DLAS2 computes singular values of a 2-by-2 triangular matrix.
DLAS2 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 is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix.
G is DOUBLE PRECISION The (1,2) element of the 2-by-2 matrix.
H is DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix.
SSMIN is DOUBLE PRECISION The smaller singular value.
SSMAX is DOUBLE PRECISION The larger singular value.
Univ. of California Berkeley
Univ. of Colorado Denver
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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