org.ejml.dense.row.CommonOps_FDRM

@Generated("org.ejml.dense.row.CommonOps_DDRM") public class CommonOps_FDRM 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_FDRM.

See Also:

Method Summary

Modifier and Type

Method

Description

static void

abs(FMatrixD1 a)

Performs absolute value of a matrix:

a = abs(a)
a_ij = abs(a_ij)

static void

abs(FMatrixD1 a, FMatrixD1 c)

Performs absolute value of a matrix:

c = abs(a)
c_ij = abs(a_ij)

static <T extends FMatrixD1> T

add(float alpha, T a, float beta, T b, T output)

Performs the following operation:

c = α * a + β * b
c_ij = α * a_ij + β * b_ij

static <T extends FMatrixD1> T

add(float alpha, T a, T b, T output)

Performs the following operation:

c = α * a + b
c_ij = α * a_ij + b_ij

static void

add(FMatrixD1 a, float val)

Performs an in-place scalar addition:

a = a + val
a_ij = a_ij + val

static <T extends FMatrixD1> T

add(T a, float val, T output)

Performs scalar addition:

c = a + val
c_ij = a_ij + val

static <T extends FMatrixD1> T

add(T a, float beta, T b, T output)

Performs the following operation:

c = a + β * b
c_ij = a_ij + β * b_ij

static <T extends FMatrixD1> T

add(T a, T b, T output)

Performs the following operation:

c = a + b
c_ij = a_ij + b_ij

static void

addEquals(FMatrixD1 a, float beta, FMatrixD1 b)

Performs the following operation:

a = a + β * b
a_ij = a_ij + β * b_ij

static void

addEquals(FMatrixD1 a, FMatrixD1 b)

Performs the following operation:

a = a + b
a_ij = a_ij + b_ij

static FMatrixRMaj

apply(FMatrixRMaj input, FOperatorUnary func)

static FMatrixRMaj

apply(FMatrixRMaj input, FOperatorUnary func, @Nullable FMatrixRMaj output)

This applies a given unary function on every value stored in the matrix

static void

changeSign(FMatrixD1 a)

Changes the sign of every element in the matrix.

a_ij = -a_ij

static <T extends FMatrixD1> T

changeSign(T input, T output)

Changes the sign of every element in the matrix.

output_ij = -input_ij

static FMatrixRMaj[]

columnsToVector(FMatrixRMaj A, @Nullable FMatrixRMaj[] v)

Converts the columns in a matrix into a set of vectors.

static FMatrixRMaj

concatColumns(FMatrixRMaj a, FMatrixRMaj b, @Nullable FMatrixRMaj output)

output = [a , b]

static FMatrixRMaj

concatColumnsMulti(FMatrixRMaj... m)

Concatenates all the matrices together along their columns.

static void

concatRows(FMatrixRMaj a, FMatrixRMaj b, FMatrixRMaj output)

output = [a ; b]

static FMatrixRMaj

concatRowsMulti(FMatrixRMaj... m)

Concatenates all the matrices together along their columns.

static int

countTrue(BMatrixRMaj A)

Counts the number of elements in A which are true

static float

det(FMatrixRMaj mat)

Returns the determinant of the matrix.

static FMatrixRMaj

diag(float... 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 FMatrixRMaj

diag(@Nullable FMatrixRMaj ret, int width, float... diagEl)

static FMatrixRMaj

diagR(int numRows, int numCols, float... 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(float alpha, FMatrixD1 a)

Performs an in-place element by element scalar division with the scalar on top.

a_ij = α/a_ij

static <T extends FMatrixD1> T

divide(float alpha, T input, T output)

Performs an element by element scalar division with the scalar on top.

b_ij = α/a_ij

static void

divide(FMatrixD1 a, float alpha)

Performs an in-place element by element scalar division with the scalar on bottom.

a_ij = a_ij/α

static <T extends FMatrixD1> T

divide(T input, float alpha, T output)

Performs an element by element scalar division with the scalar on botton.

b_ij = a_ij /α

static void

divideCols(FMatrixRMaj A, float[] values)

Divides every element in column i by value[i].

static void

divideRows(float[] values, FMatrixRMaj A)

Divides every element in row i by value[i].

static void

divideRowsCols(float[] diagA, int offsetA, FMatrixRMaj B, float[] diagC, int offsetC)

Equivalent to multiplying a matrix B by the inverse of two diagonal matrices.

static float

dot(FMatrixD1 a, FMatrixD1 b)

Computes the dot product or inner product between two vectors.

static BMatrixRMaj

elementBoolean(FMatrixRMaj input, DElementCoorBoolean func, @Nullable BMatrixRMaj output)

Applies a binary operator to even element in the input matrix.

static void

elementDiv(FMatrixD1 A, FMatrixD1 B)

Performs the an element by element division operation:

a_ij = a_ij / b_ij

static <T extends FMatrixD1> T

elementDiv(T A, T B, T output)

Performs the an element by element division operation:

c_ij = a_ij / b_ij

static <T extends FMatrixD1> T

elementExp(T A, T output)

Element-wise exp operation
c_ij = (float)Math.exp(a_ij)

static BMatrixRMaj

elementLessThan(FMatrixRMaj A, float value, @Nullable BMatrixRMaj output)

Applies the > operator to each element in A.

static BMatrixRMaj

elementLessThan(FMatrixRMaj A, FMatrixRMaj B, @Nullable BMatrixRMaj output)

Applies the < operator to each element in A.

static BMatrixRMaj

elementLessThanOrEqual(FMatrixRMaj A, float value, @Nullable BMatrixRMaj output)

Applies the ≥ operator to each element in A.

static BMatrixRMaj

elementLessThanOrEqual(FMatrixRMaj A, FMatrixRMaj B, @Nullable BMatrixRMaj output)

Applies the A ≤ B operator to each element.

static <T extends FMatrixD1> T

elementLog(T A, T output)

Element-wise log operation
c_ij = (float)Math.log(a_ij)

static float

elementMax(FMatrixD1 a)

Returns the value of the element in the matrix that has the largest value.

Max{ a_ij } for all i and j

static float

elementMax(FMatrixD1 a, ElementLocation loc)

Returns the value of the element in the matrix that has the largest value.

