LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine slas2 | ( | real | F, |
real | G, | ||
real | H, | ||
real | SSMIN, | ||
real | SSMAX | ||
) |
SLAS2 computes singular values of a 2-by-2 triangular matrix.
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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.
[in] | F | F is REAL The (1,1) element of the 2-by-2 matrix. |
[in] | G | G is REAL The (1,2) element of the 2-by-2 matrix. |
[in] | H | H is REAL The (2,2) element of the 2-by-2 matrix. |
[out] | SSMIN | SSMIN is REAL The smaller singular value. |
[out] | SSMAX | SSMAX is REAL The larger singular value. |
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.
Definition at line 109 of file slas2.f.