@inner—619

Syntax: @inner(v1, v2, smp)

Argument 1: vector, rowvector, or series, v1

Argument 2: vector, rowvector, or series, v2

Argument 3: (optional) sample, smp

Return: scalar

Syntax: @inner(o, smp)

Argument 1: matrix object or group, o

Argument 2: (optional) sample, smp

Return: scalar

If used with two vectors, v1 and v2, @inner returns the dot or inner product of the two vectors. Examples:

scalar sc1 = @inner(v1, v2) s1(1,2) = @inner(v1, r1)

If used with two series, @inner returns the inner product of the series using observations in the workfile sample. You may provide an optional sample.

If used with a matrix or sym, o, @inner returns the inner product, or moment matrix, o’o. Each element of the result is the vector inner product of two columns of the source matrix. The size of the resulting sym is the number of columns in o. Examples:

scalar sc1 = @inner(v1) sym sym1 = @inner(m1)

If used with a group, @inner returns the uncentered second moment matrix of the data in the group, g, using the observations in the sample, smp. If no sample is provided, the workfile sample is used. Examples:

sym s2 = @inner(gr1)

sym s3 = @inner(gr1, smp1)

See also @outer (p. 623).

@makediagonal—621

matrix objects and a number of columns equal to the product of the numbers of columns of the two matrix objects. The elements of the resulting matrix consist of submatrices consisting of one element of the first matrix object multiplied by the entire second matrix object. Example:

matrix m3 = @kronecker(m1,m2)

Syntax: @makediagonal(v, k)

Argument 1: vector or rowvector, v

Argument 2: (optional) integer, k

Return: matrix

Creates a square matrix with the specified vector or rowvector, v, in the k-th diagonal relative to the main diagonal, and zeroes off the diagonal. If no k value is provided or if k is set to 0, the resulting 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:

matrix m1 = @makediagonal(v1)

matrix m2 = @makediagonal(v1,1)

matrix m4 = @makediagonal(r1,-3)

M1 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)