SourcePro® 2023.1 |
SourcePro® API Reference Guide |
Encapsulates upper triangular matrices, which are 0
above the diagonal.
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#include <rw/lapack/utrimat.h>
Public Member Functions | |
RWUpperTriMat () | |
RWUpperTriMat (const RWUpperTriMat< TypeT > &rhs) | |
RWUpperTriMat (unsigned n, unsigned nAgain) | |
RWUpperTriMat (const RWMathVec< TypeT > &data, unsigned n, unsigned nAgain) | |
RWUpperTriMat (const typename rw_linear_algebra_traits< TypeT >::narrow_upper_tri_mat &re) | |
RWUpperTriMat (const RWUpperTriMat< double > &re, const RWUpperTriMat< double > &im) | |
~RWUpperTriMat () | |
RWRORef< TypeT > | bcref (int i, int j) |
TypeT | bcset (int i, int j, TypeT x) |
TypeT | bcval (int i, int j) const |
unsigned | binaryStoreSize () const |
unsigned | cols () const |
RWUpperTriMat< TypeT > | copy () const |
TypeT * | data () |
const TypeT * | data () const |
RWMathVec< TypeT > | dataVec () |
const RWMathVec< TypeT > & | dataVec () const |
RWUpperTriMat< TypeT > | deepCopy () const |
void | deepenShallowCopy () |
RWUpperTriMat< TypeT > | leadingSubmatrix (int k) |
bool | operator!= (const RWUpperTriMat< TypeT > &X) |
RWRORef< TypeT > | operator() (int i, int j) |
TypeT | operator() (int i, int j) const |
RWUpperTriMat< TypeT > & | operator*= (const RWUpperTriMat< TypeT > &m) |
RWUpperTriMat< TypeT > & | operator*= (TypeT v) |
RWUpperTriMat< TypeT > & | operator+= (const RWUpperTriMat< TypeT > &m) |
RWUpperTriMat< TypeT > & | operator-= (const RWUpperTriMat< TypeT > &m) |
RWUpperTriMat< TypeT > & | operator/= (const RWUpperTriMat< TypeT > &m) |
RWUpperTriMat< TypeT > & | operator/= (TypeT v) |
RWUpperTriMat< TypeT > & | operator= (const RWUpperTriMat< TypeT > &A) |
bool | operator== (const RWUpperTriMat< TypeT > &X) |
void | printOn (std::ostream &os) const |
RWRORef< TypeT > | ref (int i, int j) |
RWUpperTriMat< TypeT > & | reference (RWUpperTriMat< TypeT > &m) |
void | resize (unsigned m, unsigned n) |
void | restoreFrom (RWvistream &is) |
void | restoreFrom (RWFile &f) |
unsigned | rows () const |
void | saveOn (RWvostream &os) const |
void | saveOn (RWFile &f) const |
void | scanFrom (std::istream &is) |
TypeT | set (int i, int j, TypeT x) |
TypeT | val (int i, int j) const |
void | zero () |
Related Functions | |
(Note that these are not member functions.) | |
template<class TypeT > | |
RWUpperTriMat< typename rw_numeric_traits< TypeT >::norm_type > | abs (const RWUpperTriMat< TypeT > &A) |
RWUpperTriMat< double > | arg (const RWUpperTriMat< DComplex > &A) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | conj (const RWUpperTriMat< TypeT > &A) |
RWUpperTriMat< double > | imag (const RWUpperTriMat< DComplex > &A) |
double | maxValue (const RWUpperTriMat< double > &A) |
float | maxValue (const RWUpperTriMat< float > &A) |
double | minValue (const RWUpperTriMat< double > &A) |
float | minValue (const RWUpperTriMat< float > &A) |
RWUpperTriMat< double > | norm (const RWUpperTriMat< DComplex > &A) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator* (const RWUpperTriMat< TypeT > &, const RWUpperTriMat< TypeT > &) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator* (const RWUpperTriMat< TypeT > &A, TypeT x) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator* (TypeT x, const RWUpperTriMat< TypeT > &A) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator+ (const RWUpperTriMat< TypeT > &m) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator+ (const RWUpperTriMat< TypeT > &, const RWUpperTriMat< TypeT > &) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator- (const RWUpperTriMat< TypeT > &m) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator- (const RWUpperTriMat< TypeT > &, const RWUpperTriMat< TypeT > &) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator/ (const RWUpperTriMat< TypeT > &, const RWUpperTriMat< TypeT > &) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | operator/ (const RWUpperTriMat< TypeT > &A, TypeT x) |
