Package smile.math.matrix
Class BigMatrix
java.lang.Object
smile.math.matrix.IMatrix
smile.math.matrix.BigMatrix
- All Implemented Interfaces:
Serializable
,Cloneable
Big dense matrix of double precision values for more than
2 billion elements.
- See Also:
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Nested Class Summary
Modifier and TypeClassDescriptionstatic class
The Cholesky decomposition of a symmetric, positive-definite matrix.static class
Eigenvalue decomposition.static class
The LU decomposition.static class
The QR decomposition.static class
Singular Value Decomposition.Nested classes/interfaces inherited from class smile.math.matrix.IMatrix
IMatrix.Preconditioner
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Constructor Summary
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Method Summary
Modifier and TypeMethodDescriptionaat()
ReturnsA * A'
.static BigMatrix
ReturnsA * D * B
, where D is a diagonal matrix.add
(double b) A += badd
(double alpha, double[] x, double[] y) Rank-1 update A += alpha * x * y'Element-wise addition A = alpha * A + beta * BElement-wise addition A += beta * BElement-wise addition C = alpha * A + beta * Bdouble
add
(int i, int j, double b) A[i,j] += bElement-wise addition A += BElement-wise addition A = alpha * A + beta * B^2addDiag
(double b) A[i, i] += baddDiag
(double[] b) A[i, i] += b[i]ata()
ReturnsA' * A
.cholesky()
Cholesky decomposition for symmetric and positive definite matrix.cholesky
(boolean overwrite) Cholesky decomposition for symmetric and positive definite matrix.clone()
Returns a deep copy of matrix.double[]
col
(int j) Returns the j-th column.col
(int... cols) Returns the matrix of selected columns.double[]
colMeans()
Returns the mean of each column.double[]
colSds()
Returns the standard deviations of each column.double[]
colSums()
Returns the sum of each column.static BigMatrix
column
(double[] A) Returns a column vector/matrix.static BigMatrix
column
(double[] A, int offset, int length) Returns a column vector/matrix.static BigMatrix
diag
(double[] diag) Returns a square diagonal matrix.static BigMatrix
diag
(int n, double diag) Returns a square diagonal matrix.static BigMatrix
diag
(int m, int n, double diag) Returns an m-by-n diagonal matrix.static BigMatrix
diag
(org.bytedeco.javacpp.DoublePointer diag) Returns a square diagonal matrix.div
(double b) A /= bdouble
div
(int i, int j, double b) A[i,j] /= bElement-wise division A /= Beigen()
Eigenvalue Decomposition.eigen
(boolean vl, boolean vr, boolean overwrite) Eigenvalue Decomposition.boolean
boolean
Returns true if two matrices equal in given precision.static BigMatrix
eye
(int n) Returns an identity matrix.static BigMatrix
eye
(int m, int n) Returns an m-by-n identity matrix.void
fill
(double x) Fill the matrix with a value.get
(int[] rows, int[] cols) Returns the matrix of selected rows and columns.double
get
(int i, int j) ReturnsA[i,j]
.protected long
index
(int i, int j) Returns the linearized index of matrix element.inverse()
Returns the inverse of matrix.boolean
Return true if the matrix is symmetric (uplo != null && diag == null
).layout()
Returns the matrix layout.int
ld()
Returns the leading dimension.lu()
LU decomposition.lu
(boolean overwrite) LU decomposition.Matrix-matrix multiplication.Matrix-matrix multiplication.Returns matrix multiplicationA * B
.Returns matrix multiplicationA * B'
.mul
(double b) A *= bdouble
mul
(int i, int j, double b) A[i,j] *= bElement-wise multiplication A *= Bvoid
mv
(double[] work, int inputOffset, int outputOffset) Matrix-vector multiplicationA * x
.void
Matrix-vector multiplication.int
ncol()
Returns the number of columns.double
norm()
L2 matrix norm that is the maximum singular value.double
norm1()
L1 matrix norm that is the maximum of column sums.double
norm2()
L2 matrix norm that is the maximum singular value.double
normFro()
Frobenius matrix norm that is the square root of sum of squares of all elements.double
normInf()
L∞ matrix norm that is the maximum of row sums.int
nrow()
