VMath (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

java.lang.Object
- de.lmu.ifi.dbs.elki.math.linearalgebra.VMath

```
public final class VMath
extends Object
```
Class providing basic vector mathematics, for low-level vectors stored as double[]. While this is less nice syntactically, it reduces memory usage and VM overhead.

Field Summary

Fields
Modifier and Type	Field and Description
`static double`	`DELTA` A small number to handle numbers near 0 as 0.
`private static String`	`ERR_DIMENSIONS` Error message (in assertions!)
`static String`	`ERR_MATRIX_DIMENSIONS` Error message (in assertions!)
`static String`	`ERR_MATRIX_INNERDIM` Error message (in assertions!)
`static String`	`ERR_VEC_DIMENSIONS` Error message (in assertions!)

Constructor Summary

Constructors
Modifier Constructor and Description

private VMath()
Fake constructor.

Constructors
Modifier	Constructor and Description
`private`	`VMath()` Fake constructor.

Method Summary

Methods
Modifier and Type	Method and Description
`static boolean`	`almostEquals(double[][] m1, double[][] m2)` Compare two matrices with a delta parameter to take numerical errors into account.
`static boolean`	`almostEquals(double[][] m1, double[][] m2, double maxdelta)` Compare two matrices with a delta parameter to take numerical errors into account.
`static double[][]`	`appendColumns(double[][] m1, double[][] m2)` Returns a matrix which consists of this matrix and the specified columns.
`static void`	`clear(double[] v1)` Reset the Vector to 0.
`static double[]`	`columnPackedCopy(double[][] m1)` Make a one-dimensional column packed copy of the internal array.
`static double[]`	`copy(double[] v)` Returns a copy of this vector.
`static double[][]`	`copy(double[][] m1)` Make a deep copy of a matrix.
`static void`	`cross3D(double[] vo, double[] v1, double[] v2)` Cross product for 3d vectors, i.e.
`static double[][]`	`diagonal(double[] v1)` Returns a quadratic Matrix consisting of zeros and of the given values on the diagonal.
`static boolean`	`equals(double[][] m1, double[][] m2)` Test for equality
`static boolean`	`equals(double[] v1, double[] v2)` Compare for equality.
`static double`	`euclideanLength(double[] v1)` Euclidean length of the vector
`static double[]`	`getCol(double[][] m1, int col)` Get a column from a matrix as vector.
`static int`	`getColumnDimensionality(double[][] m1)` Returns the dimensionality of the columns of this matrix.
`static double[]`	`getDiagonal(double[][] m1)` getDiagonal returns array of diagonal-elements.
`static double[][]`	`getMatrix(double[][] m1, int[] r, int[] c)` Get a submatrix.
`static double[][]`	`getMatrix(double[][] m1, int[] r, int c0, int c1)` Get a submatrix.
`static double[][]`	`getMatrix(double[][] m1, int r0, int r1, int[] c)` Get a submatrix.
`static double[][]`	`getMatrix(double[][] m1, int r0, int r1, int c0, int c1)` Get a submatrix.
`static double[]`	`getRow(double[][] m1, int r)` Returns the `r`th row of this matrix as vector.
`static int`	`getRowDimensionality(double[][] m1)` Returns the dimensionality of the rows of this matrix.
`static int`	`hashCode(double[] v1)` Compute the hash code for the vector
`static int`	`hashCode(double[][] m1)` Compute hash code
`static double[][]`	`identity(int m, int n)` Generate identity matrix
`static double[][]`	`minus(double[][] m1, double[][] m2)` m3 = m1 - m2
`static double[]`	`minus(double[] v1, double d)` Compute v1 - d
`static double[]`	`minus(double[] v1, double[] v2)` Computes v1 - v2
`static double[][]`	`minusEquals(double[][] m1, double[][] m2)` m1 = m1 - m2, overwriting m1
`static double[]`	`minusEquals(double[] v1, double d)` Computes v1 = v1 - d, overwriting v1
`static double[]`	`minusEquals(double[] v1, double[] v2)` Computes v1 = v1 - v2, overwriting v1
`static double[][]`	`minusTimes(double[][] m1, double[][] m2, double s2)` m3 = m1 - s2 * m2
`static double[]`	`minusTimes(double[] v1, double[] v2, double s2)` Computes v1 - v2 * s2
`static double[][]`	`minusTimesEquals(double[][] m1, double[][] m2, double s2)` m1 = m1 - s2 * m2, overwriting m1
`static double[]`	`minusTimesEquals(double[] v1, double[] v2, double s2)` Computes v1 = v1 - v2 * s2, overwriting v1
`static double[]`	`normalize(double[] v1)` Normalizes v1 to the length of 1.0.
`static void`	`normalizeColumns(double[][] m1)` Normalizes the columns of this matrix to length of 1.0.
`static double[]`	`normalizeEquals(double[] v1)` Normalizes v1 to the length of 1.0.
`static double[][]`	`orthonormalize(double[][] m1)` Returns an orthonormalization of this matrix.
`static double[][]`	`plus(double[][] m1, double[][] m2)` m3 = m1 + m2
`static double[]`	`plus(double[] v1, double d)` Computes v1 + d
`static double[]`	`plus(double[] v1, double[] v2)` Computes v1 + v2 for vectors.
`static double[][]`	`plusEquals(double[][] m1, double[][] m2)` m1 = m1 + m2, overwriting m1
`static double[]`	`plusEquals(double[] v1, double d)` Computes v1 = v1 + d, overwriting v1
