algorithm for index numbers of triangular matrix coefficients -

-

i think must simple can't right...

i have mxm triangular matrix, coefficients of stored in vector, row row. example:

m =   [ m00 m01 m02 m03 ]        [     m11 m12 m12 ]       [         m22 m23 ]       [             m33 ]

is stored 

coef[ m00 m01 m02 m03 m11 m12 m13 m22 m23 m33 ]

now i'm looking non-recursive algorithm gives me matrix size m , coefficient array index i

unsigned int row_index(i,m)

and 

unsigned int column_index(i,m)

of matrix element refers to. so, row_index(9,4) == 3, column_index(7,4) == 2 etc. if index counting zero-based.

edit: several replies using iteration have been given. know of algebraic expressions?

here's algebraic (mostly) solution:

unsigned int row_index( unsigned int i, unsigned int m ){     double m = m;     double row = (-2*m - 1 + sqrt( (4*m*(m+1) - 8*(double)i - 7) )) / -2;     if( row == (double)(int) row ) row -= 1;     return (unsigned int) row; }   unsigned int column_index( unsigned int i, unsigned int m ){     unsigned int row = row_index( i, m);     return  - m * row + row*(row+1) / 2; }

edit: fixed row_index()


Comments

Post a Comment

Popular posts from this blog

c++ - How do I get a multi line tooltip in MFC -

-
right now, have tool tip pops when hover on edit box. problem tool tip contains multiple error messages , in 1 long line. need have each error message on own line. error messages contained in cstring new line seperating them. my existing code below. bool ontooltiptext(uint, nmhdr* pnmhdr, lresult* presult) { assert(pnmhdr->code == ttn_needtexta || pnmhdr->code == ttn_needtextw); // need handle both ansi , unicode versions of message tooltiptexta* pttta = (tooltiptexta*)pnmhdr; tooltiptextw* ptttw = (tooltiptextw*)pnmhdr; // tchar szfulltext[256]; cstring strtiptext=_t(""); uint nid = pnmhdr->idfrom; if (pnmhdr->code == ttn_needtexta && (pttta->uflags & ttf_idishwnd) || pnmhdr->code == ttn_needtextw && (ptttw->uflags & ttf_idishwnd)) { // idfrom hwnd of tool nid = ::getdlgctrlid((hwnd)nid); } //m_errprojaccel[ch] contains 1 or more error messages each...
Read more

asp.net - In javascript how to find the height and width -

-
i having .aspx , masterpage page. in masterpage loading aspx page . in aspx page design using generating table structure using code-behind server in javascript how find height , width . regards, kumar if you're looking table height , width, should it var tbl = document.getelementbyid('tbldemo'); alert(tbl.offsetwidth + '\n' + tbl.offsetheight);
Read more

c# - DataTable to EnumerableRowCollection -

-
i have datatable according client requirement can contain invalid date "00/00/1999",null,empty string.(typed datset) when collect them enumerables wish convert of invalid forms empty string. (i.e) enumerablerowcollection<datarow> query = order in _table.asenumerable() select new { orderdate= string.isnullorempty(convert.tostring(order.field<datetime>("orderdate")) || (how check date invalid date) ? string.empty : order.field<datetime>("orderdate") } how check whether date valid date or not? datetime.tryparse...like given current code: datetime date; enumerablerowcollection<datarow> query = order in _table.asenumerable() select new { orderdate= string.isnullorempty(convert.tostring(order.field<datetime>("orderdate")) || !datetime.tryparse(convert.tostring(order.field<datetime...
Read more