Octave C++ Classes

Edition 1.0 for Octave version 9.3.0

The Octave Project Developers

Copyright \begin{matrix}c \\ ◯ \end{matrix} 1996-2024 The Octave Project Developers.

This is the first edition of the documentation for Octave’s C++ classes, and is consistent with version 9.3.0 of Octave.

Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies.

Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one.

Permission is granted to copy and distribute translations of this manual into another language, under the same conditions as for modified versions.

Table of Contents

1 Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Contributors to Octave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

GNU GENERAL PUBLIC LICENSE . . . . . . . . . . . . . 2 2 A Brief Introduction to Octave. . . . . . . . . . . . . . . . 13 3 Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 Constructors and Assignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Matrix and Vector Operations . . . . . . . . . . . . . . . . 18 5 Matrix Factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6 Ranges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 7 Nonlinear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 8 Nonlinear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 9 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

9.1 Objective Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 9.2 Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 9.3 Linear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 9.4 Nonlinear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 9.5 Quadratic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 9.6 Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

10 Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

10.1 Collocation Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

11 Ordinary Differential Equations . . . . . . . . . . . . . . 45 12 Differential Algebraic Equations . . . . . . . . . . . . . 46 13 Error Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 14 Installation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

15 Bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Concept Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Function Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

1 Acknowledgements

Contributors to Octave

In addition to John W. Eaton, several people have written parts of liboctave. (This has been removed because it is the same as what is in the Octave manual.)

GNU GENERAL PUBLIC LICENSE

Version 3, 29 June 2007

Copyright \begin{matrix}c \\ ◯ \end{matrix} 2007 Free Software Foundation, Inc. https://fsf.org/

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      This is free software, and you are welcome to redistribute it
      under certain conditions; type `show c' for details.

The hypothetical commands ‘show w’ and ‘show c’ should show the appropriate parts of the General Public License. Of course, your program’s commands might be different; for a GUI interface, you would use an “about box”.

You should also get your employer (if you work as a programmer) or school, if any, to sign a “copyright disclaimer” for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see https://www.gnu.org/licenses/.

The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read

https://www.gnu.org/licenses/why-not-lgpl.html.

2 A Brief Introduction to Octave

This manual documents how to run, install and port Octave’s C++ classes, and how to report bugs.

3 Arrays

3.1 Constructors and Assignment

[Constructor] Array<T> (void)

Create an array with no elements.

[Constructor] Array<T> (int n [, const T &val])

Create an array with n elements. If the optional argument val is supplied, the elements are initialized to val; otherwise, they are left uninitialized. If n is less than zero, the current error handler is invoked (see Chapter 13 [Error Handling], page 47).

[Constructor] Array<T> (const Array<T> &a)

Create a copy of the Array<T> object a. Memory for the Array<T> class is managed using a reference counting scheme, so the cost of this operation is independent of the size of the array.

[Assignment on Array<T>] Array<T>& operator = (const Array<T> &a)

Assignment operator. Memory for the Array<T> class is managed using a reference counting scheme, so the cost of this operation is independent of the size of the array.

[Method on Array<T>] int capacity (void) const
[Method on Array<T>] int length (void) const

Return the length of the array.

[Method on Array<T>] T& elem (int n)
[Method on Array<T>] T& checkelem (int n)

If n is within the bounds of the array, return a reference to the element indexed by n; otherwise, the current error handler is invoked (see Chapter 13 [Error Handling], page 47).

[Indexing on Array<T>] T& operator () (int n)
[Method on Array<T>] T elem (int n) const
[Method on Array<T>] T checkelem (int n) const

If n is within the bounds of the array, return the value indexed by n; otherwise, call the current error handler. See Chapter 13 [Error Handling], page 47.

[Indexing on Array<T>] T operator () (int n) const
[Method on Array<T>] T& xelem (int n)
[Method on Array<T>] T xelem (int n) const

Return a reference to, or the value of, the element indexed by n. These methods never perform bounds checking.

[Method on Array<T>] void resize (int n [, const T &val])

Change the size of the array to be n elements. All elements are unchanged, except that if n is greater than the current size and the optional argument val is provided, the additional elements are initialized to val; otherwise, any additional elements are left uninitialized. In the current implementation, if n is less than the current size, the length is updated but no memory is released.

[Method on Array<T>] const T* data (void) const
[Constructor] Array2<T> Array2<T> Array2 (void)
[Constructor] Array2<T> (int n, int m)
[Constructor] Array2<T> (int n, int m, const T &val)
[Constructor] Array2<T> (const Array2<T> &a)
[Constructor] Array2<T> (const DiagArray<T> &a)
[Assignment on Array2<T>] Array2<T>& operator = (const Array2<T> &a)
[Method on Array2<T>] int dim1 (void) const
[Method on Array2<T>] int rows (void) const
[Method on Array2<T>] int dim2 (void) const
[Method on Array2<T>] int cols (void) const
[Method on Array2<T>] int columns (void) const
[Method on Array2<T>] T& elem (int i, int j)
[Method on Array2<T>] T& checkelem (int i, int j)
[Indexing on Array2<T>] T& operator () (int i, int j)
[Method on Array2<T>] void resize (int n, int m)
[Method on Array2<T>] void resize (int n, int m, const T &val)

[Constructor] Array3<T> (void)

[Constructor] Array3<T> (int n, int m, int k)
[Constructor] Array3<T> (int n, int m, int k, const T &val)
[Constructor] Array3<T> (const Array3<T> &a)
[Assignment on Array3<T>] Array3<T>& operator = (const Array3<T> &a)
[Method on Array3<T>] int dim1 (void) const
[Method on Array3<T>] int dim2 (void) const
[Method on Array3<T>] int dim3 (void) const
[Method on Array3<T>] T& elem (int i, int j, int k)
[Method on Array3<T>] T& checkelem (int i, int j, int k)
[Indexing on Array3<T>] T& operator () (int i, int j, int k)
[Method on Array3<T>] void resize (int n, int m, int k)
[Method on Array3<T>] void resize (int n, int m, int k, const T &val)
[Constructor] DiagArray<T> (void)
[Constructor] DiagArray<T> (int n)
[Constructor] DiagArray<T> (int n, const T &val)
[Constructor] DiagArray<T> (int r, int c)
[Constructor] DiagArray<T> (int r, int c, const T &val)
[Constructor] DiagArray<T> (const Array<T> &a)
[Constructor] DiagArray<T> (const DiagArray<T> &a)
[Assignment on DiagArray<T>&] operator = (const DiagArray<T> &a)

[Method on DiagArray<T>] int dim1 (void) const
[Method on DiagArray<T>] int rows (void) const
[Method on DiagArray<T>] int dim2 (void) const
[Method on DiagArray<T>] int cols (void) const
[Method on DiagArray<T>] int columns (void) const
[Method on DiagArray<T>] T& elem (int r, int c)
[Method on DiagArray<T>] T& checkelem (int r, int c)
[Indexing on DiagArray<T>] T& operator () (int r, int c)
[Method on DiagArray<T>] void resize (int n, int m)
[Method on DiagArray<T>] void resize (int n, int m, const T &val)

The real and complex ColumnVector and RowVector classes all have the following functions. These will eventually be part of an MArray<T> class, derived from the Array<T> class. Then the ColumnVector and RowVector classes will be derived from the MArray<T> class.

Element by element vector by scalar ops.

RowVector operator + (const RowVector &a, const double &s)
RowVector operator - (const RowVector &a, const double &s)
RowVector operator * (const RowVector &a, const double &s)
RowVector operator / (const RowVector &a, const double &s)

Element by element scalar by vector ops.

RowVector operator + (const double &s, const RowVector &a)
RowVector operator - (const double &s, const RowVector &a)
RowVector operator * (const double &s, const RowVector &a)
RowVector operator / (const double &s, const RowVector &a)

Element by element vector by vector ops.

RowVector operator + (const RowVector &a, const RowVector &b)
RowVector operator - (const RowVector &a, const RowVector &b)
RowVector product (const RowVector &a, const RowVector &b)
RowVector quotient (const RowVector &a, const RowVector &b)

Unary MArray ops.

RowVector operator - (const RowVector &a)

The Matrix classes share the following functions. These will eventually be part of an MArray2<T> class, derived from the Array2<T> class. Then the Matrix class will be derived from the MArray<T> class.

Element by element matrix by scalar ops.

Matrix operator + (const Matrix &a, const double &s)
Matrix operator - (const Matrix &a, const double &s)
Matrix operator * (const Matrix &a, const double &s)
Matrix operator / (const Matrix &a, const double &s)

Element by element scalar by matrix ops.

