DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]. On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and right singular vectors for abs(SSMAX), giving the decomposition [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ] [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ].
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 abs(SSMIN) is the smaller singular value.
SSMAX is DOUBLE PRECISION abs(SSMAX) is the larger singular value.
SNL is DOUBLE PRECISION
CSL is DOUBLE PRECISION The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX).
SNR is DOUBLE PRECISION
CSR is DOUBLE PRECISION The vector (CSR, SNR) is a unit right singular vector for the singular value abs(SSMAX).
Univ. of California Berkeley
Univ. of Colorado Denver
Any input parameter may be aliased with any output parameter. Barring over/underflow and assuming a guard digit in subtraction, all output quantities are correct to within a few units in the last place (ulps). 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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