Full Command and Function Reference 3-99
Model Transformation
Logarithmic y = b + m ln(x)
Exponential ln(y) = ln(b) + mx
Power ln(y) = ln(b) + m ln(x)
Access: …µ LR
Input/Output:
Level 1/Argument 1 Level 2/Item 1 Level 1/Item 2
→
Intercept: x
1
Slope: x
2
See also: BESTFIT, COLΣ, CORR, COV, EXPFIT, ΣLINE, LINFIT, LOGFIT, PREDX, PREDY,
PWRFIT, XCOL, YCOL
LSQ
Type: Command
Description: Least Squares Solution Command: Returns the minimum norm least squares solution to any
system of linear equations where A × X = B.
If B is a vector, the resulting vector has a minimum Euclidean norm ||X|| over all vector
solutions that minimize the residual Euclidean norm ||A × X – B||. If B is a matrix, each
column of the resulting matrix, X
i
, has a minimum Euclidean norm ||X
i
|| over all vector
solutions that minimize the residual Euclidean norm ||A × X
i
– B
i
||.
If A has less than full row rank (the system of equations is underdetermined), an infinite number
of solutions exist. LSQ returns the solution with the minimum Euclidean length.
If A has less than full column rank (the system of equations is overdetermined), a solution that
satisfies all the equations may not exist. LSQ returns the solution with the minimum residuals of
A × X – B.
Access: !Ø
OPERATIONS L LSQ ( Ø is the left-shift of the 5key).
!´
MATRIX LSQ ( ´ is the left-shift of the Pkey).
Flags: Singular Values (-54)
Input/Output:
Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1
[ array ]
B
[[ matrix ]]
A
→
[ array ]
x
[[ matrix ]]
B
[[ matrix ]]
A
→
[[ matrix ]]
x
See also: LQ, RANK, QR, /
LU
Type: Command
Description: LU Decomposition of a Square Matrix Command: Returns the LU decomposition of a square
matrix.
When solving an exactly determined system of equations, inverting a square matrix, or
computing the determinant of a matrix, the hp49g+/hp48gII factors a square matrix into its
Crout LU decomposition using partial pivoting.
The Crout LU decomposition of A is a lower-triangular matrix L, an upper-triangular matrix U
with ones on its diagonal, and a permutation matrix P, such that P × A = L × U. The results
satisfy P × A ≅ L × U.
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