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Mathematics Recreation Software Development Wolfram Language

problem with LUDecomposition and SparseArray

Luis Ledesma

Posted 12 years ago

POSTED BY: Luis Ledesma

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Shenghui Yang

Shenghui Yang, WOLFRAM

Posted 12 years ago

POSTED BY: Shenghui Yang

Shenghui Yang

Shenghui Yang, WOLFRAM

Posted 12 years ago

LU decomp does not guarantee a unique solution. Click link here. The permutation matrix is possible: PA = LU if P is not identity matrix. The "A" is your "kl" in the problem. Check: (l.u).Inverse[kl] // MatrixForm

POSTED BY: Shenghui Yang

Luis Ledesma

Posted 12 years ago

Shenghui Yang thanks for the link, is very explicit in the decomposition, and to say of the programs, just what I need, but that can also be done in Mathematica using the commands described above? I hope you can guide me on this topic

POSTED BY: Luis Ledesma

Bill Simpson

Posted 12 years ago

The rows are out of order In[1]:= kl = { {1, 0, 0, 0, 0, 0}, {-1, -6, -2, 0, 0, 0}, {0, -2, -8, -2, 0, 0}, {0, 0, -2, 8, 6, 0}, {0, 0, 0, 6, -4, -8}, {0, 0, 0, 0, 0, 1}}; {lu, p, c} = LUDecomposition[kl]; l = lu SparseArray[{i_, j_} /; j < i -> 1, {6, 6}] + IdentityMatrix[6]; u = lu SparseArray[{i_, j_} /; j >= i -> 1, {6, 6}]; l.u Out[5]= { {1, 0, 0, 0, 0, 0}, {0, -2, -8, -2, 0, 0}, {0, 0, -2, 8, 6, 0}, {0, 0, 0, 6, -4, -8}, {-1, -6, -2, 0, 0, 0}, {0, 0, 0, 0, 0, 1}}

The rows are out of order

In[1]:= kl = {
   {1, 0, 0, 0, 0, 0},
   {-1, -6, -2, 0, 0,  0},
   {0, -2, -8, -2, 0, 0},
   {0, 0, -2, 8, 6, 0},
   {0, 0, 0, 6, -4, -8},
   {0, 0, 0, 0, 0, 1}};
{lu, p, c} = LUDecomposition[kl];
l = lu SparseArray[{i_, j_} /; j < i -> 1, {6, 6}] + IdentityMatrix[6];
u = lu SparseArray[{i_, j_} /; j >= i -> 1, {6, 6}];
l.u

Out[5]= {
  {1, 0, 0, 0, 0, 0},
  {0, -2, -8, -2, 0, 0},
  {0, 0, -2, 8, 6, 0},
  {0, 0, 0, 6, -4, -8},
  {-1, -6, -2, 0, 0, 0},
  {0, 0, 0, 0, 0, 1}}

POSTED BY: Bill Simpson

Luis Ledesma

Posted 12 years ago

Bill Simpson thanks for the help, but I do not understand what you mean with The rows are out of order, is bad built my matrix?,anxiously await your response in order to continue using this command Shenghui Yang thanks for the link, is very explicit in the decomposition, and to say of the programs, just what I need, but that can also be done in Mathematica using the commands described above? I hope you can guide me on this topic

POSTED BY: Luis Ledesma

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