Max{ a_ij } for all i and j

static float

elementMaxAbs(FMatrixD1 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 float

elementMaxAbs(FMatrixD1 a, ElementLocation loc)

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 float

elementMin(FMatrixD1 a)

Returns the value of the element in the matrix that has the minimum value.

Min{ a_ij } for all i and j

static float

elementMin(FMatrixD1 a, ElementLocation loc)

Returns the value of the element in the matrix that has the minimum value.

Min{ a_ij } for all i and j

static float

elementMinAbs(FMatrixD1 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 float

elementMinAbs(FMatrixD1 a, ElementLocation loc)

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 BMatrixRMaj

elementMoreThan(FMatrixRMaj A, float value, @Nullable BMatrixRMaj output)

Applies the > operator to each element in A.

static BMatrixRMaj

elementMoreThanOrEqual(FMatrixRMaj A, float value, @Nullable BMatrixRMaj output)

Applies the ≥ operator to each element in A.

static void

elementMult(FMatrixD1 A, FMatrixD1 B)

Performs the an element by element multiplication operation:

a_ij = a_ij * b_ij

static <T extends FMatrixD1> T

elementMult(T A, T B, T output)

Performs the an element by element multiplication operation:

c_ij = a_ij * b_ij

static <T extends FMatrixD1> T

elementPower(float a, T B, T output)

Element-wise power operation
c_ij = a ^ b_ij

static <T extends FMatrixD1> T

elementPower(T A, float b, T output)

Element-wise power operation
c_ij = a_ij ^ b

static <T extends FMatrixD1> T

elementPower(T A, T B, T output)

Element-wise power operation
c_ij = a_ij ^ b_ij

static FMatrixRMaj

elements(FMatrixRMaj A, BMatrixRMaj marked, @Nullable FMatrixRMaj output)

Returns a row matrix which contains all the elements in A which are flagged as true in 'marked'

static float

elementSum(FMatrixD1 mat)

Computes the sum of all the elements in the matrix:

sum(i=1:m , j=1:n ; a_ij)

static float

elementSumAbs(FMatrixD1 mat)

Computes the sum of the absolute value all the elements in the matrix:

sum(i=1:m , j=1:n ; |a_ij|)

static void

extract(FMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, FMatrix dst)

Extract where the destination is reshaped to match the extracted region

static void

extract(FMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, FMatrix dst, int dstY0, int dstX0)

Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.

static void

extract(FMatrix src, int srcY0, int srcX0, FMatrix dst)

Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'.

static FMatrixRMaj

extract(FMatrixRMaj src, int[] rows, int rowsSize, int[] cols, int colsSize, @Nullable FMatrixRMaj dst)

Extracts out a matrix from source given a sub matrix with arbitrary rows and columns specified in two array lists

static FMatrixRMaj

extract(FMatrixRMaj src, int[] indexes, int length, @Nullable FMatrixRMaj dst)

Extracts the elements from the source matrix by their 1D index.

static FMatrixRMaj

extract(FMatrixRMaj src, int srcY0, int srcY1, int srcX0, int srcX1)

Creates a new matrix which is the specified submatrix of 'src'

static FMatrixRMaj

extractColumn(FMatrixRMaj a, int column, @Nullable FMatrixRMaj out)

Extracts the column from a matrix.

static FMatrixRMaj

extractDiag(FMatrixRMaj src, @Nullable FMatrixRMaj dst)

Extracts the diagonal elements 'src' write it to the 'dst' vector.

static FMatrixRMaj

extractRow(FMatrixRMaj a, int row, @Nullable FMatrixRMaj out)

Extracts the row from a matrix.

static void

fill(FMatrixD1 a, float value)

Sets every element in the matrix to the specified value.

a_ij = value

static FMatrixRMaj

identity(int width)

Creates an identity matrix of the specified size.

a_ij = 0 if i ≠ j
a_ij = 1 if i = j

static FMatrixRMaj

identity(int numRows, int numCols)

Creates a rectangular matrix which is zero except along the diagonals.

static void

insert(FMatrixRMaj src, FMatrixRMaj dst, int[] rows, int rowsSize, int[] cols, int colsSize)

Inserts into the specified elements of dst the source matrix.

static void

insert(FMatrix src, FMatrix 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(FMatrixRMaj mat)

Performs a matrix inversion operation on the specified matrix and stores the results in the same matrix.

a = a^-1

static boolean

invert(FMatrixRMaj mat, FMatrixRMaj result)

Performs a matrix inversion operation that does not modify the original and stores the results in another matrix.

static boolean

invertSPD(FMatrixRMaj mat, FMatrixRMaj result)

Matrix inverse for symmetric positive definite matrices.

static FMatrixRMaj

kron(FMatrixRMaj A, FMatrixRMaj B, @Nullable FMatrixRMaj 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}.

static FMatrixRMaj

maxCols(FMatrixRMaj input, @Nullable FMatrixRMaj output)

Finds the element with the minimum value along column in the input matrix and returns the results in a vector:

b_j = min(i=1:m ; a_ij)

static FMatrixRMaj

maxRows(FMatrixRMaj input, @Nullable FMatrixRMaj output)

Finds the element with the maximum value along each row in the input matrix and returns the results in a vector:

b_j = max(i=1:n ; a_ji)

static FMatrixRMaj

minCols(FMatrixRMaj input, @Nullable FMatrixRMaj output)

Finds the element with the minimum value along column in the input matrix and returns the results in a vector:

b_j = min(i=1:m ; a_ij)

static FMatrixRMaj

minRows(FMatrixRMaj input, @Nullable FMatrixRMaj output)

Finds the element with the minimum value along each row in the input matrix and returns the results in a vector:

b_j = min(i=1:n ; a_ji)

static <T extends FMatrix1Row> T

mult(float alpha, T a, T b, T output)

Performs the following operation:

c = α * a * b

c_ij = α ∑_k=1:n { * a_ik * b_kj}

static <T extends FMatrix1Row> T

mult(T a, T b, T output)

Performs the following operation:

c = a * b

c_ij = ∑_k=1:n { a_ik * b_kj}

static void

multAdd(float alpha, FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(FMatrix1Row a, FMatrix1Row b, FMatrix1Row c)

