slas2.f(3) [debian man page]
slas2.f(3) LAPACK slas2.f(3) NAME
slas2.f - SYNOPSIS
Functions/Subroutines subroutine slas2 (F, G, H, SSMIN, SSMAX) SLAS2 Function/Subroutine Documentation subroutine slas2 (realF, realG, realH, realSSMIN, realSSMAX) SLAS2 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. Parameters: F 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. Date: November 2011 Further Details: 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. (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. Definition at line 108 of file slas2.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 slas2.f(3)
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slasv2.f(3) LAPACK slasv2.f(3) NAME
slasv2.f - SYNOPSIS
Functions/Subroutines subroutine slasv2 (F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL) SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. Function/Subroutine Documentation subroutine slasv2 (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 ]. Parameters: F 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. Date: September 2012 Further Details: 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. (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. Definition at line 139 of file slasv2.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slasv2.f(3)