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NAME SLASV2 - compute the singular value decomposition of a 2- by-2 triangular matrix [ F G ] [ 0 H ] SYNOPSIS SUBROUTINE SLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) REAL CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN PURPOSE SLASV2 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) REAL The (1,1) entry of the 2-by-2 matrix. G (input) REAL The (1,2) entry of the 2-by-2 matrix. H (input) REAL The (2,2) entry of the 2-by-2 matrix. SSMIN (output) REAL abs(SSMIN) is the smaller singular value. SSMAX (output) REAL abs(SSMAX) is the larger singular value. SNL (output) REAL CSL (output) REAL The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX). SNR (output) REAL CSR (output) REAL The vector (CSR, SNR) is a unit right singular vector for the singular value abs(SSMAX). FURTHER DETAILS Any input parameter may be aliased with any output parameter. 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.