| lasv2(3) | LAPACK | lasv2(3) |
lasv2 - lasv2: 2x2 triangular SVD
subroutine dlasv2 (f, g, h, ssmin, ssmax, snr, csr, snl,
csl)
DLASV2 computes the singular value decomposition of a 2-by-2 triangular
matrix. subroutine slasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl)
SLASV2 computes the singular value decomposition of a 2-by-2 triangular
matrix.
DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
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
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
abs(SSMIN) is the smaller singular value.
SSMAX
SSMAX is DOUBLE PRECISION
abs(SSMAX) is the larger singular value.
SNL
SNL is DOUBLE PRECISION
CSL
CSL is DOUBLE PRECISION
The vector (CSL, SNL) is a unit left singular vector for the
singular value abs(SSMAX).
SNR
SNR is DOUBLE PRECISION
CSR
CSR is DOUBLE PRECISION
The vector (CSR, SNR) is a unit right singular vector for the
singular value abs(SSMAX).
Author
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.
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 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 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.
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| Thu Aug 7 2025 17:26:25 | Version 3.12.0 |