 | Double |
Class DoubleComplexLowerTriMatrix represents a lower triangular matrix of double-precision
complex numbers. A lower triangular matrix is a square matrix with all elements
above the main diagonal equal to zero.
Inheritance HierarchyNamespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4
SyntaxThe DoubleComplexLowerTriMatrix type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | DoubleComplexLowerTriMatrix(DoubleComplexMatrix) | Constructs a square DoubleComplexLowerTriMatrix instance by extracting the lower triangular part of a square general matrix. |
| DoubleComplexLowerTriMatrix(DoubleComplexVector) | Constructs a square DoubleComplexLowerTriMatrix instance using the data in the given vector. |
| DoubleComplexLowerTriMatrix(DoubleHermitianMatrix) | Constructs a square DoubleComplexLowerTriMatrix instance by extracting the lower triangular part of an Hermitian matrix. |
| DoubleComplexLowerTriMatrix(Int32) | Constructs a square DoubleComplexLowerTriMatrix instance with the specified size. All elements are initialized to zero. |
| DoubleComplexLowerTriMatrix(DoubleComplexMatrix, Int32) | Constructs a square DoubleComplexLowerTriMatrix instance by extracting the lower triangular part of the specified leading square submatrix of a general matrix. |
| DoubleComplexLowerTriMatrix(DoubleComplexVector, Int32) | Constructs a square DoubleComplexLowerTriMatrix instance with the specified size, and using the data in the given vector. |
Properties| Name | Description | |
|---|---|---|
 | Cols | Gets the number of columns in the matrix. |
| DataVector | Gets the data vector referenced by this matrix. |
| Item | Gets and sets the value at the specified position. Zero matrix elements are not stored, so assigning a non-zero value to a matrix element above the diagonal of the matrix raises an exception. |
| Order | Gets the order of the matrix. |
| Rows | Gets the number of rows in the matrix. |
Methods| Name | Description | |
|---|---|---|
 | Add(DoubleComplex, DoubleComplexLowerTriMatrix) | Adds a scalar and a lower triangular matrix. |
| Add(DoubleComplexLowerTriMatrix, DoubleComplex) | Adds a lower triangular matrix and a scalar. |
| Add(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Adds two lower triangular matrices. |
| Clone | Creates a deep copy of this matrix. |
| DeepenThisCopy | Guarantees that there is only one reference to the underlying data and that this data is in contiguous storage. |
| Divide(DoubleComplex, DoubleComplexLowerTriMatrix) | Divide a scalar by a lower triangular matrix. |
| Divide(DoubleComplexLowerTriMatrix, DoubleComplex) | Divide a lower triangular matrix by a scalar. |
| Divide(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Divide a lower triangular matrix by another. |
| Equals |
Tests for equality of this matrix and another matrix.
Two matrices are equal if they have the same dimensions
and all values are equal.
(Overrides ObjectEquals(Object)) |
| GetHashCode |
Returns an integer hash code for this matrix.
(Overrides ObjectGetHashCode) |
| LeadingSubmatrix | Returns the k by k upper left corner of the matrix. The matrix and the submatrix share the same data. |
| Multiply(DoubleComplex, DoubleComplexLowerTriMatrix) | Multiply a scalar and a lower triangular matrix. |
| Multiply(DoubleComplexLowerTriMatrix, DoubleComplex) | Multiply a lower triangular matrix and a scalar. |
| Multiply(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Multiply two lower triangular matrices. |
| Negate | Negation operator. |
| OnDeserialized | Checks that the matrix is square following deserialization |
| Resize | Changes the order of this matrix to that specified, adding zeros or truncating as necessary. |
| ShallowCopy | Creates a shallow copy of this matrix. |
| Subtract(DoubleComplex, DoubleComplexLowerTriMatrix) | Subtracts a lower triangular matrix from a scalar. |
| Subtract(DoubleComplexLowerTriMatrix, DoubleComplex) | Subtracts a scalar from a lower triangular matrix. |
| Subtract(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Subtracts one lower triangular matrix from another. |
| ToGeneralMatrix | Converts this triangular matrix to a general matrix. |
 | ToString |
Returns a formatted string representation of this matrix.
(Overrides ObjectToString) |
| ToString(String) | Returns a formatted string representation of this matrix. Numbers are displayed using the specified format. |
| ToTabDelimited | Returns a formatted string representation of this matrix using tabs and newlines. |
| ToTabDelimited(String) | Returns a formatted string representation of this matrix using tabs and newlines. Numbers are formatted using the specified format string. |
| Transpose | Transposes this matrix. |
Operators| Name | Description | |
|---|---|---|
 | Addition(DoubleComplex, DoubleComplexLowerTriMatrix) | Adds a scalar and a lower triangular matrix. |
| Addition(DoubleComplexLowerTriMatrix, DoubleComplex) | Adds a lower triangular matrix and a scalar. |
| Addition(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Adds two lower triangular matrices. |
| Division(DoubleComplex, DoubleComplexLowerTriMatrix) | Divide a scalar by a lower triangular matrix. |
| Division(DoubleComplexLowerTriMatrix, DoubleComplex) | Divide a lower triangular matrix by a scalar. |
| Division(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Divide a lower triangular matrix by another. |
| Equality(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Tests for equality of two lower triangular matrices. Two matrices are equal if they have the same dimensions and all values are equal. |
| (DoubleLowerTriMatrix to DoubleComplexLowerTriMatrix) | Implicitly converts a DoubleLowerTriMatrix instance into a DoubleComplexLowerTriMatrix instance. |
| (FloatComplexLowerTriMatrix to DoubleComplexLowerTriMatrix) | Implicitly converts a FloatComplexLowerTriMatrix instance into a DoubleComplexLowerTriMatrix instance. |
| Inequality(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Tests for inequality of two lower triangular matrices. Two matrices are equal if they have the same dimensions and all values are equal. |
| Multiply(DoubleComplex, DoubleComplexLowerTriMatrix) | Multiply a scalar and a lower triangular matrix. |
| Multiply(DoubleComplexLowerTriMatrix, DoubleComplex) | Multiply a lower triangular matrix and a scalar. |
| Multiply(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Multiply two lower triangular matrices. |
| Subtraction(DoubleComplex, DoubleComplexLowerTriMatrix) | Subtracts a lower triangular matrix from a scalar. |
| Subtraction(DoubleComplexLowerTriMatrix, DoubleComplex) | Subtracts a scalar from a lower triangular matrix. |
| Subtraction(DoubleComplexLowerTriMatrix, DoubleComplexLowerTriMatrix) | Subtracts one lower triangular matrix from another. |
| UnaryNegation(DoubleComplexLowerTriMatrix) | Negation operator. |
| UnaryPlus(DoubleComplexLowerTriMatrix) | Unary + operator. Just returns the input matrix. |
Remarks
The matrix is stored in a vector row by row. For efficiency, zero elements are not stored.
For example, the following 5 by 5 lower triangular matrix:
is stored in a data vector v as:
In general, A[i,j] = v[i(i+1)/2 + j].
C#
| a00 0 0 0 0 | | a10 a11 0 0 0 | A = | a20 a21 a22 0 0 | | a30 a31 a32 a33 0 | | a40 a41 a42 a43 a44 |
C#
v = [a00 a10 a11 a20 a21 a22 a30 a31 a32 a33 a40 a41 a42 a43 a44 ]
See Also