SLASV2(3F) SLASV2(3F)
SLASV2 - compute the singular value decomposition of a 2-by-2 triangular
matrix [ F G ] [ 0 H ]
SUBROUTINE SLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
REAL CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
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 ].
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).
Page 1
SLASV2(3F) SLASV2(3F)
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.
SLASV2(3F) SLASV2(3F)
SLASV2 - compute the singular value decomposition of a 2-by-2 triangular
matrix [ F G ] [ 0 H ]
SUBROUTINE SLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
REAL CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
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 ].
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).
Page 1
SLASV2(3F) SLASV2(3F)
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.
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