`static double[]`	`plusEquals(double[] v1, double[] v2)` Computes v1 = v1 + v2, overwriting v1
`static double[][]`	`plusTimes(double[][] m1, double[][] m2, double s2)` m3 = m1 + s2 * m2
`static double[]`	`plusTimes(double[] v1, double[] v2, double s2)` Computes v1 + v2 * s2
`static double[][]`	`plusTimesEquals(double[][] m1, double[][] m2, double s2)` m1 = m1 + s2 * m2, overwriting m1
`static double[]`	`plusTimesEquals(double[] v1, double[] v2, double s2)` Computes v1 = v1 + v2 * s2, overwriting v1
`static double[]`	`project(double[] v1, double[][] m2)` Projects this row vector into the subspace formed by the specified matrix v.
`static double[][]`	`random(int m, int n)` Generate matrix with random elements
`static double[]`	`randomNormalizedVector(int dimensionality)` Returns a randomly created vector of length 1.0
`static double[]`	`rotate90Equals(double[] v1)` Rotate vector by 90 degrees.
`static double[]`	`rowPackedCopy(double[][] m1)` Make a one-dimensional row packed copy of the internal array.
`static double`	`scalarProduct(double[] v1, double[] v2)` Returns the scalar product (dot product) of this vector and the specified vector v.
`static void`	`setCol(double[][] m1, int c, double[] column)` Sets the `c`th column of this matrix to the specified column.
`static void`	`setMatrix(double[][] m1, int[] r, int[] c, double[][] m2)` Set a submatrix.
`static void`	`setMatrix(double[][] m1, int[] r, int c0, int c1, double[][] m2)` Set a submatrix.
`static void`	`setMatrix(double[][] m1, int r0, int r1, int[] c, double[][] m2)` Set a submatrix.
`static void`	`setMatrix(double[][] m1, int r0, int r1, int c0, int c1, double[][] m2)` Set a submatrix.
`static void`	`setRow(double[][] m1, int r, double[] row)` Sets the `r`th row of this matrix to the specified vector.
`static double[][]`	`times(double[][] m1, double s1)` Multiply a matrix by a scalar, m3 = s1*m1
`static double[]`	`times(double[][] m1, double[] v2)` Linear algebraic matrix multiplication, m1 * v2
`static double[][]`	`times(double[][] m1, double[][] m2)` Linear algebraic matrix multiplication, m1 * m2
`static double[]`	`times(double[] v1, double s1)` Computes v1 * s1
`static double[][]`	`times(double[] v1, double[][] m2)` Matrix multiplication: v1 * m2
`static double[][]`	`timesEquals(double[][] m1, double s1)` Multiply a matrix by a scalar in place, m1 = s1 * m1
`static double[]`	`timesEquals(double[] v1, double s)` Computes v1 = v1 * s1, overwritings v1
`static double[]`	`timesMinus(double[] v1, double s1, double[] v2)` Computes v1 * s1 - v2
`static double[]`	`timesMinusEquals(double[] v1, double s1, double[] v2)` Computes v1 = v1 * s1 - v2, overwriting v1
`static double[]`	`timesMinusTimes(double[] v1, double s1, double[] v2, double s2)` Computes v1 * s1 - v2 * s2
`static double[]`	`timesMinusTimesEquals(double[] v1, double s1, double[] v2, double s2)` Computes v1 = v1 * s1 - v2 * s2, overwriting v1
`static double[]`	`timesPlus(double[] v1, double s1, double[] v2)` Computes v1 * s1 + v2
`static double[]`	`timesPlusEquals(double[] v1, double s1, double[] v2)` Computes v1 = v1 * s1 + v2, overwriting v1
`static double[]`	`timesPlusTimes(double[] v1, double s1, double[] v2, double s2)` Computes v1 * s1 + v2 * s2
`static double[]`	`timesPlusTimesEquals(double[] v1, double s1, double[] v2, double s2)` Computes v1 = v1 * s1 + v2 * s2, overwriting v1
`static double[][]`	`timesTranspose(double[][] m1, double[][] m2)` Linear algebraic matrix multiplication, m1 * m2^T
`static double[][]`	`timesTranspose(double[] v1, double[] v2)` Linear algebraic matrix multiplication, v1 * v2^T
`static double[][]`	`timesTranspose(double[] v1, double[][] m2)` Linear algebraic matrix multiplication, v1 * m2^T
`static double[][]`	`transpose(double[] v)` Transpose vector to a matrix.
`static double[][]`	`transpose(double[][] m1)` Matrix transpose
`static double[]`	`transposeTimes(double[][] m1, double[] v2)` Linear algebraic matrix multiplication, m1^T * v2
`static double[][]`	`transposeTimes(double[][] m1, double[][] m2)` Linear algebraic matrix multiplication, m1^T * m2
`static double`	`transposeTimes(double[] v1, double[] v2)` Linear algebraic matrix multiplication, v1^T * v2
`static double[][]`	`transposeTimes(double[] v1, double[][] m2)` Linear algebraic matrix multiplication, v1^T * m2
`static double`	`transposeTimesTimes(double[] a, double[][] B, double[] c)` Linear algebraic matrix multiplication, a^T * B * c
`static double[][]`	`transposeTimesTranspose(double[][] m1, double[][] m2)` Linear algebraic matrix multiplication, m1^T * m2^T.
`static double[][]`	`unitMatrix(int dim)` Returns the unit matrix of the specified dimension.
`static double[]`	`unitVector(int dimensionality, int i)` Returns the ith unit vector of the specified dimensionality.
`static double[][]`	`zeroMatrix(int dim)` Returns the zero matrix of the specified dimension.

