CommonOps (Efficient Java Matrix Library 0.25 API)

java.lang.Object
- org.ejml.ops.CommonOps

```
public class CommonOps
extends Object
```
Common matrix operations are contained here. Which specific underlying algorithm is used is not specified just the out come of the operation. Nor should calls to these functions reply on the underlying implementation. Which algorithm is used can depend on the matrix being passed in.

For more exotic and specialized generic operations see SpecializedOps.

Author:

Peter Abeles

See Also:
MatrixMatrixMult, MatrixVectorMult, SpecializedOps, MatrixFeatures

Constructor Summary

Constructors
Constructor and Description

CommonOps()

Constructors
Constructor and Description
`CommonOps()`

Method Summary

Methods
Modifier and Type	Method and Description
`static void`	`add(D1Matrix64F a, D1Matrix64F b, D1Matrix64F c)` Performs the following operation: c = a + b c_ij = a_ij + b_ij
`static void`	`add(D1Matrix64F a, double val)` Performs an in-place scalar addition: a = a + val a_ij = a_ij + val
`static void`	`add(D1Matrix64F a, double val, D1Matrix64F c)` Performs scalar addition: c = a + val c_ij = a_ij + val
`static void`	`add(D1Matrix64F a, double beta, D1Matrix64F b, D1Matrix64F c)` Performs the following operation: c = a + β * b c_ij = a_ij + β * b_ij
`static void`	`add(double alpha, D1Matrix64F a, D1Matrix64F b, D1Matrix64F c)` Performs the following operation: c = α * a + b c_ij = α * a_ij + b_ij
`static void`	`add(double alpha, D1Matrix64F a, double beta, D1Matrix64F b, D1Matrix64F c)` Performs the following operation: c = α * a + β * b c_ij = α * a_ij + β * b_ij
`static void`	`addEquals(D1Matrix64F a, D1Matrix64F b)` Performs the following operation: a = a + b a_ij = a_ij + b_ij
`static void`	`addEquals(D1Matrix64F a, double beta, D1Matrix64F b)` Performs the following operation: a = a + β * b a_ij = a_ij + β * b_ij
`static void`	`changeSign(D1Matrix64F a)` Changes the sign of every element in the matrix. a_ij = -a_ij
`static DenseMatrix64F[]`	`columnsToVector(DenseMatrix64F A, DenseMatrix64F[] v)` Converts the columns in a matrix into a set of vectors.
`static double`	`det(DenseMatrix64F mat)` Returns the determinant of the matrix.
`static DenseMatrix64F`	`diag(DenseMatrix64F ret, int width, double... diagEl)`
`static DenseMatrix64F`	`diag(double... diagEl)` Creates a new square matrix whose diagonal elements are specified by diagEl and all the other elements are zero. a_ij = 0 if i ≤ j a_ij = diag[i] if i = j
`static DenseMatrix64F`	`diagR(int numRows, int numCols, double... diagEl)` Creates a new rectangular matrix whose diagonal elements are specified by diagEl and all the other elements are zero. a_ij = 0 if i ≤ j a_ij = diag[i] if i = j
`static void`	`divide(double alpha, D1Matrix64F a)` Performs an in-place element by element scalar division. a_ij = a_ij/α
`static void`	`divide(double alpha, D1Matrix64F a, D1Matrix64F b)` Performs an element by element scalar division. b_ij = *a_ij /α
`static void`	`elementDiv(D1Matrix64F a, D1Matrix64F b)` Performs the an element by element division operation: a_ij = a_ij / b_ij
`static void`	`elementDiv(D1Matrix64F a, D1Matrix64F b, D1Matrix64F c)` Performs the an element by element division operation: c_ij = a_ij / b_ij
`static double`	`elementMax(D1Matrix64F a)` Returns the value of the element in the matrix that has the largest value. Max{ a_ij } for all i and j
`static double`	`elementMaxAbs(D1Matrix64F a)` Returns the absolute value of the element in the matrix that has the largest absolute value. Max{ \|a_ij\| } for all i and j
`static double`	`elementMin(D1Matrix64F a)` Returns the value of the element in the matrix that has the minimum value. Min{ a_ij } for all i and j
`static double`	`elementMinAbs(D1Matrix64F a)` Returns the absolute value of the element in the matrix that has the smallest absolute value. Min{ \|a_ij\| } for all i and j
`static void`	`elementMult(D1Matrix64F a, D1Matrix64F b)` Performs the an element by element multiplication operation: a_ij = a_ij * b_ij
`static void`	`elementMult(D1Matrix64F a, D1Matrix64F b, D1Matrix64F c)` Performs the an element by element multiplication operation: c_ij = a_ij * b_ij
`static double`	`elementSum(D1Matrix64F mat)` Computes the sum of all the elements in the matrix: sum(i=1:m , j=1:n ; a_ij)
`static double`	`elementSumAbs(D1Matrix64F mat)` Computes the sum of the absolute value all the elements in the matrix: sum(i=1:m , j=1:n ; \|a_ij\|)
`static DenseMatrix64F`	`extract(DenseMatrix64F src, int srcY0, int srcY1, int srcX0, int srcX1)` Creates a new matrix which is the specified submatrix of 'src'
`static void`	`extract(ReshapeMatrix64F src, int srcY0, int srcY1, int srcX0, int srcX1, ReshapeMatrix64F dst, int dstY0, int dstX0)` Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
`static void`	`extractDiag(DenseMatrix64F src, DenseMatrix64F dst)` Extracts the diagonal elements 'src' write it to the 'dst' vector.
`static void`	`fill(D1Matrix64F a, double value)` Sets every element in the matrix to the specified value. a_ij = value
`static DenseMatrix64F`	`identity(int width)` Creates an identity matrix of the specified size. a_ij = 0 if i ≠ j a_ij = 1 if i = j
`static DenseMatrix64F`	`identity(int numRows, int numCols)` Creates a rectangular matrix which is zero except along the diagonals.
`static void`	`insert(ReshapeMatrix64F src, ReshapeMatrix64F dest, int destY0, int destX0)` Inserts matrix 'src' into matrix 'dest' with the (0,0) of src at (row,col) in dest.
