https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/How-to-solve-least-squares-problem-For-dummies/m-p/837926#M6223 Hello,<BR /><BR />I'm trying to solve least squares problem. Given matrix A(mxn), m &gt; n, minimize (Ax - b)<SUP>2</SUP>. MKL Reference suggests to use <A href="http://software.intel.com/sites/products/documentation/hpc/mkl/mklman/hh_goto.htm#lse/lse_crofactor.htm" name="qrfactor"></A><A href="http://software.intel.com/sites/products/documentation/hpc/mkl/mklman/hh_goto.htm#lse/lse_crofactor.htm">QR Factorization</A>. And all calculation is done in several steps - factorization itself, normalizing matrix form, multiplying rhs, etc.<BR /><BR />However, its a little complicated and I found no straightforward explanation on how to compute result x from given A and b. For now I don't even sure how to acquire matrix R. Should I manually multiply A with Q<SUP>T</SUP>? Or should I extract it somehow from QR result?<BR /><BR />I think it'd be pretty convenient to provide manual with simple code example of function<BR /><BR />SolveLSP(int m, int n, float* A, float* b, float* x);<BR /><BR />using LAPACKE_sgeqrf(), LAPACKE_sorgqr() etc. calls, which is exactly my problem. One may assume matrix_order to be LAPACK_ROW_MAJOR.<BR /><BR />E.g. <A href="http://software.intel.com/sites/products/documentation/hpc/composerxe/en-us/ippxe/ipp_manual_lnx/hh_goto.htm#IPPM/ippm_ch7/functn_QRDecomp.htm">ippmQRDecomp</A> reference is great. Even with picture and enough explanation on storage, though one should not be concerned of it granted with simple <A href="http://software.intel.com/sites/products/documentation/hpc/composerxe/en-us/ippxe/ipp_manual_lnx/hh_goto.htm#IPPM/ippm_ch7/functn_QRBackSubst.htm">ippmQRBackSubst</A> function. <BR /><BR />Would you please grant me with such example or with some simple explanation of what functions should I call in what order?<BR /><BR />Thanks a lot.<BR /> Fri, 15 Apr 2011 10:42:11 GMT Mikhail_Matrosov 2011-04-15T10:42:11Z https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/How-to-solve-least-squares-problem-For-dummies/m-p/837926#M6223 Hello,<BR /><BR />I'm trying to solve least squares problem. Given matrix A(mxn), m &gt; n, minimize (Ax - b)<SUP>2</SUP>. MKL Reference suggests to use <A href="http://software.intel.com/sites/products/documentation/hpc/mkl/mklman/hh_goto.htm#lse/lse_crofactor.htm" name="qrfactor"></A><A href="http://software.intel.com/sites/products/documentation/hpc/mkl/mklman/hh_goto.htm#lse/lse_crofactor.htm">QR Factorization</A>. And all calculation is done in several steps - factorization itself, normalizing matrix form, multiplying rhs, etc.<BR /><BR />However, its a little complicated and I found no straightforward explanation on how to compute result x from given A and b. For now I don't even sure how to acquire matrix R. Should I manually multiply A with Q<SUP>T</SUP>? Or should I extract it somehow from QR result?<BR /><BR />I think it'd be pretty convenient to provide manual with simple code example of function<BR /><BR />SolveLSP(int m, int n, float* A, float* b, float* x);<BR /><BR />using LAPACKE_sgeqrf(), LAPACKE_sorgqr() etc. calls, which is exactly my problem. One may assume matrix_order to be LAPACK_ROW_MAJOR.<BR /><BR />E.g. <A href="http://software.intel.com/sites/products/documentation/hpc/composerxe/en-us/ippxe/ipp_manual_lnx/hh_goto.htm#IPPM/ippm_ch7/functn_QRDecomp.htm">ippmQRDecomp</A> reference is great. Even with picture and enough explanation on storage, though one should not be concerned of it granted with simple <A href="http://software.intel.com/sites/products/documentation/hpc/composerxe/en-us/ippxe/ipp_manual_lnx/hh_goto.htm#IPPM/ippm_ch7/functn_QRBackSubst.htm">ippmQRBackSubst</A> function. <BR /><BR />Would you please grant me with such example or with some simple explanation of what functions should I call in what order?<BR /><BR />Thanks a lot.<BR /> Fri, 15 Apr 2011 10:42:11 GMT https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/How-to-solve-least-squares-problem-For-dummies/m-p/837926#M6223 Mikhail_Matrosov 2011-04-15T10:42:11Z https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/How-to-solve-least-squares-problem-For-dummies/m-p/837927#M6224 If you are interested only in obtaining a least-squares solution rather than in the intermediate results such as Q and R, please look at the LAPACKE_?gels routines, and the several examples in the ../mkl/examples/lapacke/source directory. Fri, 15 Apr 2011 13:24:46 GMT https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/How-to-solve-least-squares-problem-For-dummies/m-p/837927#M6224 mecej4 2011-04-15T13:24:46Z https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/How-to-solve-least-squares-problem-For-dummies/m-p/837928#M6225 This is the best answer I didn't even dare to hear :) <BR /><BR />Thanks! Fri, 15 Apr 2011 13:41:32 GMT https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/How-to-solve-least-squares-problem-For-dummies/m-p/837928#M6225 Mikhail_Matrosov 2011-04-15T13:41:32Z