# sgeqrf.f - Man Page

SRC/sgeqrf.f

## Synopsis

### Functions/Subroutines

subroutine **sgeqrf** (m, n, a, lda, tau, work, lwork, info)**SGEQRF**

## Function/Subroutine Documentation

### subroutine sgeqrf (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

**SGEQRF** Ā

**Purpose:**

SGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * ( R ), ( 0 ) where: Q is a M-by-M orthogonal matrix; R is an upper-triangular N-by-N matrix; 0 is a (M-N)-by-N zero matrix, if M > N.

**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 REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).

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

*TAU*TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).

*WORK*WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is INTEGER The dimension of the array WORK. LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

*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.

**Further Details:**

The matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(k), where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v**T where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

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

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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