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

- Field Detail
  - DELTA
```
public static final double DELTA
```
    A small number to handle numbers near 0 as 0.
    
    See Also:
    Constant Field Values
  - ERR_VEC_DIMENSIONS
```
public static final String ERR_VEC_DIMENSIONS
```
    Error message (in assertions!) when vector dimensionalities do not agree.
    
    See Also:
    Constant Field Values
  - ERR_MATRIX_DIMENSIONS
```
public static final String ERR_MATRIX_DIMENSIONS
```
    Error message (in assertions!) when matrix dimensionalities do not agree.
    
    See Also:
    Constant Field Values
  - ERR_MATRIX_INNERDIM
```
public static final String ERR_MATRIX_INNERDIM
```
    Error message (in assertions!) when matrix dimensionalities do not agree.
    
    See Also:
    Constant Field Values
  - ERR_DIMENSIONS
```
private static final String ERR_DIMENSIONS
```
    Error message (in assertions!) when dimensionalities do not agree.
    
    See Also:
    Constant Field Values
- Constructor Detail
  - VMath
```
private VMath()
```
    Fake constructor. Static class.
- Method Detail
  - randomNormalizedVector
```
public static final double[] randomNormalizedVector(int dimensionality)
```
    Returns a randomly created vector of length 1.0
    
    Parameters:
    dimensionality - dimensionality
    
    Returns:
    Random vector of length 1.0
  - unitVector
```
public static final double[] unitVector(int dimensionality,
                  int i)
```
    Returns the ith unit vector of the specified dimensionality.
    
    Parameters:
    dimensionality - the dimensionality of the vector
    i - the index
    
    Returns:
    the ith unit vector of the specified dimensionality
  - copy
```
public static final double[] copy(double[] v)
```
    Returns a copy of this vector.
    
    Parameters:
    v - original vector
    
    Returns:
    a copy of this vector
  - transpose
```
public static final double[][] transpose(double[] v)
```
    Transpose vector to a matrix.
    
    Parameters:
    v - Vector
    
    Returns:
    Matrix
  - plus
```
public static final double[] plus(double[] v1,
            double[] v2)
```
    Computes v1 + v2 for vectors.
    
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    the sum v1 + v2
  - plusTimes
```
public static final double[] plusTimes(double[] v1,
                 double[] v2,
                 double s2)
```
    Computes v1 + v2 * s2
    
    Parameters:
    v1 - first vector
    v2 - second vector
    s2 - the scalar
    
    Returns:
    the result of v1 + v2 * s2
  - timesPlus
```
public static final double[] timesPlus(double[] v1,
                 double s1,
                 double[] v2)
```
    Computes v1 * s1 + v2
    
    Parameters:
    v1 - first vector
    s1 - the scalar for v1
    v2 - second vector
    
    Returns:
    the result of v1 * s1 + v2
  - timesPlusTimes
```
public static final double[] timesPlusTimes(double[] v1,
                      double s1,
                      double[] v2,
                      double s2)
```
    Computes v1 * s1 + v2 * s2
    
