Compute the Jacobian using finite differences. (one column at a time)
Type | Intent | Optional | Attributes | Name | ||
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class(numdiff_type), | intent(inout) | :: | me | |||
real(kind=wp), | intent(in), | dimension(:) | :: | x |
vector of variables (size |
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real(kind=wp), | intent(in), | dimension(me%n) | :: | dx |
absolute perturbation (>0) for each variable |
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real(kind=wp), | intent(out), | dimension(:) | :: | jac |
sparse jacobian vector (size
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subroutine compute_jacobian_standard(me,x,dx,jac) implicit none class(numdiff_type),intent(inout) :: me real(wp),dimension(:),intent(in) :: x !! vector of variables (size `n`) real(wp),dimension(me%n),intent(in) :: dx !! absolute perturbation (>0) !! for each variable real(wp),dimension(:),intent(out) :: jac !! sparse jacobian vector (size !! `num_nonzero_elements`) integer,dimension(:),allocatable :: nonzero_elements_in_col !! the indices of the !! nonzero Jacobian !! elements in a column integer :: i !! column counter integer :: j !! function evaluation counter real(wp),dimension(me%m) :: df !! accumulated function type(finite_diff_method) :: fd !! a finite different method (when !! specifying class rather than the method) logical :: status_ok !! error flag integer :: num_nonzero_elements_in_col !! number of nonzero elements in a column if (me%exception_raised) return ! check for exceptions ! initialize: jac = zero ! compute Jacobian matrix column-by-column: do i=1,me%n ! determine functions to compute for this column: num_nonzero_elements_in_col = count(me%sparsity%icol==i) if (num_nonzero_elements_in_col/=0) then ! there are functions to compute nonzero_elements_in_col = pack(me%sparsity%irow,mask=me%sparsity%icol==i) select case (me%mode) case(1) ! use the specified methods ! compute this column of the Jacobian: df = zero do j = 1, size(me%meth(i)%dx_factors) if (associated(me%info_function)) call me%info_function([i],j,x) call me%perturb_x_and_compute_f(x,me%meth(i)%dx_factors(j),& dx,me%meth(i)%df_factors(j),& i,nonzero_elements_in_col,df) if (me%exception_raised) return ! check for exceptions end do df(nonzero_elements_in_col) = df(nonzero_elements_in_col) / & (me%meth(i)%df_den_factor*dx(i)) case(2) ! select the method from the class so as not to violate the bounds call me%select_finite_diff_method(x(i),me%xlow(i),me%xhigh(i),& dx(i),me%class_meths(i),fd,status_ok) if (.not. status_ok) then if (me%print_messages) then write(error_unit,'(A,1X,I5)') & 'Error in compute_jacobian_standard: variable bounds violated for column: ',i end if end if ! compute this column of the Jacobian: df = zero do j = 1, size(fd%dx_factors) if (associated(me%info_function)) call me%info_function([i],j,x) call me%perturb_x_and_compute_f(x,fd%dx_factors(j),& dx,fd%df_factors(j),& i,nonzero_elements_in_col,df) if (me%exception_raised) return ! check for exceptions end do df(nonzero_elements_in_col) = df(nonzero_elements_in_col) / & (fd%df_den_factor*dx(i)) case default call me%raise_exception(23,'compute_jacobian_standard',& 'invalid mode') return end select ! put result into the output vector: jac(pack(me%sparsity%indices,mask=me%sparsity%icol==i)) = & df(nonzero_elements_in_col) end if end do end subroutine compute_jacobian_standard