# dlaorhr_col_getrfnp.f - Man Page

SRC/dlaorhr_col_getrfnp.f

## Synopsis

### Functions/Subroutines

subroutine **dlaorhr_col_getrfnp** (m, n, a, lda, d, info)**DLAORHR_COL_GETRFNP**

## Function/Subroutine Documentation

### subroutine dlaorhr_col_getrfnp (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, integer info)

**DLAORHR_COL_GETRFNP**

**Purpose:**

DLAORHR_COL_GETRFNP computes the modified LU factorization without pivoting of a real 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 DORHR_COL. In DORHR_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 DLAORHR_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.

**Parameters***M*M is INTEGER The number of rows of the matrix A. M >= 0.

*N*N is INTEGER The number of columns of the matrix A. N >= 0.

*A*A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A-S=L*U; the unit diagonal elements of L are not stored.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

*D*D is DOUBLE PRECISION array, dimension min(M,N) The diagonal elements of the diagonal M-by-N sign matrix S, D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can be only plus or minus one.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**

November 2019, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line **145** of file **dlaorhr_col_getrfnp.f**.

## Author

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## Referenced By

The man page dlaorhr_col_getrfnp(3) is an alias of dlaorhr_col_getrfnp.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK