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dlanv2(3) [debian man page]

dlanv2.f(3)							      LAPACK							       dlanv2.f(3)

NAME

       dlanv2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlanv2 (A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN)
	   DLANV2

Function/Subroutine Documentation
   subroutine dlanv2 (double precisionA, double precisionB, double precisionC, double precisionD, double precisionRT1R, double precisionRT1I,
       double precisionRT2R, double precisionRT2I, double precisionCS, double precisionSN)
       DLANV2

       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.

       Parameters:
	   A

		     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.

       Date:
	   November 2011

       Further Details:

	     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).

       Definition at line 128 of file dlanv2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       dlanv2.f(3)

Check Out this Related Man Page

dlae2.f(3)							      LAPACK								dlae2.f(3)

NAME

       dlae2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlae2 (A, B, C, RT1, RT2)
	   DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Function/Subroutine Documentation
   subroutine dlae2 (double precisionA, double precisionB, double precisionC, double precisionRT1, double precisionRT2)
       DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

       Purpose:

	    DLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
	       [  A   B  ]
	       [  B   C  ].
	    On return, RT1 is the eigenvalue of larger absolute value, and RT2
	    is the eigenvalue of smaller absolute value.

       Parameters:
	   A

		     A is DOUBLE PRECISION
		     The (1,1) element of the 2-by-2 matrix.

	   B

		     B is DOUBLE PRECISION
		     The (1,2) and (2,1) elements of the 2-by-2 matrix.

	   C

		     C is DOUBLE PRECISION
		     The (2,2) element of the 2-by-2 matrix.

	   RT1

		     RT1 is DOUBLE PRECISION
		     The eigenvalue of larger absolute value.

	   RT2

		     RT2 is DOUBLE PRECISION
		     The eigenvalue of smaller absolute value.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Further Details:

	     RT1 is accurate to a few ulps barring over/underflow.

	     RT2 may be inaccurate if there is massive cancellation in the
	     determinant A*C-B*B; higher precision or correctly rounded or
	     correctly truncated arithmetic would be needed to compute RT2
	     accurately in all cases.

	     Overflow is possible only if RT1 is within a factor of 5 of overflow.
	     Underflow is harmless if the input data is 0 or exceeds
		underflow_threshold / macheps.

       Definition at line 103 of file dlae2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012							dlae2.f(3)
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