LinAlgHelpers (ImgLib2 Javadocs 0-SNAPSHOT API)

java.lang.Object
- net.imglib2.util.LinAlgHelpers

```
public class LinAlgHelpers
extends Object
```
Basic vector and matrix operations implemented on double[] and double[][].

Author:

Tobias Pietzsch, Stephan Saalfeld

Constructor Summary

Constructors
Constructor and Description

LinAlgHelpers()

Constructors
Constructor and Description
`LinAlgHelpers()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static void`	`add(double[][] A, double[][] B, double[][] C)` set C = A + B.
`static void`	`add(double[] a, double[] b, double[] c)` set c = a + b.
`static double`	`angleFromR(double[][] R)` compute the angle of rotation from a rotation matrix.
`static void`	`axisFromR(double[][] R, double[] a)` compute the axis of rotation from a rotation matrix.
`static int`	`cols(double[][] A)`
`static void`	`copy(double[][] A, double[][] C)` set C = A, where A is a matrix.
`static void`	`cross(double[] a, double[] b, double[] c)` compute cross product, set c = a ^ b.
`static double`	`det3x3(double[] a)` Calculates the determinant of a 3x3 matrix given as a double[] (row major).
`static double`	`det3x3(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)` Calculate the determinant of a 3x3 matrix.
`static double`	`distance(double[] a, double[] b)` get the length of (a - b).
`static double`	`dot(double[] a, double[] b)` compute dot product a * b.
`static void`	`getCol(int c, double[][] A, double[] b)` extract column c of A into vector b.
`static void`	`getRow(int r, double[][] A, double[] b)` extract row r of A into vector b.
`static void`	`invert3x3(double[] m)` Invert a 3x3 matrix given as row major double[] in place.
`static double[]`	`invert3x3(double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)` Invert a 3x3 matrix given as elements in row major order.
`static void`	`invertSymmetric2x2(double[][] m, double[][] inverse)` Inverts a (invertible) symmetric 2x2 matrix.
`static void`	`invertSymmetric3x3(double[][] m, double[][] inverse)` Inverts a (invertible) symmetric 3x3 matrix.
`static double`	`length(double[] a)` get the length of a.
`static void`	`lerp(double[] a, double[] b, double t, double[] c)` set c = ( 1 - t ) * a + t * b, where a, b are vectors and t is scalar.
`static void`	`mult(double[][] A, double[][] B, double[][] C)` set C = A * B.
`static void`	`mult(double[][] A, double[] b, double[] c)` set c = A * b.
`static void`	`multABT(double[][] A, double[][] B, double[][] C)` set C = A * B^T.
`static void`	`multATB(double[][] A, double[][] B, double[][] C)` set C = A^T * B.
`static void`	`multT(double[][] A, double[] b, double[] c)` set c = A^T * b.
`static void`	`normalize(double[] a)` normalize a, i.e., scale to unit length.
`static void`	`outer(double[] a, double[] b, double[][] C)` compute outer product, set C = a * b^T.
`static void`	`quaternionApply(double[] q, double[] p, double[] qp)` Apply quaternion rotation q to 3D point p, set qp = q * p.
`static void`	`quaternionFromAngleAxis(double[] axis, double angle, double[] q)` compute a quaternion from rotation axis and angle.
`static void`	`quaternionFromR(double[][] R, double[] q)` compute a unit quaternion from a rotation matrix.
`static void`	`quaternionInvert(double[] p, double[] q)` invert quaternion, set q = p^{-1}.
`static void`	`quaternionMultiply(double[] p, double[] q, double[] pq)` compute the quaternion product pq = p * q.
`static void`	`quaternionPower(double[] q, double a, double[] qa)` compute the power of a quaternion q raised to the exponent a.
`static void`	`quaternionToR(double[] q, double[][] R)` compute a rotation matrix from a unit quaternion.
`static int`	`rows(double[] a)`
`static int`	`rows(double[][] A)`
`static void`	`scale(double[][] A, double b, double[][] C)` set C = A * b, where A is a matrix and b is scalar.
`static void`	`scale(double[] a, double b, double[] c)` set c = a * b, where a is a vector and b is scalar.
`static void`	`setCol(int c, double[] a, double[][] B)` set column c of B to vector a.
`static void`	`setRow(int r, double[] a, double[][] B)` set row r of B to vector a.
`static double`	`squareDistance(double[] a, double[] b)` get the squared length of (a - b).
`static double`	`squareLength(double[] a)` get the squared length of a.
`static void`	`subtract(double[] a, double[] b, double[] c)` set c = a - b.
`static String`	`toString(double[] a)`
`static String`	`toString(double[][] A)`
`static String`	`toString(double[][] A, String format)`
`static String`	`toString(double[] a, String format)`

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

Constructor Detail
- LinAlgHelpers
```
public LinAlgHelpers()
```

Method Detail

rows
```
public static int rows(double[] a)
```

rows
```
public static int rows(double[][] A)
```

cols
```
public static int cols(double[][] A)
```

squareLength
```
public static double squareLength(double[] a)
```
get the squared length of a.

Parameters:

a -

length

public static double length(double[] a)

get the length of a.

Parameters:: a -

squareDistance

public static double squareDistance(double[] a,
                                    double[] b)

get the squared length of (a - b).

Parameters:: a -; b -

distance

public static double distance(double[] a,
                              double[] b)

get the length of (a - b).

Parameters:: a -; b -

lerp
```
public static void lerp(double[] a,
                        double[] b,
                        double t,
                        double[] c)
```
set c = ( 1 - t ) * a + t * b, where a, b are vectors and t is scalar. Dimensions of a, b, and c must match. In place interpolation (c==a or c==b) is allowed.

scale
```
public static void scale(double[] a,
                         double b,
                         double[] c)
```
set c = a * b, where a is a vector and b is scalar. Dimensions of a and c must match. In place scaling (c==a) is permitted.

Parameters:

a -

b -

c -

scale
```
public static void scale(double[][] A,
                         double b,
                         double[][] C)
```
set C = A * b, where A is a matrix and b is scalar. Dimensions of A and C must match. In place scaling (C==A) is permitted.

Parameters:

A -

b -

C -

copy
```
public static void copy(double[][] A,
                        double[][] C)
```
set C = A, where A is a matrix. Dimensions of A and C must match.

Parameters:

A -

C -

subtract

public static void subtract(double[] a,
                            double[] b,
                            double[] c)

set c = a - b. Dimensions of a, b, and c must match. In place subtraction (c==a) is permitted.

Parameters:: a -; b -; c -

add
```
public static void add(double[] a,
                       double[] b,
                       double[] c)
```
set c = a + b. Dimensions of a, b, and c must match. In place addition (c==a) is permitted.

Parameters:

a -

b -

c -

mult
```
public static void mult(double[][] A,
                        double[] b,
                        double[] c)
```
set c = A * b. Dimensions of A, b, and c must match. That is, cols(A) == rows(b), and rows(c) == rows(A).

Parameters:

A -

b -

c -

multT
```
public static void multT(double[][] A,
                         double[] b,
                         double[] c)
```
set c = A^T * b. Dimensions of A, b, and c must match. That is, rows(A) == rows(b), and rows(c) == cols(A).

Parameters:

A -

b -

c -

mult
```
public static void mult(double[][] A,
                        double[][] B,
                        double[][] C)
```
set C = A * B. Dimensions of A, B, and C must match. That is, cols(A) == rows(B), rows(C) == rows(A), and cols(C) == cols(B).

Parameters:

A -

B -

C -

multABT
```
public static void multABT(double[][] A,
                           double[][] B,
                           double[][] C)
```
set C = A * B^T. Dimensions of A, B, and C must match. That is, cols(A) == cols(B), rows(C) == rows(A), and cols(C) == rows(B).

Parameters:

A -

B -

C -

multATB
```
public static void multATB(double[][] A,
                           double[][] B,
                           double[][] C)
```
set C = A^T * B. Dimensions of A, B, and C must match. That is, rows(A) == rows(B), rows(C) == cols(A), and cols(C) == cols(B).

Parameters:

A -

B -

C -

add
```
public static void add(double[][] A,
                       double[][] B,
                       double[][] C)
```
set C = A + B. Dimensions of A, B, and C must match. In place addition (C==A or C==B) is permitted.

Parameters:

A -

B -

C -

getCol
```
public static void getCol(int c,
                          double[][] A,
                          double[] b)
```
extract column c of A into vector b. Dimensions of A and b must match. That is, rows(A) == rows(b).

Parameters:

c -

A -

b -

setCol
```
public static void setCol(int c,
                          double[] a,
                          double[][] B)
```
set column c of B to vector a. Dimensions of a and B must match. That is, rows(a) == rows(B).

Parameters:

c -

a -

B -

getRow
```
public static void getRow(int r,
                          double[][] A,
                          double[] b)
```
extract row r of A into vector b. Dimensions of A and b must match. That is, cols(A) == rows(b).

Parameters:

r -

A -

b -

setRow

public static void setRow(int r,
                          double[] a,
                          double[][] B)

set row r of B to vector a. Dimensions of a and B must match. That is, rows(a) == cols(B).

Parameters:: r -; a -; B -

normalize
```
public static void normalize(double[] a)
```
normalize a, i.e., scale to unit length.

Parameters:

a -

dot
```
public static double dot(double[] a,
                         double[] b)
```
compute dot product a * b. Dimensions of a and b must match.

Parameters:

a -

b -

cross

public static void cross(double[] a,
                         double[] b,
                         double[] c)

compute cross product, set c = a ^ b. Dimensions of a, b, and c must equal 3.

Parameters:: a -; b -

outer
```
public static void outer(double[] a,
                         double[] b,
                         double[][] C)
```
compute outer product, set C = a * b^T. Dimensions of a, b, and C must match. That is, rows(a) == rows(C), and rows(b) == cols(C).

Parameters:

a -

b -

C -

angleFromR
```
public static double angleFromR(double[][] R)
```
compute the angle of rotation from a rotation matrix. The returned value is in the range [0, PI].

Parameters:

R - rotation matrix

axisFromR
```
public static void axisFromR(double[][] R,
                             double[] a)
```
compute the axis of rotation from a rotation matrix.

Parameters:

R - rotation matrix

a - rotation axis is stored here

quaternionFromR
```
public static void quaternionFromR(double[][] R,
                                   double[] q)
```
compute a unit quaternion from a rotation matrix.

Parameters:

R - rotation matrix.

q - unit quaternion (w, x, y, z) is stored here.

quaternionToR
```
public static void quaternionToR(double[] q,
                                 double[][] R)
```
compute a rotation matrix from a unit quaternion.

Parameters:

q - unit quaternion (w, x, y, z).

R - rotation matrix is stored here.

quaternionFromAngleAxis
```
public static void quaternionFromAngleAxis(double[] axis,
                                           double angle,
                                           double[] q)
```
compute a quaternion from rotation axis and angle.

Parameters:

axis - rotation axis as a unit vector.

angle - rotation angle [rad].

q - unit quaternion (w, x, y, z) is stored here.

quaternionMultiply
```
public static void quaternionMultiply(double[] p,
                                      double[] q,
                                      double[] pq)
```
compute the quaternion product pq = p * q. applying rotation pq corresponds to applying first q, then p (i.e. same as multiplication of rotation matrices).

Parameters:

p - unit quaternion (w, x, y, z).

q - unit quaternion (w, x, y, z).

pq - quaternion product p * q is stored here.

quaternionPower
```
public static void quaternionPower(double[] q,
                                   double a,
                                   double[] qa)
```
compute the power of a quaternion q raised to the exponent a.

Parameters:

q - unit quaternion (w, x, y, z).

a - exponent.

qa - q^a is stored here.

quaternionInvert
```
public static void quaternionInvert(double[] p,
                                    double[] q)
```
invert quaternion, set q = p^{-1}. In place inversion (p==q) is permitted.

Parameters:

p - unit quaternion (w, x, y, z).

q - inverse of p is stored here.

quaternionApply
```
public static void quaternionApply(double[] q,
                                   double[] p,
                                   double[] qp)
```
Apply quaternion rotation q to 3D point p, set qp = q * p. In place rotation (p==qp) is permitted.

Parameters:

q - unit quaternion (w, x, y, z).

p - 3D point.

qp - rotated 3D point is stored here.

det3x3
```
public static final double det3x3(double[] a)
```
Calculates the determinant of a 3x3 matrix given as a double[] (row major).

Parameters:

a -

Returns:

determinant

det3x3

public static final double det3x3(double m00,
                                  double m01,
                                  double m02,
                                  double m10,
                                  double m11,
                                  double m12,
                                  double m20,
                                  double m21,
                                  double m22)

Calculate the determinant of a 3x3 matrix.

Parameters:: m00 -; m01 -; m02 -; m10 -; m11 -; m12 -; m20 -; m21 -; m22 -
Returns:

invert3x3
```
public static final void invert3x3(double[] m)
                            throws IllegalArgumentException
```
Invert a 3x3 matrix given as row major double[] in place.

Parameters:

m - matrix

Throws:

IllegalArgumentException - if matrix is not invertible

invert3x3

public static final double[] invert3x3(double m00,
                                       double m01,
                                       double m02,
                                       double m10,
                                       double m11,
                                       double m12,
                                       double m20,
                                       double m21,
                                       double m22)
                                throws IllegalArgumentException

Invert a 3x3 matrix given as elements in row major order.

Returns:: inverted matrix as row major double[]
Throws:: IllegalArgumentException - if matrix is not invertible

invertSymmetric3x3
```
public static void invertSymmetric3x3(double[][] m,
                                      double[][] inverse)
```
Inverts a (invertible) symmetric 3x3 matrix.

Parameters:

m - symmetric matrix to invert.

inverse - inverse of m is stored here.

invertSymmetric2x2
```
public static void invertSymmetric2x2(double[][] m,
                                      double[][] inverse)
```
Inverts a (invertible) symmetric 2x2 matrix.

Parameters:

m - symmetric matrix to invert.

inverse - inverse of m is stored here.

toString

public static String toString(double[][] A)

toString

public static String toString(double[][] A,
                              String format)

toString

public static String toString(double[] a)

toString

public static String toString(double[] a,
                              String format)

Class LinAlgHelpers

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

LinAlgHelpers

Method Detail

rows

rows

cols

squareLength

length

squareDistance

distance

lerp

scale

scale

copy

subtract

add

mult

multT

mult

multABT

multATB

add

getCol

setCol

getRow

setRow

normalize

dot

cross

outer

angleFromR

axisFromR

quaternionFromR

quaternionToR

quaternionFromAngleAxis

quaternionMultiply

quaternionPower

quaternionInvert

quaternionApply

det3x3

det3x3

invert3x3

invert3x3

invertSymmetric3x3

invertSymmetric2x2

toString

toString

toString

toString