`static boolean`	`invert(DenseMatrix64F mat)` Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix. a = a^-1
`static boolean`	`invert(DenseMatrix64F mat, DenseMatrix64F result)` Performs a matrix inversion operation that does not modify the original and stores the results in another matrix.
`static void`	`kron(DenseMatrix64F A, DenseMatrix64F B, DenseMatrix64F C)` The Kronecker product of two matrices is defined as: C_ij = a_ijB where C_ij is a sub matrix inside of C ∈ ℜ ^{mk × nl}, A ∈ ℜ ^{m × n}, and B ∈ ℜ ^{k × l}.
`static void`	`mult(double alpha, RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = α * a * b c_ij = α ∑_k=1:n { * a_ik * b_kj}
`static void`	`mult(RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = a * b c_ij = ∑_k=1:n { a_ik * b_kj}
`static void`	`multAdd(double alpha, RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = c + α * a * b c_ij = c_ij + α * ∑_k=1:n { a_ik * b_kj}
`static void`	`multAdd(RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = c + a * b c_ij = c_ij + ∑_k=1:n { a_ik * b_kj}
`static void`	`multAddTransA(double alpha, RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = c + α * a^T * b c_ij =c_ij + α * ∑_k=1:n { a_ki * b_kj}
`static void`	`multAddTransA(RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = c + a^T * b c_ij = c_ij + ∑_k=1:n { a_ki * b_kj}
`static void`	`multAddTransAB(double alpha, RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = c + α * a^T * b^T c_ij = c_ij + α * ∑_k=1:n { a_ki * b_jk}
`static void`	`multAddTransAB(RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = c + a^T * b^T c_ij = c_ij + ∑_k=1:n { a_ki * b_jk}
`static void`	`multAddTransB(double alpha, RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = c + α * a * b^T c_ij = c_ij + α * ∑_k=1:n { a_ik * b_jk}
`static void`	`multAddTransB(RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = c + a * b^T c_ij = c_ij + ∑_k=1:n { a_ik * b_jk}
`static void`	`multInner(RowD1Matrix64F a, RowD1Matrix64F c)` Computes the matrix multiplication inner product: c = a^T * a c_ij = ∑_k=1:n { a_ki * a_kj}
`static void`	`multOuter(RowD1Matrix64F a, RowD1Matrix64F c)` Computes the matrix multiplication outer product: c = a * a^T c_ij = ∑_k=1:m { a_ik * a_jk}
`static void`	`multTransA(double alpha, RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = α * a^T * b c_ij = α ∑_k=1:n { a_ki * b_kj}
`static void`	`multTransA(RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = a^T * b c_ij = ∑_k=1:n { a_ki * b_kj}
`static void`	`multTransAB(double alpha, RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = α * a^T * b^T c_ij = α ∑_k=1:n { a_ki * b_jk}
`static void`	`multTransAB(RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = a^T * b^T c_ij = ∑_k=1:n { a_ki * b_jk}
`static void`	`multTransB(double alpha, RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = α * a * b^T c_ij = α ∑_k=1:n { a_ik * b_jk}
`static void`	`multTransB(RowD1Matrix64F a, RowD1Matrix64F b, RowD1Matrix64F c)` Performs the following operation: c = a * b^T c_ij = ∑_k=1:n { a_ik * b_jk}
`static void`	`pinv(DenseMatrix64F A, DenseMatrix64F invA)` Computes the Moore-Penrose pseudo-inverse: pinv(A) = (A^TA)^-1 A^T or pinv(A) = A^T(AA^T)^-1
`static DenseMatrix64F[]`	`rowsToVector(DenseMatrix64F A, DenseMatrix64F[] v)` Converts the rows in a matrix into a set of vectors.
`static DenseMatrix64F`	`rref(DenseMatrix64F A, int numUnknowns, DenseMatrix64F reduced)` Puts the augmented system matrix into reduced row echelon form (RREF).
`static void`	`scale(double alpha, D1Matrix64F a)` Performs an in-place element by element scalar multiplication. a_ij = α*a_ij
`static void`	`scale(double alpha, D1Matrix64F a, D1Matrix64F b)` Performs an element by element scalar multiplication. b_ij = α*a_ij
`static void`	`setIdentity(RowD1Matrix64F mat)` Sets all the diagonal elements equal to one and everything else equal to zero.
`static boolean`	`solve(DenseMatrix64F a, DenseMatrix64F b, DenseMatrix64F x)` Solves for x in the following equation: A*x = b
`static void`	`sub(D1Matrix64F a, D1Matrix64F b, D1Matrix64F c)` Performs the following subtraction operation: c = a - b c_ij = a_ij - b_ij
`static void`	`subEquals(D1Matrix64F a, D1Matrix64F b)` Performs the following subtraction operation: a = a - b a_ij = a_ij - b_ij
`static DenseMatrix64F`	`sumCols(DenseMatrix64F input, DenseMatrix64F output)` Computes the sum of each column in the input matrix and returns the results in a vector: b_j = sum(i=1:m ; \|a_ij\|)
`static DenseMatrix64F`	`sumRows(DenseMatrix64F input, DenseMatrix64F output)` Computes the sum of each row in the input matrix and returns the results in a vector: b_j = sum(i=1:n ; \|a_ji\|)
`static double`	`trace(RowD1Matrix64F a)` This computes the trace of the matrix: trace = ∑_i=1:n { a_ii }
`static void`	`transpose(DenseMatrix64F mat)` Performs an "in-place" transpose.
`static DenseMatrix64F`	`transpose(DenseMatrix64F A, DenseMatrix64F A_tran)` Transposes matrix 'a' and stores the results in 'b': b_ij = a_ji where 'b' is the transpose of 'a'.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - CommonOps
```
public CommonOps()
```
- Method Detail
  - mult
```
public static void mult(RowD1Matrix64F a,
        RowD1Matrix64F b,
        RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = a * b
    
    c_ij = ∑_k=1:n { a_ik * b_kj}
    
    Parameters:
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - mult
```
public static void mult(double alpha,
        RowD1Matrix64F a,
        RowD1Matrix64F b,
        RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = α * a * b
    
