SourcePro® 2023.1 |
SourcePro® API Reference Guide |
Encapsulates a symmetric band matrix. More...
#include <rw/lapack/sbndmat.h>
Public Member Functions | |
RWSymBandMat () | |
RWSymBandMat (const RWSymBandMat< TypeT > &A) | |
RWSymBandMat (unsigned n, unsigned nAgain, unsigned hb) | |
RWSymBandMat (const RWMathVec< TypeT > &data, unsigned n, unsigned nAgain, unsigned hb) | |
RWSymBandMat (const RWSymBandMat< double > &re, const RWSymBandMat< double > &im) | |
unsigned | bandwidth () const |
RWMathVec< TypeT > | bcdiagonal (int j=0) const |
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 |
RWSymBandMat< TypeT > | copy () const |
TypeT * | data () |
RWMathVec< TypeT > | dataVec () |
RWSymBandMat< TypeT > | deepCopy () const |
void | deepenShallowCopy () |
RWMathVec< TypeT > | diagonal (int j=0) const |
unsigned | halfBandwidth () const |
RWSymBandMat< TypeT > | leadingSubmatrix (int k) |
unsigned | lowerBandwidth () const |
bool | operator!= (const RWSymBandMat< TypeT > &X) |
RWRORef< TypeT > | operator() (int i, int j) |
TypeT | operator() (int i, int j) const |
RWSymBandMat< TypeT > & | operator*= (const RWSymBandMat< TypeT > &m) |
RWSymBandMat< TypeT > & | operator*= (TypeT) |
RWSymBandMat< TypeT > & | operator+= (const RWSymBandMat< TypeT > &m) |
RWSymBandMat< TypeT > & | operator-= (const RWSymBandMat< TypeT > &m) |
RWSymBandMat< TypeT > & | operator/= (const RWSymBandMat< TypeT > &m) |
RWSymBandMat< TypeT > & | operator/= (TypeT) |
RWSymBandMat< TypeT > & | operator= (const RWSymBandMat< TypeT > &A) |
bool | operator== (const RWSymBandMat< TypeT > &X) |
void | printOn (std::ostream &) const |
RWRORef< TypeT > | ref (int i, int j) |
RWSymBandMat< TypeT > & | reference (RWSymBandMat< TypeT > &m) |
void | resize (unsigned m, unsigned n) |
void | resize (unsigned n, unsigned nAgain, unsigned halfWidth) |
void | restoreFrom (RWvistream &) |
void | restoreFrom (RWFile &) |
unsigned | rows () const |
void | saveOn (RWvostream &) const |
void | saveOn (RWFile &) const |
void | scanFrom (std::istream &) |
TypeT | set (int i, int j, TypeT x) |
unsigned | upperBandwidth () const |
TypeT | val (int i, int j) const |
void | zero () |
Related Functions | |
(Note that these are not member functions.) | |
template<class TypeT > | |
RWSymBandMat< typename rw_numeric_traits< TypeT >::norm_type > | abs (const RWSymBandMat< TypeT > &A) |
RWSymBandMat< double > | arg (const RWSymBandMat< DComplex > &A) |
RWSymBandMat< DComplex > | conj (const RWSymBandMat< DComplex > &A) |
RWSymBandMat< double > | imag (const RWSymBandMat< DComplex > &A) |
double | maxValue (const RWSymBandMat< double > &A) |
float | maxValue (const RWSymBandMat< float > &A) |
double | minValue (const RWSymBandMat< double > &A) |
float | minValue (const RWSymBandMat< float > &A) |
RWSymBandMat< double > | norm (const RWSymBandMat< DComplex > &A) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator* (const RWSymBandMat< TypeT > &, const RWSymBandMat< TypeT > &) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator* (const RWSymBandMat< TypeT > &A, TypeT x) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator* (TypeT x, const RWSymBandMat< TypeT > &A) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator+ (const RWSymBandMat< TypeT > &) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator+ (const RWSymBandMat< TypeT > &, const RWSymBandMat< TypeT > &) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator- (const RWSymBandMat< TypeT > &) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator- (const RWSymBandMat< TypeT > &, const RWSymBandMat< TypeT > &) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator/ (const RWSymBandMat< TypeT > &, const RWSymBandMat< TypeT > &) |
template<class TypeT > | |
RWSymBandMat< TypeT > | operator/ (const RWSymBandMat< TypeT > &A, TypeT x) |
template<class TypeT > | |
std::ostream & | operator<< (std::ostream &s, const RWSymBandMat< TypeT > &m) |
template<class TypeT > | |
std::istream & | operator>> (std::istream &s, RWSymBandMat< TypeT > &m) |
template<class TypeT > | |
RWMathVec< TypeT > | product (const RWSymBandMat< TypeT > &A, const RWMathVec< TypeT > &x) |
template<class TypeT > | |
RWMathVec< TypeT > | product (const RWMathVec< TypeT > &x, const RWSymBandMat< TypeT > &A) |
RWSymBandMat< double > | real (const RWSymBandMat< DComplex > &A) |
template<class TypeT > | |
RWSymBandMat< TypeT > | toSymBandMat (const RWBandMat< TypeT > &A) |
template<class TypeT > | |
RWSymBandMat< TypeT > | transpose (const RWSymBandMat< TypeT > &) |
The class RWSymBandMat encapsulates symmetric band matrices. A symmetric banded matrix is symmetric, and nonzero only near the diagonal. Specifically, if h is the half bandwidth, then any entries for which \(i-j > h\) or \(j-i > h\) are defined to be 0; in addition, an entry \(A_{ij} = A_{ji}\).
