
! | abs(sigmaC - sigmaT) < TOL*abs(sigmaC) |
! | computed true |
! | |
! | If TOL .le. 0, then TOL <- macheps |
! | (machine precision) is used. |
! | |
! | IDO is the REVERSE COMMUNICATION parameter |
! | used to specify actions to be taken on return |
! | from DSAUPD. (See usage below.) |
! | |
! | It MUST initially be set to 0 before the first |
! | call to DSAUPD. |
! | |
! | INFO on entry specifies starting vector information |
! | and on return indicates error codes |
! | |
! | Initially, setting INFO=0 indicates that a |
! | random starting vector is requested to |
! | start the ARNOLDI iteration. Setting INFO to |
! | a nonzero value on the initial call is used |
! | if you want to specify your own starting |
! | vector (This vector must be placed in RESID.) |
! | |
! | The work array WORKL is used in DSAUPD as |
! | workspace. Its dimension LWORKL is set as |
! | illustrated below. |
! %-----------------------------------------------------%
!
lworkl = ncv*(ncv+8)
toll = 0.0d-3 ! 1.d-3
info = 0
ido = 0
!
! %---------------------------------------------------%
! | Specification of Algorithm Mode: |
! | |
! | This program uses the exact shift strategy |
! | (indicated by setting IPARAM(1) = 1.) |
! | IPARAM(3) specifies the maximum number of Arnoldi |
! | iterations allowed. Mode 1 of DSAUPD is used |
! | (IPARAM(7) = 1). All these options can be changed |
! | by the user. For details see the documentation in |
! | DSAUPD. |
! %---------------------------------------------------%
!
ishfts = 1
maxitr = n
mode1 = 1
!
iparam(1) = ishfts
!
iparam(3) = maxitr
!
iparam(7) = mode1
!
! %------------------------------------------------%
! | M A I N L O O P (Reverse communication loop) |
! %------------------------------------------------%
!
10 continue
!
! %---------------------------------------------%
! | Repeatedly call the routine DSAUPD and take |
! | actions indicated by parameter IDO until |
! | either convergence is indicated or maxitr |
! | has been exceeded. |
! %---------------------------------------------%
!
#ifdef DOUBLEP
call dsaupd ( ido, bmat, n, which, nev, toll, resid, &
ncv, v, ldv, iparam, ipntr, workd, workl, &
lworkl, info )
#else
call ssaupd ( ido, bmat, n, which, nev, toll, resid, &
ncv, v, ldv, iparam, ipntr, workd, workl, &
lworkl, info )
#endif
!
if (ido .eq. -1 .or. ido .eq. 1) then
!
! %---------------------------------------%
! | Perform matrix vector multiplications |
! | w <--- A*x (av()) |
! | y <--- A'*w (atv()) |
! | The user should supply his/her own |
! | matrix vector multiplication routines |
! | here that takes workd(ipntr(1)) as |
! | the input, and returns the result in |
! | workd(ipntr(2)). |
! %---------------------------------------%
!
call av (m,n,snapmatrix,workd(ipntr(1)),ax(1:m))
call atv (m,n,snapmatrix,ax,ay)
call av (m,n,snapmatrix_dx,workd(ipntr(1)),ax(1:m))
call atv (m,n,snapmatrix_dx,ax,ay_dx)
call av (m,n,snapmatrix_dy,workd(ipntr(1)),ax(1:m))
call atv (m,n,snapmatrix_dy,ax,ay_dy)
if(.false.) then
call av (m,n,snapmatrix_dz,workd(ipntr(1)),ax(1:m))
call atv (m,n,snapmatrix_dz,ax,ay_dz)
endif
open(1,file='left.dat')
write(1,*) ay(1:n)
close(1)
open(1,file='left_dx.dat')
write(1,*) ay_dx(1:n)
close(1)
open(1,file='left_dy.dat')
write(1,*) ay_dy(1:n)
close(1)
open(1,file='left_dz.dat')
write(1,*) ay_dz(1:n)
close(1)
! stop 1
workd(ipntr(2):ipntr(2)+n-1)=ay(1:n)+epsilon*(ay_dx(1:n)+ay_dy(1:n)+ay_dz(1:n))
!
