You have to assemble<div><br></div><div> a) after setting values</div><div><br></div><div> b) before using the matrix</div><div><br></div><div>Please consult the user examples where this is done correctly and the manual</div>
<div>section which explains the assembly process.</div><div><br></div><div> Matt<br><br><div class="gmail_quote">On Wed, Jul 7, 2010 at 8:13 PM, Xuan YU <span dir="ltr"><<a href="mailto:xxy113@psu.edu">xxy113@psu.edu</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div style="word-wrap:break-word"><br><div><div>On Jul 7, 2010, at 2:06 PM, Satish Balay wrote:</div><br><blockquote type="cite">
<div>On Wed, 7 Jul 2010, Xuan YU wrote:<br><br><blockquote type="cite">ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,10,PETSC_NULL,&J);CHKERRQ(ierr);<br></blockquote><br><blockquote type="cite">ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);<br>
</blockquote><blockquote type="cite">ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);<br></blockquote><br>This assembly removes the unused space here. Since no values are<br>inserted - it squezes out all of the allocated space. Perhaps you just<br>
need to remove these 2 calls as the actual matrix is assembled further<br>down the code.<br><br></div></blockquote><div><br></div><div>I removed these 2 </div><div>But got Error Message</div><div><br></div><div><div>[0]PETSC ERROR: Object is in wrong state!</div>
<div>[0]PETSC ERROR: Not for unassembled matrix!</div><div><br></div></div><div><br></div><div><br></div><div><br></div><br><blockquote type="cite"><div>Satish<br><br><blockquote type="cite">ierr = SNESComputeJacobian(ts_snes,CV_Y,&J,&J,&flag);CHKERRQ(ierr);<br>
</blockquote><blockquote type="cite">ierr = MatGetColoring(J,MATCOLORINGSL,&iscoloring);CHKERRQ(ierr);<br></blockquote><blockquote type="cite">ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);<br>
</blockquote><blockquote type="cite">ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode<br></blockquote><blockquote type="cite">(*)(void))f,(void*)&appctx);CHKERRQ(ierr);<br></blockquote><blockquote type="cite">
ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);<br></blockquote><blockquote type="cite">ierr = TSSetRHSJacobian(ts,J,J,TSDefaultComputeJacobianColor,matfdcoloring);<br></blockquote><blockquote type="cite">
<br></blockquote><blockquote type="cite">These are the Jacobian related codes.<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">
<br></blockquote><blockquote type="cite">On Jul 7, 2010, at 1:51 PM, Satish Balay wrote:<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">total: nonzeros=1830<br>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">mallocs used during MatSetValues calls =1830<br></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Looks like you are zero-ing out the non-zero structure - before<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
assembling the matrix.<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">Are you calling MatZeroRows() or MatZeroEntries() or something else -<br>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite">before assembling the matrix?<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite">Satish<br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">On Wed, 7 Jul 2010, Xuan YU wrote:<br>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">I made a change: ierr =<br></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,5,PETSC_NULL,&J);CHKERRQ(ierr);<br></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Time of the code did not change much, and got the info:<br>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Matrix Object:<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
type=seqaij, rows=1830, cols=1830<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> total: nonzeros=1830, allocated nonzeros=36600<br></blockquote>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> total number of mallocs used during MatSetValues calls =1830<br></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"> not using I-node routines<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">On Jul 7, 2010, at 12:51 PM, Satish Balay wrote:<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> total: nonzeros=1830, allocated nonzeros=29280<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> total number of mallocs used during MatSetValues calls =1830<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite">There is something wrong with your preallocation or matrix<br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite">assembly. You should see zero mallocs for efficient assembly.<br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><a href="http://www.mcs.anl.gov/petsc/petsc-as/documentation/faq.html#efficient-assembly" target="_blank">http://www.mcs.anl.gov/petsc/petsc-as/documentation/faq.html#efficient-assembly</a><br>
</blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite">satish<br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
<br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite">On Wed, 7 Jul 2010, Xuan YU wrote:<br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Hi,<br></blockquote></blockquote>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote></blockquote>
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">I finite difference Jacobian approximation for my TS model. The size<br></blockquote></blockquote></blockquote>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">of<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">the<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite">vector is 1830. I got the following info with(-ts_view):<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite">type: beuler<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
