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Hello,
I'm an MKL LAPACK engineer. MKL doesn't have matrix orthogonalization routine. Generally, MKL supports LAPACK standard, which is described at www.netlib.org/lapack,but this routine isn't standard. Anyway, we can introduce functionality in MKL if it's useful for our customers.
Michael.
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Yelu1220,
We would recommend you submit the issue against MKL to Premier support( https://premier.intel.com/ )
--Gennady
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Hi,
For such request, MKL LAPACK functionality can be used:
If we consider QR factorization of the M-by-N (M>N) matrx A=Q*R in the form where Q is square M-by-M matrix and R is an upper triangular M-by-N matrix. The equality A=Q*R can be re-written also as a product Q1*R1 where Q1 is a rectangular M-by-N submatrix of the matrix Q and R1 is M-by-M submatrix of the R. Let us note that columns of Q1 are orthonormal (they are orthogonal to each other and have norms equal to 1). The equality A=Q1*R1 can be treated as every column of A is a linear combination of Q1 columns, i.e. they span the same linear space. In other words, columns of Q1 is nothing else but a result of ortogonalization of columns A.
Of course, cases where R degenerates should be cosnsidered with some care and R must be trapezoidal if rank(A) is less than N.
QR functionality of MKL does not give Q directly- after calling DGEQRF a function DORGQR must be called.
DGEQPF might be useful for degenerate cases.
how does this works for you?
Thanks,
Chao
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Hi,
For such request, MKL LAPACK functionality can be used:
If we consider QR factorization of the M-by-N (M>N) matrx A=Q*R in the form where Q is square M-by-M matrix and R is an upper triangular M-by-N matrix. The equality A=Q*R can be re-written also as a product Q1*R1 where Q1 is a rectangular M-by-N submatrix of the matrix Q and R1 is M-by-M submatrix of the R. Let us note that columns of Q1 are orthonormal (they are orthogonal to each other and have norms equal to 1). The equality A=Q1*R1 can be treated as every column of A is a linear combination of Q1 columns, i.e. they span the same linear space. In other words, columns of Q1 is nothing else but a result of ortogonalization of columns A.
Of course, cases where R degenerates should be cosnsidered with some care and R must be trapezoidal if rank(A) is less than N.
QR functionality of MKL does not give Q directly- after calling DGEQRF a function DORGQR must be called.
DGEQPF might be useful for degenerate cases.
how does this works for you?
Thanks,
Chao
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