! %-----------------------------------------%
! | L O O P B A C K to call DSAUPD again. |
! %-----------------------------------------%
!
go to 10
!
end if
!
! %----------------------------------------%
! | Either we have convergence or there is |
! | an error. |
! %----------------------------------------%
!
if ( info .lt. 0 ) then
!
! %--------------------------%
! | Error message. Check the |
! | documentation in DSAUPD. |
! %--------------------------%
!
ewrite(3,*) ' '
ewrite(3,*) ' Error with _saupd, info = ', info
ewrite(3,*) ' Check documentation in _saupd '
ewrite(3,*) ' '
!
else
!
! %--------------------------------------------%
! | No fatal errors occurred. |
! | Post-Process using DSEUPD. |
! | |
! | Computed singular values may be extracted. |
! | |
! | Singular vectors may also be computed now |
! | if desired. (indicated by rvec = .true.) |
! | |
! | The routine DSEUPD now called to do this |
! | post processing |
! %--------------------------------------------%
!
rvec = .true.
!
#ifdef DOUBLEP
call dseupd ( rvec, 'All', select, s, v, ldv, sigma, &
bmat, n, which, nev, toll, resid, ncv, v, ldv, &
iparam, ipntr, workd, workl, lworkl, ierr )
#else
call sseupd ( rvec, 'All', select, s, v, ldv, sigma, &
bmat, n, which, nev, toll, resid, ncv, v, ldv, &
iparam, ipntr, workd, workl, lworkl, ierr )
#endif
!
! %-----------------------------------------------%
! | Singular values are returned in the first |
! | column of the two dimensional array S |
! | and the corresponding right singular vectors |
! | are returned in the first NEV columns of the |
! | two dimensional array V as requested here. |
! %-----------------------------------------------%
!
ewrite(3,*) ipntr(7)
ewrite(3,*) ipntr(7)+ncv
ewrite(3,*) (workl(ipntr(7)+ncv+j-1),j=1,ncv)
TOTAL_E=0.0
DO J=1,NCV
IF(workl(ipntr(7)+ncv+j-1).ge.0.0) THEN
TOTAL_E=TOTAL_E+sqrt(workl(ipntr(7)+ncv+j-1))
ENDIF
ENDDO
if ( ierr .ne. 0) then
!
! %------------------------------------%
! | Error condition: |
! | Check the documentation of DSEUPD. |
! %------------------------------------%
!
ewrite(3,*) ' '
ewrite(3,*) ' Error with _seupd, info = ', ierr
ewrite(3,*) ' Check the documentation of _seupd. '
ewrite(3,*) ' '
!
else
!
nconv = iparam(5)
ewrite(3,*) 'nconv',nconv
PARTIAL_E=0.0
do 20 j=1, nconv
s(j,1) = sqrt(s(j,1))
if(j.le.nsvd) then
PARTIAL_E=PARTIAL_E+s(j,1)
endif
!
! %-----------------------------%
! | Compute the left singular |
! | vectors from the formula |
! | |
! | u = Av/sigma |
! | |
! | u should have norm 1 so |
! | divide by norm(Av) instead. |
! %-----------------------------%
!
call av(m, n, snapmatrix, v(1,j), ax)
u(:,j)=ax
!call dcopy(m, ax, 1, u(1,j), 1)
temp = one/norm2(u(:,j))
!temp = one/dnrm2(m, u(1,j), 1)
u(:,j)=temp*u(:,j)
!call dscal(m, temp, u(1,j), 1)
!
! %---------------------------%
! | |
! | Compute the residual norm |
! | |
! | || A*v - sigma*u || |
! | |
! | for the NCONV accurately |
! | computed singular values |
! | and vectors. (iparam(5) |
! | indicates how many are |
! | accurate to the requested |
! | tolerance). |
! | Store the result in 2nd |
! | column of array S. |
! %---------------------------%
!
ax=ax-s(j,1)*u(:,j)
!call daxpy(m, -s(j,1), u(1,j), 1, ax, 1)
s(j,2) = norm2(ax)
!s(j,2) = dnrm2(m, ax, 1)
!
20 end do
PERCENT_E = 100.0*PARTIAL_E/TOTAL_E
ewrite(3,*) PARTIAL_E,TOTAL_E
EWRITE(3,*) 'The energry captured(%)',PERCENT_E
!