    Parameters:
    v1 - first vector
    s1 - the scalar for v1
    v2 - second vector
    s2 - the scalar for v2
    
    Returns:
    the result of v1 * s1 + v2 * s2
  - plusEquals
```
public static final double[] plusEquals(double[] v1,
                  double[] v2)
```
    Computes v1 = v1 + v2, overwriting v1
    
    Parameters:
    v1 - first vector (overwritten)
    v2 - second vector
    
    Returns:
    v1 = v1 + v2
  - plusTimesEquals
```
public static final double[] plusTimesEquals(double[] v1,
                       double[] v2,
                       double s2)
```
    Computes v1 = v1 + v2 * s2, overwriting v1
    
    Parameters:
    v1 - first vector
    v2 - another vector
    s2 - scalar vor v2
    
    Returns:
    v1 = v1 + v2 * s2
  - timesPlusEquals
```
public static final double[] timesPlusEquals(double[] v1,
                       double s1,
                       double[] v2)
```
    Computes v1 = v1 * s1 + v2, overwriting v1
    
    Parameters:
    v1 - first vector
    s1 - scalar for v1
    v2 - another vector
    
    Returns:
    v1 = v1 * s1 + v2
  - timesPlusTimesEquals
```
public static final double[] timesPlusTimesEquals(double[] v1,
                            double s1,
                            double[] v2,
                            double s2)
```
    Computes v1 = v1 * s1 + v2 * s2, overwriting v1
    
    Parameters:
    v1 - first vector
    s1 - scalar for v1
    v2 - another vector
    s2 - scalar for v2
    
    Returns:
    v1 = v1 * s1 + v2 * s2
  - plus
```
public static final double[] plus(double[] v1,
            double d)
```
    Computes v1 + d
    
    Parameters:
    v1 - vector to add to
    d - value to add
    
    Returns:
    v1 + d
  - plusEquals
```
public static final double[] plusEquals(double[] v1,
                  double d)
```
    Computes v1 = v1 + d, overwriting v1
    
    Parameters:
    v1 - vector to add to
    d - value to add
    
    Returns:
    Modified vector
  - minus
```
public static final double[] minus(double[] v1,
             double[] v2)
```
    Computes v1 - v2
    
    Parameters:
    v1 - first vector
    v2 - the vector to be subtracted from this vector
    
    Returns:
    v1 - v2
  - minusTimes
```
public static final double[] minusTimes(double[] v1,
                  double[] v2,
                  double s2)
```
    Computes v1 - v2 * s2
    
    Parameters:
    v1 - first vector
    v2 - the vector to be subtracted from this vector
    s2 - the scaling factor for v2
    
    Returns:
    v1 - v2 * s2
  - timesMinus
```
public static final double[] timesMinus(double[] v1,
                  double s1,
                  double[] v2)
```
    Computes v1 * s1 - v2
    
    Parameters:
    v1 - first vector
    s1 - the scaling factor for v1
    v2 - the vector to be subtracted from this vector
    
    Returns:
    v1 * s1 - v2
  - timesMinusTimes
```
public static final double[] timesMinusTimes(double[] v1,
                       double s1,
                       double[] v2,
                       double s2)
```
    Computes v1 * s1 - v2 * s2
    
    Parameters:
    v1 - first vector
    s1 - the scaling factor for v1
    v2 - the vector to be subtracted from this vector
    s2 - the scaling factor for v2
    
    Returns:
    v1 * s1 - v2 * s2
  - minusEquals
```
public static final double[] minusEquals(double[] v1,
                   double[] v2)
```
    Computes v1 = v1 - v2, overwriting v1
    
    Parameters:
    v1 - vector
    v2 - another vector
    
    Returns:
    v1 = v1 - v2
  - minusTimesEquals
```
public static final double[] minusTimesEquals(double[] v1,
                        double[] v2,
                        double s2)
```
    Computes v1 = v1 - v2 * s2, overwriting v1
    
    Parameters:
    v1 - vector
    v2 - another vector
    s2 - scalar for v2
    
    Returns:
    v1 = v1 - v2 * s2
  - timesMinusEquals
```
public static final double[] timesMinusEquals(double[] v1,
                        double s1,
                        double[] v2)
```
    Computes v1 = v1 * s1 - v2, overwriting v1
    
    Parameters:
    v1 - vector
    s1 - scalar for v1
    v2 - another vector
    
    Returns:
    v1 = v1 * s1 - v2
  - timesMinusTimesEquals
```
public static final double[] timesMinusTimesEquals(double[] v1,
                             double s1,
                             double[] v2,
                             double s2)
```
    Computes v1 = v1 * s1 - v2 * s2, overwriting v1
    
