lanv2

slanv2

Functions

void slanv2(
    f32* a,
    f32* b,
    f32* c,
    f32* d,
    f32* rt1r,
    f32* rt1i,
    f32* rt2r,
    f32* rt2i,
    f32* cs,
    f32* sn
);

void slanv2(f32 *a, f32 *b, f32 *c, f32 *d, f32 *rt1r, f32 *rt1i, f32 *rt2r, f32 *rt2i, f32 *cs, f32 *sn)

SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form:

 [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
 [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]

where either 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or 2) AA = DD and BB*CC < 0, so that AA +/- sqrt(BB*CC) are complex conjugate eigenvalues.

Parameters

inout

a

On entry, the (1,1) element of the input matrix. On exit, the (1,1) element of the Schur form.

inout

b

On entry, the (1,2) element of the input matrix. On exit, the (1,2) element of the Schur form.

inout

c

On entry, the (2,1) element of the input matrix. On exit, the (2,1) element of the Schur form.

inout

d

On entry, the (2,2) element of the input matrix. On exit, the (2,2) element of the Schur form.

out

rt1r

The real part of the first eigenvalue.

out

rt1i

The imaginary part of the first eigenvalue.

out

rt2r

The real part of the second eigenvalue.

out

rt2i

The imaginary part of the second eigenvalue. If the eigenvalues are a complex conjugate pair, RT1I > 0.

out

cs

Cosine of the rotation matrix.

out

sn

Sine of the rotation matrix.

dlanv2

Functions

void dlanv2(
    f64* a,
    f64* b,
    f64* c,
    f64* d,
    f64* rt1r,
    f64* rt1i,
    f64* rt2r,
    f64* rt2i,
    f64* cs,
    f64* sn
);

void dlanv2(f64 *a, f64 *b, f64 *c, f64 *d, f64 *rt1r, f64 *rt1i, f64 *rt2r, f64 *rt2i, f64 *cs, f64 *sn)

DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form:

 [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
 [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]

where either 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or 2) AA = DD and BB*CC < 0, so that AA +/- sqrt(BB*CC) are complex conjugate eigenvalues.

Parameters

inout

a

On entry, the (1,1) element of the input matrix. On exit, the (1,1) element of the Schur form.

inout

b

On entry, the (1,2) element of the input matrix. On exit, the (1,2) element of the Schur form.

inout

c

On entry, the (2,1) element of the input matrix. On exit, the (2,1) element of the Schur form.

inout

d

On entry, the (2,2) element of the input matrix. On exit, the (2,2) element of the Schur form.

out

rt1r

The real part of the first eigenvalue.

out

rt1i

The imaginary part of the first eigenvalue.

out

rt2r

The real part of the second eigenvalue.

out

rt2i

The imaginary part of the second eigenvalue. If the eigenvalues are a complex conjugate pair, RT1I > 0.

out

cs

Cosine of the rotation matrix.

out

sn

Sine of the rotation matrix.