|
|
@@ -55,7 +55,7 @@ |
|
|
|
*> where: |
|
|
|
*> |
|
|
|
*> P(K) is an N-by-N permutation matrix; |
|
|
|
*> Q(K) is an M-by-M orthogonal matrix; |
|
|
|
*> Q(K) is an M-by-M unitary matrix; |
|
|
|
*> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the |
|
|
|
*> full rank factor R with K-by-K upper-triangular |
|
|
|
*> R11(K) and K-by-N rectangular R12(K). The diagonal |
|
|
@@ -124,14 +124,14 @@ |
|
|
|
*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum |
|
|
|
*> column 2-norm of the original matrix A, which is equal |
|
|
|
*> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 ); |
|
|
|
*> e) Q(K)**H * B, the matrix B with the orthogonal |
|
|
|
*> e) Q(K)**H * B, the matrix B with the unitary |
|
|
|
*> transformation Q(K)**H applied on the left. |
|
|
|
*> |
|
|
|
*> The N-by-N permutation matrix P(K) is stored in a compact form in |
|
|
|
*> the integer array JPIV. For 1 <= j <= N, column j |
|
|
|
*> of the matrix A was interchanged with column JPIV(j). |
|
|
|
*> |
|
|
|
*> The M-by-M orthogonal matrix Q is represented as a product |
|
|
|
*> The M-by-M unitary matrix Q is represented as a product |
|
|
|
*> of elementary Householder reflectors |
|
|
|
*> |
|
|
|
*> Q(K) = H(1) * H(2) * . . . * H(K), |
|
|
@@ -300,7 +300,7 @@ |
|
|
|
*> |
|
|
|
*> 1. The elements below the diagonal of the subarray |
|
|
|
*> A(1:M,1:K) together with TAU(1:K) represent the |
|
|
|
*> orthogonal matrix Q(K) as a product of K Householder |
|
|
|
*> unitary matrix Q(K) as a product of K Householder |
|
|
|
*> elementary reflectors. |
|
|
|
*> |
|
|
|
*> 2. The elements on and above the diagonal of |
|
|
@@ -579,8 +579,8 @@ |
|
|
|
*> \verbatim |
|
|
|
*> |
|
|
|
*> November 2023, Igor Kozachenko, James Demmel, |
|
|
|
*> Computer Science Division, |
|
|
|
*> University of California, Berkeley |
|
|
|
*> EECS Department, |
|
|
|
*> University of California, Berkeley, USA. |
|
|
|
*> |
|
|
|
*> \endverbatim |
|
|
|
* |
|
|
|