    Parameters:
    v1 - vector
    s1 - scalar for v1
    v2 - another vector
    s2 - Scalar
    
    Returns:
    v1 = v1 * s1 - v2 * s2
  - minus
```
public static final double[] minus(double[] v1,
             double d)
```
    Compute v1 - d
    
    Parameters:
    v1 - original vector
    d - Value to subtract
    
    Returns:
    v1 - d
  - minusEquals
```
public static final double[] minusEquals(double[] v1,
                   double d)
```
    Computes v1 = v1 - d, overwriting v1
    
    Parameters:
    v1 - original vector
    d - Value to subtract
    
    Returns:
    v1 = v1 - d
  - times
```
public static final double[] times(double[] v1,
             double s1)
```
    Computes v1 * s1
    
    Parameters:
    v1 - original vector
    s1 - the scalar to be multiplied
    
    Returns:
    v1 * s1
  - timesEquals
```
public static final double[] timesEquals(double[] v1,
                   double s)
```
    Computes v1 = v1 * s1, overwritings v1
    
    Parameters:
    v1 - original vector
    s - scalar
    
    Returns:
    v1 = v1 * s1
  - times
```
public static final double[][] times(double[] v1,
               double[][] m2)
```
    Matrix multiplication: v1 * m2
    
    Parameters:
    v1 - vector
    m2 - other matrix
    
    Returns:
    Matrix product, v1 * m2
  - transposeTimes
```
public static final double[][] transposeTimes(double[] v1,
                        double[][] m2)
```
    Linear algebraic matrix multiplication, v1^T * m2
    
    Parameters:
    v1 - vector
    m2 - other matrix
    
    Returns:
    Matrix product, v1^T * m2
  - transposeTimes
```
public static final double transposeTimes(double[] v1,
                    double[] v2)
```
    Linear algebraic matrix multiplication, v1^T * v2
    
    Parameters:
    v1 - vector
    v2 - other vector
    
    Returns:
    Matrix product, v1^T * v2
  - timesTranspose
```
public static final double[][] timesTranspose(double[] v1,
                        double[][] m2)
```
    Linear algebraic matrix multiplication, v1 * m2^T
    
    Parameters:
    v1 - vector
    m2 - other matrix
    
    Returns:
    Matrix product, v1 * m2^T
  - timesTranspose
```
public static final double[][] timesTranspose(double[] v1,
                        double[] v2)
```
    Linear algebraic matrix multiplication, v1 * v2^T
    
    Parameters:
    v1 - vector
    v2 - other vector
    
    Returns:
    Matrix product, v1 * v2^T
  - scalarProduct
```
public static final double scalarProduct(double[] v1,
                   double[] v2)
```
    Returns the scalar product (dot product) of this vector and the specified vector v. This is the same as transposeTimes.
    
    Parameters:
    v1 - vector
    v2 - other vector
    
    Returns:
    double the scalar product of vectors v1 and v2
  - euclideanLength
```
public static final double euclideanLength(double[] v1)
```
    Euclidean length of the vector
    
    Parameters:
    v1 - vector
    
    Returns:
    euclidean length of this vector
  - normalize
```
public static final double[] normalize(double[] v1)
```
    Normalizes v1 to the length of 1.0.
    
    Parameters:
    v1 - vector
    
    Returns:
    normalized copy of v1
  - normalizeEquals
```
public static final double[] normalizeEquals(double[] v1)
```
    Normalizes v1 to the length of 1.0.
    
    Parameters:
    v1 - vector
    
    Returns:
    normalized v1
  - project
```
public static final double[] project(double[] v1,
               double[][] m2)
```
    Projects this row vector into the subspace formed by the specified matrix v.
    
    Parameters:
    m2 - the subspace matrix
    
    Returns:
    the projection of p into the subspace formed by v
  - hashCode
```
public static final int hashCode(double[] v1)
```
    Compute the hash code for the vector
    
    Parameters:
    v1 - elements
    
    Returns:
    hash code
  - equals
```
public static final boolean equals(double[] v1,
             double[] v2)
```
    Compare for equality.
    
    Parameters:
    v1 - first vector
    v2 - second vector
    
    Returns:
    comparison result
  - clear
```
public static final void clear(double[] v1)
```
    Reset the Vector to 0.
    
    Parameters:
    v1 - vector
  - rotate90Equals
```
public static final double[] rotate90Equals(double[] v1)
```
    Rotate vector by 90 degrees.
    
    Parameters:
    v1 - first vector
    
    Returns:
    modified v1, rotated by 90 degrees
  - unitMatrix
```
public static final double[][] unitMatrix(int dim)
```
    Returns the unit matrix of the specified dimension.
    
