Topic Index

Linear Algebra Module User's Guide
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Topic Index

Click on one of the letters below to jump immediately to that section of the index.

A | B | C | D | E | F | G | H | I | L | M | N | O | P | Q | R | S | T | U | V | W

A

accessing and modifying data in matrices [in 3.5 Accessing Data]
accessing components of complex matrices [in 3.5.6 Components of Complex Matrices]
accessing rows, columns, diagonals [in 3.5.5 Rows, Columns and Diagonals]
accessing the leading submatrix [in 3.7.2 Leading Submatrices]

B

balance decompositions [in 7.5 Hessenberg and Balance Decompositions]
banded matrix types [in 3.3 Matrix Precision and Shape]
banded matrix, defined [in 3.3 Matrix Precision and Shape]
bcdiagonal() [in 3.5.5 Rows, Columns and Diagonals]
BLAS [in 9.4 Basic Linear Algebra Package]
rwBlaInitStatics() [in 9.4 Basic Linear Algebra Package]
bounds checking [in 3.5.2 Bounds Checking]

C

calculating determinants [in 4.4.1 Determinants]
calculating matrix inverses [in 4.4.2 Matrix Inverses]
calculating the condition number [in 4.4.3 Condition Number]
change log [in A.1 Purpose]
changing a matrix element [in 3.5.1 Individual Elements]
Cholesky decomposition method [in 5.3 Implementations Provided]
Cholesky
   least squares factorization object [in 5.3 Implementations Provided]
classes
   general matrix [in 3.3 Matrix Precision and Shape]
   Hermitian banded matrix [in 3.3 Matrix Precision and Shape]
   Hermitian matrix [in 3.3 Matrix Precision and Shape]
   kinds of [in 2.2 Kinds of Classes]
   lower-triangular matrix [in 3.3 Matrix Precision and Shape]
   symmetric banded matrix [in 3.3 Matrix Precision and Shape]
   symmetric matrix [in 3.3 Matrix Precision and Shape]
   templatized [in A.3.1 Summary of Changes]
   upper-triangular matrix [in 3.3 Matrix Precision and Shape]
   vector [in 3.1 Defining Vectors]
cols() [in 3.5.5 Rows, Columns and Diagonals]
complete orthogonal decomposition [in 5.3 Implementations Provided]
   [in 8.1 Kinds of Decompositions]
complete orthogonal decomposition, defined [in 8.3.1 Complete Orthogonal Decomposition]
complex eigenvalues [in 7.1 Defining the Problem]
computing selected eigenvalues [in 6.4 Computing Selected Eigenvalues]
condition numbers [in 4.4.3 Condition Number]
copy constructor, defined [in 3.4 Copy Constructors - References and Copies]

D

datavec()
   interfacing with another language [in 3.5.7 Direct Access to Data]
decomposition classes
   three kinds [in 8.1 Kinds of Decompositions]
decomposition
   balance [in 7.5 Hessenberg and Balance Decompositions]
   complete orthogonal [in 8.3.1 Complete Orthogonal Decomposition]
      [in 8.3 QR Decomposition and Complete Orthogonal Decomposition]
   Hessenberg [in 2.2 Kinds of Classes]
      [in 2.3.5 Nonsymmetric Eigenvalue Decomposition Classes]
      [in 7.3 Servers]
      [in 7.5 Hessenberg and Balance Decompositions]
   QR [in 2.2 Kinds of Classes]
      [in 5.3 Implementations Provided]
      [in 8.1 Kinds of Decompositions]
      [in 8.3 QR Decomposition and Complete Orthogonal Decomposition]
   Schur [in 7.3 Servers]
      [in 7.4 Schur Decompositions]
   singular value [in 2.2 Kinds of Classes]
      [in 8.1 Kinds of Decompositions]
      [in 8.2 Singular Value Decomposition]
determinants, calculating [in 4.4.1 Determinants]
diagonal() [in 3.5.5 Rows, Columns and Diagonals]