Matrix operator + (const double &s, const Matrix &a)
Matrix operator - (const double &s, const Matrix &a)
Matrix operator * (const double &s, const Matrix &a)
Matrix operator / (const double &s, const Matrix &a)

Element by element matrix by matrix ops.

Matrix operator + (const Matrix &a, const Matrix &b)
Matrix operator - (const Matrix &a, const Matrix &b)
Matrix product (const Matrix &a, const Matrix &b)
Matrix quotient (const Matrix &a, const Matrix &b)

Unary matrix ops.

Matrix operator - (const Matrix &a)

The DiagMatrix classes share the following functions. These will eventually be part of an MDiagArray<T> class, derived from the DiagArray<T> class. Then the DiagMatrix class will be derived from the MDiagArray<T> class.

Element by element MDiagArray by scalar ops.

DiagMatrix operator * (const DiagMatrix &a, const double &s)
DiagMatrix operator / (const DiagMatrix &a, const double &s)

Element by element scalar by MDiagArray ops.

DiagMatrix operator * (const double &s, const DiagMatrix &a)

Element by element MDiagArray by MDiagArray ops.

DiagMatrix operator + (const DiagMatrix &a, const DiagMatrix &b)
DiagMatrix operator - (const DiagMatrix &a, const DiagMatrix &b)
DiagMatrix product (const DiagMatrix &a, const DiagMatrix &b)

Unary MDiagArray ops.

DiagMatrix operator - (const DiagMatrix &a)

4 Matrix and Vector Operations

Matrix (void)
Matrix (int r, int c)
Matrix (int r, int c, double val)
Matrix (const Array2<double> &a)
Matrix (const Matrix &a)
Matrix (const DiagArray<double> &a)
Matrix (const DiagMatrix &a)
Matrix& operator = (const Matrix &a)
int operator == (const Matrix &a) const
int operator != (const Matrix &a) const
Matrix& insert (const Matrix &a, int r, int c)
Matrix& insert (const RowVector &a, int r, int c)
Matrix& insert (const ColumnVector &a, int r, int c)
Matrix& insert (const DiagMatrix &a, int r, int c)
Matrix& fill (double val)
Matrix& fill (double val, int r1, int c1, int r2, int c2)
Matrix append (const Matrix &a) const
Matrix append (const RowVector &a) const
Matrix append (const ColumnVector &a) const
Matrix append (const DiagMatrix &a) const
Matrix stack (const Matrix &a) const
Matrix stack (const RowVector &a) const
Matrix stack (const ColumnVector &a) const
Matrix stack (const DiagMatrix &a) const
Matrix transpose (void) const
Matrix extract (int r1, int c1, int r2, int c2) const
RowVector row (int i) const
RowVector row (char *s) const
ColumnVector column (int i) const
ColumnVector column (char *s) const
Matrix inverse (void) const
Matrix inverse (int &info) const
Matrix inverse (int &info, double &rcond) const
ComplexMatrix fourier (void) const
ComplexMatrix ifourier (void) const
DET determinant (void) const
DET determinant (int &info) const
DET determinant (int &info, double &rcond) const
Matrix solve (const Matrix &b) const

Matrix solve (const Matrix &b, int &info) const
Matrix solve (const Matrix &b, int &info, double &rcond) const
ComplexMatrix solve (const ComplexMatrix &b) const
ComplexMatrix solve (const ComplexMatrix &b, int &info) const
ComplexMatrix solve (const ComplexMatrix &b, int &info, double
        &rcond) const
ColumnVector solve (const ColumnVector &b) const
ColumnVector solve (const ColumnVector &b, int &info) const
ColumnVector solve (const ColumnVector &b, int &info, double
        &rcond) const
ComplexColumnVector solve (const ComplexColumnVector &b) const
ComplexColumnVector solve (const ComplexColumnVector &b, int
        &info) const
ComplexColumnVector solve (const ComplexColumnVector &b, int
        &info, double &rcond) const
Matrix lssolve (const Matrix &b) const
Matrix lssolve (const Matrix &b, int &info) const
Matrix lssolve (const Matrix &b, int &info, int &rank) const
ComplexMatrix lssolve (const ComplexMatrix &b) const
ComplexMatrix lssolve (const ComplexMatrix &b, int &info) const
ComplexMatrix lssolve (const ComplexMatrix &b, int &info, int
        &rank) const
ColumnVector lssolve (const ColumnVector &b) const
ColumnVector lssolve (const ColumnVector &b, int &info) const
ColumnVector lssolve (const ColumnVector &b, int &info, int &rank)
        const
ComplexColumnVector lssolve (const ComplexColumnVector &b) const
ComplexColumnVector lssolve (const ComplexColumnVector &b, int
        &info) const
ComplexColumnVector lssolve (const ComplexColumnVector &b, int
        &info, int &rank) const
Matrix& operator += (const Matrix &a)
Matrix& operator -= (const Matrix &a)
Matrix& operator += (const DiagMatrix &a)
Matrix& operator -= (const DiagMatrix &a)
Matrix operator ! (void) const
ComplexMatrix operator + (const Matrix &a, const Complex &s)
ComplexMatrix operator - (const Matrix &a, const Complex &s)
ComplexMatrix operator * (const Matrix &a, const Complex &s)
ComplexMatrix operator / (const Matrix &a, const Complex &s)
ComplexMatrix operator + (const Complex &s, const Matrix &a)
ComplexMatrix operator - (const Complex &s, const Matrix &a)

ComplexMatrix operator * (const Complex &s, const Matrix &a)
ComplexMatrix operator / (const Complex &s, const Matrix &a)
ColumnVector operator * (const Matrix &a, const ColumnVector &b)
ComplexColumnVector operator * (const Matrix &a, const
        ComplexColumnVector &b)
Matrix operator + (const Matrix &a, const DiagMatrix &b)
Matrix operator - (const Matrix &a, const DiagMatrix &b)
Matrix operator * (const Matrix &a, const DiagMatrix &b)
ComplexMatrix operator + (const Matrix &a, const ComplexDiagMatrix
        &b)
ComplexMatrix operator - (const Matrix &a, const ComplexDiagMatrix
        &b)
ComplexMatrix operator * (const Matrix &a, const ComplexDiagMatrix
        &b)
Matrix operator * (const Matrix &a, const Matrix &b)
ComplexMatrix operator * (const Matrix &a, const ComplexMatrix &b)
ComplexMatrix operator + (const Matrix &a, const ComplexMatrix &b)
ComplexMatrix operator - (const Matrix &a, const ComplexMatrix &b)
ComplexMatrix product (const Matrix &a, const ComplexMatrix &b)
ComplexMatrix quotient (const Matrix &a, const ComplexMatrix &b)
Matrix map (d_d_Mapper f, const Matrix &a)
void map (d_d_Mapper f)
Matrix all (void) const
Matrix any (void) const
Matrix cumprod (void) const
Matrix cumsum (void) const
Matrix prod (void) const
Matrix sum (void) const
Matrix sumsq (void) const
ColumnVector diag (void) const
ColumnVector diag (int k) const
ColumnVector row_min (void) const
ColumnVector row_min_loc (void) const
ColumnVector row_max (void) const
ColumnVector row_max_loc (void) const
RowVector column_min (void) const
RowVector column_min_loc (void) const
RowVector column_max (void) const
RowVector column_max_loc (void) const
ostream& operator << (ostream &os, const Matrix &a)

istream& operator >> (istream &is, Matrix &a)
ColumnVector (void)
ColumnVector (int n)
ColumnVector (int n, double val)
ColumnVector (const Array<double> &a)
ColumnVector (const ColumnVector &a)
ColumnVector& operator = (const ColumnVector &a)
int operator == (const ColumnVector &a) const
int operator != (const ColumnVector &a) const
ColumnVector& insert (const ColumnVector &a, int r)
ColumnVector& fill (double val)
ColumnVector& fill (double val, int r1, int r2)
ColumnVector stack (const ColumnVector &a) const
RowVector transpose (void) const
ColumnVector extract (int r1, int r2) const
ColumnVector& operator += (const ColumnVector &a)
ColumnVector& operator -= (const ColumnVector &a)
ComplexColumnVector operator + (const ColumnVector &a, const
        Complex &s)
ComplexColumnVector operator - (const ColumnVector &a, const
        Complex &s)
ComplexColumnVector operator * (const ColumnVector &a, const
        Complex &s)
ComplexColumnVector operator / (const ColumnVector &a, const
        Complex &s)
ComplexColumnVector operator + (const Complex &s, const
        ColumnVector &a)
ComplexColumnVector operator - (const Complex &s, const
        ColumnVector &a)
ComplexColumnVector operator * (const Complex &s, const
        ColumnVector &a)
ComplexColumnVector operator / (const Complex &s, const
        ColumnVector &a)
Matrix operator * (const ColumnVector &a, const RowVector &a)
ComplexMatrix operator * (const ColumnVector &a, const
        ComplexRowVector &b)
ComplexColumnVector operator + (const ComplexColumnVector &a,
        const ComplexColumnVector &b)
ComplexColumnVector operator - (const ComplexColumnVector &a,
        const ComplexColumnVector &b)

