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/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/slasv2.f(3) Library Functions Manual /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/slasv2.f(3)

NAME

/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/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 (real f, real g, real h, real ssmin, real ssmax, real snr, real csr, real snl, real csl)

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.

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.
!>
!>  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 135 of file slasv2.f.

Author

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Version 3.12.0 LAPACK