las2(3) Library Functions Manual las2(3)

las2 - las2: 2x2 triangular SVD


subroutine dlas2 (f, g, h, ssmin, ssmax)
DLAS2 computes singular values of a 2-by-2 triangular matrix. subroutine slas2 (f, g, h, ssmin, ssmax)
SLAS2 computes singular values of a 2-by-2 triangular matrix.

DLAS2 computes singular values of a 2-by-2 triangular matrix.

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.

Parameters

F 
          F is DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix.

G

          G is DOUBLE PRECISION
          The (1,2) element of the 2-by-2 matrix.

H

          H is DOUBLE PRECISION
          The (2,2) element of the 2-by-2 matrix.

SSMIN

          SSMIN is DOUBLE PRECISION
          The smaller singular value.

SSMAX

          SSMAX is DOUBLE PRECISION
          The larger singular value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.
  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 104 of file dlas2.f.

SLAS2 computes singular values of a 2-by-2 triangular matrix.

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.

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.
  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 104 of file slas2.f.

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