Performs the following operation:

c = c + a * b
c_ij = c_ij + ∑_k=1:n { a_ik * b_kj}

static void

multAddTransA(float alpha, FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(FMatrix1Row a, FMatrix1Row b, FMatrix1Row c)

Performs the following operation:

c = c + a^T * b
c_ij = c_ij + ∑_k=1:n { a_ki * b_kj}

static void

multAddTransAB(float alpha, FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(float alpha, FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(FMatrix1Row a, FMatrix1Row b, FMatrix1Row c)

Performs the following operation:

c = c + a * b^T
c_ij = c_ij + ∑_k=1:n { a_ik * b_jk}

static void

multCols(FMatrixRMaj A, float[] values)

Multiplies every element in column i by value[i].

static <T extends FMatrix1Row> T

multInner(T a, T output)

Computes the matrix multiplication inner product:

c = a^T * a

c_ij = ∑_k=1:n { a_ki * a_kj}

static <T extends FMatrix1Row> T

multOuter(T a, T output)

Computes the matrix multiplication outer product:

c = a * a^T

c_ij = ∑_k=1:m { a_ik * a_jk}

static void

multRows(float[] values, FMatrixRMaj A)

Multiplies every element in row i by value[i].

static <T extends FMatrix1Row> T

multTransA(float alpha, T a, T b, T output)

Performs the following operation:

c = α * a^T * b

c_ij = α ∑_k=1:n { a_ki * b_kj}

static <T extends FMatrix1Row> T

multTransA(T a, T b, T output)

Performs the following operation:

c = a^T * b

c_ij = ∑_k=1:n { a_ki * b_kj}

static <T extends FMatrix1Row> T

multTransAB(float alpha, T a, T b, T output)

Performs the following operation:

c = α * a^T * b^T
c_ij = α ∑_k=1:n { a_ki * b_jk}

static <T extends FMatrix1Row> T

multTransAB(T a, T b, T output)

Performs the following operation:

c = a^T * b^T
c_ij = ∑_k=1:n { a_ki * b_jk}

static <T extends FMatrix1Row> T

multTransB(float alpha, T a, T b, T output)

Performs the following operation:

c = α * a * b^T
c_ij = α ∑_k=1:n { a_ik * b_jk}

static <T extends FMatrix1Row> T

multTransB(T a, T b, T output)

Performs the following operation:

c = a * b^T
c_ij = ∑_k=1:n { a_ik * b_jk}

static FMatrixRMaj

permuteRowInv(int[] pinv, FMatrixRMaj input, FMatrixRMaj output)

Applies the row permutation specified by the vector to the input matrix and save the results in the output matrix.

static void

pinv(FMatrixRMaj A, FMatrixRMaj invA)

Computes the Moore-Penrose pseudo-inverse:

pinv(A) = (A^TA)^-1 A^T
or
pinv(A) = A^T(AA^T)^-1

static void

removeColumns(FMatrixRMaj A, int col0, int col1)

Removes columns from the matrix.

static FMatrixRMaj[]

rowsToVector(FMatrixRMaj A, @Nullable FMatrixRMaj[] v)

Converts the rows in a matrix into a set of vectors.

static FMatrixRMaj

rref(FMatrixRMaj A, int numUnknowns, @Nullable FMatrixRMaj reduced)

Puts the augmented system matrix into reduced row echelon form (RREF) using Gauss-Jordan elimination with row (partial) pivots.

static void

scale(float alpha, FMatrixD1 a)

Performs an in-place element by element scalar multiplication.

a_ij = α*a_ij

static void

scale(float alpha, FMatrixD1 a, FMatrixD1 b)

Performs an element by element scalar multiplication.

b_ij = α*a_ij

static void

scaleCol(float alpha, FMatrixRMaj A, int col)

In-place scaling of a column in A

static void

scaleRow(float alpha, FMatrixRMaj A, int row)

In-place scaling of a row in A

static void

setIdentity(FMatrix1Row mat)

Sets all the diagonal elements equal to one and everything else equal to zero.

static boolean

solve(FMatrixRMaj a, FMatrixRMaj b, FMatrixRMaj x)

Solves for x in the following equation:

A*x = b

static boolean

solveSPD(FMatrixRMaj A, FMatrixRMaj b, FMatrixRMaj x)

Linear solver for systems which are symmetric positive definite.
A*x = b

static <T extends FMatrixD1> T

subtract(float val, T a, T output)

Performs matrix scalar subtraction:

c = val - a
c_ij = val - a_ij

static <T extends FMatrixD1> T

subtract(T a, float val, T output)

Performs matrix scalar subtraction:

c = a - val
c_ij = a_ij - val

static <T extends FMatrixD1> T

subtract(T a, T b, T output)

Performs the following subtraction operation:

c = a - b
c_ij = a_ij - b_ij

static void

subtractEquals(FMatrixD1 a, FMatrixD1 b)

Performs the following subtraction operation:

a = a - b
a_ij = a_ij - b_ij

static FMatrixRMaj

sumCols(FMatrixRMaj input, @Nullable FMatrixRMaj 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 FMatrixRMaj

sumRows(FMatrixRMaj input, @Nullable FMatrixRMaj 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 void

symmLowerToFull(FMatrixRMaj A)

Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.

static void

symmUpperToFull(FMatrixRMaj A)

Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.

static float

trace(FMatrix1Row a)

Computes the matrix trace:

trace = ∑_i=1:n { a_ii }
where n = min(numRows,numCols)

static void

transpose(FMatrixRMaj mat)

Performs an "in-place" transpose.

static FMatrixRMaj

transpose(FMatrixRMaj A, @Nullable FMatrixRMaj 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

Method Details
- mult
  
  public static <T extends FMatrix1Row> T mult(T a, T b, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- mult
  
  public static <T extends FMatrix1Row> T mult(float alpha, T a, T b, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- multTransA
  
  public static <T extends FMatrix1Row> T multTransA(T a, T b, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- multTransA
  
  public static <T extends FMatrix1Row> T multTransA(float alpha, T a, T b, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- multTransB
  
  public static <T extends FMatrix1Row> T multTransB(T a, T b, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- multTransB
  
  public static <T extends FMatrix1Row> T multTransB(float alpha, T a, T b, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- multTransAB
  
  public static <T extends FMatrix1Row> T multTransAB(T a, T b, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- multTransAB
  
  public static <T extends FMatrix1Row> T multTransAB(float alpha, T a, T b, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- dot
  
  public static float dot(FMatrixD1 a, FMatrixD1 b)
  
  Computes the dot product or inner product between two vectors. If the two vectors are columns vectors then it is defined as:
  dot(a,b) = a<sup>T</sup> * b
  If the vectors are column or row or both is ignored by this function.
  
