dlas2 (l) - Linux Manuals

dlas2: computes the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]

NAME

DLAS2 - computes the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]

SYNOPSIS

SUBROUTINE DLAS2(
F, G, H, SSMIN, SSMAX )

    
DOUBLE PRECISION F, G, H, SSMAX, SSMIN

PURPOSE

DLAS2 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.

ARGUMENTS

F (input) DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.
G (input) DOUBLE PRECISION
The (1,2) element of the 2-by-2 matrix.
H (input) DOUBLE PRECISION
The (2,2) element of the 2-by-2 matrix.
SSMIN (output) DOUBLE PRECISION
The smaller singular value.
SSMAX (output) DOUBLE PRECISION
The larger singular value.

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.

Pages related to dlas2

  • dlas2 (3)
  • dlascl (l) - multiplies the M by N real matrix A by the real scalar CTO/CFROM
  • dlascl2 (l) - performs a diagonal scaling on a vector
  • dlasd0 (l) - a divide and conquer approach, DLASD0 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
  • dlasd1 (l) - computes the SVD of an upper bidiagonal N-by-M matrix B,
  • dlasd2 (l) - merges the two sets of singular values together into a single sorted set
  • dlasd3 (l) - finds all the square roots of the roots of the secular equation, as defined by the values in D and Z
  • dlasd4 (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
  • dlasd5 (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
  • dlasd6 (l) - computes the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row
  • dlasd7 (l) - merges the two sets of singular values together into a single sorted set