template<class TypeT > | |
std::ostream & | operator<< (std::ostream &s, const RWUpperTriMat< TypeT > &m) |
template<class TypeT > | |
std::istream & | operator>> (std::istream &s, RWUpperTriMat< TypeT > &m) |
template<class TypeT > | |
RWMathVec< TypeT > | product (const RWUpperTriMat< TypeT > &A, const RWMathVec< TypeT > &x) |
template<class TypeT > | |
RWMathVec< TypeT > | product (const RWMathVec< TypeT > &x, const RWUpperTriMat< TypeT > &A) |
RWUpperTriMat< double > | real (const RWUpperTriMat< DComplex > &A) |
template<class TypeT > | |
RWUpperTriMat< TypeT > | toUpperTriMat (const RWGenMat< TypeT > &A) |
template<class TypeT > | |
RWLowerTriMat< TypeT > | transpose (const RWUpperTriMat< TypeT > &) |
The class RWUpperTriMat encapsulates upper triangular matrices. An upper triangular matrix is 0 above the diagonal.
The matrix is stored column-by-column. For example, the matrix:
\[ \begin{bmatrix} A_{11} & A_{12} & A_{13} & ...A_{1n} \\ 0 & A_{22} & A_{23} & ...A_{2n} \\ 0 & 0 & A_{33} & ...A_{3n} \\ & & . & \\ & & . & \\ & & . & \\ 0 & 0 & 0 & ...A_{nn} \end{bmatrix} \]
is stored as follows:
[ A11 A12 A22 A13 A23 A33 ... A1n A2n A3n ... Ann ]
The mapping between the array and storage vector is as follows:
\[ A(i+1,j+1) \rightarrow vec \left [\frac{j(j+1)}{2+i} \right ] \]
RWUpperTriMat< TypeT >::RWUpperTriMat | ( | ) |
Default constructor. Builds a matrix of size 0 x 0. This constructor is necessary to declare a matrix with no explicit constructor or to declare an array of matrices.
RWUpperTriMat< TypeT >::RWUpperTriMat | ( | const RWUpperTriMat< TypeT > & | rhs | ) |
Builds a copy of its argument, rhs. Note that the new matrix references the data of rhs. To construct a matrix with its own copy of the data, you can use copy() or deepenShallowCopy().
RWUpperTriMat< TypeT >::RWUpperTriMat | ( | unsigned | n, |
unsigned | nAgain | ||
) |
Defines an uninitialized matrix of size n x n.
RWUpperTriMat< TypeT >::RWUpperTriMat | ( | const RWMathVec< TypeT > & | data, |
unsigned | n, | ||
unsigned | nAgain | ||
) |
Constructs a size n x n matrix using the data in the passed vector. This data must be stored in the format described in the Storage Scheme section. The resultant matrix references the data in vector data.
RWUpperTriMat< TypeT >::RWUpperTriMat | ( | const typename rw_linear_algebra_traits< TypeT >::narrow_upper_tri_mat & | re | ) |
Constructs a complex matrix from the real part supplied. The imaginary part is assumed to be 0.
RWUpperTriMat< TypeT >::RWUpperTriMat | ( | const RWUpperTriMat< double > & | re, |
const RWUpperTriMat< double > & | im | ||
) |
Constructs a complex matrix from the real and imaginary parts supplied.
RWUpperTriMat< TypeT >::~RWUpperTriMat | ( | ) |
Destructor.
RWRORef<TypeT> RWUpperTriMat< TypeT >::bcref | ( | int | i, |
int | j | ||
) |
Returns a reference to the ij th element of the matrix, after doing bounds checking.
TypeT RWUpperTriMat< TypeT >::bcset | ( | int | i, |
int | j, | ||
TypeT | x | ||
) |
Sets the ij th element of the matrix equal to x, after doing bounds checking.
