<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 14 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:SimSun;
panose-1:2 1 6 0 3 1 1 1 1 1;}
@font-face
{font-family:SimSun;
panose-1:2 1 6 0 3 1 1 1 1 1;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:SimSun;
panose-1:2 1 6 0 3 1 1 1 1 1;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
{mso-style-priority:99;
mso-style-link:"Balloon Text Char";
margin:0in;
margin-bottom:.0001pt;
font-size:8.0pt;
font-family:"Tahoma","sans-serif";}
span.EmailStyle17
{mso-style-type:personal;
font-family:"Calibri","sans-serif";
color:#1F497D;}
span.BalloonTextChar
{mso-style-name:"Balloon Text Char";
mso-style-priority:99;
mso-style-link:"Balloon Text";
font-family:"Tahoma","sans-serif";}
span.EmailStyle20
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.25in 1.0in 1.25in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Sorry, I forgot to reply to the user group again. Here’s my question again.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Thanks,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Shuangshuang<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> Jin, Shuangshuang <br><b>Sent:</b> Tuesday, June 11, 2013 3:43 PM<br><b>To:</b> 'Hong Zhang'<br><b>Subject:</b> RE: [petsc-users] MATELEMENTAL<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Hi, Hong, does that mean in my code where my J is 12x12,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>If I use one processor, I should set the matrix size as: <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> ierr = MatSetSizes(J, 12, 12, 12, 12); CHKERRQ(ierr);<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>If I use two processor, I should write:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> ierr = MatSetSizes(J, 6, 6, 12, 12); CHKERRQ(ierr);<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>and for three processors, should be:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'> ierr = MatSetSizes(J, 4, 4, 12, 12); CHKERRQ(ierr);<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>which means, the number of local rows = the number of global rows / the number of processors?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Thanks,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Shuangshuang<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> Hong Zhang [<a href="mailto:hzhang@mcs.anl.gov">mailto:hzhang@mcs.anl.gov</a>] <br><b>Sent:</b> Tuesday, June 11, 2013 3:05 PM<br><b>To:</b> Jin, Shuangshuang<br><b>Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><br><b>Subject:</b> Re: [petsc-users] MATELEMENTAL<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Shuangshuang,</span><o:p></o:p></p><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>In ex38.c, m and n are local block sizes, not global. When running np=2 on a matrix with global sizes 12 by 12, you should give</span><o:p></o:p></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>mpiexec -n 2 ./ex38 -Cexp_view_ownership 1 -m 6 -n 6</span><o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Hong</span><o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div></div><div><p class=MsoNormal style='margin-bottom:12.0pt'><o:p> </o:p></p><div><p class=MsoNormal>On Tue, Jun 11, 2013 at 3:22 PM, Jin, Shuangshuang <<a href="mailto:Shuangshuang.Jin@pnnl.gov" target="_blank">Shuangshuang.Jin@pnnl.gov</a>> wrote:<o:p></o:p></p><div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Hello, I’m trying to set my Jacobian matrix to MATELEMENTAL type.<o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>According to an Elemental matrix example code: /src/mat/examples/tests/ex38.c, I wrote my piece of code as following:<o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatCreate(PETSC_COMM_WORLD, &J); CHKERRQ(ierr); // J: Jacobian matrix<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatSetSizes(J, 12, 12, PETSC_DECIDE, PETSC_DECIDE); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatSetType(J, MATELEMENTAL); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatSetFromOptions(J); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatSetUp(J); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> PetscInt nrows,ncols;<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> const PetscInt *rows,*cols;<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> IS isrows,iscols;<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> PetscScalar *v;<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatGetOwnershipIS(J, &isrows, &iscols); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> // Set local matrix entries<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = ISGetLocalSize(isrows, &nrows); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = ISGetIndices(isrows, &rows); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = ISGetLocalSize(iscols, &ncols); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = ISGetIndices(iscols, &cols); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = PetscMalloc(nrows*ncols*sizeof(*v), &v); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> printf("nrows=%d, ncols=%d\n",nrows,ncols);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> for (i = 0; i < nrows; i++) {<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> for (j = 0; j < ncols; j++) {<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> v[i*ncols+j] = jacVal[i][j]; // jacVal stores the value of the 12*12 Jacobian matrix<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> }<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> }<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatSetValues(J, nrows, rows, ncols, cols, v, INSERT_VALUES); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = ISRestoreIndices(isrows, &rows); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = ISRestoreIndices(iscols, &cols); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = ISDestroy(&isrows); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> ierr = ISDestroy(&iscols); CHKERRQ(ierr);<o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>This works for one processor. When it goes to multiple processor, it will fail. <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>I notice that when the # of processor equals to 1, the nrows and ncols will be 12 each, which are the dimension of the Jacobian matrix.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>However, when the # of processor goes up, for example, to 2, nrows=24, ncols=12, then it will fail because the index of my jac[i][j] are withn [0, 11].<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>My question is, to use MATELEMENTAL, what is the rule to fit the values of my 12x12 matrix into a 24X12 arrays by the two level for loops?<o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>And I don’t understand what the set means here:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[d3m956@olympus tests]$ mpiexec -n 1 ex38 -Cexp_view_ownership 1 -m 12 -n 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Ownership of explicit C:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Row index set:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Number of indices in set 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>0 0<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>1 1<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>2 2<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>3 3<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>4 4<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>5 5<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>6 6<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>7 7<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>8 8<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>9 9<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>10 10<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>11 11<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Column index set:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Number of indices in set 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>0 0<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>1 1<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>2 2<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>3 3<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>4 4<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>5 5<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>6 6<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>7 7<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>8 8<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>9 9<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>10 10<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>11 11<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>nrows=12, ncols=12<o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[d3m956@olympus tests]$ mpiexec -n 2 ex38 -Cexp_view_ownership 1 -m 12 -n 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Ownership of explicit C:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Row index set:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] Number of indices in set 24<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 0 0<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 1 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 2 1<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 3 13<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 4 2<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 5 14<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 6 3<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 7 15<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 8 4<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 9 16<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 10 5<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 11 17<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 12 6<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 13 18<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 14 7<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 15 19<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 16 8<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 17 20<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 18 9<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 19 21<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 20 10<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 21 22<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 22 11<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 23 23<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>nrows=24, ncols=12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] Number of indices in set 24<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 0 0<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 1 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 2 1<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 3 13<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 4 2<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 5 14<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 6 3<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 7 15<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 8 4<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 9 16<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 10 5<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 11 17<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 12 6<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 13 18<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 14 7<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 15 19<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 16 8<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 17 20<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 18 9<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 19 21<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 20 10<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 21 22<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 22 11<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 23 23<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Column index set:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] Number of indices in set 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 0 0<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 1 1<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 2 2<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 3 3<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 4 4<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 5 5<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 6 6<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 7 7<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 8 8<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 9 9<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 10 10<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[0] 11 11<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] Number of indices in set 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 0 12<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 1 13<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 2 14<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 3 15<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 4 16<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 5 17<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 6 18<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 7 19<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 8 20<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 9 21<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 10 22<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>[1] 11 23<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>nrows=24, ncols=12<o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Thanks,<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Calibri","sans-serif"'>Shuangshuang<o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div><div><p class=MsoNormal> <span style='font-family:"Calibri","sans-serif"'><o:p></o:p></span></p></div></div></div><p class=MsoNormal><o:p> </o:p></p></div></div></body></html>