  Parameters:
  
  a - Vector
  
  b - Vector
  
  Returns:
  
  Dot product of the two vectors
- multInner
  
  public static <T extends FMatrix1Row> T multInner(T a, @Nullable T output)
  
  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_FDRM.innerProd(FMatrixD1, FMatrixD1)
  
  Parameters:
  
  a - The matrix being multiplied. Not modified.
  
  output - Where the results of the operation are stored. Modified.
- multOuter
  
  public static <T extends FMatrix1Row> T multOuter(T a, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- multAdd
  
  public static void multAdd(FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(float alpha, FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(float alpha, FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(float alpha, FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(float alpha, FMatrix1Row a, FMatrix1Row b, FMatrix1Row 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(FMatrixRMaj a, FMatrixRMaj b, FMatrixRMaj 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_FDRM instead.
  
  It is ok for 'b' and 'x' to be the same matrix.
  
  Parameters:
  
  a - A matrix that is m by n. Not modified.
  
  b - A matrix that is n by k. Not modified.
  
  x - A matrix that is m by k. Modified.
  
  Returns:
  
  true if it could invert the matrix false if it could not.
- solveSPD
  
  public static boolean solveSPD(FMatrixRMaj A, FMatrixRMaj b, FMatrixRMaj x)
  
  Linear solver for systems which are symmetric positive definite.
  A*x = b
  Parameters:
  
  A - A matrix that is n by n and SPD. Not modified.
  
  b - A matrix that is n by k. Not modified.
  
  x - A matrix that is n by k. Modified.
  
  Returns:
  
  true if it could invert the matrix false if it could not.
  
  See Also:
  
  UnrolledCholesky_FDRM
  
  LinearSolverFactory_FDRM
- transpose
  
  public static void transpose(FMatrixRMaj 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(FMatrixRMaj, FMatrixRMaj) is invoked.
  
  Parameters:
  
  mat - The matrix that is to be transposed. Modified.
- transpose
  
  public static FMatrixRMaj transpose(FMatrixRMaj A, @Nullable @Nullable FMatrixRMaj 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 float trace(FMatrix1Row a)
  
  Computes the matrix trace:
  
  trace = ∑_i=1:n { a_ii }
  where n = min(numRows,numCols)
  
  Parameters:
  
  a - (Input) A matrix
- det
  
  public static float det(FMatrixRMaj mat)
  
  Returns the determinant of the matrix. If the inverse of the matrix is also needed, then using LUDecomposition_F32 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(FMatrixRMaj 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(FMatrixRMaj mat, FMatrixRMaj 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_FDRM 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.
- invertSPD
  
  public static boolean invertSPD(FMatrixRMaj mat, FMatrixRMaj result)
  
  Matrix inverse for symmetric positive definite matrices. For small matrices an unrolled cholesky is used. Otherwise a standard decomposition.
  Parameters:
  
  mat - (Input) SPD matrix
  
  result - (Output) Inverted matrix.
  
  Returns:
  
  true if it could invert the matrix false if it could not.
  
  See Also:
  
  UnrolledCholesky_FDRM
  
  LinearSolverFactory_FDRM.chol(int)
- pinv
  
  public static void pinv(FMatrixRMaj A, FMatrixRMaj 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_FDRM 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 FMatrixRMaj[] columnsToVector(FMatrixRMaj A, @Nullable @Nullable FMatrixRMaj[] v)
  
  Converts the columns in a matrix into a set of vectors.
  
  Parameters:
  
  A - Matrix. Not modified.
  
  Returns:
  
  An array of vectors.
- rowsToVector
  
  public static FMatrixRMaj[] rowsToVector(FMatrixRMaj A, @Nullable @Nullable FMatrixRMaj[] v)
  
  Converts the rows in a matrix into a set of vectors.
  
  Parameters:
  
  A - Matrix. Not modified.
  
  Returns:
  
  An array of vectors.
- setIdentity
  
  public static void setIdentity(FMatrix1Row 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 FMatrixRMaj 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 FMatrixRMaj 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 FMatrixRMaj diag(float... 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, float...)
- diag
  
  public static FMatrixRMaj diag(@Nullable @Nullable FMatrixRMaj ret, int width, float... diagEl)
  See Also:
  
  diag(float...)
- diagR
  
  public static FMatrixRMaj diagR(int numRows, int numCols, float... 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(float...)
- kron
  
  public static FMatrixRMaj kron(FMatrixRMaj A, FMatrixRMaj B, @Nullable @Nullable FMatrixRMaj 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. Nullable. Modified.
- extract
  
  public static void extract(FMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, FMatrix 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 void extract(FMatrix src, int srcY0, int srcY1, int srcX0, int srcX1, FMatrix dst)
  
  Extract where the destination is reshaped to match the extracted region
  
  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.
- extract
  
  public static void extract(FMatrix src, int srcY0, int srcX0, FMatrix dst)
  
  Extracts a submatrix from 'src' and inserts it in a submatrix in 'dst'. Uses the shape of dst to determine the size of the matrix extracted.
  
  Parameters:
  
  src - The original matrix which is to be copied. Not modified.
  
  srcY0 - Start row in src.
  
  srcX0 - Start column in src.
  
  dst - Where the matrix is extracted into.
- extract
  
  public static FMatrixRMaj extract(FMatrixRMaj 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.
- extract
  
  public static FMatrixRMaj extract(FMatrixRMaj src, int[] rows, int rowsSize, int[] cols, int colsSize, @Nullable @Nullable FMatrixRMaj dst)
  
  Extracts out a matrix from source given a sub matrix with arbitrary rows and columns specified in two array lists
  
  Parameters:
  
  src - Source matrix. Not modified.
  
  rows - array of row indexes
  
  rowsSize - maximum element in row array
  
  cols - array of column indexes
  
  colsSize - maximum element in column array
  
  dst - output matrix. Must be correct shape.
- extract
  
  public static FMatrixRMaj extract(FMatrixRMaj src, int[] indexes, int length, @Nullable @Nullable FMatrixRMaj dst)
  
  Extracts the elements from the source matrix by their 1D index.
  