ComplexColumnVector product (const ComplexColumnVector &a, const
        ComplexColumnVector &b)
ComplexColumnVector quotient (const ComplexColumnVector &a, const
        ComplexColumnVector &b)
ColumnVector map (d_d_Mapper f, const ColumnVector &a)
void map (d_d_Mapper f)
double min (void) const
double max (void) const
ostream& operator << (ostream &os, const ColumnVector &a)
RowVector (void)
RowVector (int n)
RowVector (int n, double val)
RowVector (const Array<double> &a)
RowVector (const RowVector &a)
RowVector& operator = (const RowVector &a)
int operator == (const RowVector &a) const
int operator != (const RowVector &a) const
RowVector& insert (const RowVector &a, int c)
RowVector& fill (double val)
RowVector& fill (double val, int c1, int c2)
RowVector append (const RowVector &a) const
ColumnVector transpose (void) const
RowVector extract (int c1, int c2) const
RowVector& operator += (const RowVector &a)
RowVector& operator -= (const RowVector &a)
ComplexRowVector operator + (const RowVector &a, const Complex &s)
ComplexRowVector operator - (const RowVector &a, const Complex &s)
ComplexRowVector operator * (const RowVector &a, const Complex &s)
ComplexRowVector operator / (const RowVector &a, const Complex &s)
ComplexRowVector operator + (const Complex &s, const RowVector &a)
ComplexRowVector operator - (const Complex &s, const RowVector &a)
ComplexRowVector operator * (const Complex &s, const RowVector &a)
ComplexRowVector operator / (const Complex &s, const RowVector &a)
double operator * (const RowVector &a, ColumnVector &b)
Complex operator * (const RowVector &a, const ComplexColumnVector
        &b)
RowVector operator * (const RowVector &a, const Matrix &b)
ComplexRowVector operator * (const RowVector &a, const
        ComplexMatrix &b)

ComplexRowVector operator + (const RowVector &a, const
        ComplexRowVector &b)
ComplexRowVector operator - (const RowVector &a, const
        ComplexRowVector &b)
ComplexRowVector product (const RowVector &a, const
        ComplexRowVector &b)
ComplexRowVector quotient (const RowVector &a, const
        ComplexRowVector &b)
RowVector map (d_d_Mapper f, const RowVector &a)
void map (d_d_Mapper f)
double min (void) const
double max (void) const
ostream& operator << (ostream &os, const RowVector &a)
DiagMatrix (void)
DiagMatrix (int n)
DiagMatrix (int n, double val)
DiagMatrix (int r, int c)
DiagMatrix (int r, int c, double val)
DiagMatrix (const RowVector &a)
DiagMatrix (const ColumnVector &a)
DiagMatrix (const DiagArray<double> &a)
DiagMatrix (const DiagMatrix &a)
DiagMatrix& operator = (const DiagMatrix &a)
int operator == (const DiagMatrix &a) const
int operator != (const DiagMatrix &a) const
DiagMatrix& fill (double val)
DiagMatrix& fill (double val, int beg, int end)
DiagMatrix& fill (const ColumnVector &a)
DiagMatrix& fill (const RowVector &a)
DiagMatrix& fill (const ColumnVector &a, int beg)
DiagMatrix& fill (const RowVector &a, int beg)
DiagMatrix transpose (void) const
Matrix extract (int r1, int c1, int r2, int c2) const
RowVector row (int i) const
RowVector row (char *s) const
ColumnVector column (int i) const
ColumnVector column (char *s) const
DiagMatrix inverse (void) const
DiagMatrix inverse (int &info) const
DiagMatrix& operator += (const DiagMatrix &a)

DiagMatrix& operator -= (const DiagMatrix &a)
Matrix operator + (const DiagMatrix &a, double s)
Matrix operator - (const DiagMatrix &a, double s)
ComplexMatrix operator + (const DiagMatrix &a, const Complex &s)
ComplexMatrix operator - (const DiagMatrix &a, const Complex &s)
ComplexDiagMatrix operator * (const DiagMatrix &a, const Complex
        &s)
ComplexDiagMatrix operator / (const DiagMatrix &a, const Complex
        &s)
Matrix operator + (double s, const DiagMatrix &a)
Matrix operator - (double s, const DiagMatrix &a)
ComplexMatrix operator + (const Complex &s, const DiagMatrix &a)
ComplexMatrix operator - (const Complex &s, const DiagMatrix &a)
ComplexDiagMatrix operator * (const Complex &s, const DiagMatrix
        &a)
ColumnVector operator * (const DiagMatrix &a, const ColumnVector
        &b)
ComplexColumnVector operator * (const DiagMatrix &a, const
        ComplexColumnVector &b)
ComplexDiagMatrix operator + (const DiagMatrix &a, const
        ComplexDiagMatrix &b)
ComplexDiagMatrix operator - (const DiagMatrix &a, const
        ComplexDiagMatrix &b)
ComplexDiagMatrix product (const DiagMatrix &a, const
        ComplexDiagMatrix &b)
Matrix operator + (const DiagMatrix &a, const Matrix &b)
Matrix operator - (const DiagMatrix &a, const Matrix &b)
Matrix operator * (const DiagMatrix &a, const Matrix &b)
ComplexMatrix operator + (const DiagMatrix &a, const ComplexMatrix
        &b)
ComplexMatrix operator - (const DiagMatrix &a, const ComplexMatrix
        &b)
ComplexMatrix operator * (const DiagMatrix &a, const ComplexMatrix
        &b)
ColumnVector diag (void) const
ColumnVector diag (int k) const
ostream& operator << (ostream &os, const DiagMatrix &a)
ComplexMatrix (void)
ComplexMatrix (int r, int c)
ComplexMatrix (int r, int c, const Complex &val)

ComplexMatrix (const Matrix &a)
ComplexMatrix (const Array2<Complex> &a)
ComplexMatrix (const ComplexMatrix &a)
ComplexMatrix (const DiagMatrix &a)
ComplexMatrix (const DiagArray<Complex> &a)
ComplexMatrix (const ComplexDiagMatrix &a)
ComplexMatrix& operator = (const ComplexMatrix &a)
int operator == (const ComplexMatrix &a) const
int operator != (const ComplexMatrix &a) const
ComplexMatrix& insert (const Matrix &a, int r, int c)
ComplexMatrix& insert (const RowVector &a, int r, int c)
ComplexMatrix& insert (const ColumnVector &a, int r, int c)
ComplexMatrix& insert (const DiagMatrix &a, int r, int c)
ComplexMatrix& insert (const ComplexMatrix &a, int r, int c)
ComplexMatrix& insert (const ComplexRowVector &a, int r, int c)
ComplexMatrix& insert (const ComplexColumnVector &a, int r, int c)
ComplexMatrix& insert (const ComplexDiagMatrix &a, int r, int c)
ComplexMatrix& fill (double val)
ComplexMatrix& fill (const Complex &val)
ComplexMatrix& fill (double val, int r1, int c1, int r2, int c2)
ComplexMatrix& fill (const Complex &val, int r1, int c1, int r2,
        int c2)
ComplexMatrix append (const Matrix &a) const
ComplexMatrix append (const RowVector &a) const
ComplexMatrix append (const ColumnVector &a) const
ComplexMatrix append (const DiagMatrix &a) const
ComplexMatrix append (const ComplexMatrix &a) const
ComplexMatrix append (const ComplexRowVector &a) const
ComplexMatrix append (const ComplexColumnVector &a) const
ComplexMatrix append (const ComplexDiagMatrix &a) const
ComplexMatrix stack (const Matrix &a) const
ComplexMatrix stack (const RowVector &a) const
ComplexMatrix stack (const ColumnVector &a) const
ComplexMatrix stack (const DiagMatrix &a) const
ComplexMatrix stack (const ComplexMatrix &a) const
ComplexMatrix stack (const ComplexRowVector &a) const
ComplexMatrix stack (const ComplexColumnVector &a) const
ComplexMatrix stack (const ComplexDiagMatrix &a) const
ComplexMatrix transpose (void) const
Matrix real (const ComplexMatrix &a)
Matrix imag (const ComplexMatrix &a)
ComplexMatrix conj (const ComplexMatrix &a)
ComplexMatrix extract (int r1, int c1, int r2, int c2) const