Returns the number of rows.static BigMatrix
of
(double[][] A) Returns a matrix from a two-dimensional array.qr()
QR Decomposition.qr
(boolean overwrite) QR Decomposition.static BigMatrix
rand
(int m, int n) Returns a uniformly distributed random matrix in [0, 1).static BigMatrix
rand
(int m, int n, double lo, double hi) Returns a random matrix of uniform distribution.static BigMatrix
rand
(int m, int n, Distribution distribution) Returns a random matrix.static BigMatrix
randn
(int m, int n) Returns a random matrix of standard normal distribution.replaceNaN
(double x) Replaces NaN's with given value.static BigMatrix
row
(double[] A) Returns a row vector/matrix.static BigMatrix
row
(double[] A, int offset, int length) Returns a row vector/matrix.double[]
row
(int i) Returns the i-th row.row
(int... rows) Returns the matrix of selected rows.double[]
rowMeans()
Returns the mean of each row.double[]
rowSds()
Returns the standard deviations of each row.double[]
rowSums()
Returns the sum of each row.scale
(double[] center, double[] scale) Centers and scales the columns of matrix.void
set
(int i, int j, double x) SetsA[i,j] = x
.Sets the matrix value.long
size()
Returns the number of stored matrix elements.Standardizes the columns of matrix.sub
(double b) A -= bdouble
sub
(int i, int j, double b) A[i,j] -= bElement-wise subtraction A -= Bsubmatrix
(int i, int j, int k, int l) Returns the submatrix which top left at (i, j) and bottom right at (k, l).double
sum()
Returns the sum of all elements.svd()
Singular Value Decomposition.svd
(boolean vectors, boolean overwrite) Singular Value Decomposition.Returns matrix multiplicationA' * B
.double[][]
toArray()
Return the two-dimensional array of matrix.static BigMatrix
toeplitz
(double[] a) Returns a symmetric Toeplitz matrix in which each descending diagonal from left to right is constant.static BigMatrix
toeplitz
(double[] kl, double[] ku) Returns a Toeplitz matrix in which each descending diagonal from left to right is constant.Returns the transpose of matrix.transpose
(boolean share) Returns the transpose of matrix.Gets the flag if a triangular matrix has unit diagonal elements.triangular
(Diag diag) Sets/unsets if the matrix is triangular.Returns matrix multiplicationA' * B'
.void
tv
(double[] work, int inputOffset, int outputOffset) Matrix-vector multiplicationA' * x
.uplo()
Gets the format of packed matrix.Sets the format of packed matrix.double
xAx
(double[] x) Returns the quadratic formx' * A * x
.
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Constructor Details
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BigMatrix
public BigMatrix(int m, int n) Constructor of zero matrix.- Parameters:
m
- the number of rows.n
- the number of columns.
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BigMatrix
public BigMatrix(int m, int n, double a) Constructor. Fills the matrix with given value.- Parameters:
m
- the number of rows.n
- the number of columns.a
- the initial value.
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BigMatrix
public BigMatrix(int m, int n, int ld, org.bytedeco.javacpp.DoublePointer A) Constructor.- Parameters:
m
- the number of rows.n
- the number of columns.ld
- the leading dimension.A
- the matrix storage.
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Method Details
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of
Returns a matrix from a two-dimensional array.- Parameters:
A
- the two-dimensional array.- Returns:
- the matrix.
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column
Returns a column vector/matrix.- Parameters:
A
- the column vector.- Returns:
- the column vector/matrix.
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column
Returns a column vector/matrix.- Parameters:
A
- the column vector.offset
- the offset of the subarray to be used; must be non-negative and no larger than array.length.length
- the length of the subarray to be used; must be non-negative and no larger than array.length - offset.- Returns:
- the column vector/matrix.
