lasv2 - lasv2: 2x2 triangular SVD

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 lasv2(3)

subroutinedlasv2(doubleprecisionf,doubleprecisiong,doubleprecisionh,doubleprecisionssmin,doubleprecisionssmax,doubleprecisionsnr,doubleprecisioncsr,doubleprecisionsnl,doubleprecisioncsl)DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. 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 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 ]. 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 abs(SSMIN) is the smaller singular value. SSMAX SSMAX is DOUBLE PRECISION abs(SSMAX) is the larger singular value. SNL SNL is DOUBLE PRECISION CSL CSL is DOUBLE PRECISION The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX). SNR SNR is DOUBLE PRECISION CSR CSR is DOUBLE PRECISION The vector (CSR, SNR) is a unit right singular vector for the singular value abs(SSMAX). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold. subroutineslasv2(realf,realg,realh,realssmin,realssmax,realsnr,realcsr,realsnl,realcsl)SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. 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 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 ]. 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 abs(SSMIN) is the smaller singular value. SSMAX SSMAX is REAL abs(SSMAX) is the larger singular value. SNL SNL is REAL CSL CSL is REAL The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX). SNR SNR is REAL CSR CSR is REAL The vector (CSR, SNR) is a unit right singular vector for the singular value abs(SSMAX). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold.

lasv2 - lasv2: 2x2 triangular SVD

Functions subroutine dlasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl) DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. subroutine slasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl) SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.