dlae2(l) [redhat man page]

DLAE2(l)								 )								  DLAE2(l)

NAME

       DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]

SYNOPSIS

       SUBROUTINE DLAE2( A, B, C, RT1, RT2 )

	   DOUBLE	 PRECISION A, B, C, RT1, RT2

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.

ARGUMENTS

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

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

       C       (input) DOUBLE PRECISION
	       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.

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.

       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 							  DLAE2(l)

DLAEV2(l)								 )								 DLAEV2(l)

NAME

       DLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]

SYNOPSIS

       SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

	   DOUBLE	  PRECISION A, B, C, CS1, RT1, RT2, SN1

PURPOSE

       DLAEV2  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) DOUBLE PRECISION
	       The (1,1) element of the 2-by-2 matrix.

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

       C       (input) DOUBLE PRECISION
	       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) DOUBLE PRECISION 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 							 DLAEV2(l)