maximum steps=50<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">maximum time=50<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">total number of nonlinear solver iterations=647<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">total number of linear solver iterations=647<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">SNES Object:<br></blockquote></blockquote>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">type: ls<br></blockquote></blockquote></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> line search variant: SNESLineSearchCubic<br></blockquote></blockquote></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> alpha=0.0001, maxstep=1e+08, minlambda=1e-12<br></blockquote></blockquote></blockquote>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">maximum iterations=50, maximum function evaluations=10000<br></blockquote></blockquote>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">tolerances: relative=1e-08, absolute=1e-50, solution=1e-08<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">total number of linear solver iterations=50<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">total number of function evaluations=51<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">KSP Object:<br></blockquote></blockquote>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> type: gmres<br></blockquote></blockquote></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt<br></blockquote></blockquote>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Orthogonalization with no iterative refinement<br></blockquote>
</blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> GMRES: happy breakdown tolerance 1e-30<br></blockquote>
</blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> maximum iterations=10000, initial guess is zero<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> tolerances: relative=1e-05, absolute=1e-50, divergence=10000<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> left preconditioning<br></blockquote>
</blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> using PRECONDITIONED norm type for convergence test<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">PC Object:<br></blockquote></blockquote>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> type: ilu<br></blockquote></blockquote></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> ILU: out-of-place factorization<br></blockquote></blockquote></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> 0 levels of fill<br></blockquote></blockquote></blockquote></blockquote></blockquote>
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> tolerance for zero pivot 1e-12<br></blockquote></blockquote></blockquote></blockquote></blockquote>
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> using diagonal shift to prevent zero pivot<br></blockquote></blockquote></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> matrix ordering: natural<br></blockquote></blockquote></blockquote></blockquote></blockquote>
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> factor fill ratio given 1, needed 1<br></blockquote></blockquote></blockquote></blockquote></blockquote>
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> Factored matrix follows:<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> Matrix Object:<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> type=seqaij, rows=1830, cols=1830<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> package used to perform factorization: petsc<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> total: nonzeros=1830, allocated nonzeros=1830<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> total number of mallocs used during MatSetValues calls =0<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> not using I-node routines<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> linear system matrix = precond matrix:<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> Matrix Object:<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> type=seqaij, rows=1830, cols=1830<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> total: nonzeros=1830, allocated nonzeros=29280<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> total number of mallocs used during MatSetValues calls =1830<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"> not using I-node routines<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">50 output time step takes me 11.877s. So I guess there is something<br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">not<br></blockquote></blockquote></blockquote>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">appropriate with my Jacobian Matrix. Could you please tell me how to<br></blockquote>
</blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">speed<br></blockquote></blockquote></blockquote></blockquote>
</blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">up<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">my code?<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite">Thanks!<br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Xuan YU<br></blockquote></blockquote>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><a href="mailto:xxy113@psu.edu" target="_blank">xxy113@psu.edu</a><br>
</blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote>
</blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite">Xuan YU (俞烜)<br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite">
<blockquote type="cite"><a href="mailto:xxy113@psu.edu" target="_blank">xxy113@psu.edu</a><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote>
</blockquote></blockquote><blockquote type="cite"><blockquote type="cite"><blockquote type="cite"><br></blockquote></blockquote></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">Xuan YU (俞烜)<br>
</blockquote><blockquote type="cite"><a href="mailto:xxy113@psu.edu" target="_blank">xxy113@psu.edu</a><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">
<br></blockquote><blockquote type="cite"><br></blockquote></div></blockquote></div><font color="#888888"><br><div> <div style="word-wrap:break-word"><span style="border-collapse:separate;color:rgb(0, 0, 0);font-family:Helvetica;font-size:medium;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><div style="word-wrap:break-word">
<div>Xuan YU (<span style="font-family:arial;font-size:16px;white-space:pre-wrap">俞烜<span style="font-family:Helvetica;font-size:medium;white-space:normal">)</span></span></div><div><a href="mailto:xxy113@psu.edu" target="_blank">xxy113@psu.edu</a></div>
<div><br></div></div></span><br></div><br> </div><br></font></div></blockquote></div><br><br clear="all"><br>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<br>
</div>