! %-------------------------------%
! | Display computed residuals |
! %-------------------------------%
#ifdef DOUBLEP
call dmout(6, nconv, 2, s, maxncv, -6, &
'Singular values and direct residuals')
#else
call smout(6, nconv, 2, s, maxncv, -6, &
'Singular values and direct residuals')
#endif
end if
!
! %------------------------------------------%
! | Print additional convergence information |
! %------------------------------------------%
!
if ( info .eq. 1) then
ewrite(3,*) ' '
ewrite(3,*) ' Maximum number of iterations reached.'
ewrite(3,*) ' '
else if ( info .eq. 3) then
ewrite(3,*) ' '
ewrite(3,*) ' No shifts could be applied during implicit', &
' Arnoldi update, try increasing NCV.'
ewrite(3,*) ' '
end if
!
ewrite(3,*) ' '
ewrite(3,*) ' _SVD '
ewrite(3,*) ' ==== '
ewrite(3,*) ' '
ewrite(3,*) ' Size of the matrix is ', n
ewrite(3,*) ' The number of Ritz values requested is ', nev
ewrite(3,*) ' The number of Arnoldi vectors generated', &
' (NCV) is ', ncv
ewrite(3,*) ' What portion of the spectrum: ', which
ewrite(3,*) ' The number of converged Ritz values is ', &
nconv
ewrite(3,*) ' The number of Implicit Arnoldi update', &
' iterations taken is ', iparam(3)
ewrite(3,*) ' The number of OP*x is ', iparam(9)
ewrite(3,*) ' The convergence criterion is ', toll
ewrite(3,*) ' '
!
end if
!
! %-------------------------%
! | Done with program dsvd. |
! %-------------------------%
!
9000 continue
if (nconv .ne. nsvd_total) then
write(*,*) 'convergence error in svd computation'
stop
end if
do j = nsvd,1,-1
svdval(nconv+1-j)= s(j,1) ! decreasing order
enddo
do j = nsvd,1,-1
do i=1,m
usv(i,nconv+1-j) = u(i,j)
enddo
enddo
ewrite(3,*) 'the end of snapsvd'
1000 format (1X, E24.16, 1X, E24.16)
2000 format (100(1X,E24.16))
DEALLOCATE(v)
DEALLOCATE(u)
DEALLOCATE(s)
DEALLOCATE(workl)
DEALLOCATE(workd)
DEALLOCATE(resid)
DEALLOCATE(ax)
DEALLOCATE(select)
DEALLOCATE(ay)
DEALLOCATE(ay_dx)
DEALLOCATE(ay_dy)
DEALLOCATE(ay_dz)
#else
FLAbort("No ARPACK support - cannot run reduced model.")
#endif
return
end subroutine snapsvd_H1
!********************
!
! ------------------------------------------------------------------
! matrix vector subroutines
!
!-------------------------------------------------------------------
!
subroutine av (m, n, snapmatrix, x, w)
!
! computes w <- A*x
! include 'paramnew.h'
real x(n), w(m), psum
integer i,j,m,n
real snapmatrix(m,n)
! if (n .ne. nrsnapshots) then
! write(*,*)'matrix dimension error: no of snapshots'
! stop
! end if
! if(m .ne. istate) then
! write(*,*)'matrix dimension error: state dimension'
! stop
! end if
do i=1,m
psum = 0.0d0
do j=1,n
psum = psum + snapmatrix(i,j)*x(j)
enddo
w(i) = psum
enddo
return
end subroutine av
!
!-------------------------------------------------------------------
!
subroutine atv (m, n, snapmatrix, w, y)
!
! computes y <- A'*w
! include 'paramnew.h'
integer m, n
real w(m), y(n),psum
integer i,j
real snapmatrix(m,n)
! if (n .ne. nrsnapshots .or. m .ne. istate) then
! write(*,*)'transpose matrix dimension error'
! stop
! end if
do j=1,n
psum = 0.0d0
do i=1,m
psum = psum + snapmatrix(i,j)*w(i)
enddo
y(j) = psum
enddo
return
end subroutine atv
end module snapsvd_module
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