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row
Returns a row vector/matrix.- Parameters:
A
- the row vector.- Returns:
- the row vector/matrix.
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row
Returns a row vector/matrix.- Parameters:
A
- the row vector.offset
- the offset of the subarray to be used; must be non-negative and no larger than array.length.length
- the length of the subarray to be used; must be non-negative and no larger than array.length - offset.- Returns:
- the row vector/matrix.
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rand
Returns a random matrix.- Parameters:
m
- the number of rows.n
- the number of columns.distribution
- the distribution of random number.- Returns:
- the matrix.
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randn
Returns a random matrix of standard normal distribution.- Parameters:
m
- the number of rows.n
- the number of columns.- Returns:
- the matrix.
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rand
Returns a uniformly distributed random matrix in [0, 1).- Parameters:
m
- the number of rows.n
- the number of columns.- Returns:
- the random matrix.
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rand
Returns a random matrix of uniform distribution.- Parameters:
m
- the number of rows.n
- the number of columns.lo
- the lower bound of uniform distribution.hi
- the upper bound of uniform distribution.- Returns:
- the matrix.
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eye
Returns an identity matrix.- Parameters:
n
- the number of rows/columns.- Returns:
- the matrix.
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eye
Returns an m-by-n identity matrix.- Parameters:
m
- the number of rows.n
- the number of columns.- Returns:
- the matrix.
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diag
Returns a square diagonal matrix.- Parameters:
n
- the number of rows/columns.diag
- the diagonal value.- Returns:
- the matrix.
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diag
Returns an m-by-n diagonal matrix.- Parameters:
m
- the number of rows.n
- the number of columns.diag
- the diagonal value.- Returns:
- the matrix.
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diag
Returns a square diagonal matrix.- Parameters:
diag
- the diagonal elements.- Returns:
- the matrix.
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diag
Returns a square diagonal matrix.- Parameters:
diag
- the diagonal elements.- Returns:
- the matrix.
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toeplitz
Returns a symmetric Toeplitz matrix in which each descending diagonal from left to right is constant.- Parameters:
a
- A[i, j] = a[i - j] fori >= j
(or a[j - i] whenj > i
)- Returns:
- the matrix.
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toeplitz
Returns a Toeplitz matrix in which each descending diagonal from left to right is constant.- Parameters:
kl
-A[i, j] = kl[i - j]
fori > j
ku
-A[i, j] = ku[j - i]
fori <= j
- Returns:
- the matrix.
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nrow
public int nrow()Description copied from class:IMatrix
Returns the number of rows. -
ncol
public int ncol()Description copied from class:IMatrix
Returns the number of columns. -
size
public long size()Description copied from class:IMatrix
Returns the number of stored matrix elements. For conventional matrix, it is simply nrow * ncol. But it is usually much less for band, packed or sparse matrix. -
layout
Returns the matrix layout.- Returns:
- the matrix layout.
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ld
public int ld()Returns the leading dimension.- Returns:
- the leading dimension.
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isSymmetric
public boolean isSymmetric()Return true if the matrix is symmetric (uplo != null && diag == null
).- Returns:
- true if the matrix is symmetric.
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uplo
Sets the format of packed matrix.- Parameters:
uplo
- the format of packed matrix.- Returns:
- this matrix.
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uplo
Gets the format of packed matrix.- Returns:
- the format of packed matrix.
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triangular
Sets/unsets if the matrix is triangular.- Parameters:
diag
- if not null, it specifies if the triangular matrix has unit diagonal elements.- Returns:
- this matrix.
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triangular
Gets the flag if a triangular matrix has unit diagonal elements. Returns null if the matrix is not triangular.- Returns:
- the flag if a triangular matrix has unit diagonal elements.
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clone
Returns a deep copy of matrix. -
toArray
public double[][] toArray()Return the two-dimensional array of matrix.- Returns:
- the two-dimensional array of matrix.