    c_ij = α ∑_k=1:n { * a_ik * b_kj}
    
    Parameters:
    alpha - Scaling factor.
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multTransA
```
public static void multTransA(RowD1Matrix64F a,
              RowD1Matrix64F b,
              RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = a^T * b
    
    c_ij = ∑_k=1:n { a_ki * b_kj}
    
    Parameters:
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multTransA
```
public static void multTransA(double alpha,
              RowD1Matrix64F a,
              RowD1Matrix64F b,
              RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = α * a^T * b
    
    c_ij = α ∑_k=1:n { a_ki * b_kj}
    
    Parameters:
    alpha - Scaling factor.
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multTransB
```
public static void multTransB(RowD1Matrix64F a,
              RowD1Matrix64F b,
              RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = a * b^T
    c_ij = ∑_k=1:n { a_ik * b_jk}
    
    Parameters:
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multTransB
```
public static void multTransB(double alpha,
              RowD1Matrix64F a,
              RowD1Matrix64F b,
              RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = α * a * b^T
    c_ij = α ∑_k=1:n { a_ik * b_jk}
    
    Parameters:
    alpha - Scaling factor.
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multTransAB
```
public static void multTransAB(RowD1Matrix64F a,
               RowD1Matrix64F b,
               RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = a^T * b^T
    c_ij = ∑_k=1:n { a_ki * b_jk}
    
    Parameters:
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multTransAB
```
public static void multTransAB(double alpha,
               RowD1Matrix64F a,
               RowD1Matrix64F b,
               RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = α * a^T * b^T
    c_ij = α ∑_k=1:n { a_ki * b_jk}
    
    Parameters:
    alpha - Scaling factor.
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multInner
```
public static void multInner(RowD1Matrix64F a,
             RowD1Matrix64F c)
```
    Computes the matrix multiplication inner product:
    
    c = a^T * a
    
    c_ij = ∑_k=1:n { a_ki * a_kj}
    
    Is faster than using a generic matrix multiplication by taking advantage of symmetry. For vectors there is an even faster option, see VectorVectorMult.innerProd(org.ejml.data.D1Matrix64F, org.ejml.data.D1Matrix64F)
    
    Parameters:
    a - The matrix being multiplied. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multOuter
```
public static void multOuter(RowD1Matrix64F a,
             RowD1Matrix64F c)
```
    Computes the matrix multiplication outer product:
    
    c = a * a^T
    
    c_ij = ∑_k=1:m { a_ik * a_jk}
    
    Is faster than using a generic matrix multiplication by taking advantage of symmetry.
    
