Table 6 List of functions implemented for the Matrix<M,N> class.
From: A new advance on dimensional-aware scalar, vector and matrix operations in C++
Operation | Method | Description | Note |
|---|---|---|---|
\({\mathcal {A}}_{i-1,j-1}\) | a(i,j) | Element access (1-based) | |
\({\mathcal {A}}_{i,j}\) | a[i,j] | Element access (0-based) | |
a.rowMajor(x) | Element access (row-major) | ||
a.colMajor(x) | Element access (column-major) | ||
m | a.rows | Rows count | |
n | a.columns | Columns count | |
\({\mathcal {A}}_{i,*}\) | a.row() | Returns a specified row | |
\({\mathcal {A}}_{*,j}\) | a.col() | Returns a specified column | |
\(m=n\) | a.square | Check if square | |
\( {\mathcal {A}}_{i_2,*} \leftarrow {\mathcal {A}}_{i_2,*} + {\mathcal {A}}_{i_1,*}\) | a.rowAdd(i1, i2) | Row addition and store | \(*\) |
\( {\mathcal {A}}_{i_2,*} \leftarrow {\mathcal {A}}_{i_2,*} - {\mathcal {A}}_{i_1,*}\) | a.rowSub(i1, i2) | Row subtraction and store | \(*\) |
\( {\mathcal {A}}_{i,*} \leftarrow {\mathcal {A}}_{i,*} \cdot s\) | a.rowMul(i, s) | Row multiplication | \(*\) |
\( {\mathcal {A}}_{i,*} \leftarrow {\mathcal {A}}_{i,*} / s\) | a.rowDiv(i, s) | Row division | \(*\) |
\( {\mathcal {A}}_{i_1,*} \leftrightarrow {\mathcal {A}}_{i_2,*}\) | a.rowSwap(i1, i2) | Row swap | \(*\) |
a.reverseRows() | Reverse the rows | \(*\) | |
a.shuffleRows() | Shuffles the rows | \(*\) | |
a.sortRows() | Sorts the rows | \(*\) | |
\( {\mathcal {A}}_{*,j_2} \leftarrow {\mathcal {A}}_{*,j_2} + {\mathcal {A}}_{*,j_1}\) | a.colAdd(j1, j2) | Column addition and store | \(*\) |
\( {\mathcal {A}}_{*,j_2} \leftarrow {\mathcal {A}}_{*,j_2} - {\mathcal {A}}_{*,j_1}\) | a.colSub(j1, j2) | Column subtraction and store | \(*\) |
\( {\mathcal {A}}_{*,j} \leftarrow {\mathcal {A}}_{*,j} \cdot s\) | a.colMul(j, s) | Column multiplication | \(*\) |
\( {\mathcal {A}}_{*,j} \leftarrow {\mathcal {A}}_{*,j} / s\) | a.colDiv(j, s) | Column division | \(*\) |
\( {\mathcal {A}}_{*,j_1} \leftrightarrow {\mathcal {A}}_{*,j_2}\) | a.colSwap(j1, j2) | Column swap | \(*\) |
a.reverseCols() | Reverse the columns | \(*\) | |
a.shuffleCols() | Shuffle the columns | \(*\) | |
a.sortCols() | Sorts the columns | \(*\) | |
\(o({\mathcal {A}})\) | a.order() | Order | \(\dagger \) |
\(O({\mathcal {A}})\) | a.orders() | Order (in \(m \times n \) form) | |
\(\text {adj}({\mathcal {A}})\) | a.adj() | Ajugate | \(\dagger \) |
\(c_{m,n}\) | a.cofactor(m,n) | Cofactor element | \(\dagger \) |
\(C_{m,n}\) | a.cofactors(m,n) | Cofactor matrix | \(\dagger \) |
\(\det ({\mathcal {A}})\) | a.det() | Determinant | \(\dagger \) |
\(\text {tr}({\mathcal {A}})\) | a.tr() | Trace | \(\dagger \) |
\({\mathcal {A}}^T\) | a.t() | Transpose | \(*\) |
\({\overline{A}}\) | a.conj() | Conjugate | \(*\) |
\({\mathcal {A}}^H\) | a.conjT() | Conjugate transpose | \(*\) |
\({\mathcal {A}}_{i,j} \leftarrow 0 \quad \text {if} |{A}_{i,j}| < t \) | a.zap(t) | Set to zero small elements | \(*\) |
\({\mathcal {A}}^{-1}\) | a.inv() | Inverse | \(\dagger \) |
\({\mathcal {A}}^{+}\) | a.pseudoInv() | Moore–Penrose inverse | |
\({\mathcal {A}}[m;n]\) | a.sub(n,m) | Submatrix | |
\(m_{m,n}\) | a.minor(m,n) | Minor element | \(\dagger \) |
\(M_{m,n}\) | a.minors(m,n) | Minor matrix | \(\dagger \) |
\(({\mathcal {A}}_{1,1},{\mathcal {A}}_{2,2}, \ldots , {\mathcal {A}}_{n,n})\) | a.diagonal() | Diagonal elements | \(\dagger \) |
\({\mathcal {A}}_{1,1} \cdot {\mathcal {A}}_{2,2} \cdot \ldots \cdot {\mathcal {A}}_{n,n})\) | a.diagonalProduct() | Product of the diagonal elements | \(\dagger \) |
\(\langle {\mathcal {A}}, {\mathcal {B}} \rangle _F\) | a.frobenius(b) | Frobenius inner product | |
\(\sum {\mathcal {A}}_{i,j}\) | a.grandSum() | Sum of all elements | |
\({\mathcal {A}} \oplus {\mathcal {B}}\) | a.directSum(b) | Direct sum | |
\({\mathcal {A}} \otimes {\mathcal {I}}_b + {\mathcal {I}}_a \otimes {\mathcal {B}}\) | a.kroneckerSum(b) | Kronecker sum | |
\({\mathcal {A}} \otimes {\mathcal {B}}\) | a.kroneckerProduct(b) | Kronecker product | |
\({\mathcal {A}}_{i,j} \cdot {\mathcal {B}}_{i,j}\) | a.elementwiseProduct() | Element-wise product | |
\({\mathcal {A}}_{i,j} / {\mathcal {B}}_{i,j}\) | a.elementwiseDivision() | Element-wise divisison | |
a.reduction(type) | Performs the reduction of the matrix | \(*\) |
