las2 - las2: 2x2 triangular SVD

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subroutinedlas2(doubleprecisionf,doubleprecisiong,doubleprecisionh,doubleprecisionssmin,doubleprecisionssmax)DLAS2 computes singular values of a 2-by-2 triangular matrix. Purpose: 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. ParametersF F is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix. G G is DOUBLE PRECISION The (1,2) element of the 2-by-2 matrix. H H is DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix. SSMIN SSMIN is DOUBLE PRECISION The smaller singular value. SSMAX SSMAX is DOUBLE PRECISION The larger singular value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold. subroutineslas2(realf,realg,realh,realssmin,realssmax)SLAS2 computes singular values of a 2-by-2 triangular matrix. Purpose: SLAS2 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. ParametersF F is REAL The (1,1) element of the 2-by-2 matrix. G G is REAL The (1,2) element of the 2-by-2 matrix. H H is REAL The (2,2) element of the 2-by-2 matrix. SSMIN SSMIN is REAL The smaller singular value. SSMAX SSMAX is REAL The larger singular value. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold.

las2 - las2: 2x2 triangular SVD

Functions subroutine dlas2 (f, g, h, ssmin, ssmax) DLAS2 computes singular values of a 2-by-2 triangular matrix. subroutine slas2 (f, g, h, ssmin, ssmax) SLAS2 computes singular values of a 2-by-2 triangular matrix.