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set
Sets the matrix value. If the matrices have the same layout, this matrix will share the underlying storage with b.- Parameters:
b
- the right hand side of assignment.- Returns:
- this matrix.
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index
protected long index(int i, int j) Returns the linearized index of matrix element.- Parameters:
i
- the row index.j
- the column index.- Returns:
- the linearized index.
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get
public double get(int i, int j) Description copied from class:IMatrix
ReturnsA[i,j]
. -
set
public void set(int i, int j, double x) Description copied from class:IMatrix
SetsA[i,j] = x
. -
get
Returns the matrix of selected rows and columns. Negative index -i means the i-th row/column from the end.- Parameters:
rows
- the row indices.cols
- the column indices.- Returns:
- the submatrix.
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row
public double[] row(int i) Returns the i-th row. Negative index -i means the i-th row from the end.- Parameters:
i
- the row index.- Returns:
- the row.
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col
public double[] col(int j) Returns the j-th column. Negative index -j means the j-th row from the end.- Parameters:
j
- the column index.- Returns:
- the column.
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row
Returns the matrix of selected rows.- Parameters:
rows
- the row indices.- Returns:
- the submatrix.
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col
Returns the matrix of selected columns.- Parameters:
cols
- the column indices.- Returns:
- the submatrix.
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submatrix
Returns the submatrix which top left at (i, j) and bottom right at (k, l). The content of the submatrix will be that of this matrix. Changes to this matrix's content will be visible in the submatrix, and vice versa.- Parameters:
i
- the beginning row, inclusive.j
- the beginning column, inclusive,k
- the ending row, inclusive.l
- the ending column, inclusive.- Returns:
- the submatrix.
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fill
public void fill(double x) Fill the matrix with a value.- Parameters:
x
- the value.
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transpose
Returns the transpose of matrix. The transpose shares the storage with this matrix. Changes to this matrix's content will be visible in the transpose, and vice versa.- Returns:
- the transpose of matrix.
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transpose
Returns the transpose of matrix.- Parameters:
share
- if true, the transpose shares the storage with this matrix. Changes to this matrix's content will be visible in the transpose, and vice versa.- Returns:
- the transpose of matrix.
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equals
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equals
Returns true if two matrices equal in given precision.- Parameters:
o
- the other matrix.epsilon
- a number close to zero.- Returns:
- true if two matrices equal in given precision.
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add
public double add(int i, int j, double b) A[i,j] += b- Parameters:
i
- the row index.j
- the column index.b
- the operand.- Returns:
- the updated cell value.
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sub
public double sub(int i, int j, double b) A[i,j] -= b- Parameters:
i
- the row index.j
- the column index.b
- the operand.- Returns:
- the updated cell value.
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mul
public double mul(int i, int j, double b) A[i,j] *= b- Parameters:
i
- the row index.j
- the column index.b
- the operand.- Returns:
- the updated cell value.
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div
public double div(int i, int j, double b) A[i,j] /= b- Parameters:
i
- the row index.j
- the column index.b
- the operand.- Returns:
- the updated cell value.
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addDiag
A[i, i] += b- Parameters:
b
- the operand.- Returns:
- this matrix.
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addDiag
A[i, i] += b[i]- Parameters:
b
- the operand.- Returns:
- this matrix.
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add
A += b- Parameters:
b
- the operand.- Returns:
- this matrix.
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sub
A -= b- Parameters:
b
- the operand.- Returns:
- this matrix.
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mul
A *= b- Parameters:
b
- the operand.- Returns:
- this matrix.
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div
A /= b- Parameters:
b
- the operand.- Returns:
- this matrix.
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add
Element-wise addition A += B- Parameters:
B
- the operand.- Returns:
- this matrix.
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sub
Element-wise subtraction A -= B- Parameters:
B
- the operand.- Returns:
- this matrix.
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mul
Element-wise multiplication A *= B- Parameters:
B
- the operand.- Returns:
- this matrix.
