---
name: "srotg.f90"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/srotg.f90"
---

# srotg.f90(3)

## NAME

BLAS/SRC/srotg.f90

## SYNOPSIS

### Functions/Subroutines

subroutine **srotg** (a, b, c, s)\
 **SROTG**

## Function/Subroutine Documentation

### subroutine srotg (real(wp) a, real(wp) b, real(wp) c, real(wp) s)

**SROTG**

**Purpose:**

```
!>
!> SROTG constructs a plane rotation
!>    [  c  s ] [ a ] = [ r ]
!>    [ -s  c ] [ b ]   [ 0 ]
!> satisfying c**2 + s**2 = 1.
!>
!> The computation uses the formulas
!>    sigma = sgn(a)    if |a| >  |b|
!>          = sgn(b)    if |b| >= |a|
!>    r = sigma*sqrt( a**2 + b**2 )
!>    c = 1; s = 0      if r = 0
!>    c = a/r; s = b/r  if r != 0
!> The subroutine also computes
!>    z = s    if |a| > |b|,
!>      = 1/c  if |b| >= |a| and c != 0
!>      = 1    if c = 0
!> This allows c and s to be reconstructed from z as follows:
!>    If z = 1, set c = 0, s = 1.
!>    If |z| < 1, set c = sqrt(1 - z**2) and s = z.
!>    If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).
!>
!>
```

**See also**

**lartg:          generate plane rotation, more accurate than BLAS rot**,

**lartgp:         generate plane rotation, more accurate than BLAS rot**

**Parameters**

*A*

```
!>          A is REAL
!>          On entry, the scalar a.
!>          On exit, the scalar r.
!>
```

*B*

```
!>          B is REAL
!>          On entry, the scalar b.
!>          On exit, the scalar z.
!>
```

*C*

```
!>          C is REAL
!>          The scalar c.
!>
```

*S*

```
!>          S is REAL
!>          The scalar s.
!>
```

**Author**

Edward Anderson, Lockheed Martin

**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 **91** of file **srotg.f90**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.