  Parameters:
  
  src - Source matrix. Not modified.
  
  indexes - array of row indexes
  
  length - maximum element in row array
  
  dst - output matrix. Must be a vector of the correct length.
- insert
  
  public static void insert(FMatrixRMaj src, FMatrixRMaj dst, int[] rows, int rowsSize, int[] cols, int colsSize)
  Inserts into the specified elements of dst the source matrix.
  for i in len(rows): for j in len(cols): dst(rows[i],cols[j]) = src(i,j)
  Parameters:
  
  src - Source matrix. Not modified.
  
  dst - output matrix. Must be correct shape.
  
  rows - array of row indexes.
  
  rowsSize - maximum element in row array
  
  cols - array of column indexes
  
  colsSize - maximum element in column array
- extractDiag
  
  public static FMatrixRMaj extractDiag(FMatrixRMaj src, @Nullable @Nullable FMatrixRMaj 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.
- extractRow
  
  public static FMatrixRMaj extractRow(FMatrixRMaj a, int row, @Nullable @Nullable FMatrixRMaj out)
  
  Extracts the row from a matrix.
  
  Parameters:
  
  a - Input matrix
  
  row - Which row is to be extracted
  
  out - output. Storage for the extracted row. If null then a new vector will be returned.
  
  Returns:
  
  The extracted row.
- extractColumn
  
  public static FMatrixRMaj extractColumn(FMatrixRMaj a, int column, @Nullable @Nullable FMatrixRMaj out)
  
  Extracts the column from a matrix.
  
  Parameters:
  
  a - Input matrix
  
  column - Which column is to be extracted
  
  out - output. Storage for the extracted column. If null then a new vector will be returned.
  
  Returns:
  
  The extracted column.
- removeColumns
  
  public static void removeColumns(FMatrixRMaj A, int col0, int col1)
  
  Removes columns from the matrix.
  
  Parameters:
  
  A - Matrix. Modified
  
  col0 - First column
  
  col1 - Last column, inclusive.
- insert
  
  public static void insert(FMatrix src, FMatrix 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 float elementMax(FMatrixD1 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.
- elementMax
  
  public static float elementMax(FMatrixD1 a, ElementLocation loc)
  
  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.
  
  loc - (Output) Location of selected element.
  
  Returns:
  
  The max element value of the matrix.
- elementMaxAbs
  
  public static float elementMaxAbs(FMatrixD1 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.
- elementMaxAbs
  
  public static float elementMaxAbs(FMatrixD1 a, ElementLocation loc)
  
  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.
  
  loc - (Output) Location of element element.
  
  Returns:
  
  The max abs element value of the matrix.
- elementMin
  
  public static float elementMin(FMatrixD1 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.
- elementMin
  
  public static float elementMin(FMatrixD1 a, ElementLocation loc)
  
  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.
  
  loc - (Output) Location of selected element.
  
  Returns:
  
  The value of element in the matrix with the minimum value.
- elementMinAbs
  
  public static float elementMinAbs(FMatrixD1 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.
- elementMinAbs
  
  public static float elementMinAbs(FMatrixD1 a, ElementLocation loc)
  
  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 - (Input) A matrix. Not modified.
  
  loc - (Output) Location of selected element.
  
  Returns:
  
  The max element value of the matrix.
- elementMult
  
  public static void elementMult(FMatrixD1 A, FMatrixD1 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 <T extends FMatrixD1> T elementMult(T A, T B, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- elementDiv
  
  public static void elementDiv(FMatrixD1 A, FMatrixD1 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 <T extends FMatrixD1> T elementDiv(T A, T B, @Nullable T output)
  
  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.
  
  output - Where the results of the operation are stored. Modified.
- elementSum
  
  public static float elementSum(FMatrixD1 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 float elementSumAbs(FMatrixD1 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.
- elementPower
  
  public static <T extends FMatrixD1> T elementPower(T A, T B, @Nullable T output)
  
  Element-wise power operation
  c_ij = a_ij ^ b_ij
  
  Parameters:
  
  A - left side
  
  B - right side
  
  output - output (modified)
- elementPower
  
  public static <T extends FMatrixD1> T elementPower(float a, T B, @Nullable T output)
  
  Element-wise power operation
  c_ij = a ^ b_ij
  
  Parameters:
  
  a - left scalar
  
  B - right side
  
  output - output (modified)
- elementPower
  
  public static <T extends FMatrixD1> T elementPower(T A, float b, @Nullable T output)
  
  Element-wise power operation
  c_ij = a_ij ^ b
  
  Parameters:
  
  A - left side
  
  b - right scalar
  
  output - output (modified)
- elementLog
  
  public static <T extends FMatrixD1> T elementLog(T A, @Nullable T output)
  
  Element-wise log operation
  c_ij = (float)Math.log(a_ij)
  
  Parameters:
  
  A - (input) A matrix
  
  output - (input/output) Storage for results. can be null. (modified)
  
  Returns:
  
  The results
- elementExp
  
  public static <T extends FMatrixD1> T elementExp(T A, @Nullable T output)
  
  Element-wise exp operation
  c_ij = (float)Math.exp(a_ij)
  
  Parameters:
  
  A - (input) A matrix
  
  output - (input/output) Storage for results. can be null. (modified)
  
  Returns:
  
  The results
- multRows
  
  public static void multRows(float[] values, FMatrixRMaj A)
  
  Multiplies every element in row i by value[i].
  
  Parameters:
  
  values - array. Not modified.
  
  A - Matrix. Modified.
- divideRows
  
  public static void divideRows(float[] values, FMatrixRMaj A)
  
  Divides every element in row i by value[i].
  
  Parameters:
  
  values - array. Not modified.
  
  A - Matrix. Modified.
- multCols
  
  public static void multCols(FMatrixRMaj A, float[] values)
  
  Multiplies every element in column i by value[i].
  
  Parameters:
  
  A - Matrix. Modified.
  
  values - array. Not modified.
- divideCols
  
  public static void divideCols(FMatrixRMaj A, float[] values)
  
  Divides every element in column i by value[i].
  
