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NAME DLASV2 - compute the singular value decomposition of a 2- by-2 triangular matrix [ F G ] [ 0 H ] SYNOPSIS SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN PURPOSE DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]. On return, abs(SSMAX) is the larger singu- lar value, abs(SSMIN) is the smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and right singular vec- tors for abs(SSMAX), giving the decomposition [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ] [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ]. ARGUMENTS F (input) DOUBLE PRECISION The (1,1) entry of the 2-by-2 matrix. G (input) DOUBLE PRECISION The (1,2) entry of the 2-by-2 matrix. H (input) DOUBLE PRECISION The (2,2) entry of the 2-by-2 matrix. SSMIN (output) DOUBLE PRECISION abs(SSMIN) is the smaller singular value. SSMAX (output) DOUBLE PRECISION abs(SSMAX) is the larger singular value. SNL (output) DOUBLE PRECISION CSL (output) DOUBLE PRECISION The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX). SNR (output) DOUBLE PRECISION CSR (output) DOUBLE PRECISION The vector (CSR, SNR) is a unit right singular vector for the singu- lar value abs(SSMAX). FURTHER DETAILS Any input parameter may be aliased with any output parame- ter. Barring over/underflow and assuming a guard digit in sub- traction, 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 entry 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.