As an example of the storage scheme, consider the following 9 x 9 matrix with a half bandwidth of two:
\[ \begin{bmatrix} & A_{11} & A_{12} & A_{13} & 0 & 0 & 0 & 0 & 0 & 0 \\ & A_{12} & A_{22} & A_{23} & A_{24} & 0 & 0 & 0 & 0 & 0 \\ & A_{13} & A_{23} & A_{33} & A_{34} & A_{35} & 0 & 0 & 0 & 0 \\ & 0 & A_{24} & A_{34} & A_{44} & A_{45} & A_{46} & 0 & 0 & 0 \\ & 0 & 0 & A_{35} & A_{45} & A_{55} & A_{56} & A_{57} & 0 & 0 \\ & 0 & 0 & 0 & A_{46} & A_{56} & A_{66} & A_{67} & A_{68} & 0 \\ & 0 & 0 & 0 & 0 & A_{57} & A_{67} & A_{77} & A_{78} & A_{79} \\ & 0 & 0 & 0 & 0 & 0 & A_{68} & A_{78} & A_{88} & A_{89} \\ & 0 & 0 & 0 & 0 & 0 & 0 & A_{79} & A_{89} & A_{99} \\ \end{bmatrix} \]
The upper triangle is stored column by column. For convenience, there are some unused locations left in the vector of data. These are indicated as XXX
in the following illustration of the storage vector:
[ XXX XXX A11 XXX A12 A22 A13 A23 A33 A24 A34 A44 A35 A45 A55 A46 A56 A66 A57 A67 A77 A68 A78 A88 A79 A89 A99 ]
The mapping between the array and storage vector is as follows:
\[ A(i + 1, j + 1) \to \left\{ \begin{array}{l l} \text{vec}[i + \text{halfwidth} + j*\text{halfwidth}] & \quad \text{if } j \geq i \\ \text{vec}[j + \text{halfwidth} + i*\text{halfwidth}] & \quad \text{if } j < i \\ \end{array} \right. \]
RWSymBandMat< TypeT >::RWSymBandMat | ( | ) |
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.
RWSymBandMat< TypeT >::RWSymBandMat | ( | const RWSymBandMat< TypeT > & | A | ) |
Build a copy of its argument, A. Note that the new matrix references A's data. To construct a matrix with its own copy of the data, you can use either the copy() or deepenShallowCopy() member functions.
RWSymBandMat< TypeT >::RWSymBandMat | ( | unsigned | n, |
unsigned | nAgain, | ||
unsigned | hb | ||
) |
Defines an uninitialized matrix of size n x nAgain with half bandwidth hb.
RWSymBandMat< TypeT >::RWSymBandMat | ( | const RWMathVec< TypeT > & | data, |
unsigned | n, | ||
unsigned | nAgain, | ||
unsigned | hb | ||
) |
Constructs an n x nAgain matrix with half bandwidth hb 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.
RWSymBandMat< TypeT >::RWSymBandMat | ( | const RWSymBandMat< double > & | re, |
const RWSymBandMat< double > & | im | ||
) |
Constructs a complex matrix from the real and imaginary parts supplied. If no imaginary part is supplied, it is assumed to be 0.
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Returns the bandwidth of the matrix. The bandwidth is twice the half bandwidth plus 1 for the main diagonal.
RWMathVec<TypeT> RWSymBandMat< TypeT >::bcdiagonal | ( | int | j = 0 | ) | const |
Returns a reference to the j th diagonal of the matrix, after doing bounds checking. The main diagonal is indexed by 0, diagonals in the upper triangle are indexed with positive integers, diagonals in the lower triangle are indexed with negative integers.
RWRORef<TypeT> RWSymBandMat< TypeT >::bcref | ( | int | i, |
int | j | ||
) |
Returns a reference to the ij th element of the matrix, after doing bounds checking.
TypeT RWSymBandMat< TypeT >::bcset | ( | int | i, |
int | j, | ||
TypeT | x | ||
) |
Sets the ij th element of the matrix equal to x, after doing bounds checking.
