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DLASV2(l)) DLASV2(l)DLASV2 - compute the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]NAMESUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMINSYNOPSISDLASV2 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 ] [ CSRPURPOSE] = [ SSMAX 0 ] [-SNRCSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ].-SNLF (input) DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix. G (input) DOUBLE PRECISION The (1,2) element of the 2-by-2 matrix. H (input) DOUBLE PRECISION The (2,2) element 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 singu- lar 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).ARGUMENTSAny 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 over- flow. (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 per- turbations of size near the underflow threshold.FURTHER DETAILSLAPACK version 3.015 June 2000 DLASV2(l)

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