Thanks for the explanation and advice Karli,
Your comment :
"matrix_range objects operate on the original entries of the full
matrix. That is, whenever you manipulate A, B, C, or D, the entries in
the original matrix are changed as well."
Solves my problem.
I thought this created separate matrices. My solution becomes quite
simple as I can create sub matrices variables from the required output
matrix and write the solution directly without worrying about copying
memory.
I have just tested and is working a treat.
On 7/06/2016 3:15 PM, Karl Rupp wrote:
> Hi Alan,
>
> I'm not sure whether I understand your question correctly.
> matrix_range objects operate on the original entries of the full
> matrix. That is, whenever you manipulate A, B, C, or D, the entries in
> the original matrix are changed as well. This is probably not what you
> want.
>
> I think that you should instead extract the entries representing A, B,
> C, and D into smaller matrix objects (let's call them mA, mB, mC, mD),
> then compute the inverse based on the Schur complement according to
> your formula, and finally put everything back into the original
> matrix. This way you only need matrix_range objects for extracting the
> entries from the original matrix to mA, mB, mC, mD, and for writing
> the entries from mA, mB, mC, mD back into the original matrix. This is
> then achieved via direct assignments from/to matrix_range objects:
>
> mA = A; // extract from original matrix
> // compute something
> A = mA; // write back to original matrix
>
> Best regards,
> Karli
>
>
>
> On 06/07/2016 05:40 AM, Alan wrote:
>> Hi,
>>
>> I am inverting a large matrix using partitioning.
>> i.e.
>>
>> [ A B C D ] − 1 = [ A − 1 + A − 1 B ( D − C A − 1 B ) − 1 C A − 1 −
>> A − 1 B ( D − C A − 1 B ) − 1 − ( D − C A − 1 B ) − 1 C A − 1 ( D −
>> C A − 1 B ) − 1 ] , {\displaystyle {\begin{bmatrix}\mathbf {A}
>> &\mathbf {B} \\\mathbf {C} &\mathbf {D}
>> \end{bmatrix}}^{-1}={\begin{bmatrix}\mathbf {A} ^{-1}+\mathbf {A}
>> ^{-1}\mathbf {B} (\mathbf {D} -\mathbf {CA} ^{-1}\mathbf {B}
>> )^{-1}\mathbf {CA} ^{-1}&-\mathbf {A} ^{-1}\mathbf {B} (\mathbf {D}
>> -\mathbf {CA} ^{-1}\mathbf {B} )^{-1}\\-(\mathbf {D} -\mathbf {CA}
>> ^{-1}\mathbf {B} )^{-1}\mathbf {CA} ^{-1}&(\mathbf {D} -\mathbf {CA}
>> ^{-1}\mathbf {B} )^{-1}\end{bmatrix}},}
>>
>> {\displaystyle \,}
>>
>>
>> I form the submatrices as follows:
>> viennacl::range r1(0,partition);
>> viennacl::range r2(partition,u);
>> viennacl::matrix_range<viennacl::matrix<double>>
>> A(viennacl_Norm,r1,r1);
>> viennacl::matrix_range<viennacl::matrix<double>>
>> B(viennacl_Norm,r1,r2);
>> viennacl::matrix_range<viennacl::matrix<double>>
>> C(viennacl_Norm,r2,r1);
>> viennacl::matrix_range<viennacl::matrix<double>>
>> D(viennacl_Norm,r2,r2);
>>
>> I then manipulate the sub matrices using the above formula (code not
>> shown).
>>
>> I then wish to recreate the full inverted matrix from its parts.
>>
>> I currently can only do this using a very inefficient method (element by
>> element copy using for loops) which defeats the original reason for
>> partitioning.
>> for(int i = 0; i < partition;i++)
>> for(int k = 0; k < partition;k++)
>> viennacl_Norm_i(i,k) = A1(i,k);
>> for(int i = 0; i < partition;i++)
>> for(int k = 0; k < u-partition;k++)
>> viennacl_Norm_i(i,partition+k) = B1(i,k);
>> for(int i = 0; i < u-partition;i++)
>> for(int k = 0; k < partition;k++)
>> viennacl_Norm_i(partition+i,k) = C1(i,k);
>> for(int i = 0; i < u-partition;i++)
>> for(int k = 0; k < u-partition;k++)
>> viennacl_Norm_i(partition+i,partition+k) = D1(i,k);
>>
>>
>> Is there a function that does the reverse of matrix_range class that
>> puts sub matrices back into the full matrix ?
>>
>> Regards,
>>
>> Alan Buchanan
>>
>>
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