SLAS2(3F) SLAS2(3F)
SLAS2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H
]
SUBROUTINE SLAS2( F, G, H, SSMIN, SSMAX )
REAL F, G, H, SSMAX, SSMIN
SLAS2 computes the singular values of the 2-by-2 matrix
[ F G ]
[ 0 H ]. On return, SSMIN is the smaller singular value and SSMAX
is the larger singular value.
F (input) REAL
The (1,1) element of the 2-by-2 matrix.
G (input) REAL
The (1,2) element of the 2-by-2 matrix.
H (input) REAL
The (2,2) element of the 2-by-2 matrix.
SSMIN (output) REAL
The smaller singular value.
SSMAX (output) REAL
The larger singular value.
FURTHER DETAILS
Barring over/underflow, all output quantities are correct to within a few
units in the last place (ulps), even in the absence of a guard digit in
addition/subtraction.
In IEEE arithmetic, the code works correctly if one matrix element is
infinite.
Overflow will not occur unless the largest singular value itself
overflows, or is within a few ulps of overflow. (On machines with partial
overflow, like the Cray, overflow may occur if the largest singular value
is within a factor of 2 of overflow.)
Underflow is harmless if underflow is gradual. Otherwise, results may
correspond to a matrix modified by perturbations of size near the
underflow threshold.
SLAS2(3F) SLAS2(3F)
SLAS2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H
]
SUBROUTINE SLAS2( F, G, H, SSMIN, SSMAX )
REAL F, G, H, SSMAX, SSMIN
SLAS2 computes the singular values of the 2-by-2 matrix
[ F G ]
[ 0 H ]. On return, SSMIN is the smaller singular value and SSMAX
is the larger singular value.
F (input) REAL
The (1,1) element of the 2-by-2 matrix.
G (input) REAL
The (1,2) element of the 2-by-2 matrix.
H (input) REAL
The (2,2) element of the 2-by-2 matrix.
SSMIN (output) REAL
The smaller singular value.
SSMAX (output) REAL
The larger singular value.
FURTHER DETAILS
Barring over/underflow, all output quantities are correct to within a few
units in the last place (ulps), even in the absence of a guard digit in
addition/subtraction.
In IEEE arithmetic, the code works correctly if one matrix element is
infinite.
Overflow will not occur unless the largest singular value itself
overflows, or is within a few ulps of overflow. (On machines with partial
overflow, like the Cray, overflow may occur if the largest singular value
is within a factor of 2 of overflow.)
Underflow is harmless if underflow is gradual. Otherwise, results may
correspond to a matrix modified by perturbations of size near the
underflow threshold.
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