TypeT RWUpperTriMat< TypeT >::bcval | ( | int | i, |
int | j | ||
) | const |
Returns the value of the ij th element of the matrix, after doing bounds checking.
unsigned RWUpperTriMat< TypeT >::binaryStoreSize | ( | ) | const |
Returns the number of bytes that it would take to write the matrix to a file using saveOn().
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Returns the number of columns in the matrix.
RWUpperTriMat<TypeT> RWUpperTriMat< TypeT >::copy | ( | ) | const |
Creates a copy of this matrix with distinct data. The stride of the data vector in the new matrix is guaranteed to be 1.
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Returns a pointer to the first item of data in the vector storing the matrix's data. You can use this (with caution!) to pass the matrix's data to C or FORTRAN subroutines. Be aware that the stride of the data vector may not be 1.
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Returns a pointer to the first item of data in the vector storing the matrix's data. You can use this (with caution!) to pass the matrix's data to C or FORTRAN subroutines. Be aware that the stride of the data vector may not be 1.
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Returns the matrix's data vector. This is where the explicitly stored entries in the matrix are kept.
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Returns the matrix's data vector. This is where the explicitly stored entries in the matrix are kept.
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Creates a copy of this matrix with distinct data. The stride of the data vector in the new matrix is guaranteed to be 1.
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Ensures that the data in the matrix is not shared by any other matrix or vector. Also ensures that the stride in the data vector is equal to 1. If necessary, a new copy of the data vector is made.
RWUpperTriMat<TypeT> RWUpperTriMat< TypeT >::leadingSubmatrix | ( | int | k | ) |
Returns the k x k upper left corner of the matrix. The submatrix and the matrix share the same data.
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Inequality operator. Returns false
if two matrices have the same size and their elements are all exactly the same. Otherwise this function returns true
. Be aware that floating point arithmetic is not exact; matrices that are theoretically equal are not always numerically equal.
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Accesses the ij th element. A reference type is returned, so this operator can be used for assigning or accessing an element. In this case, using this operator is equivalent to calling the ref() member function. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK
is defined before including the header file.
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Accesses the ij th element. A value is returned, so this operator can be used only for accessing an element. Using this operator is equivalent to calling the val() member function. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK
is defined before including the header file.
RWUpperTriMat<TypeT>& RWUpperTriMat< TypeT >::operator*= | ( | const RWUpperTriMat< TypeT > & | m | ) |
Performs element-by-element arithmetic on the data in the matrices. This function does element-by-element multiplication, not inner product style matrix multiplication. You can use the product() global function to do matrix-matrix inner product multiplication.
RWUpperTriMat<TypeT>& RWUpperTriMat< TypeT >::operator*= | ( | TypeT | v | ) |
Performs the indicated operation on each element of the matrix.
RWUpperTriMat<TypeT>& RWUpperTriMat< TypeT >::operator+= | ( | const RWUpperTriMat< TypeT > & | m | ) |
Performs element-by-element arithmetic on the data in the matrices.
RWUpperTriMat<TypeT>& RWUpperTriMat< TypeT >::operator-= | ( | const RWUpperTriMat< TypeT > & | m | ) |
Performs element-by-element arithmetic on the data in the matrices.
RWUpperTriMat<TypeT>& RWUpperTriMat< TypeT >::operator/= | ( | const RWUpperTriMat< TypeT > & | m | ) |
Performs element-by-element arithmetic on the data in the matrices.
RWUpperTriMat<TypeT>& RWUpperTriMat< TypeT >::operator/= | ( | TypeT | v | ) |
Performs the indicated operation on each element of the matrix.
RWUpperTriMat<TypeT>& RWUpperTriMat< TypeT >::operator= | ( | const RWUpperTriMat< TypeT > & | A | ) |
Sets the matrix elements equal to the elements of A. The two matrices must be the same size. To make the matrix reference the same data as A, use reference().
bool RWUpperTriMat< TypeT >::operator== | ( | const RWUpperTriMat< TypeT > & | X | ) |
Equality operator. Returns true
if two matrices have the same size and their elements are all exactly the same. Otherwise this function returns false
. Be aware that floating point arithmetic is not exact; matrices that are theoretically equal are not always numerically equal.
void RWUpperTriMat< TypeT >::printOn | ( | std::ostream & | os | ) | const |
Prints the matrix to an output stream in human readable format.