    Parameters:
    a - The matrix being multiplied. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multAdd
```
public static void multAdd(RowD1Matrix64F a,
           RowD1Matrix64F b,
           RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = c + a * b
    c_ij = c_ij + ∑_k=1:n { a_ik * b_kj}
    
    Parameters:
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multAdd
```
public static void multAdd(double alpha,
           RowD1Matrix64F a,
           RowD1Matrix64F b,
           RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = c + α * a * b
    c_ij = c_ij + α * ∑_k=1:n { a_ik * b_kj}
    
    Parameters:
    alpha - scaling factor.
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multAddTransA
```
public static void multAddTransA(RowD1Matrix64F a,
                 RowD1Matrix64F b,
                 RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = c + a^T * b
    c_ij = c_ij + ∑_k=1:n { a_ki * b_kj}
    
    Parameters:
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multAddTransA
```
public static void multAddTransA(double alpha,
                 RowD1Matrix64F a,
                 RowD1Matrix64F b,
                 RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = c + α * a^T * b
    c_ij =c_ij + α * ∑_k=1:n { a_ki * b_kj}
    
    Parameters:
    alpha - scaling factor
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multAddTransB
```
public static void multAddTransB(RowD1Matrix64F a,
                 RowD1Matrix64F b,
                 RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = c + a * b^T
    c_ij = c_ij + ∑_k=1:n { a_ik * b_jk}
    
    Parameters:
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multAddTransB
```
public static void multAddTransB(double alpha,
                 RowD1Matrix64F a,
                 RowD1Matrix64F b,
                 RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = c + α * a * b^T
    c_ij = c_ij + α * ∑_k=1:n { a_ik * b_jk}
    