ComplexRowVector row (int i) const
ComplexRowVector row (char *s) const
ComplexColumnVector column (int i) const
ComplexColumnVector column (char *s) const
ComplexMatrix inverse (void) const
ComplexMatrix inverse (int &info) const
ComplexMatrix inverse (int &info, double &rcond) const
ComplexMatrix fourier (void) const
ComplexMatrix ifourier (void) const
ComplexDET determinant (void) const
ComplexDET determinant (int &info) const
ComplexDET determinant (int &info, double &rcond) const
ComplexMatrix solve (const Matrix &b) const
ComplexMatrix solve (const Matrix &b, int &info) const
ComplexMatrix solve (const Matrix &b, int &info, double &rcond)
        const
ComplexMatrix solve (const ComplexMatrix &b) const
ComplexMatrix solve (const ComplexMatrix &b, int &info) const
ComplexMatrix solve (const ComplexMatrix &b, int &info, double
        &rcond) const
ComplexColumnVector solve (const ComplexColumnVector &b) const
ComplexColumnVector solve (const ComplexColumnVector &b, int
        &info) const
ComplexColumnVector solve (const ComplexColumnVector &b, int
        &info, double &rcond) const
ComplexMatrix lssolve (const ComplexMatrix &b) const
ComplexMatrix lssolve (const ComplexMatrix &b, int &info) const
ComplexMatrix lssolve (const ComplexMatrix &b, int &info, int
        &rank) const
ComplexColumnVector lssolve (const ComplexColumnVector &b) const
ComplexColumnVector lssolve (const ComplexColumnVector &b, int
        &info) const
ComplexColumnVector lssolve (const ComplexColumnVector &b, int
        &info, int &rank) const
ComplexMatrix& operator += (const DiagMatrix &a)
ComplexMatrix& operator -= (const DiagMatrix &a)
ComplexMatrix& operator += (const ComplexDiagMatrix &a)
ComplexMatrix& operator -= (const ComplexDiagMatrix &a)
ComplexMatrix& operator += (const Matrix &a)
ComplexMatrix& operator -= (const Matrix &a)
ComplexMatrix& operator += (const ComplexMatrix &a)
ComplexMatrix& operator -= (const ComplexMatrix &a)
Matrix operator ! (void) const

ComplexMatrix operator + (const ComplexMatrix &a, double s)
ComplexMatrix operator - (const ComplexMatrix &a, double s)
ComplexMatrix operator * (const ComplexMatrix &a, double s)
ComplexMatrix operator / (const ComplexMatrix &a, double s)
ComplexMatrix operator + (double s, const ComplexMatrix &a)
ComplexMatrix operator - (double s, const ComplexMatrix &a)
ComplexMatrix operator * (double s, const ComplexMatrix &a)
ComplexMatrix operator / (double s, const ComplexMatrix &a)
ComplexColumnVector operator * (const ComplexMatrix &a, const
        ColumnVector &b)
ComplexColumnVector operator * (const ComplexMatrix &a, const
        ComplexColumnVector &b)
ComplexMatrix operator + (const ComplexMatrix &a, const DiagMatrix
        &b)
ComplexMatrix operator - (const ComplexMatrix &a, const DiagMatrix
        &b)
ComplexMatrix operator * (const ComplexMatrix &a, const DiagMatrix
        &b)
ComplexMatrix operator + (const ComplexMatrix &a, const
        ComplexDiagMatrix &b)
ComplexMatrix operator - (const ComplexMatrix &a, const
        ComplexDiagMatrix &b)
ComplexMatrix operator * (const ComplexMatrix &a, const
        ComplexDiagMatrix &b)
ComplexMatrix operator + (const ComplexMatrix &a, const Matrix &b)
ComplexMatrix operator - (const ComplexMatrix &a, const Matrix &b)
ComplexMatrix operator * (const ComplexMatrix &a, const Matrix &b)
ComplexMatrix operator * (const ComplexMatrix &a, const
        ComplexMatrix &b)
ComplexMatrix product (const ComplexMatrix &a, const Matrix &b)
ComplexMatrix quotient (const ComplexMatrix &a, const Matrix &b)
ComplexMatrix map (c_c_Mapper f, const ComplexMatrix &a)
Matrix map (d_c_Mapper f, const ComplexMatrix &a)
void map (c_c_Mapper f)
Matrix all (void) const
Matrix any (void) const
ComplexMatrix cumprod (void) const
ComplexMatrix cumsum (void) const
ComplexMatrix prod (void) const
ComplexMatrix sum (void) const
ComplexMatrix sumsq (void) const
ComplexColumnVector diag (void) const

ComplexColumnVector diag (int k) const
ComplexColumnVector row_min (void) const
ComplexColumnVector row_min_loc (void) const
ComplexColumnVector row_max (void) const
ComplexColumnVector row_max_loc (void) const
ComplexRowVector column_min (void) const
ComplexRowVector column_min_loc (void) const
ComplexRowVector column_max (void) const
ComplexRowVector column_max_loc (void) const
ostream& operator << (ostream &os, const ComplexMatrix &a)
istream& operator >> (istream &is, ComplexMatrix &a)
ComplexColumnVector (void)
ComplexColumnVector (int n)
ComplexColumnVector (int n, const Complex &val)
ComplexColumnVector (const ColumnVector &a)
ComplexColumnVector (const Array<Complex> &a)
ComplexColumnVector (const ComplexColumnVector &a)
ComplexColumnVector& operator = (const ComplexColumnVector &a)
int operator == (const ComplexColumnVector &a) const
int operator != (const ComplexColumnVector &a) const
ComplexColumnVector& insert (const ColumnVector &a, int r)
ComplexColumnVector& insert (const ComplexColumnVector &a, int r)
ComplexColumnVector& fill (double val)
ComplexColumnVector& fill (const Complex &val)
ComplexColumnVector& fill (double val, int r1, int r2)
ComplexColumnVector& fill (const Complex &val, int r1, int r2)
ComplexColumnVector stack (const ColumnVector &a) const
ComplexColumnVector stack (const ComplexColumnVector &a) const
ComplexRowVector transpose (void) const
ColumnVector real (const ComplexColumnVector &a)
ColumnVector imag (const ComplexColumnVector &a)
ComplexColumnVector conj (const ComplexColumnVector &a)
ComplexColumnVector extract (int r1, int r2) const
ComplexColumnVector& operator += (const ColumnVector &a)
ComplexColumnVector& operator -= (const ColumnVector &a)
ComplexColumnVector& operator += (const ComplexColumnVector &a)
ComplexColumnVector& operator -= (const ComplexColumnVector &a)
ComplexColumnVector operator + (const ComplexColumnVector &a,
        double s)

ComplexColumnVector operator - (const ComplexColumnVector &a,
        double s)
ComplexColumnVector operator * (const ComplexColumnVector &a,
        double s)
ComplexColumnVector operator / (const ComplexColumnVector &a,
        double s)
ComplexColumnVector operator + (double s, const
        ComplexColumnVector &a)
ComplexColumnVector operator - (double s, const
        ComplexColumnVector &a)
ComplexColumnVector operator * (double s, const
        ComplexColumnVector &a)
ComplexColumnVector operator / (double s, const
        ComplexColumnVector &a)
ComplexMatrix operator * (const ComplexColumnVector &a, const
        ComplexRowVector &b)
ComplexColumnVector operator + (const ComplexColumnVector &a,
        const ColumnVector &b)
ComplexColumnVector operator - (const ComplexColumnVector &a,
        const ColumnVector &b)
ComplexColumnVector product (const ComplexColumnVector &a, const
        ColumnVector &b)
ComplexColumnVector quotient (const ComplexColumnVector &a, const
        ColumnVector &b)
ComplexColumnVector map (c_c_Mapper f, const ComplexColumnVector
        &a)
ColumnVector map (d_c_Mapper f, const ComplexColumnVector &a)
void map (c_c_Mapper f)
Complex min (void) const
Complex max (void) const
ostream& operator << (ostream &os, const ComplexColumnVector &a)
ComplexRowVector (void)
ComplexRowVector (int n)
ComplexRowVector (int n, const Complex &val)
ComplexRowVector (const RowVector &a)
ComplexRowVector (const Array<Complex> &a)
ComplexRowVector (const ComplexRowVector &a)
ComplexRowVector& operator = (const ComplexRowVector &a)
int operator == (const ComplexRowVector &a) const
int operator != (const ComplexRowVector &a) const
ComplexRowVector& insert (const RowVector &a, int c)
ComplexRowVector& insert (const ComplexRowVector &a, int c)
ComplexRowVector& fill (double val)