E

eigenvalue decomposition server object, defined [in 6.3 Servers]
eigenvalues, complex [in 7.1 Defining the Problem]
error checking
   testing the factorization [in 4.2.1 Error Checking]
example
   computing eigenvalues and eigenvectors [in 6.2 Decomposition Object]
      [in 7.2 Decomposition Object]
   computing eigenvalues in a range [in 6.4 Computing Selected Eigenvalues]
   computing eigenvectors only [in 6.2 Decomposition Object]
   computing the ith through jth eigenvalues [in 6.4 Computing Selected Eigenvalues]
   data in a tridiagonal matrix [in 3.5.7 Direct Access to Data]
   element access with val() and set() [in 3.5.4 val() and set()]
   modifying real and imaginary matrix parts [in 3.5.6 Components of Complex Matrices]
   operating on explicitly stored elements [in 3.5.7 Direct Access to Data]
   printing the components of an SVD [in 8.2 Singular Value Decomposition]
   runtime error caused by bounds check [in 3.5.2 Bounds Checking]
   runtime error with operator()(int,int) [in 3.5.3 Changing Elements with operator()()]
   side effects of operator()(int,int) [in 3.5.3 Changing Elements with operator()()]
   solving a least squares problem [in 5.2 Solving a Least Squares Problem]
   solving several systems of equations [in 4.3 Solving Several Systems of Equations]
   subscripting [in 3.1 Defining Vectors]
   tridiagonal matrix class [in 3.2 Defining Matrices]
   two objects referencing the same data [in 3.4 Copy Constructors - References and Copies]
   type conversions between tridiagonal matrices [in 3.6.1 Converting Precisions]
   undetected out-of-bounds reference [in 3.5.2 Bounds Checking]
   using a server object for more control [in 8.2.1 SVD Server Objects]
   using a server object to adjust an algorithm's parameters [in 6.4 Computing Selected Eigenvalues]
   using a specific algorithm for a computation [in 6.3 Servers]
   using real() and imag() [in 3.5.6 Components of Complex Matrices]
   using RWHessEigServer<double> to return selected eigenvectors [in 7.3 Servers]

F

factorization and decomposition, distinction between [in 2.2.1 A Note on Terminology]
factorization classes [in 4.1 Defining Factorizations]
factorization, defined [in 4.1 Defining Factorizations]
fail() [in 4.2.1 Error Checking]

L

leading submatrix [in 3.7.2 Leading Submatrices]
leadingSubmatrix() [in 3.7.2 Leading Submatrices]
least squares factorization objects
   three implementations [in 5.3 Implementations Provided]
least squares factorizations [in 5.1 Defining the Problem]
least squares problem, defined [in 5.1 Defining the Problem]
Linear Algebra Module
   capabilities [in 1.2 Product Features]
   design features [in 2.1 The Class Concept]
   kinds of classes [in 2.2 Kinds of Classes]
lower-triangular matrix types [in 3.3 Matrix Precision and Shape]
lower-triangular matrix, defined [in 3.3 Matrix Precision and Shape]

M

mapping, defined [in 3.2 Defining Matrices]
matrices
   accessing data [in 3.5 Accessing Data]
   accessing rows and columns [in 3.5.5 Rows, Columns and Diagonals]
   direct access to data [in 3.5.7 Direct Access to Data]
   storage patterns [in 3.5.7 Direct Access to Data]
   type conversion [in 3.6 Type Conversion]
matrix classes
   modifying data [in 3.5 Accessing Data]
matrix shapes and available types, list [in 3.3 Matrix Precision and Shape]
multiple threads
   with Rogue Wave BLAS library [in 9.4 Basic Linear Algebra Package]

N

nonsymmetric eigenvalue class, basic [in 7.2 Decomposition Object]
nonsymmetric eigenvalue problem, basic [in 7.1 Defining the Problem]
nonsymmetric eigenvalue servers [in 7.3 Servers]

O

object-oriented design in the Linear Algebra Module [in 2.1 The Class Concept]
operator double() [in 9.3 Helper Class Member Functions]
operator()()
   bounds checking [in 3.5.2 Bounds Checking]
operator()(int, int) [in 9.1 Function operator()(int, int)]
   changing a matrix element [in 3.5.1 Individual Elements]
   changing matrix elements [in 3.5.3 Changing Elements with operator()()]
   limitations [in 3.5.4 val() and set()]
   side effects [in 3.5.3 Changing Elements with operator()()]
operator=(double x) [in 9.3 Helper Class Member Functions]
orthogonal design
   in the Linear Algebra Module [in 2.1 The Class Concept]

P

performance
   and Rogue Wave BLAS [in 9.4 Basic Linear Algebra Package]
positive definite factorization [in 4.1 Defining Factorizations]
   [in 4.3 Solving Several Systems of Equations]
positive definite matrices
   example [in 6.3 Servers]
precision, defined [in 3.3 Matrix Precision and Shape]
precisions, converting [in 3.6.1 Converting Precisions]

Q

QR decomposition, defined [in 8.3 QR Decomposition and Complete Orthogonal Decomposition]
QR [in 8.3 QR Decomposition and Complete Orthogonal Decomposition]
least squares factorization object [in 5.3 Implementations Provided]