    Parameters:
    alpha - Scaling factor.
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - multAddTransAB
```
public static void multAddTransAB(RowD1Matrix64F a,
                  RowD1Matrix64F b,
                  RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = c + a^T * b^T
    c_ij = c_ij + ∑_k=1:n { a_ki * b_jk}
    
    Parameters:
    a - The left matrix in the multiplication operation. Not Modified.
    b - The right matrix in the multiplication operation. Not Modified.
    c - Where the results of the operation are stored. Modified.
  - multAddTransAB
```
public static void multAddTransAB(double alpha,
                  RowD1Matrix64F a,
                  RowD1Matrix64F b,
                  RowD1Matrix64F c)
```
    Performs the following operation:
    
    c = c + α * a^T * b^T
    c_ij = c_ij + α * ∑_k=1:n { a_ki * b_jk}
    
    Parameters:
    alpha - Scaling factor.
    a - The left matrix in the multiplication operation. Not Modified.
    b - The right matrix in the multiplication operation. Not Modified.
    c - Where the results of the operation are stored. Modified.
  - solve
```
public static boolean solve(DenseMatrix64F a,
            DenseMatrix64F b,
            DenseMatrix64F x)
```
    Solves for x in the following equation:
    
    A*x = b
    
    If the system could not be solved then false is returned. If it returns true that just means the algorithm finished operating, but the results could still be bad because 'A' is singular or nearly singular.
    
    If repeat calls to solve are being made then one should consider using LinearSolverFactory instead.
    
    It is ok for 'b' and 'x' to be the same matrix.
    
    Parameters:
    a - A matrix that is m by m. Not modified.
    b - A matrix that is m by n. Not modified.
    x - A matrix that is m by n. Modified.
    
    Returns:
    true if it could invert the matrix false if it could not.
  - transpose
```
public static void transpose(DenseMatrix64F mat)
```
    Performs an "in-place" transpose.
    
    For square matrices the transpose is truly in-place and does not require additional memory. For non-square matrices, internally a temporary matrix is declared and transpose(org.ejml.data.DenseMatrix64F, org.ejml.data.DenseMatrix64F) is invoked.
    
    Parameters:
    mat - The matrix that is to be transposed. Modified.
  - transpose
```
public static DenseMatrix64F transpose(DenseMatrix64F A,
                       DenseMatrix64F A_tran)
```
    Transposes matrix 'a' and stores the results in 'b':
    
    b_ij = a_ji
    where 'b' is the transpose of 'a'.
    
    Parameters:
    A - The original matrix. Not modified.
    A_tran - Where the transpose is stored. If null a new matrix is created. Modified.
    
    Returns:
    The transposed matrix.
  - trace
```
public static double trace(RowD1Matrix64F a)
```
    This computes the trace of the matrix:
    
    trace = ∑_i=1:n { a_ii }
    
    The trace is only defined for square matrices.
    
    Parameters:
    a - A square matrix. Not modified.
  - det
```
public static double det(DenseMatrix64F mat)
```
    Returns the determinant of the matrix. If the inverse of the matrix is also needed, then using LUDecompositionAlt_D64 directly (or any similar algorithm) can be more efficient.
    
    Parameters:
    mat - The matrix whose determinant is to be computed. Not modified.
    
    Returns:
    The determinant.
  - invert
```
public static boolean invert(DenseMatrix64F mat)
```
    Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix.
    
    a = a^-1
    
    If the algorithm could not invert the matrix then false is returned. If it returns true that just means the algorithm finished. The results could still be bad because the matrix is singular or nearly singular.
    
    Parameters:
    mat - The matrix that is to be inverted. Results are stored here. Modified.
    
    Returns:
    true if it could invert the matrix false if it could not.
  - invert
```
public static boolean invert(DenseMatrix64F mat,
             DenseMatrix64F result)
```
    Performs a matrix inversion operation that does not modify the original and stores the results in another matrix. The two matrices must have the same dimension.
    
    b = a^-1
    
    If the algorithm could not invert the matrix then false is returned. If it returns true that just means the algorithm finished. The results could still be bad because the matrix is singular or nearly singular.
    
    For medium to large matrices there might be a slight performance boost to using LinearSolverFactory instead.
    
    Parameters:
    mat - The matrix that is to be inverted. Not modified.
    result - Where the inverse matrix is stored. Modified.
    
    Returns:
    true if it could invert the matrix false if it could not.
  - pinv
```
public static void pinv(DenseMatrix64F A,
        DenseMatrix64F invA)
```
    Computes the Moore-Penrose pseudo-inverse:
    
    pinv(A) = (A^TA)^-1 A^T
    or
    pinv(A) = A^T(AA^T)^-1
    
    Internally it uses SolvePseudoInverseSvd to compute the inverse. For performance reasons, this should only be used when a matrix is singular or nearly singular.
    
    Parameters:
    A - A m by n Matrix. Not modified.
    invA - Where the computed pseudo inverse is stored. n by m. Modified.
  - columnsToVector
```
public static DenseMatrix64F[] columnsToVector(DenseMatrix64F A,
                               DenseMatrix64F[] v)
```
    Converts the columns in a matrix into a set of vectors.
    
    Parameters:
    A - Matrix. Not modified.
    v -
    
    Returns:
    An array of vectors.