TypeT RWSymBandMat< TypeT >::bcval | ( | int | i, |
int | j | ||
) | const |
Returns the value of the ij th element of the matrix, after doing bounds checking.
unsigned RWSymBandMat< 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.
RWSymBandMat<TypeT> RWSymBandMat< 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 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 ensure that the stride in the data vector is equal to 1. If necessary, a new copy of the data vector is made.
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Returns a reference to the j th diagonal of the matrix. The main diagonal is indexed by 0, diagonals in the upper triangle are indexed with positive integers, and diagonals in the lower triangle are indexed with negative integers. Bounds checking is done if the preprocessor symbol RWBOUNDS_CHECK
is defined when the header file is read. The member function bcdiagonal() does the same thing with guaranteed bounds checking.
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Returns the half bandwidth of the matrix.
RWSymBandMat<TypeT> RWSymBandMat< 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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Returns the lower bandwidth of the matrix.
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Two matrices are considered equal if they have the same size and their elements are all exactly the same. Be aware that floating point arithmetic is not exact; matrices that are theoretically equal are not always numerically equal.
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Returns a reference to the ij th element of the matrix. 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. 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.
RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator*= | ( | const RWSymBandMat< TypeT > & | m | ) |
Performs element-by-element arithmetic on the data in the matrices.
RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator*= | ( | TypeT | ) |
Performs the indicated operation on each element of the matrix.
RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator+= | ( | const RWSymBandMat< TypeT > & | m | ) |
Performs element-by-element arithmetic on the data in the matrices.
RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator-= | ( | const RWSymBandMat< TypeT > & | m | ) |
Performs element-by-element arithmetic on the data in the matrices.
RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator/= | ( | const RWSymBandMat< TypeT > & | m | ) |
Performs element-by-element arithmetic on the data in the matrices.
RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator/= | ( | TypeT | ) |
Performs the indicated operation on each element of the matrix.
RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::operator= | ( | const RWSymBandMat< 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 the reference() member function.
bool RWSymBandMat< TypeT >::operator== | ( | const RWSymBandMat< TypeT > & | X | ) |
Two matrices are considered equal if they have the same size and their elements are all exactly the same. Be aware that floating point arithmetic is not exact; matrices that are theoretically equal are not always numerically equal.
void RWSymBandMat< TypeT >::printOn | ( | std::ostream & | ) | const |
Prints the matrix to an output stream in human readable format.
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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.
RWSymBandMat<TypeT>& RWSymBandMat< TypeT >::reference | ( | RWSymBandMat< TypeT > & | m | ) |
Makes this matrix a reference to the argument matrix. 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 the operator=() member operator.
void RWSymBandMat< TypeT >::resize | ( | unsigned | m, |
unsigned | n | ||
) |
Resizes the matrix or changes both its size and half bandwidth. Any new entries in the matrix are set to 0. Both arguments must be the same.
void RWSymBandMat< TypeT >::resize | ( | unsigned | n, |
unsigned | nAgain, | ||
unsigned | halfWidth | ||
) |
Resizes the matrix or changes both its size and half bandwidth. Any new entries in the matrix are set to 0. Both arguments must be the same.
void RWSymBandMat< TypeT >::restoreFrom | ( | RWvistream & | ) |
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 RWSymBandMat< TypeT >::restoreFrom | ( | RWFile & | ) |
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Returns the number of rows in the matrix.
void RWSymBandMat< TypeT >::saveOn | ( | RWvostream & | ) | const |
Stores a matrix to an RWvostream, the Rogue Wave virtual output stream class. The matrix can be read using the restoreFrom() member function.
void RWSymBandMat< TypeT >::saveOn | ( | RWFile & | ) | const |
Stores a matrix to an RWFile. The matrix can be read using the restoreFrom() member function.
void RWSymBandMat< TypeT >::scanFrom | ( | std::istream & | ) |
Reads a matrix from an input stream. The format of the matrix is the same as the format output by the printOn() member function: first the half bandwidth, followed by the matrix itself. Below is a sample matrix showing the format. Note that extra white space and text preceding the bandwidth specification are ignored. Only the symmetric part of the relevant band of the matrix is used.
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Sets the ij th element 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 upper bandwidth of the matrix.
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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 minimum entry in the matrix.
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Returns the minimum 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 operation on the arguments. To do inner product matrix multiplication, you can use the product() global function.
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Performs element-by-element operations on the arguments.
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Performs element-by-element operations on the arguments.
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Unary plus operator. Returns a copy of the matrix.
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Performs element-by-element operation on the arguments.
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Unary minus operator. Returns a copy of matrix's negation.
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Performs element-by-element operation on the arguments.
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Performs element-by-element operation on the arguments.
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Performs element-by-element operations 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 symmetric part of a banded matrix. The symmetric part of the banded matrix A is \((A + A^{T})/2\).
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Returns the transpose of the argument matrix.
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