I just bought MatLab for a school project a few hours ago, and I've never used this software before. I need to run the code my professor has posted, but the message "'convection_hat' requires more input arguments to run" comes up. Is there something wrong with the code she posted? I'd really appreciated any help, as I'm totally lost at the moment. Here is the code:
function d_theta_hat = convection_hat( t, theta_hat_vec ) global F N tol del_x del_y lap_inv; % theta_hat = Fourier transform of Theta given in ODE call.
% t = time
% return Fourier Transform of -u \cdot \grad theta
% where v = -\lap \inv P ( \theta \cdot \grad \inv \theta )
% and u = v / \norm{\grad v}_{L^2}
theta_hat = reshape( theta_hat_vec, N, N ); % g = \theta \grad\inv \theta
% To convolve accurately we need to "circularly" convolve, which matlab
% doesn't have in 2D. Instead we ifft, multipliy and fft back.
linv_theta_hat = lap_inv .* theta_hat; theta = ifft2( theta_hat, 'symmetric' ); g_hat(:, :, 1) = fft2( theta .* ifft2( del_x .* linv_theta_hat, 'symmetric' ) ); g_hat(:, :, 2) = fft2( theta .* ifft2( del_y .* linv_theta_hat, 'symmetric' ) ); % div_g_hat = (\divergence g)^\hat
div_g_hat = del_x .* g_hat(:, :, 1) + del_y .* g_hat( :, :, 2 ); % v = -\lap\inv P g
v_hat(:, :, 1) = -lap_inv .* ( g_hat(:,:,1) - del_x .* lap_inv .* div_g_hat ); v_hat(:, :, 2) = -lap_inv .* ( g_hat(:,:,2) - del_y .* lap_inv .* div_g_hat ); v_hat_norm1 = del_x.*v_hat(:,:,1); v_hat_norm2 = del_x.*v_hat(:,:,2); v_hat_norm3 = del_y.*v_hat(:,:,1); v_hat_norm4 = del_y.*v_hat(:,:,2); norm_v_hat = sqrt( norm( v_hat_norm1(:), 2 )^2 + ... norm( v_hat_norm2(:), 2 )^2 + norm( v_hat_norm3(:), 2 )^2 + ... norm( v_hat_norm4(:), 2 )^2 ); norm_v = norm_v_hat / N^2; % L2 conversion factor for DFT.
% Compare norm_v relative to norm_g
linv_g_hat( :, :, 1 ) = lap_inv .* g_hat(:, :, 1); linv_g_hat( :, :, 2 ) = lap_inv .* g_hat(:, :, 2); norm_linv_g = norm( linv_g_hat(:), 2 ) / N^2; if norm_v < norm_linv_g *tol; disp( sprintf( ... 'Possible saddle point: t=%.3f, norm_v=%.9f, norm_g=%.9f', ... t, norm_v, norm_linv_g ) ); end u(:, :, 1) = F*ifft2( v_hat(:, :, 1), 'symmetric' ) / norm_v; u(:, :, 2) = F*ifft2( v_hat(:, :, 2), 'symmetric' ) / norm_v; d_theta_hat = -fft2( ... u(:,:,1) .* ifft2( del_x.*theta_hat, 'symmetric' ) + ... u(:,:,2) .* ifft2( del_y.*theta_hat, 'symmetric' ) ); % Finally we need our output to be used in ode23 or ode45 functions, so we
% need reshape it.
d_theta_hat = d_theta_hat(:);end
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