  - rowsToVector
```
public static DenseMatrix64F[] rowsToVector(DenseMatrix64F A,
                            DenseMatrix64F[] v)
```
    Converts the rows in a matrix into a set of vectors.
    
    Parameters:
    A - Matrix. Not modified.
    v -
    
    Returns:
    An array of vectors.
  - setIdentity
```
public static void setIdentity(RowD1Matrix64F mat)
```
    Sets all the diagonal elements equal to one and everything else equal to zero. If this is a square matrix then it will be an identity matrix.
    
    Parameters:
    mat - A square matrix.
    See Also:
    identity(int)
  - identity
```
public static DenseMatrix64F identity(int width)
```
    Creates an identity matrix of the specified size.
    
    a_ij = 0 if i ≠ j
    a_ij = 1 if i = j
    
    Parameters:
    width - The width and height of the identity matrix.
    
    Returns:
    A new instance of an identity matrix.
  - identity
```
public static DenseMatrix64F identity(int numRows,
                      int numCols)
```
    Creates a rectangular matrix which is zero except along the diagonals.
    
    Parameters:
    numRows - Number of rows in the matrix.
    numCols - NUmber of columns in the matrix.
    
    Returns:
    A matrix with diagonal elements equal to one.
  - diag
```
public static DenseMatrix64F diag(double... diagEl)
```
    Creates a new square matrix whose diagonal elements are specified by diagEl and all the other elements are zero.
    
    a_ij = 0 if i ≤ j
    a_ij = diag[i] if i = j
    
    Parameters:
    diagEl - Contains the values of the diagonal elements of the resulting matrix.
    
    Returns:
    A new matrix.
    See Also:
    diagR(int, int, double...)
  - diag
```
public static DenseMatrix64F diag(DenseMatrix64F ret,
                  int width,
                  double... diagEl)
```
  - diagR
```
public static DenseMatrix64F diagR(int numRows,
                   int numCols,
                   double... diagEl)
```
    Creates a new rectangular matrix whose diagonal elements are specified by diagEl and all the other elements are zero.
    
    a_ij = 0 if i ≤ j
    a_ij = diag[i] if i = j
    
    Parameters:
    numRows - Number of rows in the matrix.
    numCols - Number of columns in the matrix.
    diagEl - Contains the values of the diagonal elements of the resulting matrix.
    
    Returns:
    A new matrix.
    See Also:
    diag(double...)
  - kron
```
public static void kron(DenseMatrix64F A,
        DenseMatrix64F B,
        DenseMatrix64F C)
```
    The Kronecker product of two matrices is defined as:
    C_ij = a_ijB
    where C_ij is a sub matrix inside of C ∈ ℜ ^{m*k × n*l}, A ∈ ℜ ^{m × n}, and B ∈ ℜ ^{k × l}.
    
    Parameters:
    A - The left matrix in the operation. Not modified.
    B - The right matrix in the operation. Not modified.
    C - Where the results of the operation are stored. Modified.
  - extract
```
public static void extract(ReshapeMatrix64F src,
           int srcY0,
           int srcY1,
           int srcX0,
           int srcX1,
           ReshapeMatrix64F dst,
           int dstY0,
           int dstX0)
```
    Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.
    
    s_{i-y0 , j-x0} = o_ij for all y0 ≤ i < y1 and x0 ≤ j < x1
    
    where 's_ij' is an element in the submatrix and 'o_ij' is an element in the original matrix.
    
    Parameters:
    src - The original matrix which is to be copied. Not modified.
    srcX0 - Start column.
    srcX1 - Stop column+1.
    srcY0 - Start row.
    srcY1 - Stop row+1.
    dst - Where the submatrix are stored. Modified.
    dstY0 - Start row in dst.
    dstX0 - start column in dst.
  - extract
```
public static DenseMatrix64F extract(DenseMatrix64F src,
                     int srcY0,
                     int srcY1,
                     int srcX0,
                     int srcX1)
```
    Creates a new matrix which is the specified submatrix of 'src'
    
    s_{i-y0 , j-x0} = o_ij for all y0 ≤ i < y1 and x0 ≤ j < x1
    
    where 's_ij' is an element in the submatrix and 'o_ij' is an element in the original matrix.
    
    Parameters:
    src - The original matrix which is to be copied. Not modified.
    srcX0 - Start column.
    srcX1 - Stop column+1.
    srcY0 - Start row.
    srcY1 - Stop row+1.
    
    Returns:
    Extracted submatrix.
  - extractDiag
```
public static void extractDiag(DenseMatrix64F src,
               DenseMatrix64F dst)
```
    Extracts the diagonal elements 'src' write it to the 'dst' vector. 'dst' can either be a row or column vector.
    
    Parameters:
    src - Matrix whose diagonal elements are being extracted. Not modified.
    dst - A vector the results will be written into. Modified.
  - insert
```
public static void insert(ReshapeMatrix64F src,
          ReshapeMatrix64F dest,
          int destY0,
          int destX0)
```
    Inserts matrix 'src' into matrix 'dest' with the (0,0) of src at (row,col) in dest. This is equivalent to calling extract(src,0,src.numRows,0,src.numCols,dest,destY0,destX0).
    
    Parameters:
    src - matrix that is being copied into dest. Not modified.
    dest - Where src is being copied into. Modified.
    destY0 - Start row for the copy into dest.
    destX0 - Start column for the copy into dest.
  - elementMax
```
public static double elementMax(D1Matrix64F a)
```
    Returns the value of the element in the matrix that has the largest value.
    
    Max{ a_ij } for all i and j
    
    Parameters:
    a - A matrix. Not modified.
    
    Returns:
    The max element value of the matrix.
  - elementMaxAbs
```
public static double elementMaxAbs(D1Matrix64F a)
