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zlaev2(3) [debian man page]

zlaev2.f(3)							      LAPACK							       zlaev2.f(3)

NAME

       zlaev2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1)
	   ZLAEV2

Function/Subroutine Documentation
   subroutine zlaev2 (complex*16A, complex*16B, complex*16C, double precisionRT1, double precisionRT2, double precisionCS1, complex*16SN1)
       ZLAEV2

       Purpose:

	    ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
	       [  A	    B  ]
	       [  CONJG(B)  C  ].
	    On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
	    eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
	    eigenvector for RT1, giving the decomposition

	    [ CS1  CONJG(SN1) ] [    A	   B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
	    [-SN1     CS1     ] [ CONJG(B) C ] [ SN1	 CS1	 ]   [	0  RT2 ].

       Parameters:
	   A

		     A is COMPLEX*16
		    The (1,1) element of the 2-by-2 matrix.

	   B

		     B is COMPLEX*16
		    The (1,2) element and the conjugate of the (2,1) element of
		    the 2-by-2 matrix.

	   C

		     C is COMPLEX*16
		    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.

	   CS1

		     CS1 is DOUBLE PRECISION

	   SN1

		     SN1 is COMPLEX*16
		    The vector (CS1, SN1) is a unit right eigenvector for RT1.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       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.

	     CS1 and SN1 are accurate to a few ulps barring over/underflow.

	     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 122 of file zlaev2.f.

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

Version 3.4.1							  Sun May 26 2013						       zlaev2.f(3)

Check Out this Related Man Page

ZLAEV2(l)								 )								 ZLAEV2(l)

NAME

       ZLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]

SYNOPSIS

       SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

	   DOUBLE	  PRECISION CS1, RT1, RT2

	   COMPLEX*16	  A, B, C, SN1

PURPOSE

       ZLAEV2  computes  the  eigendecomposition  of  a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]. On return, RT1 is the eigenvalue of larger
       absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposi-
       tion

       [ CS1  CONJG(SN1) ] [	A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ] [-SN1     CS1     ] [ CONJG(B) C ] [ SN1	 CS1	 ]   [	0  RT2 ].

ARGUMENTS

       A      (input) COMPLEX*16
	      The (1,1) element of the 2-by-2 matrix.

       B      (input) COMPLEX*16
	      The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.

       C      (input) COMPLEX*16
	      The (2,2) element of the 2-by-2 matrix.

       RT1    (output) DOUBLE PRECISION
	      The eigenvalue of larger absolute value.

       RT2    (output) DOUBLE PRECISION
	      The eigenvalue of smaller absolute value.

       CS1    (output) DOUBLE PRECISION
	      SN1    (output) COMPLEX*16 The vector (CS1, SN1) is a unit right eigenvector for RT1.

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 trun-
       cated arithmetic would be needed to compute RT2 accurately in all cases.

       CS1 and SN1 are accurate to a few ulps barring over/underflow.

       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.

LAPACK version 3.0						   15 June 2000 							 ZLAEV2(l)
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