    Parameters:
    dim - the dimensionality of the unit matrix
    
    Returns:
    the unit matrix of the specified dimension
  - zeroMatrix
```
public static final double[][] zeroMatrix(int dim)
```
    Returns the zero matrix of the specified dimension.
    
    Parameters:
    dim - the dimensionality of the unit matrix
    
    Returns:
    the zero matrix of the specified dimension
  - random
```
public static final double[][] random(int m,
                int n)
```
    Generate matrix with random elements
    
    Parameters:
    m - Number of rows.
    n - Number of columns.
    
    Returns:
    An m-by-n matrix with uniformly distributed random elements.
  - identity
```
public static final double[][] identity(int m,
                  int n)
```
    Generate identity matrix
    
    Parameters:
    m - Number of rows.
    n - Number of columns.
    
    Returns:
    An m-by-n matrix with ones on the diagonal and zeros elsewhere.
  - diagonal
```
public static final double[][] diagonal(double[] v1)
```
    Returns a quadratic Matrix consisting of zeros and of the given values on the diagonal.
    
    Parameters:
    v1 - the values on the diagonal
    
    Returns:
    the resulting matrix
  - copy
```
public static final double[][] copy(double[][] m1)
```
    Make a deep copy of a matrix.
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    a new matrix containing the same values as this matrix
  - rowPackedCopy
```
public static final double[] rowPackedCopy(double[][] m1)
```
    Make a one-dimensional row packed copy of the internal array.
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    Matrix elements packed in a one-dimensional array by rows.
  - columnPackedCopy
```
public static final double[] columnPackedCopy(double[][] m1)
```
    Make a one-dimensional column packed copy of the internal array.
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    Matrix elements packed in a one-dimensional array by columns.
  - getMatrix
```
public static final double[][] getMatrix(double[][] m1,
                   int r0,
                   int r1,
                   int c0,
                   int c1)
```
    Get a submatrix.
    
    Parameters:
    m1 - Input matrix
    r0 - Initial row index
    r1 - Final row index
    c0 - Initial column index
    c1 - Final column index
    
    Returns:
    m1(r0:r1,c0:c1)
  - getMatrix
```
public static final double[][] getMatrix(double[][] m1,
                   int[] r,
                   int[] c)
```
    Get a submatrix.
    
    Parameters:
    m1 - Input matrix
    r - Array of row indices.
    c - Array of column indices.
    
    Returns:
    m1(r(:),c(:))
  - getMatrix
```
public static final double[][] getMatrix(double[][] m1,
                   int[] r,
                   int c0,
                   int c1)
```
    Get a submatrix.
    
    Parameters:
    m1 - Input matrix
    r - Array of row indices.
    c0 - Initial column index
    c1 - Final column index
    
    Returns:
    m1(r(:),c0:c1)
  - getMatrix
```
public static final double[][] getMatrix(double[][] m1,
                   int r0,
                   int r1,
                   int[] c)
```
    Get a submatrix.
    
    Parameters:
    m1 - Input matrix
    r0 - Initial row index
    r1 - Final row index
    c - Array of column indices.
    
    Returns:
    m1(r0:r1,c(:))
  - setMatrix
```
public static final void setMatrix(double[][] m1,
             int r0,
             int r1,
             int c0,
             int c1,
             double[][] m2)
```
    Set a submatrix.
    
    Parameters:
    m1 - Original matrix
    r0 - Initial row index
    r1 - Final row index
    c0 - Initial column index
    c1 - Final column index
    m2 - New values for m1(r0:r1,c0:c1)
  - setMatrix
```
public static final void setMatrix(double[][] m1,
             int[] r,
             int[] c,
             double[][] m2)
```
    Set a submatrix.
    
    Parameters:
    m1 - Original matrix
    r - Array of row indices.
    c - Array of column indices.
    m2 - New values for m1(r(:),c(:))
  - setMatrix
```
public static final void setMatrix(double[][] m1,
             int[] r,
             int c0,
             int c1,
             double[][] m2)
```
    Set a submatrix.
    
    Parameters:
    m1 - Input matrix
    r - Array of row indices.
    c0 - Initial column index
    c1 - Final column index
    m2 - New values for m1(r(:),c0:c1)
  - setMatrix
```
public static final void setMatrix(double[][] m1,
             int r0,
             int r1,
             int[] c,
             double[][] m2)
```
    Set a submatrix.
    
    Parameters:
    m1 - Input matrix
    r0 - Initial row index
    r1 - Final row index
    c - Array of column indices.
    m2 - New values for m1(r0:r1,c(:))
  - getRow
```
public static final double[] getRow(double[][] m1,
              int r)
```
    Returns the rth row of this matrix as vector.
    