```
    Returns the absolute value of the element in the matrix that has the largest absolute value.
    
    Max{ |a_ij| } for all i and j
    
    Parameters:
    a - A matrix. Not modified.
    
    Returns:
    The max abs element value of the matrix.
  - elementMin
```
public static double elementMin(D1Matrix64F a)
```
    Returns the value of the element in the matrix that has the minimum value.
    
    Min{ a_ij } for all i and j
    
    Parameters:
    a - A matrix. Not modified.
    
    Returns:
    The value of element in the matrix with the minimum value.
  - elementMinAbs
```
public static double elementMinAbs(D1Matrix64F a)
```
    Returns the absolute value of the element in the matrix that has the smallest absolute value.
    
    Min{ |a_ij| } for all i and j
    
    Parameters:
    a - A matrix. Not modified.
    
    Returns:
    The max element value of the matrix.
  - elementMult
```
public static void elementMult(D1Matrix64F a,
               D1Matrix64F b)
```
    Performs the an element by element multiplication operation:
    
    a_ij = a_ij * b_ij
    
    Parameters:
    a - The left matrix in the multiplication operation. Modified.
    b - The right matrix in the multiplication operation. Not modified.
  - elementMult
```
public static void elementMult(D1Matrix64F a,
               D1Matrix64F b,
               D1Matrix64F c)
```
    Performs the an element by element multiplication operation:
    
    c_ij = a_ij * b_ij
    
    Parameters:
    a - The left matrix in the multiplication operation. Not modified.
    b - The right matrix in the multiplication operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - elementDiv
```
public static void elementDiv(D1Matrix64F a,
              D1Matrix64F b)
```
    Performs the an element by element division operation:
    
    a_ij = a_ij / b_ij
    
    Parameters:
    a - The left matrix in the division operation. Modified.
    b - The right matrix in the division operation. Not modified.
  - elementDiv
```
public static void elementDiv(D1Matrix64F a,
              D1Matrix64F b,
              D1Matrix64F c)
```
    Performs the an element by element division operation:
    
    c_ij = a_ij / b_ij
    
    Parameters:
    a - The left matrix in the division operation. Not modified.
    b - The right matrix in the division operation. Not modified.
    c - Where the results of the operation are stored. Modified.
  - elementSum
```
public static double elementSum(D1Matrix64F mat)
```
    Computes the sum of all the elements in the matrix:
    
    sum(i=1:m , j=1:n ; a_ij)
    
    Parameters:
    mat - An m by n matrix. Not modified.
    
    Returns:
    The sum of the elements.
  - elementSumAbs
```
public static double elementSumAbs(D1Matrix64F mat)
```
    Computes the sum of the absolute value all the elements in the matrix:
    
    sum(i=1:m , j=1:n ; |a_ij|)
    
    Parameters:
    mat - An m by n matrix. Not modified.
    
    Returns:
    The sum of the absolute value of each element.
  - sumRows
```
public static DenseMatrix64F sumRows(DenseMatrix64F input,
                     DenseMatrix64F output)
```
    Computes the sum of each row in the input matrix and returns the results in a vector:
    
    b_j = sum(i=1:n ; |a_ji|)
    
    Parameters:
    input - INput matrix whose rows are summed.
    output - Optional storage for output. Must be a vector. If null a row vector is returned. Modified.
    
    Returns:
    Vector containing the sum of each row in the input.
  - sumCols
```
public static DenseMatrix64F sumCols(DenseMatrix64F input,
                     DenseMatrix64F output)
```
    Computes the sum of each column in the input matrix and returns the results in a vector:
    
    b_j = sum(i=1:m ; |a_ij|)
    
    Parameters:
    input - INput matrix whose rows are summed.
    output - Optional storage for output. Must be a vector. If null a column vector is returned. Modified.
    
    Returns:
    Vector containing the sum of each row in the input.
  - addEquals
```
public static void addEquals(D1Matrix64F a,
             D1Matrix64F b)
```
    Performs the following operation:
    
    a = a + b
    a_ij = a_ij + b_ij
    
    Parameters:
    a - A Matrix. Modified.
    b - A Matrix. Not modified.
  - addEquals
```
public static void addEquals(D1Matrix64F a,
             double beta,
             D1Matrix64F b)
```
    Performs the following operation:
    
    a = a + β * b
    a_ij = a_ij + β * b_ij
    
    Parameters:
    beta - The number that matrix 'b' is multiplied by.
    a - A Matrix. Modified.
    b - A Matrix. Not modified.
  - add
```
public static void add(D1Matrix64F a,
       D1Matrix64F b,
       D1Matrix64F c)
```
    Performs the following operation:
    
    c = a + b
    c_ij = a_ij + b_ij
    
    Matrix C can be the same instance as Matrix A and/or B.
    
    Parameters:
    a - A Matrix. Not modified.
    b - A Matrix. Not modified.
    c - A Matrix where the results are stored. Modified.
  - add
```
public static void add(D1Matrix64F a,
       double beta,
       D1Matrix64F b,
       D1Matrix64F c)
```
    Performs the following operation:
    
    c = a + β * b
    c_ij = a_ij + β * b_ij
    
    Matrix C can be the same instance as Matrix A and/or B.
    
    Parameters:
    a - A Matrix. Not modified.
    beta - Scaling factor for matrix b.
    b - A Matrix. Not modified.
    c - A Matrix where the results are stored. Modified.
  - add
```
public static void add(double alpha,
       D1Matrix64F a,
       double beta,
       D1Matrix64F b,
       D1Matrix64F c)
```
    Performs the following operation:
    
