SLAPY3(l) ) SLAPY3(l)
NAME
SLAPY3 - return sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow
SYNOPSIS
REAL FUNCTION SLAPY3( X, Y, Z )
REAL X, Y, Z
PURPOSE
SLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause unnecessary overflow.
ARGUMENTS
X (input) REAL
Y (input) REAL Z (input) REAL X, Y and Z specify the values x, y and z.
LAPACK version 3.0 15 June 2000 SLAPY3(l)
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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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