    Parameters:
    m1 - Input matrix
    r - the index of the row to be returned
    
    Returns:
    the rth row of this matrix
  - setRow
```
public static final void setRow(double[][] m1,
          int r,
          double[] row)
```
    Sets the rth row of this matrix to the specified vector.
    
    Parameters:
    m1 - Original matrix
    r - the index of the column to be set
    row - the value of the column to be set
  - getCol
```
public static final double[] getCol(double[][] m1,
              int col)
```
    Get a column from a matrix as vector.
    
    Parameters:
    m1 - Matrix to extract the column from
    col - Column number
    
    Returns:
    Column
  - setCol
```
public static final void setCol(double[][] m1,
          int c,
          double[] column)
```
    Sets the cth column of this matrix to the specified column.
    
    Parameters:
    m1 - Input matrix
    c - the index of the column to be set
    column - the value of the column to be set
  - transpose
```
public static final double[][] transpose(double[][] m1)
```
    Matrix transpose
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    m1^T as copy
  - plus
```
public static final double[][] plus(double[][] m1,
              double[][] m2)
```
    m3 = m1 + m2
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    
    Returns:
    m1 + m1 in a new Matrix
  - plusTimes
```
public static final double[][] plusTimes(double[][] m1,
                   double[][] m2,
                   double s2)
```
    m3 = m1 + s2 * m2
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    s2 - scalar
    
    Returns:
    m1 + s2 * m2 in a new Matrix
  - plusEquals
```
public static final double[][] plusEquals(double[][] m1,
                    double[][] m2)
```
    m1 = m1 + m2, overwriting m1
    
    Parameters:
    m1 - input matrix
    m2 - another matrix
    
    Returns:
    m1 = m1 + m2
  - plusTimesEquals
```
public static final double[][] plusTimesEquals(double[][] m1,
                         double[][] m2,
                         double s2)
```
    m1 = m1 + s2 * m2, overwriting m1
    
    Parameters:
    m1 - input matrix
    m2 - another matrix
    s2 - scalar for s2
    
    Returns:
    m1 = m1 + s2 * m2, overwriting m1
  - minus
```
public static final double[][] minus(double[][] m1,
               double[][] m2)
```
    m3 = m1 - m2
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    
    Returns:
    m1 - m2 in a new matrix
  - minusTimes
```
public static final double[][] minusTimes(double[][] m1,
                    double[][] m2,
                    double s2)
```
    m3 = m1 - s2 * m2
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    s2 - Scalar
    
    Returns:
    m1 - s2 * m2 in a new Matrix
  - minusEquals
```
public static final double[][] minusEquals(double[][] m1,
                     double[][] m2)
```
    m1 = m1 - m2, overwriting m1
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    
    Returns:
    m1 - m2, overwriting m1
  - minusTimesEquals
```
public static final double[][] minusTimesEquals(double[][] m1,
                          double[][] m2,
                          double s2)
```
    m1 = m1 - s2 * m2, overwriting m1
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    s2 - Scalar
    
    Returns:
    m1 = m1 - s2 * m2, overwriting m1
  - times
```
public static final double[][] times(double[][] m1,
               double s1)
```
    Multiply a matrix by a scalar, m3 = s1*m1
    
    Parameters:
    m1 - Input matrix
    s1 - scalar
    
    Returns:
    s1*m1, in a new matrix
  - timesEquals
```
public static final double[][] timesEquals(double[][] m1,
                     double s1)
```
    Multiply a matrix by a scalar in place, m1 = s1 * m1
    
    Parameters:
    m1 - Input matrix
    s1 - scalar
    
    Returns:
    m1 = s1 * m1, overwriting m1
  - times
```
public static final double[][] times(double[][] m1,
               double[][] m2)
```
    Linear algebraic matrix multiplication, m1 * m2
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    
    Returns:
    Matrix product, m1 * m2
  - times
```
public static final double[] times(double[][] m1,
             double[] v2)
```
    Linear algebraic matrix multiplication, m1 * v2
    
    Parameters:
    m1 - Input matrix
    v2 - a vector
    
    Returns:
    Matrix product, m1 * v2
  - transposeTimes
```
public static final double[] transposeTimes(double[][] m1,
                      double[] v2)
```
    Linear algebraic matrix multiplication, m1^T * v2
    
    Parameters:
    m1 - Input matrix
    v2 - another matrix
    
    Returns:
    Matrix product, m1^T * v2
  - transposeTimes
```
public static final double[][] transposeTimes(double[][] m1,
                        double[][] m2)
```
    Linear algebraic matrix multiplication, m1^T * m2
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    
    Returns:
    Matrix product, m1^T * m2
  - transposeTimesTimes
```
public static double transposeTimesTimes(double[] a,
                         double[][] B,
                         double[] c)
```
    Linear algebraic matrix multiplication, a^T * B * c
    