R

real() [in 3.5.6 Components of Complex Matrices]
referencing data [in 3.4 Copy Constructors - References and Copies]
reverse mapping [in 4.1 Defining Factorizations]
rows() [in 3.5.5 Rows, Columns and Diagonals]
runtime error
   caused by bounds checking [in 3.5.2 Bounds Checking]
   from changing elements [in 3.5.3 Changing Elements with operator()()]
   from singularity [in 4.2.1 Error Checking]
   when a reference is read-only [in 9.3 Helper Class Member Functions]
rwBlaInitStatics() [in 9.4 Basic Linear Algebra Package]
RWBOUNDS_CHECK [in 3.5.5 Rows, Columns and Diagonals]
   [in 3.5.2 Bounds Checking]
RWCJRef<T> [in 9.2 Matrix Entry Helper Classes]
RWEigDecomp<double> [in 7.2 Decomposition Object]
RWGenFact<float>
   used as temporary variable [in 4.2 Solving a System of Equations]
RWHessEigServer<double> [in 7.3 Servers]
RWHessEigServer<doublle> [in 7.3 Servers]
RWNGRef<T> [in 9.2 Matrix Entry Helper Classes]
RWROCJRef<T> [in 9.2 Matrix Entry Helper Classes]
RWRORef<T> [in 9.2 Matrix Entry Helper Classes]
RWSchurEigServer<double> [in 7.3 Servers]
RWSymEigDecomp<double> [in 6.2 Decomposition Object]
RWSymRangeEigServer<double> [in 6.4 Computing Selected Eigenvalues]
RWSymSomeEigServer<double> [in 6.4 Computing Selected Eigenvalues]
   [in 6.4 Computing Selected Eigenvalues]

S

Schur decomposition, defined [in 7.4 Schur Decompositions]
servers [in 6.3 Servers]
   [in 7.3 Servers]
set() [in 3.5.4 val() and set()]
shape, defined [in 3.3 Matrix Precision and Shape]
shapes, converting [in 3.6.2 Converting Shapes]
singular value decomposition objects [in 8.2.1 SVD Server Objects]
singular value decomposition, defined [in 8.2 Singular Value Decomposition]
skew symmetric matrix, defined [in 3.3 Matrix Precision and Shape]
solving
   a least squares problem [in 5.2 Solving a Least Squares Problem]
   a numerically underdetermined system of equations [in 5.4 Solving a Numerically Underdetermined System]
   a system of equations [in 4.2 Solving a System of Equations]
   several systems of equations [in 4.3 Solving Several Systems of Equations]
storage patterns [in 3.5.7 Direct Access to Data]
submatrices
   accessing with subscripting [in 3.7.1 General Matrices]
   two mechanisms for extraction and operation [in 3.7 Submatrices]
subscripting operator [in 3.5.3 Changing Elements with operator()()]
subscripting [in 3.7.1 General Matrices]
SVD
   least squares factorization object [in 5.3 Implementations Provided]
symmetric banded matrix types [in 3.3 Matrix Precision and Shape]
symmetric banded matrix, defined [in 3.3 Matrix Precision and Shape]
symmetric eigenvalue decomposition object [in 6.2 Decomposition Object]
symmetric eigenvalue problem, basic [in 6.1 Defining the Problem]
symmetric eigenvalue servers, table [in 6.3 Servers]
symmetric matrix types [in 3.3 Matrix Precision and Shape]
symmetric matrix, defined [in 3.3 Matrix Precision and Shape]

T

table
   symmetric eigenvalue servers in the Linear Algebra Module [in 6.3 Servers]
temporary variable [in 4.2 Solving a System of Equations]
tolerance, defined [in 5.4 Solving a Numerically Underdetermined System]
toSymMat() [in 3.6.2 Converting Shapes]
type conversion
   precisions [in 3.6.1 Converting Precisions]
   shapes [in 3.6.2 Converting Shapes]
   two kinds [in 3.6 Type Conversion]
   with explicit functions [in 3.6.2 Converting Shapes]
type conversions
   between RWGenMat<T> matrices [in 3.6.1 Converting Precisions]

U

upper-triangular matrix types [in 3.3 Matrix Precision and Shape]
upper-triangular matrix, defined [in 3.3 Matrix Precision and Shape]

V

val() [in 3.5.4 val() and set()]
vector classes in the Linear Algebra Module [in 3.1 Defining Vectors]
vector space, defined [in 3.1 Defining Vectors]
vector, defined [in 3.1 Defining Vectors]

W

well-conditioned matrix, defined [in 4.4.3 Condition Number]

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