Stata User's Guide

14.8 Matrix functions

In addition to the functions listed below, see [P] matrix svd for singular value decomposition,

[P] matrix symeigen for eigenvalues and eigenvectors of symmetric matrices, and see [P] matrix

eigenvalues for eigenvalues of nonsymmetric matrices. For a full description of the matrix functions,

see [D] functions.

Matrix functions returning matrices:

cholesky(M) I(n) nullmat(matname)

corr(M) inv(M) sweep(M,i)

diag(v) invsym(M) vec(M)

get(systemname) J(r,c,z) vecdiag(M)

hadamard(M,N) matuniform(r,c)

Matrix functions returning scalars:

colnumb(M,s) el(M,i,j) rownumb(M,s)

colsof(M) issymmetric(M) rowsof(M)

det(M) matmissing(M) trace(M)

diag0cnt(M) mreldif(X,Y )

[ U ] 14.9 Subscripting 173

14.9 Subscripting

1. In matrix and scalar expressions, you may refer to matname[r,c], where r and c are scalar

expressions, to obtain one element of matname as a scalar.

Examples:

matrix A = A / A[1,1]

generate newvar = oldvar / A[2,2]

2. In matrix expressions, you may refer to matname[sr,sc], where sr and sc are string expressions,

to obtain a submatrix with one element. The element returned is based on searching the row and

column names.

Examples:

matrix B = V["price","price"]

generate sdif = dif / sqrt(V["price","price"])

3. In matrix expressions, you may mix these two syntaxes and refer to matname[r,sc] or to

matname[sr,c].

Example:

matrix b = b * R[1,"price"]

4. In matrix expressions, you may use matname[r1..r2,c1..c2] to refer to submatrices; r1, r2, c1,

and c2 may be scalar expressions. If r2 evaluates to missing, it is taken as referring to the last

row of matname; if c2 evaluates to missing, it is taken as referring to the last column of matname.

Thus matname[r1...,c1...] is allowed.

Examples:

matrix S = Z[1..4, 1..4]

matrix R = Z[5..., 5...]

5. In matrix expressions, you may refer to matname[sr1..sr2,sc1..sc2] to refer to submatrices

where sr1, sr2, sc1, and sc2, are string expressions. The matrix returned is based on looking up

the row and column names.

If the string evaluates to an equation name only, all the rows or columns for the equation are

returned.

Examples:

matrix S = Z["price".."weight", "price".."weight"]

matrix L = D["mpg:price".."mpg:weight", "mpg:price".."mpg:weight"]

matrix T1 = C["mpg:", "mpg:"]

matrix T2 = C["mpg:", "price:"]

6. In matrix expressions, any of the above syntaxes may be combined.

Examples:

matrix T1 = C["mpg:", "price:weight".."price:displ"]

matrix T2 = C["mpg:", "price:weight"...]

matrix T3 = C["mpg:price", 2..5]

matrix T4 = C["mpg:price", 2]

174 [ U ] 14 Matrix expressions

7. When defining an element of a matrix, use

matrix matname[i,j] = expression

where i and j are scalar expressions. The matrix matname must already exist.

Example:

matrix A = J(2,2,0)

matrix A[1,2] = sqrt(2)

8. To replace a submatrix within a matrix, use the same syntax. If the expression on the right evaluates

to a scalar or 11 matrix, the element is replaced. If it evaluates to a matrix, the submatrix with

top-left element at (i; j) is replaced. The matrix matname must already exist.

Example:

matrix A = J(4,4,0)

matrix A[2,2] = C'*C

14.10 Using matrices in scalar expressions

Scalar expressions are documented as exp in the Stata manuals:

generate newvar = exp if exp : : :

replace newvar = exp if exp : : :

regress : : : if exp : : :

if exp {: : : }

while exp {: : : }

Most importantly, scalar expressions occur in generate and replace, in the if exp modifier allowed

on the end of many commands, and in the if and while commands for program control.

You will rarely need to refer to a matrix in any of these situations except when using the if and

while commands.

In any case, you may refer to matrices in any of these situations, but the expression cannot require

evaluation

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