lartg#

Functions

void slartg(
    const f32  f,
    const f32  g,
          f32* c,
          f32* s,
          f32* r
);
void slartg(const f32 f, const f32 g, f32 *c, f32 *s, f32 *r)#

SLARTG generates a plane rotation so that.

[ C S ] . [ F ] = [ R ] [ -S C ] [ G ] [ 0 ]

where C**2 + S**2 = 1.

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).

Parameters

in
f

The first component of vector to be rotated.

in
g

The second component of vector to be rotated.

out
c

The cosine of the rotation.

out
s

The sine of the rotation.

out
r

The nonzero component of the rotated vector.

Functions

void dlartg(
    const f64  f,
    const f64  g,
          f64* c,
          f64* s,
          f64* r
);
void dlartg(const f64 f, const f64 g, f64 *c, f64 *s, f64 *r)#

DLARTG generates a plane rotation so that.

[ C S ] . [ F ] = [ R ] [ -S C ] [ G ] [ 0 ]

where C**2 + S**2 = 1.

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).

Parameters

in
f

The first component of vector to be rotated.

in
g

The second component of vector to be rotated.

out
c

The cosine of the rotation.

out
s

The sine of the rotation.

out
r

The nonzero component of the rotated vector.

Functions

void clartg(
    const c64  f,
    const c64  g,
          f32* c,
          c64* s,
          c64* r
);
void clartg(const c64 f, const c64 g, f32 *c, c64 *s, c64 *r)#

CLARTG generates a plane rotation so that.

[ C S ] . [ F ] = [ R ] [ -conjg(S) C ] [ G ] [ 0 ]

where C is real and C**2 + |S|**2 = 1.

The mathematical formulas used for C and S are

sgn(x) = { x / |x|, x != 0 { 1, x = 0

R = sgn(F) * sqrt(|F|**2 + |G|**2)

C = |F| / sqrt(|F|**2 + |G|**2)

S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2)

Special conditions: If G=0, then C=1 and S=0. If F=0, then C=0 and S is chosen so that R is real.

When F and G are real, the formulas simplify to C = F/R and S = G/R, and the returned values of C, S, and R should be identical to those returned by SLARTG.

Parameters

in
f

The first component of vector to be rotated.

in
g

The second component of vector to be rotated.

out
c

The cosine of the rotation.

out
s

The sine of the rotation.

out
r

The nonzero component of the rotated vector.

Functions

void zlartg(
    const c128  f,
    const c128  g,
          f64*  c,
          c128* s,
          c128* r
);
void zlartg(const c128 f, const c128 g, f64 *c, c128 *s, c128 *r)#

ZLARTG generates a plane rotation so that.

[ C S ] . [ F ] = [ R ] [ -conjg(S) C ] [ G ] [ 0 ]

where C is real and C**2 + |S|**2 = 1.

The mathematical formulas used for C and S are

sgn(x) = { x / |x|, x != 0 { 1, x = 0

R = sgn(F) * sqrt(|F|**2 + |G|**2)

C = |F| / sqrt(|F|**2 + |G|**2)

S = sgn(F) * conjg(G) / sqrt(|F|**2 + |G|**2)

Special conditions: If G=0, then C=1 and S=0. If F=0, then C=0 and S is chosen so that R is real.

When F and G are real, the formulas simplify to C = F/R and S = G/R, and the returned values of C, S, and R should be identical to those returned by DLARTG.

Parameters

in
f

The first component of vector to be rotated.

in
g

The second component of vector to be rotated.

out
c

The cosine of the rotation.

out
s

The sine of the rotation.

out
r

The nonzero component of the rotated vector.

On this page

This Page