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div
Element-wise division A /= B- Parameters:
B
- the operand.- Returns:
- this matrix.
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add
Element-wise addition A += beta * B- Parameters:
beta
- the scalar alpha.B
- the operand.- Returns:
- this matrix.
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add
Element-wise addition C = alpha * A + beta * B- Parameters:
alpha
- the scalar alpha.A
- the operand.beta
- the scalar beta.B
- the operand.- Returns:
- this matrix.
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add
Element-wise addition A = alpha * A + beta * B- Parameters:
alpha
- the scalar alpha.beta
- the scalar beta.B
- the operand.- Returns:
- this matrix.
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add2
Element-wise addition A = alpha * A + beta * B^2- Parameters:
alpha
- the scalar alpha.beta
- the scalar beta.B
- the operand.- Returns:
- this matrix.
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add
Rank-1 update A += alpha * x * y'- Parameters:
alpha
- the scalar alpha.x
- the column vector.y
- the row vector.- Returns:
- this matrix.
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replaceNaN
Replaces NaN's with given value.- Parameters:
x
- a real number.- Returns:
- this matrix.
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sum
public double sum()Returns the sum of all elements.- Returns:
- the sum of all elements.
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norm1
public double norm1()L1 matrix norm that is the maximum of column sums.- Returns:
- L1 matrix norm.
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norm2
public double norm2()L2 matrix norm that is the maximum singular value.- Returns:
- L2 matrix norm.
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norm
public double norm()L2 matrix norm that is the maximum singular value.- Returns:
- L2 matrix norm.
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normInf
public double normInf()L∞ matrix norm that is the maximum of row sums.- Returns:
- L∞ matrix norm.
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normFro
public double normFro()Frobenius matrix norm that is the square root of sum of squares of all elements.- Returns:
- Frobenius matrix norm.
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xAx
public double xAx(double[] x) Returns the quadratic formx' * A * x
. The left upper submatrix of A is used in the computation based on the size of x.- Parameters:
x
- the vector.- Returns:
- the quadratic form.
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rowSums
public double[] rowSums()Returns the sum of each row.- Returns:
- the sum of each row.
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rowMeans
public double[] rowMeans()Returns the mean of each row.- Returns:
- the mean of each row.
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rowSds
public double[] rowSds()Returns the standard deviations of each row.- Returns:
- the standard deviations of each row.
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colSums
public double[] colSums()Returns the sum of each column.- Returns:
- the sum of each column.
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colMeans
public double[] colMeans()Returns the mean of each column.- Returns:
- the mean of each column.
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colSds
public double[] colSds()Returns the standard deviations of each column.- Returns:
- the standard deviations of each column.
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standardize
Standardizes the columns of matrix.- Returns:
- a new matrix with zero mean and unit variance for each column.
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scale
Centers and scales the columns of matrix.- Parameters:
center
- column center. If null, no centering.scale
- column scale. If null, no scaling.- Returns:
- a new matrix with zero mean and unit variance for each column.
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inverse
Returns the inverse of matrix.- Returns:
- the inverse of matrix.
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mv
Description copied from class:IMatrix
Matrix-vector multiplication.
where op is the transpose operation.y = alpha * op(A) * x + beta * y
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mv
public void mv(double[] work, int inputOffset, int outputOffset) Description copied from class:IMatrix
Matrix-vector multiplicationA * x
. -
tv
public void tv(double[] work, int inputOffset, int outputOffset) Description copied from class:IMatrix
Matrix-vector multiplicationA' * x
. -
mm
Matrix-matrix multiplication.C := A*B
- Parameters:
transA
- normal, transpose, or conjugate transpose operation on the matrix A.A
- the operand.transB
- normal, transpose, or conjugate transpose operation on the matrix B.B
- the operand.- Returns:
- this matrix.