ComplexRowVector& fill (const Complex &val)
ComplexRowVector& fill (double val, int c1, int c2)
ComplexRowVector& fill (const Complex &val, int c1, int c2)
ComplexRowVector append (const RowVector &a) const
ComplexRowVector append (const ComplexRowVector &a) const
ComplexColumnVector transpose (void) const
RowVector real (const ComplexRowVector &a)
RowVector imag (const ComplexRowVector &a)
ComplexRowVector conj (const ComplexRowVector &a)
ComplexRowVector extract (int c1, int c2) const
ComplexRowVector& operator += (const RowVector &a)
ComplexRowVector& operator -= (const RowVector &a)
ComplexRowVector& operator += (const ComplexRowVector &a)
ComplexRowVector& operator -= (const ComplexRowVector &a)
ComplexRowVector operator + (const ComplexRowVector &a, double s)
ComplexRowVector operator - (const ComplexRowVector &a, double s)
ComplexRowVector operator * (const ComplexRowVector &a, double s)
ComplexRowVector operator / (const ComplexRowVector &a, double s)
ComplexRowVector operator + (double s, const ComplexRowVector &a)
ComplexRowVector operator - (double s, const ComplexRowVector &a)
ComplexRowVector operator * (double s, const ComplexRowVector &a)
ComplexRowVector operator / (double s, const ComplexRowVector &a)
Complex operator * (const ComplexRowVector &a, const ColumnVector
        &b)
Complex operator * (const ComplexRowVector &a, const
        ComplexColumnVector &b)
ComplexRowVector operator * (const ComplexRowVector &a, const
        ComplexMatrix &b)
ComplexRowVector operator + (const ComplexRowVector &a, const
        RowVector &b)
ComplexRowVector operator - (const ComplexRowVector &a, const
        RowVector &b)
ComplexRowVector product (const ComplexRowVector &a, const
        RowVector &b)
ComplexRowVector quotient (const ComplexRowVector &a, const
        RowVector &b)
ComplexRowVector map (c_c_Mapper f, const ComplexRowVector &a)
RowVector map (d_c_Mapper f, const ComplexRowVector &a)
void map (c_c_Mapper f)
Complex min (void) const
Complex max (void) const
ostream& operator << (ostream &os, const ComplexRowVector &a)

ComplexDiagMatrix (void)
ComplexDiagMatrix (int n)
ComplexDiagMatrix (int n, const Complex &val)
ComplexDiagMatrix (int r, int c)
ComplexDiagMatrix (int r, int c, const Complex &val)
ComplexDiagMatrix (const RowVector &a)
ComplexDiagMatrix (const ComplexRowVector &a)
ComplexDiagMatrix (const ColumnVector &a)
ComplexDiagMatrix (const ComplexColumnVector &a)
ComplexDiagMatrix (const DiagMatrix &a)
ComplexDiagMatrix (const DiagArray<Complex> &a)
ComplexDiagMatrix (const ComplexDiagMatrix &a)
ComplexDiagMatrix& operator = (const ComplexDiagMatrix &a)
int operator == (const ComplexDiagMatrix &a) const
int operator != (const ComplexDiagMatrix &a) const
ComplexDiagMatrix& fill (double val)
ComplexDiagMatrix& fill (const Complex &val)
ComplexDiagMatrix& fill (double val, int beg, int end)
ComplexDiagMatrix& fill (const Complex &val, int beg, int end)
ComplexDiagMatrix& fill (const ColumnVector &a)
ComplexDiagMatrix& fill (const ComplexColumnVector &a)
ComplexDiagMatrix& fill (const RowVector &a)
ComplexDiagMatrix& fill (const ComplexRowVector &a)
ComplexDiagMatrix& fill (const ColumnVector &a, int beg)
ComplexDiagMatrix& fill (const ComplexColumnVector &a, int beg)
ComplexDiagMatrix& fill (const RowVector &a, int beg)
ComplexDiagMatrix& fill (const ComplexRowVector &a, int beg)
ComplexDiagMatrix transpose (void) const
DiagMatrix real (const ComplexDiagMatrix &a)
DiagMatrix imag (const ComplexDiagMatrix &a)
ComplexDiagMatrix conj (const ComplexDiagMatrix &a)
ComplexMatrix extract (int r1, int c1, int r2, int c2) const
ComplexRowVector row (int i) const
ComplexRowVector row (char *s) const
ComplexColumnVector column (int i) const
ComplexColumnVector column (char *s) const
ComplexDiagMatrix inverse (int &info) const
ComplexDiagMatrix inverse (void) const
ComplexDiagMatrix& operator += (const DiagMatrix &a)
ComplexDiagMatrix& operator -= (const DiagMatrix &a)
ComplexDiagMatrix& operator += (const ComplexDiagMatrix &a)
ComplexDiagMatrix& operator -= (const ComplexDiagMatrix &a)
ComplexMatrix operator + (const ComplexDiagMatrix &a, double s)

ComplexMatrix operator - (const ComplexDiagMatrix &a, double s)
ComplexMatrix operator + (const ComplexDiagMatrix &a, const
        Complex &s)
ComplexMatrix operator - (const ComplexDiagMatrix &a, const
        Complex &s)
ComplexDiagMatrix operator * (const ComplexDiagMatrix &a, double
        s)
ComplexDiagMatrix operator / (const ComplexDiagMatrix &a, double
        s)
ComplexMatrix operator + (double s, const ComplexDiagMatrix &a)
ComplexMatrix operator - (double s, const ComplexDiagMatrix &a)
ComplexMatrix operator + (const Complex &s, const
        ComplexDiagMatrix &a)
ComplexMatrix operator - (const Complex &s, const
        ComplexDiagMatrix &a)
ComplexDiagMatrix operator * (double s, const ComplexDiagMatrix
        &a)
ComplexColumnVector operator * (const ComplexDiagMatrix &a, const
        ColumnVector &b)
ComplexColumnVector operator * (const ComplexDiagMatrix &a, const
        ComplexColumnVector &b)
ComplexDiagMatrix operator + (const ComplexDiagMatrix &a, const
        DiagMatrix &b)
ComplexDiagMatrix operator - (const ComplexDiagMatrix &a, const
        DiagMatrix &b)
ComplexDiagMatrix product (const ComplexDiagMatrix &a, const
        DiagMatrix &b)
ComplexMatrix operator + (const ComplexDiagMatrix &a, const Matrix
        &b)
ComplexMatrix operator - (const ComplexDiagMatrix &a, const Matrix
        &b)
ComplexMatrix operator * (const ComplexDiagMatrix &a, const Matrix
        &b)
ComplexMatrix operator + (const ComplexDiagMatrix &a, const
        ComplexMatrix &b)
ComplexMatrix operator - (const ComplexDiagMatrix &a, const
        ComplexMatrix &b)
ComplexMatrix operator * (const ComplexDiagMatrix &a, const
        ComplexMatrix &b)
ComplexColumnVector diag (void) const
ComplexColumnVector diag (int k) const
ostream& operator << (ostream &os, const ComplexDiagMatrix &a)

5 Matrix Factorizations

AEPBALANCE (void)
AEPBALANCE (const Matrix &a, const char *balance_job)
AEPBALANCE (const AEPBALANCE &a)
AEPBALANCE& operator = (const AEPBALANCE &a)
Matrix balanced_matrix (void) const
Matrix balancing_matrix (void) const
ostream& operator << (ostream &os, const AEPBALANCE &a)
ComplexAEPBALANCE (void)
ComplexAEPBALANCE (const ComplexMatrix &a, const char
        *balance_job)
ComplexAEPBALANCE (const ComplexAEPBALANCE &a)
ComplexAEPBALANCE& operator = (const ComplexAEPBALANCE &a)
ComplexMatrix balanced_matrix (void) const
ComplexMatrix balancing_matrix (void) const
ostream& operator << (ostream &os, const ComplexAEPBALANCE &a)
DET (void)
DET (const DET &a)
DET& operator = (const DET &a)
int value_will_overflow (void) const
int value_will_underflow (void) const
double coefficient (void) const
int exponent (void) const
double value (void) const
ostream& operator << (ostream &os, const DET &a)
ComplexDET (void)
ComplexDET (const ComplexDET &a)
ComplexDET& operator = (const ComplexDET &a)
int value_will_overflow (void) const
int value_will_underflow (void) const
Complex coefficient (void) const
int exponent (void) const
Complex value (void) const
ostream& operator << (ostream &os, const ComplexDET &a)
GEPBALANCE (void)
GEPBALANCE (const Matrix &a, const Matrix &, const char
        *balance_job)
GEPBALANCE (const GEPBALANCE &a)
GEPBALANCE& operator = (const GEPBALANCE &a)

