slasv2 (l) - Linux Manuals

slasv2: computes the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]

NAME

SLASV2 - computes the singular value decomposition of a 2-by-2 triangular matrix [ F G ] [ 0 H ]

SYNOPSIS

SUBROUTINE SLASV2(
F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )

    
REAL CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN

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 ].

ARGUMENTS

F (input) REAL
The (1,1) element of the 2-by-2 matrix.
G (input) REAL
The (1,2) element of the 2-by-2 matrix.
H (input) REAL
The (2,2) element of the 2-by-2 matrix.
SSMIN (output) REAL
abs(SSMIN) is the smaller singular value.
SSMAX (output) REAL
abs(SSMAX) is the larger singular value.
SNL (output) REAL
CSL (output) REAL The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX).
SNR (output) REAL
CSR (output) REAL The vector (CSR, SNR) is a unit right singular vector for the singular value abs(SSMAX).

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.

Pages related to slasv2

  • slasv2 (3)
  • slas2 (l) - computes the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]
  • slascl (l) - multiplies the M by N real matrix A by the real scalar CTO/CFROM
  • slascl2 (l) - performs a diagonal scaling on a vector
  • slasd0 (l) - a divide and conquer approach, SLASD0 computes the singular value decomposition (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where M = N + SQRE
  • slasd1 (l) - computes the SVD of an upper bidiagonal N-by-M matrix B,
  • slasd2 (l) - merges the two sets of singular values together into a single sorted set
  • slasd3 (l) - finds all the square roots of the roots of the secular equation, as defined by the values in D and Z
  • slasd4 (l) - subroutine compute the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0
  • slasd5 (l) - subroutine compute the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO The diagonal entries in the array D are assumed to satisfy 0 <= D(i) < D(j) for i < j