LANV2 - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void lanv2(T *a, T *b, T *c, T *d, T *rt1r, T *rt1i, T *rt2r, T *rt2i, T *cs, T *sn)#

LANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Purpose:

   LANV2 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 + or - sqrt(BB*CC) are complex
   conjugate eigenvalues.
Parameters:
  • A[inout] A is REAL

  • B[inout] B is REAL

  • C[inout] C is REAL

  • D[inout]

    D is REAL

    On entry, the elements of the input matrix. On exit, they are overwritten by the elements of the standardised Schur form.

  • RT1R[out] RT1R is REAL

  • RT1I[out] RT1I is REAL

  • RT2R[out] RT2R is REAL

  • RT2I[out]

    RT2I is REAL

    The real and imaginary parts of the eigenvalues. If the eigenvalues are a complex conjugate pair, RT1I > 0.

  • CS[out] CS is REAL

  • SN[out]

    SN is REAL

    Parameters of the rotation matrix.