Matrix balanced_a_matrix (void) const
Matrix balanced_b_matrix (void) const
Matrix left_balancing_matrix (void) const
Matrix right_balancing_matrix (void) const
ostream& operator << (ostream &os, const GEPBALANCE &a)
CHOL (void)
CHOL (const Matrix &a)
CHOL (const Matrix &a, int &info)
CHOL (const CHOL &a)
CHOL& operator = (const CHOL &a)
Matrix chol_matrix (void) const
ostream& operator << (ostream &os, const CHOL &a)
ComplexCHOL (void)
ComplexCHOL (const ComplexMatrix &a)
ComplexCHOL (const ComplexMatrix &a, int &info)
ComplexCHOL (const ComplexCHOL &a)
ComplexCHOL& operator = (const ComplexCHOL &a)
ComplexMatrix chol_matrix (void) const
ostream& operator << (ostream &os, const ComplexCHOL &a)
HESS (void)
HESS (const Matrix &a)
HESS (const Matrix&a, int &info)
HESS (const HESS &a)
HESS& operator = (const HESS &a)
Matrix hess_matrix (void) const
Matrix unitary_hess_matrix (void) const
ostream& operator << (ostream &os, const HESS &a)
ComplexHESS (void)
ComplexHESS (const ComplexMatrix &a)
ComplexHESS (const ComplexMatrix &a, int &info)
ComplexHESS (const ComplexHESS &a)
ComplexHESS& operator = (const ComplexHESS &a)
ComplexMatrix hess_matrix (void) const
ComplexMatrix unitary_hess_matrix (void) const
ostream& operator << (ostream &os, const ComplexHESS &a)
SCHUR (void)
SCHUR (const Matrix &a, const char *ord)
SCHUR (const Matrix &a, const char *ord, int &info)
SCHUR (const SCHUR &a, const char *ord)
SCHUR& operator = (const SCHUR &a)

Matrix schur_matrix (void) const
Matrix unitary_matrix (void) const
ostream& operator << (ostream &os, const SCHUR &a)
ComplexSCHUR (void)
ComplexSCHUR (const ComplexMatrix &a, const char *ord)
ComplexSCHUR (const ComplexMatrix &a, const char *ord, int &info)
ComplexSCHUR (const ComplexSCHUR &a, const char *ord)
ComplexSCHUR& operator = (const ComplexSCHUR &a)
ComplexMatrix schur_matrix (void) const
ComplexMatrix unitary_matrix (void) const
ostream& operator << (ostream &os, const ComplexSCHUR &a)
SVD (void)
SVD (const Matrix &a)
SVD (const Matrix &a, int &info)
SVD (const SVD &a)
SVD& operator = (const SVD &a)
DiagMatrix singular_values (void) const
Matrix left_singular_matrix (void) const
Matrix right_singular_matrix (void) const
ostream& operator << (ostream &os, const SVD &a)
ComplexSVD (void)
ComplexSVD (const ComplexMatrix &a)
ComplexSVD (const ComplexMatrix &a, int &info)
ComplexSVD (const ComplexSVD &a)
ComplexSVD& operator = (const ComplexSVD &a)
DiagMatrix singular_values (void) const
ComplexMatrix left_singular_matrix (void) const
ComplexMatrix right_singular_matrix (void) const
ostream& operator << (ostream &os, const ComplexSVD &a)
EIG (void)
EIG (const Matrix &a)
EIG (const Matrix &a, int &info)
EIG (const ComplexMatrix &a)
EIG (const ComplexMatrix &a, int &info)
EIG (const EIG &a)
EIG& operator = (const EIG &a)
ComplexColumnVector eigenvalues (void) const
ComplexMatrix eigenvectors (void) const
ostream& operator << (ostream &os, const EIG &a)

LU (void)
LU (const Matrix &a)
LU (const LU &a)
LU& operator = (const LU &a)
Matrix L (void) const
Matrix U (void) const
Matrix P (void) const
ostream& operator << (ostream &os, const LU &a)
ComplexLU (void)
ComplexLU (const ComplexMatrix &a)
ComplexLU (const ComplexLU &a)
ComplexLU& operator = (const ComplexLU &a)
ComplexMatrix L (void) const
ComplexMatrix U (void) const
Matrix P (void) const
ostream& operator << (ostream &os, const ComplexLU &a)
QR (void)
QR (const Matrix &A)
QR (const QR &a)
QR& operator = (const QR &a)
Matrix Q (void) const
Matrix R (void) const
ostream& operator << (ostream &os, const QR &a)
ComplexQR (void)
ComplexQR (const ComplexMatrix &A)
ComplexQR (const ComplexQR &a)
ComplexQR& operator = (const ComplexQR &a)
ComplexMatrix Q (void) const
ComplexMatrix R (void) const
ostream& operator << (ostream &os, const ComplexQR &a)

6 Ranges

FIXME: The Range class is obsolete.

7 Nonlinear Functions

NLFunc (void)
NLFunc (const nonlinear_fcn)
NLFunc (const nonlinear_fcn, const jacobian_fcn)
NLFunc (const NLFunc &a)
NLFunc& operator = (const NLFunc &a)
nonlinear_fcn function (void) const;
NLFunc& set_function (const nonlinear_fcn f)
jacobian_fcn jacobian_function (void) const;
NLFunc& set_jacobian_function (const jacobian_fcn j)

8 Nonlinear Equations

NLEqn_options (void)
NLEqn_options (const NLEqn_options &opt)
NLEqn_options& operator = (const NLEqn_options &opt)
void init (void)
void copy (const NLEqn_options &opt)
void set_default_options (void)
void set_tolerance (double val)
double tolerance (void)
NLEqn (void)
NLEqn (const ColumnVector&, const NLFunc)
NLEqn (const NLEqn &a)
NLEqn& operator = (const NLEqn &a)
void resize (int n)
void set_states (const ColumnVector &x)
ColumnVector states (void) const
int size (void) const
ColumnVector solve (void)
ColumnVector solve (const ColumnVector &x)
ColumnVector solve (int &info)
ColumnVector solve (const ColumnVector &x, int &info)

9 Optimization

9.1 Objective Functions

Objective (void)
Objective (const objective_fcn)
Objective (const objective_fcn, const gradient_fcn)
Objective (const Objective &a)
Objective& operator = (const Objective &a)
objective_fcn objective_function (void) const;
Objective& set_objective_function (const objective_fcn)
gradient_fcn gradient_function (void) const;
Objective& set_gradient_function (const gradient_fcn)

9.2 Bounds

Bounds (void)
Bounds (int n)
Bounds (const ColumnVector lb, const ColumnVector ub)
Bounds (const Bounds &a)
Bounds& operator = (const Bounds &a)
Bounds& resize (int n)
double lower_bound (int index) const;
double upper_bound (int index) const;
ColumnVector lower_bounds (void) const;
ColumnVector upper_bounds (void) const;
int size (void) const;
Bounds& set_bound (int index, double low, double high)
Bounds& set_bounds (double low, double high)
Bounds& set_bounds (const ColumnVector lb, const ColumnVector ub)
Bounds& set_lower_bound (int index, double low)
Bounds& set_upper_bound (int index, double high)
Bounds& set_lower_bounds (double low)
Bounds& set_upper_bounds (double high)
Bounds& set_lower_bounds (const ColumnVector lb)
Bounds& set_upper_bounds (const ColumnVector ub)
ostream& operator << (ostream &os, const Bounds &b)

9.3 Linear Constraints

LinConst (void)
LinConst (int nclin, int nx)
LinConst (int nclin_eq, int nclin_ineq, int nx)
LinConst (const ColumnVector &lb, const Matrix &A, const
        ColumnVector &ub)
LinConst (const Matrix &A_eq, const ColumnVector &b_eq, const
        Matrix &A_ineq, const ColumnVector &b_ineq)
LinConst (const LinConst &a)
LinConst& operator = (const LinConst &a)
LinConst& resize (int nclin, int n)
Matrix constraint_matrix (void) const;
LinConst& set_constraint_matrix (const Matrix &A)
Matrix eq_constraint_matrix (void) const;
Matrix ineq_constraint_matrix (void) const;
ColumnVector eq_constraint_vector (void) const;
ColumnVector ineq_constraint_vector (void) const;
ostream& operator << (ostream &os, const LinConst &b)

9.4 Nonlinear Constraints

NLConst (void)
NLConst (int n)
NLConst (const ColumnVector lb, const NLFunc f, const ColumnVector
        ub)
NLConst (const NLConst &a)
NLConst& operator = (const NLConst &a)