  Parameters:
  
  A - Matrix. Modified.
  
  values - array. Not modified.
- divideRowsCols
  
  public static void divideRowsCols(float[] diagA, int offsetA, FMatrixRMaj B, float[] diagC, int offsetC)
  
  Equivalent to multiplying a matrix B by the inverse of two diagonal matrices. B = inv(A)*B*inv(C), where A=diag(a) and C=diag(c).
  
  Parameters:
  
  diagA - Array of length offsteA + B.numRows
  
  offsetA - First index in A
  
  B - Rectangular matrix
  
  diagC - Array of length indexC + B.numCols
  
  offsetC - First index in C
- sumRows
  
  public static FMatrixRMaj sumRows(FMatrixRMaj input, @Nullable @Nullable FMatrixRMaj 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. Reshaped into a column. Modified.
  
  Returns:
  
  Vector containing the sum of each row in the input.
- minRows
  
  public static FMatrixRMaj minRows(FMatrixRMaj input, @Nullable @Nullable FMatrixRMaj output)
  
  Finds the element with the minimum value along each row in the input matrix and returns the results in a vector:
  
  b_j = min(i=1:n ; a_ji)
  
  Parameters:
  
  input - Input matrix
  
  output - Optional storage for output. Reshaped into a column. Modified.
  
  Returns:
  
  Vector containing the sum of each row in the input.
- maxRows
  
  public static FMatrixRMaj maxRows(FMatrixRMaj input, @Nullable @Nullable FMatrixRMaj output)
  
  Finds the element with the maximum value along each row in the input matrix and returns the results in a vector:
  
  b_j = max(i=1:n ; a_ji)
  
  Parameters:
  
  input - Input matrix
  
  output - Optional storage for output. Reshaped into a column. Modified.
  
  Returns:
  
  Vector containing the sum of each row in the input.
- sumCols
  
  public static FMatrixRMaj sumCols(FMatrixRMaj input, @Nullable @Nullable FMatrixRMaj 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
  
  output - Optional storage for output. Reshaped into a row vector. Modified.
  
  Returns:
  
  Vector containing the sum of each column
- minCols
  
  public static FMatrixRMaj minCols(FMatrixRMaj input, @Nullable @Nullable FMatrixRMaj output)
  
  Finds the element with the minimum value along column in the input matrix and returns the results in a vector:
  
  b_j = min(i=1:m ; a_ij)
  
  Parameters:
  
  input - Input matrix
  
  output - Optional storage for output. Reshaped into a row vector. Modified.
  
  Returns:
  
  Vector containing the minimum of each column
- maxCols
  
  public static FMatrixRMaj maxCols(FMatrixRMaj input, @Nullable @Nullable FMatrixRMaj output)
  
  Finds the element with the minimum value along column in the input matrix and returns the results in a vector:
  
  b_j = min(i=1:m ; a_ij)
  
  Parameters:
  
  input - Input matrix
  
  output - Optional storage for output. Reshaped into a row vector. Modified.
  
  Returns:
  
  Vector containing the maximum of each column
- addEquals
  
  public static void addEquals(FMatrixD1 a, FMatrixD1 b)
  
  Performs the following operation:
  
  a = a + b
  a_ij = a_ij + b_ij
  
  Parameters:
  
  a - (input/output) A Matrix. Modified.
  
  b - (input) A Matrix. Not modified.
- addEquals
  
  public static void addEquals(FMatrixD1 a, float beta, FMatrixD1 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 - (input/output) A Matrix. Modified.
  
  b - (input) A Matrix. Not modified.
- add
  
  public static <T extends FMatrixD1> T add(T a, T b, @Nullable T output)
  
  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.
  
  output - (output) A Matrix where the results are stored. Can be null. Modified.
  
  Returns:
  
  The results.
- add
  
  public static <T extends FMatrixD1> T add(T a, float beta, T b, @Nullable T output)
  
  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.
  
  output - (output) A Matrix where the results are stored. Can be null. Modified.
  
  Returns:
  
  The results.
- add
  
  public static <T extends FMatrixD1> T add(float alpha, T a, float beta, T b, @Nullable T output)
  
  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.
  
  output - (output) A Matrix where the results are stored. Can be null. Modified.
  
  Returns:
  
  The results.
- add
  
  public static <T extends FMatrixD1> T add(float alpha, T a, T b, T output)
  
  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.
  
  output - (output) A Matrix where the results are stored. Can be null. Modified.
  
  Returns:
  
  The results.
- add
  
  public static void add(FMatrixD1 a, float 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 <T extends FMatrixD1> T add(T a, float val, T output)
  
  Performs scalar addition:
  
  c = a + val
  c_ij = a_ij + val
  
  Parameters:
  
  a - A matrix. Not modified.
  
  val - The value that's added to each element.
  
  output - (output) Storage for results. Can be null. Modified.
  
  Returns:
  
  The resulting matrix
- subtract
  
  public static <T extends FMatrixD1> T subtract(T a, float val, @Nullable T output)
  
  Performs matrix scalar subtraction:
  
  c = a - val
  c_ij = a_ij - val
  
  Parameters:
  
  a - (input) A matrix. Not modified.
  
  val - (input) The value that's subtracted to each element.
  
  output - (output) Storage for results. Can be null. Modified.
  
  Returns:
  
  The resulting matrix
- subtract
  
  public static <T extends FMatrixD1> T subtract(float val, T a, @Nullable T output)
  
  Performs matrix scalar subtraction:
  
  c = val - a
  c_ij = val - a_ij
  
  Parameters:
  
  val - (input) The value that's subtracted to each element.
  
  a - (input) A matrix. Not modified.
  
  output - (output) Storage for results. Can be null. Modified.
  
  Returns:
  
  The resulting matrix
- subtractEquals
  
  public static void subtractEquals(FMatrixD1 a, FMatrixD1 b)
  
  Performs the following subtraction operation:
  
  a = a - b
  a_ij = a_ij - b_ij
  
  Parameters:
  
  a - (input) A Matrix. Modified.
  
  b - (input) A Matrix. Not modified.
- subtract
  
  public static <T extends FMatrixD1> T subtract(T a, T b, @Nullable T output)
  
  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 - (input) A Matrix. Not modified.
  
  b - (input) A Matrix. Not modified.
  
  output - (output) A Matrix. Can be null. Modified.
  
