lanv2 - lanv2: 2x2 Schur factor

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subroutinedlanv2(doubleprecisiona,doubleprecisionb,doubleprecisionc,doubleprecisiond,doubleprecisionrt1r,doubleprecisionrt1i,doubleprecisionrt2r,doubleprecisionrt2i,doubleprecisioncs,doubleprecisionsn)DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. Purpose: 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 + or - sqrt(BB*CC) are complex conjugate eigenvalues. ParametersA A is DOUBLE PRECISION B B is DOUBLE PRECISION C C is DOUBLE PRECISION D D is DOUBLE PRECISION On entry, the elements of the input matrix. On exit, they are overwritten by the elements of the standardised Schur form. RT1R RT1R is DOUBLE PRECISION RT1I RT1I is DOUBLE PRECISION RT2R RT2R is DOUBLE PRECISION RT2I RT2I is DOUBLE PRECISION The real and imaginary parts of the eigenvalues. If the eigenvalues are a complex conjugate pair, RT1I > 0. CS CS is DOUBLE PRECISION SN SN is DOUBLE PRECISION Parameters of the rotation matrix. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: Modified by V. Sima, Research Institute for Informatics, Bucharest, Romania, to reduce the risk of cancellation errors, when computing real eigenvalues, and to ensure, if possible, that abs(RT1R) >= abs(RT2R). subroutineslanv2(reala,realb,realc,reald,realrt1r,realrt1i,realrt2r,realrt2i,realcs,realsn)SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. Purpose: 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 + or - sqrt(BB*CC) are complex conjugate eigenvalues. ParametersA A is REAL B B is REAL C C is REAL D 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 RT1R is REAL RT1I RT1I is REAL RT2R RT2R is REAL RT2I RT2I is REAL The real and imaginary parts of the eigenvalues. If the eigenvalues are a complex conjugate pair, RT1I > 0. CS CS is REAL SN SN is REAL Parameters of the rotation matrix. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: Modified by V. Sima, Research Institute for Informatics, Bucharest, Romania, to reduce the risk of cancellation errors, when computing real eigenvalues, and to ensure, if possible, that abs(RT1R) >= abs(RT2R).

lanv2 - lanv2: 2x2 Schur factor

Functions subroutine dlanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn) DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. subroutine slanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn) SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.