dlaev2.f(3) [debian man page]
dlaev2.f(3) LAPACK dlaev2.f(3) NAME
dlaev2.f - SYNOPSIS
Functions/Subroutines subroutine dlaev2 (A, B, C, RT1, RT2, CS1, SN1) DLAEV2 Function/Subroutine Documentation subroutine dlaev2 (double precisionA, double precisionB, double precisionC, double precisionRT1, double precisionRT2, double precisionCS1, double precisionSN1) DLAEV2 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 ]. Parameters: A A is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix. B B is DOUBLE PRECISION The (1,2) element and the conjugate of the (2,1) element 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. CS1 CS1 is DOUBLE PRECISION SN1 SN1 is DOUBLE PRECISION 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 dlaev2.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dlaev2.f(3)
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zlaev2.f(3) LAPACK zlaev2.f(3) NAME
zlaev2.f - SYNOPSIS
Functions/Subroutines subroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1) ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Function/Subroutine Documentation subroutine zlaev2 (complex*16A, complex*16B, complex*16C, double precisionRT1, double precisionRT2, double precisionCS1, complex*16SN1) ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. 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: 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 zlaev2.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 zlaev2.f(3)