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slaev2.f(3) [debian man page]

slaev2.f(3)							      LAPACK							       slaev2.f(3)

NAME

       slaev2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slaev2 (A, B, C, RT1, RT2, CS1, SN1)
	   SLAEV2

Function/Subroutine Documentation
   subroutine slaev2 (realA, realB, realC, realRT1, realRT2, realCS1, realSN1)
       SLAEV2

       Purpose:

	    SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
	       [  A   B  ]
	       [  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  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1	0  ]
	       [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]	 [  0  RT2 ].

       Parameters:
	   A

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

	   B

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

	   C

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

	   RT1

		     RT1 is REAL
		     The eigenvalue of larger absolute value.

	   RT2

		     RT2 is REAL
		     The eigenvalue of smaller absolute value.

	   CS1

		     CS1 is REAL

	   SN1

		     SN1 is REAL
		     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 121 of file slaev2.f.

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

Version 3.4.1							  Sun May 26 2013						       slaev2.f(3)

Check Out this Related Man Page

SLAEV2(l)								 )								 SLAEV2(l)

NAME

       SLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]

SYNOPSIS

       SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

	   REAL 	  A, B, C, CS1, RT1, RT2, SN1

PURPOSE

       SLAEV2  computes  the  eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ 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  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
	  [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].

ARGUMENTS

       A       (input) REAL
	       The (1,1) element of the 2-by-2 matrix.

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

       C       (input) REAL
	       The (2,2) element of the 2-by-2 matrix.

       RT1     (output) REAL
	       The eigenvalue of larger absolute value.

       RT2     (output) REAL
	       The eigenvalue of smaller absolute value.

       CS1     (output) REAL
	       SN1     (output) REAL 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 							 SLAEV2(l)
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