9.5 Quadratic Programming

QP (void)
QP (const ColumnVector &x, const Matrix &H)
QP (const ColumnVector &x, const Matrix &H, const ColumnVector &c)
QP (const ColumnVector &x, const Matrix &H, const Bounds &b)
QP (const ColumnVector &x, const Matrix &H, const LinConst &lc)
QP (const ColumnVector &x, const Matrix &H, const ColumnVector &c,
        const Bounds &b)
QP (const ColumnVector &x, const Matrix &H, const ColumnVector &c,
        const LinConst &lc)
QP (const ColumnVector &x, const Matrix &H, const Bounds &b, const
        LinConst &lc)
QP (const ColumnVector &x, const Matrix &H, const ColumnVector &c,
        const Bounds &b, const LinConst &lc)
virtual ColumnVector minimize (void)

virtual ColumnVector minimize (double &objf)
virtual ColumnVector minimize (double &objf, int &inform)
virtual ColumnVector minimize (double &objf, int &inform,
        ColumnVector &lambda) = 0;
virtual ColumnVector minimize (const ColumnVector &x)
virtual ColumnVector minimize (const ColumnVector &x, double
        &objf)
virtual ColumnVector minimize (const ColumnVector &x, double
        &objf, int &inform)
virtual ColumnVector minimize (const ColumnVector &x, double
        &objf, int &inform, ColumnVector &lambda)
ColumnVector minimize (double &objf, int &inform, ColumnVector
        &lambda)

9.6 Nonlinear Programming

NLP (void)
NLP (const ColumnVector &x, const Objective &phi)
NLP (const ColumnVector &x, const Objective &phi, const Bounds &b)
NLP (const ColumnVector &x, const Objective &phi, const Bounds &b,
        const LinConst &lc)
NLP (const ColumnVector &x, const Objective &phi, const Bounds &b,
        const LinConst &lc, const NLConst &nlc)
NLP (const ColumnVector &x, const Objective &phi, const LinConst
        &lc)
NLP (const ColumnVector &x, const Objective &phi, const LinConst
        &lc, const NLConst &nlc)
NLP (const ColumnVector &x, const Objective &phi, const NLConst
        &nlc)
NLP (const ColumnVector &x, const Objective &phi, const Bounds &b,
        const NLConst &nlc)
NLP& operator = (const NLP &a)
int size (void) const
ColumnVector minimize (void)
ColumnVector minimize (double &objf)
ColumnVector minimize (double &objf, int &inform)
ColumnVector minimize (double &objf, int &inform, ColumnVector
        &lambda)
ColumnVector minimize (const ColumnVector &x)
ColumnVector minimize (const ColumnVector &x, double &objf)
ColumnVector minimize (const ColumnVector &x, double &objf, int
        &inform)
ColumnVector minimize (const ColumnVector &x, double &objf, int
        &inform, ColumnVector &lambda)

10 Quadrature

Quad (integrand_fcn fcn)
Quad (integrand_fcn fcn, double abs, double rel)
virtual double integrate (void)
virtual double integrate (int &ier)
virtual double integrate (int &ier, int &neval)
virtual double integrate (int &ier, int &neval, double &abserr) =
        0
Quad_options (void)
Quad_options (const Quad_options &opt)
Quad_options& operator = (const Quad_options &opt)
void init (void)
void copy (const Quad_options &opt)
void set_default_options (void)
void set_absolute_tolerance (double val)
void set_relative_tolerance (double val)
double absolute_tolerance (void)
double relative_tolerance (void)
DefQuad (integrand_fcn fcn)
DefQuad (integrand_fcn fcn, double ll, double ul)
DefQuad (integrand_fcn fcn, double ll, double ul, double abs,
        double rel)
DefQuad (integrand_fcn fcn, double ll, double ul, const
        ColumnVector &sing)
DefQuad (integrand_fcn fcn, const ColumnVector &sing, double abs,
        double rel)
DefQuad (integrand_fcn fcn, const ColumnVector &sing)
DefQuad (integrand_fcn fcn, double ll, double ul, const
        ColumnVector &sing, double abs, double rel)
IndefQuad (integrand_fcn fcn)
IndefQuad (integrand_fcn fcn, double b, IntegralType t)
IndefQuad (integrand_fcn fcn, double b, IntegralType t, double
        abs, double rel)
IndefQuad (integrand_fcn fcn, double abs, double rel)

10.1 Collocation Weights

CollocWt (void)
CollocWt (int n, int inc_l, int inc_r)
CollocWt (int n, int inc_l, int inc_r, double l, double r)
CollocWt (int n, double a, double b, int inc_l, int inc_r)

CollocWt (int n, int inc_l, int inc_r, double l, double r)
CollocWt (const CollocWt&)
CollocWt& operator = (const CollocWt&)
CollocWt& resize (int ncol)
CollocWt& add_left (void)
CollocWt& add_right (void)
CollocWt& delete_left (void)
CollocWt& delete_right (void)
CollocWt& set_left (double val)
CollocWt& set_right (double val)
CollocWt& set_alpha (double val)
CollocWt& set_beta (double val)
int ncol (void) const
int left_included (void) const
int right_included (void) const
double left (void) const
double right (void) const
double width (void) const
double alpha (void) const
double beta (void) const
ColumnVector roots (void)
ColumnVector quad (void)
ColumnVector quad_weights (void)
Matrix first (void)
Matrix second (void)
ostream& operator << (ostream &os, const CollocWt &c)

11 Ordinary Differential Equations

ODE_options (void)
ODE_options (const ODE_options &opt)
ODE_options& operator = (const ODE_options &opt)
void init (void)
void copy (const ODE_options &opt)
void set_default_options (void)
void set_absolute_tolerance (double val)
void set_initial_step_size (double val)
void set_maximum_step_size (double val)
void set_minimum_step_size (double val)
void set_relative_tolerance (double val)
double absolute_tolerance (void)
double initial_step_size (void)
double maximum_step_size (void)
double minimum_step_size (void)
double relative_tolerance (void)
ODE (void)
ODE (int n)
ODE (const ColumnVector &state, double time, const ODEFunc &f)
virtual int size (void) const
virtual ColumnVector state (void) const
virtual double time (void) const
virtual void force_restart (void)
virtual void initialize (const ColumnVector &x, double t)
virtual void set_stop_time (double t)
virtual void clear_stop_time (void)
virtual ColumnVector integrate (double t)
void integrate (int nsteps, double tstep, ostream &s)
Matrix integrate (const ColumnVector &tout)
Matrix integrate (const ColumnVector &tout, const ColumnVector
        &tcrit)

12 Differential Algebraic Equations

DAE (void)
DAE (int n)
DAE (const ColumnVector &x, double time, DAEFunc &f)
DAE (const ColumnVector &x, ColumnVector &xdot, double time,
        DAEFunc &f)
ColumnVector deriv (void)
virtual void initialize (const ColumnVector &x, double t)
virtual void initialize (const ColumnVector &x, ColumnVector
        &xdot, double t)
ColumnVector integrate (double t)
Matrix integrate (const ColumnVector &tout, Matrix &xdot_out)
Matrix integrate (const ColumnVector &tout, Matrix &xdot_out,
        const ColumnVector &tcrit)

47

13 Error Handling

48

14 Installation

49

15 Bugs Concept Index

A

acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

B

bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 bugs, known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

C

collocation weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 copyright . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

D

DAE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

F

factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

I

installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 installation trouble. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

K

known causes of trouble . . . . . . . . . . . . . . . . . . . . . . . . 49

L

linear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

M

matrix factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 matrix manipulations . . . . . . . . . . . . . . . . . . . . . . . . . . 18

N

NLP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 nonlinear Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 41 nonlinear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 nonlinear functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 nonlinear programming . . . . . . . . . . . . . . . . . . . . . . . . 42 numerical integration . . . . . . . . . . . . . . . . . . . . . . . . . . 43

O

objective functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 ODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 orthogonal collocation. . . . . . . . . . . . . . . . . . . . . . . . . . 43

Q

QP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 quadratic programming . . . . . . . . . . . . . . . . . . . . . . . . 41 quadrature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

R

ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

T

troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

V

vector manipulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

W

warranty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Function Index

A

absolute_tolerance . . . . . . . . . . . . . . . . . . . . . . . 43, 45 add_left . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 add_right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 AEPBALANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 27 alpha. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 any . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 27 append. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 22, 25, 30 Array<T> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Array2<T> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Array3<T> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

B

balanced_a_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 balanced_b_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 balanced_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 balancing_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Bounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

