DLASV2(3F) DLASV2(3F)
DLASV2 - compute the singular value decomposition of a 2-by-2 triangular
matrix [ F G ] [ 0 H ]
SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
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 ].
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
abs(SSMIN) is the smaller singular value.
SSMAX (output) DOUBLE PRECISION
abs(SSMAX) is the larger singular value.
SNL (output) DOUBLE PRECISION
CSL (output) DOUBLE PRECISION The vector (CSL, SNL) is a unit
left singular vector for the singular value abs(SSMAX).
SNR (output) DOUBLE PRECISION
CSR (output) DOUBLE PRECISION 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
DLASV2(3F) DLASV2(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.
DLASV2(3F) DLASV2(3F)
DLASV2 - compute the singular value decomposition of a 2-by-2 triangular
matrix [ F G ] [ 0 H ]
SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )
DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN
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 ].
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
abs(SSMIN) is the smaller singular value.
SSMAX (output) DOUBLE PRECISION
abs(SSMAX) is the larger singular value.
SNL (output) DOUBLE PRECISION
CSL (output) DOUBLE PRECISION The vector (CSL, SNL) is a unit
left singular vector for the singular value abs(SSMAX).
SNR (output) DOUBLE PRECISION
CSR (output) DOUBLE PRECISION 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
DLASV2(3F) DLASV2(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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