    c = α * a + β * b
    c_ij = α * a_ij + β * b_ij
    
    Matrix C can be the same instance as Matrix A and/or B.
    
    Parameters:
    alpha - A scaling factor for matrix a.
    a - A Matrix. Not modified.
    beta - A scaling factor for matrix b.
    b - A Matrix. Not modified.
    c - A Matrix where the results are stored. Modified.
  - add
```
public static void add(double alpha,
       D1Matrix64F a,
       D1Matrix64F b,
       D1Matrix64F c)
```
    Performs the following operation:
    
    c = α * a + b
    c_ij = α * a_ij + b_ij
    
    Matrix C can be the same instance as Matrix A and/or B.
    
    Parameters:
    alpha - A scaling factor for matrix a.
    a - A Matrix. Not modified.
    b - A Matrix. Not modified.
    c - A Matrix where the results are stored. Modified.
  - add
```
public static void add(D1Matrix64F a,
       double val)
```
    Performs an in-place scalar addition:
    
    a = a + val
    a_ij = a_ij + val
    
    Parameters:
    a - A matrix. Modified.
    val - The value that's added to each element.
  - add
```
public static void add(D1Matrix64F a,
       double val,
       D1Matrix64F c)
```
    Performs scalar addition:
    
    c = a + val
    c_ij = a_ij + val
    
    Parameters:
    a - A matrix. Not modified.
    c - A matrix. Modified.
    val - The value that's added to each element.
  - subEquals
```
public static void subEquals(D1Matrix64F a,
             D1Matrix64F b)
```
    Performs the following subtraction operation:
    
    a = a - b
    a_ij = a_ij - b_ij
    
    Parameters:
    a - A Matrix. Modified.
    b - A Matrix. Not modified.
  - sub
```
public static void sub(D1Matrix64F a,
       D1Matrix64F b,
       D1Matrix64F c)
```
    Performs the following subtraction operation:
    
    c = a - b
    c_ij = a_ij - b_ij
    
    Matrix C can be the same instance as Matrix A and/or B.
    
    Parameters:
    a - A Matrix. Not modified.
    b - A Matrix. Not modified.
    c - A Matrix. Modified.
  - scale
```
public static void scale(double alpha,
         D1Matrix64F a)
```
    Performs an in-place element by element scalar multiplication.
    
    a_ij = α*a_ij
    
    Parameters:
    a - The matrix that is to be scaled. Modified.
    alpha - the amount each element is multiplied by.
  - scale
```
public static void scale(double alpha,
         D1Matrix64F a,
         D1Matrix64F b)
```
    Performs an element by element scalar multiplication.
    
    b_ij = α*a_ij
    
    Parameters:
    alpha - the amount each element is multiplied by.
    a - The matrix that is to be scaled. Not modified.
    b - Where the scaled matrix is stored. Modified.
  - divide
```
public static void divide(double alpha,
          D1Matrix64F a)
```
    Performs an in-place element by element scalar division.
    
    a_ij = a_ij/α
    
    Parameters:
    a - The matrix whose elements are to be divided. Modified.
    alpha - the amount each element is divided by.
  - divide
```
public static void divide(double alpha,
          D1Matrix64F a,
          D1Matrix64F b)
```
    Performs an element by element scalar division.
    
    b_ij = *a_ij /α
    
    Parameters:
    alpha - the amount each element is divided by.
    a - The matrix whose elements are to be divided. Not modified.
    b - Where the results are stored. Modified.
  - changeSign
```
public static void changeSign(D1Matrix64F a)
```
    Changes the sign of every element in the matrix.
    
    a_ij = -a_ij
    
    Parameters:
    a - A matrix. Modified.
  - fill
```
public static void fill(D1Matrix64F a,
        double value)
```
    Sets every element in the matrix to the specified value.
    
    a_ij = value
    
    Parameters:
    a - A matrix whose elements are about to be set. Modified.
    value - The value each element will have.
  - rref
```
public static DenseMatrix64F rref(DenseMatrix64F A,
                  int numUnknowns,
                  DenseMatrix64F reduced)
```
    Puts the augmented system matrix into reduced row echelon form (RREF). A matrix is said to be in RREF is the following conditions are true:
    1. If a row has non-zero entries, then the first non-zero entry is 1. This is known as the leading one.
    2. If a column contains a leading one then all other entries in that column are zero.
    3. If a row contains a leading 1, then each row above contains a leading 1 further to the left.
    [1] Page 19 in, Otter Bretscherm "Linear Algebra with Applications" Prentice-Hall Inc, 1997
    Parameters:
    A - Input matrix. Unmodified.
    numUnknowns - Number of unknowns/columns that are reduced. Set to -1 to default to Math.min(A.numRows,A.numCols), which works for most systems.
    reduced - Storage for reduced echelon matrix. If null then a new matrix is returned. Modified.
    
    Returns:
    Reduced echelon form of A

Class CommonOps

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

CommonOps

Method Detail

mult

mult

multTransA

multTransA

multTransB

multTransB

multTransAB

multTransAB

multInner

multOuter

multAdd

multAdd

multAddTransA

multAddTransA

multAddTransB

multAddTransB

multAddTransAB

multAddTransAB

solve

transpose

transpose

trace

det

invert

invert

pinv

columnsToVector

rowsToVector

setIdentity

identity

identity

diag

diag

diagR

kron

extract

extract

extractDiag

insert

elementMax

elementMaxAbs

elementMin

elementMinAbs

elementMult

elementMult

elementDiv

elementDiv

elementSum

elementSumAbs

sumRows

sumCols

addEquals

addEquals

add

add

add

add

add

add

subEquals

sub

scale

scale

divide

divide

changeSign

fill

rref