  Returns:
  
  The resulting matrix
- scale
  
  public static void scale(float alpha, FMatrixD1 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(float alpha, FMatrixD1 a, FMatrixD1 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.
- scaleRow
  
  public static void scaleRow(float alpha, FMatrixRMaj A, int row)
  
  In-place scaling of a row in A
  
  Parameters:
  
  alpha - scale factor
  
  A - matrix
  
  row - which row in A
- scaleCol
  
  public static void scaleCol(float alpha, FMatrixRMaj A, int col)
  
  In-place scaling of a column in A
  
  Parameters:
  
  alpha - scale factor
  
  A - matrix
  
  col - which row in A
- divide
  
  public static void divide(float alpha, FMatrixD1 a)
  
  Performs an in-place element by element scalar division with the scalar on top.
  
  a_ij = α/a_ij
  
  Parameters:
  
  a - (input/output) The matrix whose elements are divide the scalar. Modified.
  
  alpha - top value in division
- divide
  
  public static void divide(FMatrixD1 a, float alpha)
  
  Performs an in-place element by element scalar division with the scalar on bottom.
  
  a_ij = a_ij/α
  
  Parameters:
  
  a - (input/output) The matrix whose elements are to be divided. Modified.
  
  alpha - the amount each element is divided by.
- divide
  
  public static <T extends FMatrixD1> T divide(float alpha, T input, T output)
  
  Performs an element by element scalar division with the scalar on top.
  
  b_ij = α/a_ij
  
  Parameters:
  
  alpha - The numerator.
  
  input - The matrix whose elements are the divisor. Not modified.
  
  output - Where the results are stored. Modified. Can be null.
  
  Returns:
  
  The resulting matrix
- divide
  
  public static <T extends FMatrixD1> T divide(T input, float alpha, @Nullable T output)
  
  Performs an element by element scalar division with the scalar on botton.
  
  b_ij = a_ij /α
  
  Parameters:
  
  input - The matrix whose elements are to be divided. Not modified.
  
  alpha - the amount each element is divided by.
  
  output - Where the results are stored. Modified. Can be null.
  
  Returns:
  
  The resulting matrix
- changeSign
  
  public static void changeSign(FMatrixD1 a)
  
  Changes the sign of every element in the matrix.
  
  a_ij = -a_ij
  
  Parameters:
  
  a - A matrix. Modified.
- changeSign
  
  public static <T extends FMatrixD1> T changeSign(T input, @Nullable T output)
  
  Changes the sign of every element in the matrix.
  
  output_ij = -input_ij
  
  Parameters:
  
  input - A matrix. Modified.
- fill
  
  public static void fill(FMatrixD1 a, float 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 FMatrixRMaj rref(FMatrixRMaj A, int numUnknowns, @Nullable @Nullable FMatrixRMaj reduced)
  Puts the augmented system matrix into reduced row echelon form (RREF) using Gauss-Jordan elimination with row (partial) pivots. A matrix is said to be in RREF is the following conditions are true:
  
  If a row has non-zero entries, then the first non-zero entry is 1. This is known as the leading one.
  
  If a column contains a leading one then all other entries in that column are zero.
  
  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 A.numCols, which works for most applications.
  
  reduced - Storage for reduced echelon matrix. If null then a new matrix is returned. Modified.
  
  Returns:
  
  Reduced echelon form of A
  
  See Also:
  
  RrefGaussJordanRowPivot_FDRM
- elementLessThan
  
  public static BMatrixRMaj elementLessThan(FMatrixRMaj A, float value, @Nullable @Nullable BMatrixRMaj output)
  
  Applies the > operator to each element in A. Results are stored in a boolean matrix.
  Parameters:
  
  A - Input matrx
  
  value - value each element is compared against
  
  output - (Optional) Storage for results. Can be null. Is reshaped.
  
  Returns:
  
  Boolean matrix with results
  
  See Also:
  
  for a more generalized element wise binary operator
- elementLessThanOrEqual
  
  public static BMatrixRMaj elementLessThanOrEqual(FMatrixRMaj A, float value, @Nullable @Nullable BMatrixRMaj output)
  
  Applies the ≥ operator to each element in A. Results are stored in a boolean matrix.
  Parameters:
  
  A - Input matrix
  
  value - value each element is compared against
  
  output - (Optional) Storage for results. Can be null. Is reshaped.
  
  Returns:
  
  Boolean matrix with results
  
  See Also:
  
  for a more generalized element wise binary operator
- elementMoreThan
  
  public static BMatrixRMaj elementMoreThan(FMatrixRMaj A, float value, @Nullable @Nullable BMatrixRMaj output)
  
  Applies the > operator to each element in A. Results are stored in a boolean matrix.
  Parameters:
  
  A - Input matrix
  
  value - value each element is compared against
  
  output - (Optional) Storage for results. Can be null. Is reshaped.
  
  Returns:
  
  Boolean matrix with results
  
  See Also:
  
  for a more generalized element wise binary operator
- elementMoreThanOrEqual
  
  public static BMatrixRMaj elementMoreThanOrEqual(FMatrixRMaj A, float value, @Nullable @Nullable BMatrixRMaj output)
  
  Applies the ≥ operator to each element in A. Results are stored in a boolean matrix.
  Parameters:
  
  A - Input matrix
  
  value - value each element is compared against
  
  output - (Optional) Storage for results. Can be null. Is reshaped.
  
  Returns:
  
  Boolean matrix with results
  
  See Also:
  
  for a more generalized element wise binary operator
- elementLessThan
  
  public static BMatrixRMaj elementLessThan(FMatrixRMaj A, FMatrixRMaj B, @Nullable @Nullable BMatrixRMaj output)
  
  Applies the < operator to each element in A. Results are stored in a boolean matrix.
  Parameters:
  
  A - Input matrix
  
  B - Input matrix
  
  output - (Optional) Storage for results. Can be null. Is reshaped.
  