C

capacity on Method on Array<T> . . . . . . . . . . . . . . 14
checkelem on Method on Array<T> . . . . . . . . . . . . . 14
checkelem on Method on Array2<T> . . . . . . . . . . . . 15
checkelem on Method on Array3<T> . . . . . . . . . . . . 15
checkelem on Method on DiagArray<T> . . . . . . . . 16

chol_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 CHOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 clear_stop_time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 CollocWt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43, 44

cols on Method on Array2<T> . . . . . . . . . . . . . . . . . 15
cols on Method on DiagArray<T> . . . . . . . . . . . . . . 16

column. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 23, 26, 31 column_max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28 column_max_loc. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28 column_min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28 column_min_loc. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28

columns on Method on Array2<T> . . . . . . . . . . . . . . 15
columns on Method on DiagArray<T>. . . . . . . . . . . 16

ColumnVector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 ComplexAEPBALANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ComplexCHOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ComplexColumnVector. . . . . . . . . . . . . . . . . . . . . . . . . . 28 ComplexDET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ComplexDiagMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 ComplexHESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ComplexLU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 ComplexMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24, 25 ComplexQR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 ComplexRowVector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 ComplexSCHUR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 ComplexSVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 conj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25, 28, 30, 31 constraint_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 copy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39, 43, 45 cumprod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 27 cumsum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 27

D

DAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 data on Method on Array<T>. . . . . . . . . . . . . . . . . . . 15 DefQuad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 delete_left . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 delete_right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 deriv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 26 DET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 diag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 24, 27, 32 DiagArray<T>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 DiagMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

                                                dim1 on Method on Array2<T> . . . . . . . . . . . . . . . . . 15
                                                dim1 on Method on Array3<T> . . . . . . . . . . . . . . . . . 15
                                                dim1 on Method on DiagArray<T> . . . . . . . . . . . . . . 16
                                                dim2 on Method on Array2<T> . . . . . . . . . . . . . . . . . 15
                                                dim2 on Method on Array3<T> . . . . . . . . . . . . . . . . . 15
                                                dim2 on Method on DiagArray<T> . . . . . . . . . . . . . . 16
                                                dim3 on Method on Array3<T> . . . . . . . . . . . . . . . . . 15

E

eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 eigenvectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 EIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 elem on Method on Array<T>. . . . . . . . . . . . . . . . . . . 14

                                                elem on Method on Array2<T> . . . . . . . . . . . . . . . . . 15
                                                elem on Method on Array3<T> . . . . . . . . . . . . . . . . . 15
                                                elem on Method on DiagArray<T> . . . . . . . . . . . . . . 16

eq_constraint_matrix . . . . . . . . . . . . . . . . . . . . . . . . 41 eq_constraint_vector . . . . . . . . . . . . . . . . . . . . . . . . 41 exponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 extract . . . . . . . . . . . . . . 18, 21, 22, 23, 25, 28, 30, 31

F

fill . . . . . . . . . . . . . . 18, 21, 22, 23, 25, 28, 29, 30, 31 first. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 force_restart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 fourier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 26 function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Function Index 52

G

GEPBALANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 gradient_function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

H

hess_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 HESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

I

ifourier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 26 imag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25, 28, 30, 31 IndefQuad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 ineq_constraint_matrix . . . . . . . . . . . . . . . . . . . . . . 41 ineq_constraint_vector . . . . . . . . . . . . . . . . . . . . . . 41 init. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39, 43, 45 initial_step_size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 initialize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45, 46 insert . . . . . . . . . . . . . . . . . . . . . . 18, 21, 22, 25, 28, 29 integrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43, 45, 46 inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 23, 26, 31

J

jacobian_function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

L

left . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 left_balancing_matrix . . . . . . . . . . . . . . . . . . . . . . . 34 left_included . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 left_singular_matrix . . . . . . . . . . . . . . . . . . . . . . . . 35

length on Method on Array<T> . . . . . . . . . . . . . . . . 14

LinConst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 lower_bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 lower_bounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 lssolve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19, 26 L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 LU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

M

map . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 22, 23, 27, 29, 30 Matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22, 23, 29, 30 maximum_step_size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22, 23, 29, 30 minimize. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41, 42 minimum_step_size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

N

ncol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 NLConst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 NLEqn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 NLEqn_options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 NLFunc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 NLP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

O

Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 objective_function . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 ODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 ODE_options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 operator !. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19, 26 operator != . . . . . . . . . . 18, 21, 22, 23, 25, 28, 29, 31

operator () on Indexing on Array<T> . . . . . . . . 14
operator () on Indexing on Array2<T> . . . . . . . 15
operator () on Indexing on Array3<T> . . . . . . . 15
operator () on Indexing on DiagArray<T> . . . . 16

operator *. 16, 17, 19, 20, 21, 22, 24, 27, 29, 30, 32 operator + … 16, 17, 19, 20, 21, 22, 23, 24, 27, 28,

29, 30, 31, 32

operator += . . . . . . . . . . 19, 21, 22, 23, 26, 28, 30, 31 operator - … 16, 17, 19, 20, 21, 22, 23, 24, 27, 28,

29, 30, 31, 32

operator -= . . . . . . . . . . 19, 21, 22, 23, 26, 28, 30, 31 operator /. 16, 17, 19, 20, 21, 22, 24, 27, 29, 30, 32 operator << . . 20, 22, 23, 24, 28, 29, 30, 32, 33, 34,

35, 36, 40, 41, 44

operator = … 18, 21, 22, 23, 25, 28, 29, 31, 33, 34,

35, 36, 38, 39, 40, 41, 42, 43, 44, 45

operator = on Assignment on Array<T> . . . . . . . 14
operator = on Assignment on Array2<T> . . . . . . 15
operator = on Assignment on Array3<T> . . . . . . 15
operator = on Assignment on DiagArray<T>& . 15

operator == . . . . . . . . . . 18, 21, 22, 23, 25, 28, 29, 31 operator >>. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28

P

prod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 27 product . . . . . . . 16, 17, 20, 22, 23, 24, 27, 29, 30, 32 P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Q

Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 QP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 QR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Quad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 quad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Quad_options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 quad_weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 quotient . . . . . . . . . . . . . 16, 17, 20, 22, 23, 27, 29, 30

Function Index 53

R

real . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25, 28, 30, 31 relative_tolerance . . . . . . . . . . . . . . . . . . . . . . . 43, 45 resize. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39, 40, 41, 44

resize on Method on Array<T> . . . . . . . . . . . . . . . . 14
resize on Method on Array2<T> . . . . . . . . . . . . . . . 15
resize on Method on Array3<T> . . . . . . . . . . . . . . . 15
resize on Method on DiagArray<T> . . . . . . . . . . . . 16

right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 right_balancing_matrix . . . . . . . . . . . . . . . . . . . . . . 34 right_included . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 right_singular_matrix . . . . . . . . . . . . . . . . . . . . . . . 35 roots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 row . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 23, 26, 31 row_max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28 row_max_loc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28 row_min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28 row_min_loc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 28

rows on Method on Array2<T> . . . . . . . . . . . . . . . . . 15
rows on Method on DiagArray<T> . . . . . . . . . . . . . . 16

R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 RowVector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

S

schur_matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 SCHUR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 second. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 set_absolute_tolerance . . . . . . . . . . . . . . . . . . 43, 45 set_alpha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 set_beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 set_bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 set_bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 set_constraint_matrix . . . . . . . . . . . . . . . . . . . . . . . 41 set_default_options . . . . . . . . . . . . . . . . . . 39, 43, 45 set_function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 set_gradient_function . . . . . . . . . . . . . . . . . . . . . . . 40 set_initial_step_size . . . . . . . . . . . . . . . . . . . . . . . 45 set_jacobian_function . . . . . . . . . . . . . . . . . . . . . . . 38 set_left . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 set_lower_bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 set_lower_bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 set_maximum_step_size . . . . . . . . . . . . . . . . . . . . . . . 45 set_minimum_step_size . . . . . . . . . . . . . . . . . . . . . . . 45 set_objective_function . . . . . . . . . . . . . . . . . . . . . . 40 set_relative_tolerance . . . . . . . . . . . . . . . . . . 43, 45 set_right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 set_states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 set_stop_time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 set_tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 set_upper_bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 set_upper_bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 singular_values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39, 40, 42, 45 solve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 19, 26, 39 stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 21, 25, 28 state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 27 sumsq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20, 27 SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

T

time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 transpose. . . . . . . . . . . . 18, 21, 22, 23, 25, 28, 30, 31

U

unitary_hess_matrix. . . . . . . . . . . . . . . . . . . . . . . . . . 34 unitary_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 upper_bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 upper_bounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

V

value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 value_will_overflow. . . . . . . . . . . . . . . . . . . . . . . . . . 33 value_will_underflow . . . . . . . . . . . . . . . . . . . . . . . . 33

W

width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

X

                                                xelem on Method on Array<T> . . . . . . . . . . . . . . . . . 14