# sqrt11.f - Man Page

TESTING/LIN/sqrt11.f

## Synopsis

### Functions/Subroutines

real function **sqrt11** (m, k, a, lda, tau, work, lwork)**SQRT11**

## Function/Subroutine Documentation

### real function sqrt11 (integer m, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork)

**SQRT11**

**Purpose:**

SQRT11 computes the test ratio || Q'*Q - I || / (eps * m) where the orthogonal matrix Q is represented as a product of elementary transformations. Each transformation has the form H(k) = I - tau(k) v(k) v(k)' where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored in A(k+1:m,k).

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

*K*K is INTEGER The number of columns of A whose subdiagonal entries contain information about orthogonal transformations.

*A*A is REAL array, dimension (LDA,K) The (possibly partial) output of a QR reduction routine.

*LDA*LDA is INTEGER The leading dimension of the array A.

*TAU*TAU is REAL array, dimension (K) The scaling factors tau for the elementary transformations as computed by the QR factorization routine.

*WORK*WORK is REAL array, dimension (LWORK)

*LWORK*LWORK is INTEGER The length of the array WORK. LWORK >= M*M + M.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **97** of file **sqrt11.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sqrt11(3) is an alias of sqrt11.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK