MatrixD

Instance Constructors

new MatrixD(b: MatrixD)

Construct a matrix and assign values from matrix u.
Construct a matrix and assign values from matrix u.
b
the matrix of values to assign
new MatrixD(u: Array[VectorD])

Construct a matrix and assign values from array of vectors u.
Construct a matrix and assign values from array of vectors u.
u
the 2D array of values to assign
new MatrixD(dim: (Int, Int), u: Double*)

Construct a matrix from repeated values.
Construct a matrix from repeated values.
dim
the (row, column) dimensions
u
the repeated values
new MatrixD(u: Array[Array[Double]])

Construct a matrix and assign values from array of arrays u.
Construct a matrix and assign values from array of arrays u.
u
the 2D array of values to assign
new MatrixD(dim1: Int, dim2: Int, x: Double)

Construct a dim1 by dim2 matrix and assign each element the value x.
Construct a dim1 by dim2 matrix and assign each element the value x.
dim1
the row dimension
dim2
the column dimesion
x
the scalar value to assign
new MatrixD(dim1: Int)

Construct a dim1 by dim1 square matrix.
Construct a dim1 by dim1 square matrix.
dim1
the row and column dimension
new MatrixD(d1: Int, d2: Int, v: Array[Array[Double]] = null)

d1
the first/row dimension
d2
the second/column dimension
v
the 2D array used to store matrix elements

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
def *(x: Double): MatrixD

Multiply this matrix by scalar x.
Multiply this matrix by scalar x.
x
the scalar to multiply by

Definition Classes
MatrixD → Matrix
def *(u: VectorD): VectorD

Multiply this matrix by vector u.
Multiply this matrix by vector u.
u
the vector to multiply by

Definition Classes
MatrixD → Matrix
def *(b: MatrixD): MatrixD

Multiply this matrix by matrix b, transposing b to improve efficiency.
Multiply this matrix by matrix b, transposing b to improve efficiency. Use 'times' method to skip the transpose step.
b
the matrix to multiply by (requires sameCrossDimensions)
def **(u: VectorD): MatrixD

Multiply this matrix by vector u to produce another matrix (a_ij * u_j) E.g., multiply a matrix by a diagonal matrix represented as a vector.
Multiply this matrix by vector u to produce another matrix (a_ij * u_j) E.g., multiply a matrix by a diagonal matrix represented as a vector.
u
the vector to multiply by

Definition Classes
MatrixD → Matrix
def **=(u: VectorD): MatrixD

Multiply in-place this matrix by vector u to produce another matrix (a_ij * u_j)
Multiply in-place this matrix by vector u to produce another matrix (a_ij * u_j)
u
the vector to multiply by

Definition Classes
MatrixD → Matrix
def *=(x: Double): MatrixD

Multiply in-place this matrix by scalar x.
Multiply in-place this matrix by scalar x.
x
the scalar to multiply by

Definition Classes
MatrixD → Matrix
def *=(b: MatrixD): MatrixD

Multiply in-place this matrix by matrix b, transposing b to improve efficiency.
Multiply in-place this matrix by matrix b, transposing b to improve efficiency. Use 'times_ip' method to skip the transpose step.
b
the matrix to multiply by (requires square and sameCrossDimensions)
def +(x: Double): MatrixD

Add this matrix and scalar x.
Add this matrix and scalar x.
x
the scalar to add

Definition Classes
MatrixD → Matrix
def +(u: VectorD): MatrixD

Add this matrix and vector u.
Add this matrix and vector u.
u
the vector to add
def +(b: Matrix): MatrixD

Add this matrix and matrix b.
Add this matrix and matrix b.
b
the matrix to add (requires leDimensions)

Definition Classes
MatrixD → Matrix
def +(b: MatrixD): MatrixD

Add this matrix and matrix b.
Add this matrix and matrix b.
b
the matrix to add (requires leDimensions)
def ++(u: VectorD): MatrixD

Concatenate this matrix and (row) vector u, i.e., append u.
Concatenate this matrix and (row) vector u, i.e., append u.
u
the vector to be concatenated as the new last row in matrix

Definition Classes
MatrixD → Matrix
def +=(x: Double): MatrixD

Add in-place this matrix and scalar x.
Add in-place this matrix and scalar x.
x
the scalar to add

Definition Classes
MatrixD → Matrix
def +=(b: MatrixD): MatrixD

Add in-place this matrix and matrix b.
Add in-place this matrix and matrix b.
b
the matrix to add (requires leDimensions)
def -(x: Double): MatrixD

From this matrix subtract scalar x.
From this matrix subtract scalar x.
x
the scalar to subtract

Definition Classes
MatrixD → Matrix
def -(b: MatrixD): MatrixD

From this matrix subtract matrix b.
From this matrix subtract matrix b.
b
the matrix to subtract (requires leDimensions)
def -=(x: Double): MatrixD

From this matrix subtract in-place scalar x.
From this matrix subtract in-place scalar x.
x
the scalar to subtract

Definition Classes
MatrixD → Matrix
def -=(b: MatrixD): MatrixD

From this matrix subtract in-place matrix b.
From this matrix subtract in-place matrix b.
b
the matrix to subtract (requires leDimensions)
def /(x: Double): MatrixD

Divide this matrix by scalar x.
Divide this matrix by scalar x.
x
the scalar to divide by

Definition Classes
MatrixD → Matrix
def /=(x: Double): MatrixD

Divide in-place this matrix by scalar x.
Divide in-place this matrix by scalar x.
x
the scalar to divide by

Definition Classes
MatrixD → Matrix
def :+(u: VectorD): MatrixD

Concatenate this matrix and (column) vector u, i.e., append u.
Concatenate this matrix and (column) vector u, i.e., append u.
u
the vector to be concatenated as the new last column in matrix
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def apply(i: Int, jr: Range): VectorD

Get a slice this matrix row-wise at index i and column-wise on range jr.
Get a slice this matrix row-wise at index i and column-wise on range jr. Ex: u = a(2, 3..5)
i
the row index
jr
the column range

Definition Classes
MatrixD → Matrix
def apply(ir: Range, j: Int): VectorD

Get a slice this matrix row-wise on range ir and column-wise at index j.
Get a slice this matrix row-wise on range ir and column-wise at index j. Ex: u = a(2..4, 3)
ir
the row range
j
the column index

Definition Classes
MatrixD → Matrix
def apply(ir: Range, jr: Range): MatrixD

Get a slice this matrix row-wise on range ir and column-wise on range jr.
Get a slice this matrix row-wise on range ir and column-wise on range jr. Ex: b = a(2..4, 3..5)
ir
the row range
jr
the column range

Definition Classes
MatrixD → Matrix
def apply(i: Int): VectorD

Get this matrix's vector at the i-th index position (i-th row).
Get this matrix's vector at the i-th index position (i-th row).
i
the row index

Definition Classes
MatrixD → Matrix
def apply(i: Int, j: Int): Double

Get this matrix's element at the i,j-th index position.
Get this matrix's element at the i,j-th index position.
i
the row index
j
the column index

Definition Classes
MatrixD → Matrix
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clean(thres: Double, relative: Boolean = true): MatrixD

Clean values in matrix at or below the threshold by setting them to zero.
Clean values in matrix at or below the threshold by setting them to zero. Iterative algorithms give approximate values and if very close to zero, may throw off other calculations, e.g., in computing eigenvectors.
thres
the cutoff threshold (a small value)
relative
whether to use relative or absolute cutoff

Definition Classes
MatrixD → Matrix
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
def col(col: Int, from: Int = 0): VectorD

Get column 'col' from the matrix, returning it as a vector.
Get column 'col' from the matrix, returning it as a vector.
col
the column to extract from the matrix
from
the position to start extracting from

Definition Classes
MatrixD → Matrix
val d1: Int

the first/row dimension
val d2: Int

the second/column dimension
def det: Double

Compute the determinant of this matrix.
Compute the determinant of this matrix. The value of the determinant indicates, among other things, whether there is a unique solution to a system of linear equations (a nonzero determinant).

Definition Classes
MatrixD → Matrix
def diag(p: Int, q: Int): MatrixD

Form a matrix [Ip, this, Iq] where Ir is a r by r identity matrix, by positioning the three matrices Ip, this and Iq along the diagonal.
Form a matrix [Ip, this, Iq] where Ir is a r by r identity matrix, by positioning the three matrices Ip, this and Iq along the diagonal. Fill the rest of matrix with zeros.
p
the size of identity matrix Ip
q
the size of identity matrix Iq

Definition Classes
MatrixD → Matrix
def diag(p: Int): MatrixD

Form a matrix [Ip, this] where Ip is a p by p identity matrix, by positioning the two matrices Ip and this along the diagonal.
Form a matrix [Ip, this] where Ip is a p by p identity matrix, by positioning the two matrices Ip and this along the diagonal. Fill the rest of matrix with zeros.
p
the size of identity matrix Ip
def diag(b: MatrixD): MatrixD

Combine this matrix with matrix b, placing them along the diagonal and filling in the bottom left and top right regions with zeros; [this, b].
Combine this matrix with matrix b, placing them along the diagonal and filling in the bottom left and top right regions with zeros; [this, b].
b
the matrix to combine with this matrix
lazy val dim1: Int

Dimension 1
Dimension 1

Definition Classes
MatrixD → Matrix
lazy val dim2: Int

Dimension 2
Dimension 2

Definition Classes
MatrixD → Matrix
def dot(u: VectorD): VectorD

Compute the dot product of 'this' matrix and vector 'u', by first transposing 'this' matrix and then multiplying by 'u' (ie., 'a dot u = a.t * u').
Compute the dot product of 'this' matrix and vector 'u', by first transposing 'this' matrix and then multiplying by 'u' (ie., 'a dot u = a.t * u').
u
the vector to multiply by (requires same first dimensions)
def dot(b: MatrixD): MatrixD

Compute the dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (ie., 'a dot b = a.t * b').
Compute the dot product of 'this' matrix and matrix 'b', by first transposing 'this' matrix and then multiplying by 'b' (ie., 'a dot b = a.t * b').
b
the matrix to multiply by (requires same first dimensions)
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
var fString: String

Format string used for printing vector values (change using setFormat)
Format string used for printing vector values (change using setFormat)

Attributes
protected
Definition Classes
Matrix
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
def flaw(method: String, message: String): Unit

Show the flaw by printing the error message.
Show the flaw by printing the error message.
method
the method where the error occurred
message
the error message

Definition Classes
Error
def foreach[U](f: (Array[Double]) ⇒ U): Unit

Iterate over the matrix row by row.
Iterate over the matrix row by row.
f
the function to apply

Definition Classes
Matrix
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
def getDiag(k: Int = 0): VectorD

Get the kth diagonal of this matrix.
Get the kth diagonal of this matrix. Assumes dim2 >= dim1.
k
how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)

Definition Classes
MatrixD → Matrix
def hashCode(): Int

Definition Classes
AnyRef → Any
def inverse: MatrixD

Invert this matrix (requires a squareMatrix) and use partial pivoting.
Invert this matrix (requires a squareMatrix) and use partial pivoting.

Definition Classes
MatrixD → Matrix
def inverse_ip: MatrixD

Invert in-place this matrix (requires a squareMatrix) and uses partial pivoting.
Invert in-place this matrix (requires a squareMatrix) and uses partial pivoting. Note: this method turns the orginal matrix into the identity matrix. The inverse is returned and is captured by assignment.

Definition Classes
MatrixD → Matrix
def inverse_npp: MatrixD

Invert this matrix (requires a squareMatrix) and does not use partial pivoting.
Invert this matrix (requires a squareMatrix) and does not use partial pivoting.

Definition Classes
MatrixD → Matrix
def isBidiagonal: Boolean

Check whether this matrix is bidiagonal (has non-zreo elements only in main diagonal and superdiagonal).
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def isNonnegative: Boolean

Check whether this matrix is nonnegative (has no negative elements).
Check whether this matrix is nonnegative (has no negative elements).

Definition Classes
MatrixD → Matrix
def isRectangular: Boolean

Check whether this matrix is rectangular (all rows have the same number of columns).
Check whether this matrix is rectangular (all rows have the same number of columns).

Definition Classes
MatrixD → Matrix
def isSquare: Boolean

Check whether this matrix is square (same row and column dimensions).
Check whether this matrix is square (same row and column dimensions).

Definition Classes
Matrix
def isSymmetric: Boolean

Check whether this matrix is symmetric.
Check whether this matrix is symmetric.

Definition Classes
Matrix
def leDimensions(b: Matrix): Boolean

Check whether this matrix dimensions are less than or equal to (le) those of the other Matrix.
Check whether this matrix dimensions are less than or equal to (le) those of the other Matrix.
b
the other matrix

Definition Classes
Matrix
def lud: (MatrixD, MatrixD)

Factor this matrix into the product of lower and upper triangular matrices (l, u) using the LU Factorization algorithm.
Factor this matrix into the product of lower and upper triangular matrices (l, u) using the LU Factorization algorithm. This version uses partial pivoting.

Definition Classes
MatrixD → Matrix
def lud_ip: (MatrixD, MatrixD)

Factor in-place this matrix into the product of lower and upper triangular matrices (l, u) using the LU Factorization algorithm.
Factor in-place this matrix into the product of lower and upper triangular matrices (l, u) using the LU Factorization algorithm. This version uses partial pivoting.

Definition Classes
MatrixD → Matrix
def lud_npp: (MatrixD, MatrixD)

Factor this matrix into the product of upper and lower triangular matrices (l, u) using the LU Factorization algorithm.
Factor this matrix into the product of upper and lower triangular matrices (l, u) using the LU Factorization algorithm. This version uses no partial pivoting.
def mag: Double

Find the magnitude of this matrix, the element value farthest from zero.
Find the magnitude of this matrix, the element value farthest from zero.

Definition Classes
Matrix
def max(e: Int = dim1): Double

Find the maximum element in this matrix.
Find the maximum element in this matrix.
e
the ending row index (exclusive) for the search

Definition Classes
MatrixD → Matrix
def mean: VectorD

Compute the column means of this matrix.
def min(e: Int = dim1): Double

Find the minimum element in this matrix.
Find the minimum element in this matrix.
e
the ending row index (exclusive) for the search

Definition Classes
MatrixD → Matrix
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def norm1: Double

Compute the 1-norm of this matrix, i.e., the maximum 1-norm of the column vectors.
Compute the 1-norm of this matrix, i.e., the maximum 1-norm of the column vectors. This is useful for comparing matrices (a - b).norm1

Definition Classes
MatrixD → Matrix
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
def nullspace: VectorD

Compute the (right) nullspace of this m by n matrix (requires n = m + 1) by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.
Compute the (right) nullspace of this m by n matrix (requires n = m + 1) by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1. The nullspace of matrix a is "this vector v times any scalar s", i.e., a*(v*s) = 0. The left nullspace of matrix a is the same as the right nullspace of a.t (a transpose). FIX: need a more robust algorithm for computing nullspace (@see Fac_QR.scala)

Definition Classes
MatrixD → Matrix
See also
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces /solving-ax-0-pivot-variables-special-solutions/MIT18_06SCF11_Ses1.7sum.pdf
def nullspace_ip: VectorD

Compute the (right) nullspace in-place of this m by n matrix (requires n = m + 1) by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1.
Compute the (right) nullspace in-place of this m by n matrix (requires n = m + 1) by performing Gauss-Jordan reduction and extracting the negation of the last column augmented by 1. The nullspace of matrix a is "this vector v times any scalar s", i.e., a*(v*s) = 0. The left nullspace of matrix a is the same as the right nullspace of a.t (a transpose).

Definition Classes
MatrixD → Matrix
val range1: Range

Range for the storage array on dimension 1 (rows)
Range for the storage array on dimension 1 (rows)

Attributes
protected
Definition Classes
Matrix
val range2: Range

Range for the storage array on dimension 2 (columns)
Range for the storage array on dimension 2 (columns)

Attributes
protected
Definition Classes
Matrix
def rank: Int

Determine the rank of this m by n matrix by taking the upper triangular matrix from the LU Decomposition and counting the number of non-zero diagonal elements.
Determine the rank of this m by n matrix by taking the upper triangular matrix from the LU Decomposition and counting the number of non-zero diagonal elements.

Definition Classes
Matrix
def reduce: MatrixD

Use Gauss-Jordan reduction on this matrix to make the left part embed an identity matrix.
Use Gauss-Jordan reduction on this matrix to make the left part embed an identity matrix. A constraint on this m by n matrix is that n >= m.

Definition Classes
MatrixD → Matrix
def reduce_ip: Unit

Use Gauss-Jordan reduction in-place on this matrix to make the left part embed an identity matrix.
Use Gauss-Jordan reduction in-place on this matrix to make the left part embed an identity matrix. A constraint on this m by n matrix is that n >= m.

Definition Classes
MatrixD → Matrix
def sameCrossDimensions(b: Matrix): Boolean

Check whether this matrix and the other matrix have the same cross dimensions.
Check whether this matrix and the other matrix have the same cross dimensions.
b
the other matrix

Definition Classes
Matrix
def sameDimensions(b: Matrix): Boolean

Check whether this matrix and the other Matrix have the same dimensions.
Check whether this matrix and the other Matrix have the same dimensions.
b
the other matrix

Definition Classes
Matrix
def selectCols(colIndex: Array[Int]): MatrixD

Select columns from this matrix according to the given index/basis.
Select columns from this matrix according to the given index/basis. Ex: Can be used to divide a matrix into a basis and a non-basis.
colIndex
the column index positions (e.g., (0, 2, 5))

Definition Classes
MatrixD → Matrix
def selectRows(rowIndex: Array[Int]): MatrixD

Select rows from this matrix according to the given index/basis.
Select rows from this matrix according to the given index/basis.
rowIndex
the row index positions (e.g., (0, 2, 5))

Definition Classes
MatrixD → Matrix
def set(i: Int, u: VectorD, j: Int = 0): Unit

Set this matrix's ith row starting at column j to the vector u.
Set this matrix's ith row starting at column j to the vector u.
i
the row index
u
the vector value to assign
j
the starting column index

Definition Classes
MatrixD → Matrix
def set(u: Array[Array[Double]]): Unit

Set all the values in this matrix as copies of the values in 2D array u.
Set all the values in this matrix as copies of the values in 2D array u.
u
the 2D array of values to assign

Definition Classes
MatrixD → Matrix
def set(x: Double): Unit

Set all the elements in this matrix to the scalar x.
Set all the elements in this matrix to the scalar x.
x
the scalar value to assign

Definition Classes
MatrixD → Matrix
def setCol(col: Int, u: VectorD): Unit

Set column 'col' of the matrix to a vector.
Set column 'col' of the matrix to a vector.
col
the column to set
u
the vector to assign to the column

Definition Classes
MatrixD → Matrix
def setDiag(x: Double): Unit

Set the main diagonal of this matrix to the scalar x.
Set the main diagonal of this matrix to the scalar x. Assumes dim2 >= dim1.
x
the scalar to set the diagonal to

Definition Classes
MatrixD → Matrix
def setDiag(u: VectorD, k: Int = 0): Unit

Set the kth diagonal of this matrix to the vector u.
Set the kth diagonal of this matrix to the vector u. Assumes dim2 >= dim1.
u
the vector to set the diagonal to
k
how far above the main diagonal, e.g., (-1, 0, 1) for (sub, main, super)

Definition Classes
MatrixD → Matrix
def setFormat(newFormat: String): Unit

Set the format to the newFormat.
Set the format to the newFormat.
newFormat
the new format string

Definition Classes
Matrix
def slice(r_from: Int, r_end: Int, c_from: Int, c_end: Int): MatrixD

Slice this matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
Slice this matrix row-wise 'r_from' to 'r_end' and column-wise 'c_from' to 'c_end'.
r_from
the start of the row slice
r_end
the end of the row slice
c_from
the start of the column slice
c_end
the end of the column slice

Definition Classes
MatrixD → Matrix
def slice(from: Int, end: Int): MatrixD

Slice this matrix row-wise 'from' to 'end'.
Slice this matrix row-wise 'from' to 'end'.
from
the start row of the slice (inclusive)
end
the end row of the slice (exclusive)

Definition Classes
MatrixD → Matrix
def sliceCol(from: Int, end: Int): MatrixD

Slice this matrix column-wise 'from' to 'end'.
Slice this matrix column-wise 'from' to 'end'.
from
the start column of the slice (inclusive)
end
the end column of the slice (exclusive)
def sliceExclude(row: Int, col: Int): MatrixD

Slice this matrix excluding the given row and/or column.
Slice this matrix excluding the given row and/or column.
row
the row to exclude (0 until dim1, set to dim1 to keep all rows)
col
the column to exclude (0 until dim2, set to dim2 to keep all columns)

Definition Classes
MatrixD → Matrix
def solve(b: VectorD): VectorD

Solve for x in the equation a*x = b where a is this matrix (see lud above).
Solve for x in the equation a*x = b where a is this matrix (see lud above).
b
the constant vector.

Definition Classes
MatrixD → Matrix
def solve(lu: (Matrix, Matrix), b: VectorD): VectorD

Solve for x in the equation l*u*x = b (see lud above).
Solve for x in the equation l*u*x = b (see lud above).
lu
the lower and upper triangular matrices
b
the constant vector

Definition Classes
MatrixD → Matrix
def solve(l: Matrix, u: Matrix, b: VectorD): VectorD

Solve for x in the equation l*u*x = b (see lud above).
Solve for x in the equation l*u*x = b (see lud above).
l
the lower triangular matrix
u
the upper triangular matrix
b
the constant vector

Definition Classes
MatrixD → Matrix
def sum: Double

Compute the sum of this matrix, i.e., the sum of its elements.
Compute the sum of this matrix, i.e., the sum of its elements.

Definition Classes
MatrixD → Matrix
def sumAbs: Double

Compute the abs sum of this matrix, i.e., the sum of the absolute value of its elements.
Compute the abs sum of this matrix, i.e., the sum of the absolute value of its elements. This is useful for comparing matrices (a - b).sumAbs

Definition Classes
MatrixD → Matrix
def sumLower: Double

Compute the sum of the lower triangular region of this matrix.
Compute the sum of the lower triangular region of this matrix.

Definition Classes
MatrixD → Matrix
def swap(i: Int, k: Int, col: Int = 0): Unit

Swap the elements in rows 'i' and 'k' starting from column 'col'.
Swap the elements in rows 'i' and 'k' starting from column 'col'.
i
the first row in the swap
k
the second row in the swap
col
the starting column for the swap (default 0 => whole row)
def swapCol(j: Int, l: Int, row: Int = 0): Unit

Swap the elements in columns 'j' and 'l' starting from row 'row'.
Swap the elements in columns 'j' and 'l' starting from row 'row'.
j
the first column in the swap
l
the second column in the swap
row
the starting row for the swap (default 0 => whole column)
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def t: MatrixD

Transpose this matrix (rows => columns).
Transpose this matrix (rows => columns).

Definition Classes
MatrixD → Matrix
def times(b: MatrixD): MatrixD

Multiply this matrix by matrix b without first transposing b.
Multiply this matrix by matrix b without first transposing b.
b
the matrix to multiply by (requires sameCrossDimensions)
def times_d(b: Matrix): MatrixD

Multiply this matrix by matrix b using dot product (concise solution).
Multiply this matrix by matrix b using dot product (concise solution).
b
the matrix to multiply by (requires sameCrossDimensions)
def times_ip(b: MatrixD): Unit

Multiply in-place this matrix by matrix b without first transposing b.
Multiply in-place this matrix by matrix b without first transposing b. If b and this reference the same matrix (b == this), a copy of the this matrix is made.
b
the matrix to multiply by (requires square and sameCrossDimensions)
def times_s(b: MatrixD): MatrixD

Multiply this matrix by matrix b using the Strassen matrix multiplication algorithm.
Multiply this matrix by matrix b using the Strassen matrix multiplication algorithm. Both matrices (this and b) must be square. Although the algorithm is faster than the traditional cubic algorithm, its requires more memory and is often less stable (due to round-off errors). FIX: could be make more efficient using a virtual slice (vslice) method.
b
the matrix to multiply by (it has to be a square matrix)

See also
http://en.wikipedia.org/wiki/Strassen_algorithm
def toString(): String

Convert this real (double precision) matrix to a string.
Convert this real (double precision) matrix to a string.

Definition Classes
MatrixD → AnyRef → Any
def trace: Double

Compute the trace of this matrix, i.e., the sum of the elements on the main diagonal.
Compute the trace of this matrix, i.e., the sum of the elements on the main diagonal. Should also equal the sum of the eigenvalues.

Definition Classes
MatrixD → Matrix
See also
Eigen.scala
def update(i: Int, jr: Range, u: VectorD): Unit

Set a slice this matrix row-wise at index i and column-wise on range jr.
Set a slice this matrix row-wise at index i and column-wise on range jr. Ex: a(2, 3..5) = u
i
the row index
jr
the column range
u
the vector to assign

Definition Classes
MatrixD → Matrix
def update(ir: Range, j: Int, u: VectorD): Unit

Set a slice this matrix row-wise on range ir and column-wise at index j.
Set a slice this matrix row-wise on range ir and column-wise at index j. Ex: a(2..4, 3) = u
ir
the row range
j
the column index
u
the vector to assign

Definition Classes
MatrixD → Matrix
def update(ir: Range, jr: Range, b: MatrixD): Unit

Set a slice this matrix row-wise on range ir and column-wise on range jr.
Set a slice this matrix row-wise on range ir and column-wise on range jr. Ex: a(2..4, 3..5) = b
ir
the row range
jr
the column range
b
the matrix to assign
def update(i: Int, u: VectorD): Unit

Set this matrix's row at the i-th index position to the vector u.
Set this matrix's row at the i-th index position to the vector u.
i
the row index
u
the vector value to assign

Definition Classes
MatrixD → Matrix
def update(i: Int, j: Int, x: Double): Unit

Set this matrix's element at the i,j-th index position to the scalar x.
Set this matrix's element at the i,j-th index position to the scalar x.
i
the row index
j
the column index
x
the scalar value to assign

Definition Classes
MatrixD → Matrix
final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
def write(fileName: String): Unit

Write this matrix to a CSV-formatted text file.
Write this matrix to a CSV-formatted text file.
fileName
the name of file holding the data
def ~^(p: Int): MatrixD

Raise this matrix to the pth power (for some integer p >= 2).
Raise this matrix to the pth power (for some integer p >= 2). Caveat: should be replace by a divide and conquer algorithm.
p
the power to raise this matrix to

Definition Classes
MatrixD → Matrix

Related Docs: object MatrixD | package linalgebra

class MatrixD extends Matrix with Error with Serializable

Instance Constructors

new MatrixD(b: MatrixD)

new MatrixD(u: Array[VectorD])

new MatrixD(dim: (Int, Int), u: Double*)

new MatrixD(u: Array[Array[Double]])

new MatrixD(dim1: Int, dim2: Int, x: Double)

new MatrixD(dim1: Int)

new MatrixD(d1: Int, d2: Int, v: Array[Array[Double]] = null)

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

def *(x: Double): MatrixD

def *(u: VectorD): VectorD

def *(b: MatrixD): MatrixD

def **(u: VectorD): MatrixD

def **=(u: VectorD): MatrixD

def *=(x: Double): MatrixD

def *=(b: MatrixD): MatrixD

def +(x: Double): MatrixD

def +(u: VectorD): MatrixD

def +(b: Matrix): MatrixD

def +(b: MatrixD): MatrixD

def ++(u: VectorD): MatrixD

def +=(x: Double): MatrixD

def +=(b: MatrixD): MatrixD

def -(x: Double): MatrixD

def -(b: MatrixD): MatrixD

def -=(x: Double): MatrixD

def -=(b: MatrixD): MatrixD

def /(x: Double): MatrixD

def /=(x: Double): MatrixD

def :+(u: VectorD): MatrixD

final def ==(arg0: Any): Boolean

def apply(i: Int, jr: Range): VectorD

def apply(ir: Range, j: Int): VectorD

def apply(ir: Range, jr: Range): MatrixD

def apply(i: Int): VectorD

def apply(i: Int, j: Int): Double

final def asInstanceOf[T0]: T0

def clean(thres: Double, relative: Boolean = true): MatrixD

def clone(): AnyRef

def col(col: Int, from: Int = 0): VectorD

val d1: Int

val d2: Int

def det: Double

def diag(p: Int, q: Int): MatrixD

def diag(p: Int): MatrixD

def diag(b: MatrixD): MatrixD

lazy val dim1: Int

lazy val dim2: Int

def dot(u: VectorD): VectorD

def dot(b: MatrixD): MatrixD

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

var fString: String

def finalize(): Unit

def flaw(method: String, message: String): Unit

def foreach[U](f: (Array[Double]) ⇒ U): Unit

final def getClass(): Class[_]

def getDiag(k: Int = 0): VectorD

def hashCode(): Int

def inverse: MatrixD

def inverse_ip: MatrixD

def inverse_npp: MatrixD

def isBidiagonal: Boolean

final def isInstanceOf[T0]: Boolean

def isNonnegative: Boolean

def isRectangular: Boolean

def isSquare: Boolean

def isSymmetric: Boolean

def leDimensions(b: Matrix): Boolean

def lud: (MatrixD, MatrixD)

def lud_ip: (MatrixD, MatrixD)

def lud_npp: (MatrixD, MatrixD)

def mag: Double

def max(e: Int = dim1): Double

def mean: VectorD