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mm
public BigMatrix mm(Transpose transA, BigMatrix A, Transpose transB, BigMatrix B, double alpha, double beta) Matrix-matrix multiplication.C := alpha*A*B + beta*C
- Parameters:
transA
- normal, transpose, or conjugate transpose operation on the matrix A.A
- the operand.transB
- normal, transpose, or conjugate transpose operation on the matrix B.B
- the operand.alpha
- the scalar alpha.beta
- the scalar beta.- Returns:
- this matrix.
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ata
ReturnsA' * A
.- Returns:
A' * A
.
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aat
ReturnsA * A'
.- Returns:
A * A'
.
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adb
public static BigMatrix adb(Transpose transA, BigMatrix A, double[] D, Transpose transB, BigMatrix B) ReturnsA * D * B
, where D is a diagonal matrix.- Parameters:
transA
- normal, transpose, or conjugate transpose operation on the matrix A.A
- the operand.D
- the diagonal matrix.transB
- normal, transpose, or conjugate transpose operation on the matrix B.B
- the operand.- Returns:
- the multiplication.
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mm
Returns matrix multiplicationA * B
.- Parameters:
B
- the operand.- Returns:
- the multiplication.
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mt
Returns matrix multiplicationA * B'
.- Parameters:
B
- the operand.- Returns:
- the multiplication.
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tm
Returns matrix multiplicationA' * B
.- Parameters:
B
- the operand.- Returns:
- the multiplication.
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tt
Returns matrix multiplicationA' * B'
.- Parameters:
B
- the operand.- Returns:
- the multiplication.
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lu
LU decomposition.- Returns:
- LU decomposition.
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lu
LU decomposition.- Parameters:
overwrite
- The flag if the decomposition overwrites this matrix.- Returns:
- LU decomposition.
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cholesky
Cholesky decomposition for symmetric and positive definite matrix.- Returns:
- Cholesky decomposition.
- Throws:
ArithmeticException
- if the matrix is not positive definite.
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cholesky
Cholesky decomposition for symmetric and positive definite matrix.- Parameters:
overwrite
- The flag if the decomposition overwrites this matrix.- Returns:
- Cholesky decomposition.
- Throws:
ArithmeticException
- if the matrix is not positive definite.
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qr
QR Decomposition.- Returns:
- QR decomposition.
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qr
QR Decomposition.- Parameters:
overwrite
- The flag if the decomposition overwrites this matrix.- Returns:
- QR decomposition.
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svd
Singular Value Decomposition. Returns a compact SVD of m-by-n matrix A:m > n
— Only the first n columns of U are computed, and S is n-by-n.m = n
— Equivalent to full SVD.m < n
— Only the first m columns of V are computed, and S is m-by-m.
- Returns:
- singular value decomposition.
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svd
Singular Value Decomposition. Returns a compact SVD of m-by-n matrix A:m > n
— Only the first n columns of U are computed, and S is n-by-n.m = n
— Equivalent to full SVD.m < n
— Only the first m columns of V are computed, and S is m-by-m.
- Parameters:
vectors
- The flag if computing the singular vectors.overwrite
- The flag if the decomposition overwrites this matrix.- Returns:
- singular value decomposition.
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eigen
Eigenvalue Decomposition. For a symmetric matrix, all eigenvalues are real values. Otherwise, the eigenvalues may be complex numbers.By default
eigen
does not always return the eigenvalues and eigenvectors in sorted order. Use theEVD.sort
function to put the eigenvalues in descending order and reorder the corresponding eigenvectors.- Returns:
- eign value decomposition.
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eigen
Eigenvalue Decomposition. For a symmetric matrix, all eigenvalues are real values. Otherwise, the eigenvalues may be complex numbers.By default
eigen
does not always return the eigenvalues and eigenvectors in sorted order. Use thesort
function to put the eigenvalues in descending order and reorder the corresponding eigenvectors.- Parameters:
vl
- The flag if computing the left eigenvectors.vr
- The flag if computing the right eigenvectors.overwrite
- The flag if the decomposition overwrites this matrix.- Returns:
- eigen value decomposition.
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