  Returns:
  
  Boolean matrix with results
  
  See Also:
  
  for a more generalized element wise binary operator
- elementLessThanOrEqual
  
  public static BMatrixRMaj elementLessThanOrEqual(FMatrixRMaj A, FMatrixRMaj B, @Nullable @Nullable BMatrixRMaj output)
  
  Applies the A ≤ B operator to each element. Results are stored in a boolean matrix.
  Parameters:
  
  A - Input matrix
  
  B - Input matrix
  
  output - (Optional) Storage for results. Can be null. Is reshaped.
  
  Returns:
  
  Boolean matrix with results
  
  See Also:
  
  for a more generalized element wise binary operator
- elements
  
  public static FMatrixRMaj elements(FMatrixRMaj A, BMatrixRMaj marked, @Nullable @Nullable FMatrixRMaj output)
  
  Returns a row matrix which contains all the elements in A which are flagged as true in 'marked'
  
  Parameters:
  
  A - Input matrix
  
  marked - Input matrix marking elements in A
  
  output - Storage for output row vector. Can be null. Will be reshaped.
  
  Returns:
  
  Row vector with marked elements
- countTrue
  
  public static int countTrue(BMatrixRMaj A)
  
  Counts the number of elements in A which are true
  
  Parameters:
  
  A - input matrix
  
  Returns:
  
  number of true elements
- concatColumns
  
  public static FMatrixRMaj concatColumns(FMatrixRMaj a, FMatrixRMaj b, @Nullable @Nullable FMatrixRMaj output)
  
  output = [a , b]
- concatColumnsMulti
  
  public static FMatrixRMaj concatColumnsMulti(FMatrixRMaj... m)
  
  Concatenates all the matrices together along their columns. If the rows do not match the upper elements are set to zero.
  A = [ m[0] , ... , m[n-1] ]
  
  Parameters:
  
  m - Set of matrices
  
  Returns:
  
  Resulting matrix
- concatRows
  
  public static void concatRows(FMatrixRMaj a, FMatrixRMaj b, FMatrixRMaj output)
  
  output = [a ; b]
- concatRowsMulti
  
  public static FMatrixRMaj concatRowsMulti(FMatrixRMaj... m)
  
  Concatenates all the matrices together along their columns. If the rows do not match the upper elements are set to zero.
  A = [ m[0] ; ... ; m[n-1] ]
  
  Parameters:
  
  m - Set of matrices
  
  Returns:
  
  Resulting matrix
- permuteRowInv
  
  public static FMatrixRMaj permuteRowInv(int[] pinv, FMatrixRMaj input, FMatrixRMaj output)
  
  Applies the row permutation specified by the vector to the input matrix and save the results in the output matrix. output[perm[j],:] = input[j,:]
  
  Parameters:
  
  pinv - (Input) Inverse permutation vector. Specifies new order of the rows.
  
  input - (Input) Matrix which is to be permuted
  
  output - (Output) Matrix which has the permutation stored in it. Is reshaped.
- abs
  
  public static void abs(FMatrixD1 a, FMatrixD1 c)
  
  Performs absolute value of a matrix:
  
  c = abs(a)
  c_ij = abs(a_ij)
  
  Parameters:
  
  a - A matrix. Not modified.
  
  c - A matrix. Modified.
- abs
  
  public static void abs(FMatrixD1 a)
  
  Performs absolute value of a matrix:
  
  a = abs(a)
  a_ij = abs(a_ij)
  
  Parameters:
  
  a - A matrix. Modified.
- symmLowerToFull
  
  public static void symmLowerToFull(FMatrixRMaj A)
  
  Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.
  
  Parameters:
  
  A - (Input) Lower triangular matrix (Output) symmetric matrix
- symmUpperToFull
  
  public static void symmUpperToFull(FMatrixRMaj A)
  
  Given a symmetric matrix which is represented by a lower triangular matrix convert it back into a full symmetric matrix.
  
  Parameters:
  
  A - (Input) Lower triangular matrix (Output) symmetric matrix
- apply
  
  public static FMatrixRMaj apply(FMatrixRMaj input, FOperatorUnary func, @Nullable @Nullable FMatrixRMaj output)
  This applies a given unary function on every value stored in the matrix
  output[i,j] = func(input[i,j])
  A and B can be the same instance.
  Parameters:
  
  input - (Input) input matrix. Not modified
  
  func - Unary function accepting a float
  
  output - (Output) Matrix. Can be same instance as A. Modified.
  
  Returns:
  
  The output matrix
- apply
  
  public static FMatrixRMaj apply(FMatrixRMaj input, FOperatorUnary func)
- elementBoolean
  
  public static BMatrixRMaj elementBoolean(FMatrixRMaj input, DElementCoorBoolean func, @Nullable @Nullable BMatrixRMaj output)
  Applies a binary operator to even element in the input matrix. In the lambda, the coordinate (row, col), and the value at that element is provided. This is designed to enable arbitrary operations.
  For example, to apply an arbitrary boolean operatorto elements between two matrices, you can do the following:
  BMatrixRMaj found = CommonOps_FDRM.elementBoolean(A, ( row, col, value ) -> B.get(row, col) < value, null);
  Parameters:
  
  input - Input matrix
  
  func - Element wise function that outputs a boolean value
  
  output - (Optional) Output matrix.
  
  Returns:
  
  Resulting binary matrix

Class CommonOps_FDRM

Method Summary

Methods inherited from class java.lang.Object

Method Details

mult

mult

multTransA

multTransA

multTransB

multTransB

multTransAB

multTransAB

dot

multInner

multOuter

multAdd

multAdd

multAddTransA

multAddTransA

multAddTransB

multAddTransB

multAddTransAB

multAddTransAB

solve

solveSPD

transpose

transpose

trace

det

invert

invert

invertSPD

pinv

columnsToVector

rowsToVector

setIdentity

identity

identity

diag

diag

diagR

kron

extract

extract

extract

extract

extract

extract

insert

extractDiag

extractRow

extractColumn

removeColumns

insert

elementMax

elementMax

elementMaxAbs

elementMaxAbs

elementMin

elementMin

elementMinAbs

elementMinAbs

elementMult

elementMult

elementDiv

elementDiv

elementSum

elementSumAbs

elementPower

elementPower

elementPower

elementLog

elementExp

multRows

divideRows

multCols

divideCols

divideRowsCols

sumRows

minRows