# dlartg.f90 - Man Page

SRC/dlartg.f90

## Synopsis

### Functions/Subroutines

subroutine **dlartg** (f, g, c, s, r)**DLARTG** generates a plane rotation with real cosine and real sine.

## Function/Subroutine Documentation

### subroutine dlartg (real(wp) f, real(wp) g, real(wp) c, real(wp) s, real(wp) r)

**DLARTG** generates a plane rotation with real cosine and real sine.

**Purpose:**

DLARTG generates a plane rotation so that [ C S ] . [ F ] = [ R ] [ -S C ] [ G ] [ 0 ] where C**2 + S**2 = 1. The mathematical formulas used for C and S are R = sign(F) * sqrt(F**2 + G**2) C = F / R S = G / R Hence C >= 0. The algorithm used to compute these quantities incorporates scaling to avoid overflow or underflow in computing the square root of the sum of squares. This version is discontinuous in R at F = 0 but it returns the same C and S as ZLARTG for complex inputs (F,0) and (G,0). This is a more accurate version of the BLAS1 routine DROTG, with the following other differences: F and G are unchanged on return. If G=0, then C=1 and S=0. If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any floating point operations (saves work in DBDSQR when there are zeros on the diagonal). Below, wp=>dp stands for double precision from LA_CONSTANTS module.

**Parameters***F*F is REAL(wp) The first component of vector to be rotated.

*G*G is REAL(wp) The second component of vector to be rotated.

*C*C is REAL(wp) The cosine of the rotation.

*S*S is REAL(wp) The sine of the rotation.

*R*R is REAL(wp) The nonzero component of the rotated vector.

**Author**Edward Anderson, Lockheed Martin

**Date**July 2016

**Contributors:**Weslley Pereira, University of Colorado Denver, USA

**Further Details:**

Anderson E. (2017) Algorithm 978: Safe Scaling in the Level 1 BLAS ACM Trans Math Softw 44:1--28 https://doi.org/10.1145/3061665

Definition at line **110** of file **dlartg.f90**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlartg(3) is an alias of dlartg.f90(3).

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