Create a matrix with vector placed on a diagonal.
Syntax: @makediagonal(v[, k])
v: vector, rowvector
k: (optional) integer
Return: sym or matrix
Create a square matrix with v placed in the k-th diagonal relative to the main diagonal, and zeros off the diagonal.
• If no k value is provided or if k is set to 0, the resulting sym matrix will have the same number of rows and columns as the length of v, and will have v in the main diagonal.
• If a value for k is provided, the matrix has the same number of rows and columns as the number of elements in the vector plus k, and will place v in the diagonal offset from the main by k.
Examples
sym s1 = @makediagonal(v1)
matrix m2 = @makediagonal(v1,1)
matrix m4 = @makediagonal(r1,-3)
S1 will contain V1 in the main diagonal; M2 will contain V1 in the diagonal immediately above the main diagonal; M4 will contain R1 in the diagonal 3 positions below the main diagonal. Using the optional k parameter may be useful in creating covariance matrices for AR models. For example, you can create an AR(1) correlation matrix by issuing the commands:
matrix(10,10) m1
vector(9) rho = .3
m1 = @makediagonal(rho,-1) + @makediagonal(rho,+1)
m1 = m1 + @identity(10)
Note that to make a diagonal matrix with the same elements on the diagonal, you may use @identity, multiplied by the scalar value.
Cross-references