dlasv2()

subroutine dlasv2	(	double precision	F,
		double precision	G,
		double precision	H,
		double precision	SSMIN,
		double precision	SSMAX,
		double precision	SNR,
		double precision	CSR,
		double precision	SNL,
		double precision	CSL
	)

DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Download DLASV2 + dependencies [TGZ] [ZIP] [TXT]

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 ].

Parameters

[in]	F	F is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix.
[in]	G	G is DOUBLE PRECISION The (1,2) element of the 2-by-2 matrix.
[in]	H	H is DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix.
[out]	SSMIN	SSMIN is DOUBLE PRECISION abs(SSMIN) is the smaller singular value.
[out]	SSMAX	SSMAX is DOUBLE PRECISION abs(SSMAX) is the larger singular value.
[out]	SNL	SNL is DOUBLE PRECISION
[out]	CSL	CSL is DOUBLE PRECISION The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX).
[out]	SNR	SNR is DOUBLE PRECISION
[out]	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.

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.