public interface launhr_col_getrfnp
LAUNHR_COL_GETRFNP computes the modified LU factorization without
pivoting of a complex general M-by-N matrix A. The factorization has
the form:
A - S = L * U,
where:
S is a m-by-n diagonal sign matrix with the diagonal D, so that
D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
i-1 steps of Gaussian elimination. This means that the diagonal
element at each step of "modified" Gaussian elimination is
at least one in absolute value (so that division-by-zero not
not possible during the division by the diagonal element);
L is a M-by-N lower triangular matrix with unit diagonal elements
(lower trapezoidal if M > N);
and U is a M-by-N upper triangular matrix
(upper trapezoidal if M < N).
This routine is an auxiliary routine used in the Householder
reconstruction routine CUNHR_COL. In CUNHR_COL, this routine is
applied to an M-by-N matrix A with orthonormal columns, where each
element is bounded by one in absolute value. With the choice of
the matrix S above, one can show that the diagonal element at each
step of Gaussian elimination is the largest (in absolute value) in
the column on or below the diagonal, so that no pivoting is required
for numerical stability [1].
For more details on the Householder reconstruction algorithm,
including the modified LU factorization, see [1].
This is the blocked right-looking version of the algorithm,
calling Level 3 BLAS to update the submatrix. To factorize a block,
this routine calls the recursive routine LAUNHR_COL_GETRFNP2.
[1] "Reconstructing Householder vectors from tall-skinny QR",
G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
E. Solomonik, J. Parallel Distrib. Comput.,
vol. 85, pp. 3-31, 2015.
Subroutines
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
m |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
n |
|
|
complex(kind=sp),
|
intent(inout) |
|
|
:: |
a(lda,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lda |
|
|
complex(kind=sp),
|
intent(out) |
|
|
:: |
d(*) |
|
|
integer(kind=ilp),
|
intent(out) |
|
|
:: |
info |
|
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
m |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
n |
|
|
complex(kind=dp),
|
intent(inout) |
|
|
:: |
a(lda,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lda |
|
|
complex(kind=dp),
|
intent(out) |
|
|
:: |
d(*) |
|
|
integer(kind=ilp),
|
intent(out) |
|
|
:: |
info |
|
Module Procedures
