claev2(l) [redhat man page]
CLAEV2(l) ) CLAEV2(l) NAME
CLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ] SYNOPSIS
SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) REAL CS1, RT1, RT2 COMPLEX A, B, C, SN1 PURPOSE
CLAEV2 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 The (1,1) element of the 2-by-2 matrix. B (input) COMPLEX The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. C (input) COMPLEX 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) COMPLEX 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 CLAEV2(l)
Check Out this Related Man Page
claev2.f(3) LAPACK claev2.f(3) NAME
claev2.f - SYNOPSIS
Functions/Subroutines subroutine claev2 (A, B, C, RT1, RT2, CS1, SN1) CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Function/Subroutine Documentation subroutine claev2 (complexA, complexB, complexC, realRT1, realRT2, realCS1, complexSN1) CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: CLAEV2 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 The (1,1) element of the 2-by-2 matrix. B B is COMPLEX The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. C C is COMPLEX 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 COMPLEX 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: 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. 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 claev2.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 claev2.f(3)