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| '''Matrices''' are a data type used for meta programming in the Stata programming language. See also [[Stata/Scalars|scalars]]. | '''Matrices''' are a fundamental data type in Stata, like [[Stata/Scalars|scalars]]. Note that [[Stata/Mata|Mata]] does not use this data type. |
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| == Definition == | == Description == |
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| To define a matrix, use either the `matrix` or `matrix input` command. The latter only allows literals in the definition, while the former allows expressions like `1/3` or `_pi`. The former also allows assignment by matrix arithmetic. | Matrices are collections of numeric values. |
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| The matrix's values are bounded by parentheses (`(` and `)`). Values in a row are delimited with a comma (`,`). Rows are delimited with a backslash (`\`). | Many commands return matrices; for example: |
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| . matrix input A = (1,2\3,4) . matrix list A A[2,2] c1 c2 r1 1 2 r2 3 4 |
correlate foo bar baz, covariance matrix cov = r(C) |
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Matrices can be defined with other matrices as well. {{{ . matrix B = (A,A) . matrix list B B[2,4] c1 c2 c1 c2 r1 1 2 1 2 r2 3 4 3 4 . matrix C = (A\A) . matrix list C C[4,2] c1 c2 r1 1 2 r2 3 4 r1 1 2 r2 3 4 }}} A '''vector''' is simply a special case of a matrix. === Rows and Columns === A newly-defined matrix's rows and columns have sequential names (`r1`, `r2`, and so on). Many commands return matrices with names rows and columns. Many more commands are able to parse passed matrices ''only'' because rows and columns are named in a structured way. |
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| Matrixes can be joined in either direction. | To declare a matrix, try: |
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| . matrix A = (1) . matrix B = A , (2) . matrix list B B[1,2] c1 c2 r1 1 2 . matrix C = B \ (3,4) . matrix list C C[2,2] c1 c2 r1 1 2 r2 3 4 |
matrix A = (1, 2 \ 3, 4) matrix input B = (5, 6 \ 1/3, _pi) |
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| A matrix is indexed by `NAME[ROW,COL]`. Indexing starts at 1. `C[1,2]` is 2 in the above example. | The '''`matrix input`''' subcommand allows for expressions as seen above, but otherwise does not differ. Matrix elements can be accessed by subscripting (row then column) while indexing from 1. Following from the above example, `A[1,2]` returns 2. To instead show the values of an entire matrix, try `matrix list A`. To join matrices horizontally, try {{{ matrix C = (A, B) }}} To join matrices vertically, try {{{ matrix C = (A \ B) }}} A '''vector''' is simply a special case of a matrix. |
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| === Arithmetic === | === Row and Column Names === |
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| Addition (and subtraction) is defined for any like-sized matrices. | A new matrix uses sequential names for rows and columns (i.e., `r1`, `c1`, and so on). |
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| Multiplication is defined for any ''a x b'' and ''b x c'' matrices, the result being ''a x c''. | Commands that return matrices usually name the rows and columns. Commands that consume matrices often assume a common structure, and therefore require that specific names be used. |
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| The transpose of matrix `A` is defined with `A'`. | To assign names, try: |
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| The negation of matrix `A` is defined with `-A`. Division by [[Stata/Scalars|scalar]] is performed with the forward slash (`/`) operator. The Kronecker product is performed with the hash (`#`) operator. |
{{{ matrix rownames A = foo bar baz matrix colnames A = ham spam eggs }}} |
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| === Functions === | === Operators === |
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| Matrices support these functions. | Most operators work as expected. Note that the slash (`/`) performs element-wise scalar division. |
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| ||'''Function''' || ||`cholesky(M)` || ||`corr(M)` || ||`diag(v)` || ||`get(systemname)` || ||`hadamard(M,N)` || ||`I(n)` || ||`inv(M)` || ||`invsym(M)` || ||`J(r,c,z)` || ||`matuniform(r,c)` || ||`nullmat(matname)`|| ||`sweep(M,i)` || ||`vec(M)` || ||`vecdiag(M)` || Matrices also support these functions which return a scalar. ||'''Function''' || ||`coleqnumb(M,s)` || ||`colnfreeparms(M)`|| ||`colnumb(M,s)` || ||`colsof(M)` || ||`det(M)` || ||`diag0cnt(M)` || ||`el(M,i,j)` || ||`issymmetric(M)` || ||`matmissing(M)` || ||`mreldif(X,Y)` || ||`roweqnumb(M,s)` || ||`rownfreeparms(M)`|| ||`rownumb(M,s)` || ||`rowsof(M)` || ||`trace(M)` || |
New operators include: * apostrophe (`'`) for [[LinearAlgebra/Transposition|transposition]], as in `A'` |
Stata Matrices
Matrices are a fundamental data type in Stata, like scalars.
Note that Mata does not use this data type.
Description
Matrices are collections of numeric values.
Many commands return matrices; for example:
correlate foo bar baz, covariance matrix cov = r(C)
Usage
To declare a matrix, try:
matrix A = (1, 2 \ 3, 4) matrix input B = (5, 6 \ 1/3, _pi)
The matrix input subcommand allows for expressions as seen above, but otherwise does not differ.
Matrix elements can be accessed by subscripting (row then column) while indexing from 1. Following from the above example, A[1,2] returns 2.
To instead show the values of an entire matrix, try matrix list A.
To join matrices horizontally, try
matrix C = (A, B)
To join matrices vertically, try
matrix C = (A \ B)
A vector is simply a special case of a matrix.
Row and Column Names
A new matrix uses sequential names for rows and columns (i.e., r1, c1, and so on).
Commands that return matrices usually name the rows and columns. Commands that consume matrices often assume a common structure, and therefore require that specific names be used.
To assign names, try:
matrix rownames A = foo bar baz matrix colnames A = ham spam eggs
Operators
Most operators work as expected. Note that the slash (/) performs element-wise scalar division.
New operators include:
apostrophe (') for transposition, as in A'
See also
Stata manual section 14: Matrix expressions