Model

Transformation

 

 

Logarithmic

y = b + m ln(x)

 

 

Exponential

ln(y) = ln(b) + mx

 

 

Power

ln(y) = ln(b) + m ln(x)

 

 

Access: …µLR

Input/Output:

Level 1/Argument 1

Level 2/Item 1

Level 1/Item 2

 

 

 

→

Intercept: x1

Slope: x2

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, Xi, has a minimum Euclidean norm Xi over all vector solutions that minimize the residual Euclidean norm A × Xi – Bi.

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 LLSQ

( 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

 

LQ, RANK,

 

 

 

 

See also:

QR, /

 

 

 

 

 

 

 

 

 

LU

Command

 

 

 

Type:

 

 

 

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 calculator 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.

 

 

 

Access:

!Ø FACTORIZATION LU

( Ø is the left-shift of the 5key).

 

!´MATRIX FACTOR LU

( ´is the left-shift of the Pkey).

Full Command and Function Reference 3-139