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inline |
Returns a reference to the ij th element of the matrix. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK
is defined when the header file is read. The member function bcref() does the same thing with guaranteed bounds checking.
RWUpperTriMat<TypeT>& RWUpperTriMat< TypeT >::reference | ( | RWUpperTriMat< TypeT > & | m | ) |
Makes this matrix a reference to the matrix m. The two matrices share the same data. The matrices do not have to be the same size before calling reference(). To copy a matrix into another of the same size, use operator=().
void RWUpperTriMat< TypeT >::resize | ( | unsigned | m, |
unsigned | n | ||
) |
Resizes the matrix. Any new entries in the matrix are set to 0. Both arguments must be the same.
void RWUpperTriMat< TypeT >::restoreFrom | ( | RWvistream & | is | ) |
Reads in a matrix from an RWvistream, the Rogue Wave virtual input stream class. The matrix must have been stored to the stream using the saveOn() member function.
void RWUpperTriMat< TypeT >::restoreFrom | ( | RWFile & | f | ) |
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Returns the number of rows in the matrix.
void RWUpperTriMat< TypeT >::saveOn | ( | RWvostream & | os | ) | const |
Stores a matrix to an RWvostream, the Rogue Wave virtual output stream class. The matrix can be read using restoreFrom().
void RWUpperTriMat< TypeT >::saveOn | ( | RWFile & | f | ) | const |
Stores a matrix to an RWFile. The matrix can be read using the restoreFrom() member function.
void RWUpperTriMat< TypeT >::scanFrom | ( | std::istream & | is | ) |
Reads a matrix from an input stream. The format of the matrix is the same as the format output by printOn(). Below is a sample matrix that could be input. Note that extra white space and any text preceding the dimension specification are ignored. Only the upper triangle of the matrix is used.
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Sets the ij thelement of the matrix equal to x. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK
is defined when the header file is read. The member function bcset() does the same thing with guaranteed bounds checking.
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Returns the value of the ij th element of the matrix. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK
is defined when the header file is read. The member function bcval() does the same thing with guaranteed bounds checking.
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Sets every element of the matrix to 0.
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Returns a matrix whose entries are the absolute value of the argument. The absolute value of a complex number is considered to be the sum of the absolute values of its real and imaginary parts. To get the norm of a complex matrix, you can use the norm() function.
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Returns a matrix where each element is the argument of the corresponding element in the matrix A.
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Returns a matrix where each element is the complex conjugate of the corresponding element in the matrix A.
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Returns a matrix where each element is the imaginary part of the corresponding element in the matrix A.
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Returns the maximum entry in the matrix.
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Returns the maximum entry in the matrix.
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Returns the maximum entry in the matrix.
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Returns the maximum entry in the matrix.
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Returns a matrix where each element is the norm (magnitude) of the corresponding element in the matrix A.
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Performs element-by-element operations on the arguments. To do inner product matrix multiplication, you can use the product() global function.
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Performs element-by-element multiplication on the arguments.
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Performs element-by-element multiplication on the arguments.
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Unary plus operator. Returns a copy of the matrix m.
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Performs element-by-element addition on the arguments.
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Unary minus operator. Returns the negation of the matrix m.
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Performs element-by-element subtraction on the arguments.
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Performs element-by-element division on the arguments.
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Performs element-by-element division on the arguments.
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Writes the matrix to the stream. This is equivalent to calling the printOn() member function.
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Reads the matrix from the stream. This is equivalent to calling the scanFrom() member function.
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Returns the inner product (matrix-vector product) of A and x.
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Returns the inner product (matrix-vector product) of x and A. This is equal to the product of A transpose and x.
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Returns a matrix where each element is the real part of the corresponding element in the matrix A.
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Extracts the upper triangular part of a square matrix.
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Returns the transpose of the argument matrix. The transpose is made to reference the same data as the argument matrix.
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