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. More...

Public Member Functions
pure subroutine	claunhr_col_getrfnp (m, n, a, lda, d, info)

	la_claunhr_col_getrfnp

	la_wlaunhr_col_getrfnp

pure subroutine	zlaunhr_col_getrfnp (m, n, a, lda, d, info)

	la_zlaunhr_col_getrfnp

Detailed Description

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.

Member Function/Subroutine Documentation

◆ claunhr_col_getrfnp()

pure subroutine la_lapack::launhr_col_getrfnp::claunhr_col_getrfnp	(	integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(*), intent(out)	d,
		integer(ilp), intent(out)	info
	)

◆ la_claunhr_col_getrfnp()

la_lapack::launhr_col_getrfnp::la_claunhr_col_getrfnp

◆ la_wlaunhr_col_getrfnp()

la_lapack::launhr_col_getrfnp::la_wlaunhr_col_getrfnp

◆ la_zlaunhr_col_getrfnp()

la_lapack::launhr_col_getrfnp::la_zlaunhr_col_getrfnp

◆ zlaunhr_col_getrfnp()

pure subroutine la_lapack::launhr_col_getrfnp::zlaunhr_col_getrfnp	(	integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		complex(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(*), intent(out)	d,
		integer(ilp), intent(out)	info
	)

The documentation for this interface was generated from the following file:

la_lapack.f90