    Parameters:
    B - matrix
    c - vector on the right
    
    Returns:
    Matrix product, a^T * B * c
  - timesTranspose
```
public static final double[][] timesTranspose(double[][] m1,
                        double[][] m2)
```
    Linear algebraic matrix multiplication, m1 * m2^T
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    
    Returns:
    Matrix product, m1 * m2^T
  - transposeTimesTranspose
```
public static final double[][] transposeTimesTranspose(double[][] m1,
                                 double[][] m2)
```
    Linear algebraic matrix multiplication, m1^T * m2^T. Computed as (m2*m1)^T
    
    Parameters:
    m1 - Input matrix
    m2 - another matrix
    
    Returns:
    Matrix product, m1^T * m2^T
  - getDiagonal
```
public static final double[] getDiagonal(double[][] m1)
```
    getDiagonal returns array of diagonal-elements.
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    values on the diagonal of the Matrix
  - normalizeColumns
```
public static final void normalizeColumns(double[][] m1)
```
    Normalizes the columns of this matrix to length of 1.0.
    
    Parameters:
    m1 - Input matrix
  - appendColumns
```
public static final double[][] appendColumns(double[][] m1,
                       double[][] m2)
```
    Returns a matrix which consists of this matrix and the specified columns.
    
    Parameters:
    m1 - Input matrix
    m2 - the columns to be appended
    
    Returns:
    the new matrix with the appended columns
  - orthonormalize
```
public static final double[][] orthonormalize(double[][] m1)
```
    Returns an orthonormalization of this matrix.
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    the orthonormalized matrix
  - hashCode
```
public static final int hashCode(double[][] m1)
```
    Compute hash code
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    Hash code
  - equals
```
public static final boolean equals(double[][] m1,
             double[][] m2)
```
    Test for equality
    
    Parameters:
    m1 - Input matrix
    m2 - Other matrix
    
    Returns:
    Equality
  - almostEquals
```
public static final boolean almostEquals(double[][] m1,
                   double[][] m2,
                   double maxdelta)
```
    Compare two matrices with a delta parameter to take numerical errors into account.
    
    Parameters:
    m1 - Input matrix
    m2 - other matrix to compare with
    maxdelta - maximum delta allowed
    
    Returns:
    true if delta smaller than maximum
  - almostEquals
```
public static final boolean almostEquals(double[][] m1,
                   double[][] m2)
```
    Compare two matrices with a delta parameter to take numerical errors into account.
    
    Parameters:
    m1 - Input matrix
    m2 - other matrix to compare with
    
    Returns:
    almost equals with delta DELTA
  - getRowDimensionality
```
public static final int getRowDimensionality(double[][] m1)
```
    Returns the dimensionality of the rows of this matrix.
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    the number of rows.
  - getColumnDimensionality
```
public static final int getColumnDimensionality(double[][] m1)
```
    Returns the dimensionality of the columns of this matrix.
    
    Parameters:
    m1 - Input matrix
    
    Returns:
    the number of columns.
  - cross3D
```
public static void cross3D(double[] vo,
           double[] v1,
           double[] v2)
```
    Cross product for 3d vectors, i.e. vo = v1 x v2
    
    Parameters:
    vo - Output vector
    v1 - First input vector
    v2 - Second input vector

Class VMath

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

DELTA

ERR_VEC_DIMENSIONS

ERR_MATRIX_DIMENSIONS

ERR_MATRIX_INNERDIM

ERR_DIMENSIONS

Constructor Detail

VMath

Method Detail

randomNormalizedVector

unitVector

copy

transpose

plus

plusTimes

timesPlus

timesPlusTimes

plusEquals

plusTimesEquals

timesPlusEquals

timesPlusTimesEquals

plus

plusEquals

minus

minusTimes

timesMinus

timesMinusTimes

minusEquals

minusTimesEquals

timesMinusEquals

timesMinusTimesEquals

minus

minusEquals

times

timesEquals

times

transposeTimes

transposeTimes

timesTranspose

timesTranspose

scalarProduct

euclideanLength

normalize

normalizeEquals

project

hashCode

equals

clear

rotate90Equals

unitMatrix

zeroMatrix

random

identity

diagonal

copy

rowPackedCopy

columnPackedCopy

getMatrix

getMatrix

getMatrix

getMatrix

setMatrix

setMatrix

setMatrix

setMatrix

getRow

setRow

getCol

setCol

transpose

plus

plusTimes

plusEquals

plusTimesEquals

minus