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APPSPACK::Matrix Class Reference

#include <APPSPACK_Matrix.hpp>

Collaboration diagram for APPSPACK::Matrix:

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List of all members.

Detailed Description

Stores a matrix A. All indices begin at zero.

Vectorized storage

When interfacing with BLAS and LAPACK routines it is necessary to first write matrix elements to a vector of columns, and/or a vector of rows. To enhance computational efficiency when such a copy is made, it will be automatically be stored. If A is written to a vector by columns, a copy is stored in fmatvec and fmatvecSet is set to true. Similarly, if A is written to vector by rows, a copy is stored in fmatvecT and fmatvecTSet is set to true. To ensure that the vectorized forms of A are kept current, both fmatvecSet and fmatvecTSet are set to false upon instantiation and whenever a non-const method is called.

Warning:
To ensure that vectorized storage of A is kept current, it is crucial that every non-const method call method Matrix::matrixChanged() which resets fmatvecSet and fmatvecTSet to false.
See also:
Matrix::copyToFortranVector();

Definition at line 69 of file APPSPACK_Matrix.hpp.

Public Types

enum  TransposeType { Transpose, NoTranspose }
 Indicator for transpose operations. More...

Public Member Functions

 Matrix ()
 Constructor. Creates an empty matrix.
 Matrix (const Matrix &B, TransposeType ttype=NoTranspose)
 Copy constructor.
 Matrix (const Matrix &B, const Vector &s, TransposeType ttype=NoTranspose)
 Copy constructor with scaling.
 Matrix (double **Aptr, int nrows, int ncols)
 Resizes A to be nrows by ncols. Sets A(i,j) = Aptr[i][j].
 ~Matrix ()
 Destructor.
Accessors
bool empty () const
 Returns true if A is empty, i.e., the number of rows is zero.
int getNrows () const
 Returns number of rows in A.
int getNcols () const
 Returns number of columns in A.
const Vector & getRow (int i) const
 Return ith row of A.
Modifiers
void getRowPointers (vector< double * > &Aptr)
 On exit Aptr[i] points to row i of A.
void clear ()
 Empty the matrix A.
void addRow (const Vector &r)
 Append a copy of r to the bottom of A.
void deleteRow (int i)
 Deletes the ith row of A.
void addRow (const Vector &r, double alpha)
 Append alpha * r (i.e., a scaled copy of r) to the bottom of A.
void addMatrix (const Matrix &B)
 Append copies of the rows of matrix B to the bottom of A.
void addMatrix (const Matrix &B, double alpha)
 Append the matrix alpha * B (i.e., a scaled copy of B) to the bottom of A.
void addMatrix (const Matrix &B, const Vector &s)
 Append matrix B scaled columnwise to the bottom of A.
void addUniqueRows (const Matrix &B, double epsilon)
 Selectivly appends the rows which are unique to B to the bottom of A.
void operator= (const Matrix &B)
 Copy matrix (A = B).
void transpose (const Matrix &B)
 Copy transposed matrix (A = B').
void scale (const Matrix &B, const Vector &s)
 Copy and scale matrix.
void scale (const Vector &s)
 Scale matrix.
void setToIdentity (int n)
 Sets A = I, an n by n identity matrix.
void normalize ()
 Normalizes the rows of A.
Calculations involving A
void multVec (const Vector &x, Vector &y, TransposeType ttype=NoTranspose) const
 Compute y = Ax (or y = A'x if ttype = Transpose).
void svd (Matrix &U, Vector &s, Matrix &VT) const
 Compute the singular value decomposition (SVD) of A.
void multMat (const Matrix &B, TransposeType ttype=NoTranspose)
 On exit A = A*B if ttype = NoTranspose, and A = A*B' otherwise.
void multMat (const Matrix &B, Matrix &C, TransposeType ttype=NoTranspose) const
 On exit C = A*B if ttype = NoTranspose, and C = A*B' otherwise.
void nullSpace (Matrix &ZT, double tol) const
 On exit the rows of ZT form an orthonormal basis for null(A).
bool getRighInvAndNullBasis (Matrix &RT, Matrix &NT, double tol) const
 Computes right inverse and null space basis matrix for A (if possible).
void pruneDependentRows (Vector &b, double epsilon)
 Deletes dependent rows of A and corresponding entries in b. On exit, Ax = b forms a consistent system.
void constrainedLSQR (Vector &x, const Vector &b) const
 Solve a constrained least-squares problem for the case when A has full row rank.
Printing help
ostream & leftshift (ostream &stream) const
 Print object to the given stream

Private Member Functions

void matrixChanged ()
 Sets fmatvecSet and fmatvecTSet to false.
const Vector & getMatrixVector (TransposeType ttype=NoTranspose) const
 Private member variables fmatvec and fmatvecTSet should never be access directly. Instead method getMatrixVector() should be called. If ttype equals NoTranspose, A is returns as a single vector stored column-wise. If ttype equals Transpose, A is returns as a single vector stored row-wise.
void copyToFortranVector (Vector &Avec, TransposeType ttype=NoTranspose) const
 Converts A to a Fortran-style vector.
void copyFromFortranVector (const Vector &Avec, int nrows, int ncols, TransposeType ttype=NoTranspose)
 Unpack A from a Fortran-style vector.
void resize (int m, int n)
 Resize A to have m rows and n columns.
void copySubMatrix (int istart, int iextent, const Matrix &B)
 Sets A equal to the specified block-row submatrix of B.
void multMatWithBlas (const APPSPACK::Matrix &Bin, APPSPACK::Matrix &C, TransposeType ttype) const
 Performs a matrix multiply using Blas 3 routine DGEMM_F77().
void multMatWithoutBlas (const APPSPACK::Matrix &Bin, APPSPACK::Matrix &C, TransposeType ttype) const
 Performs a matrix multiply by hand without blas subroutines.
void multVecWithBlas (const Vector &x, Vector &y, TransposeType ttype=NoTranspose) const
 Performs a matrix-vector multiply with Blas subroutine DGEMV_F77().
void multVecWithoutBlas (const Vector &x, Vector &y, TransposeType ttype=NoTranspose) const
 Performs a matrix-vector multiply by hand without blas subroutines.

Private Attributes

vector< Vector > matrix
 The matrix A.
Vectorized matrix storage.
Vector fmatvec
bool fmatvecSet
Vector fmatvecT
bool fmatvecTSet

Member Enumeration Documentation

enum APPSPACK::Matrix::TransposeType
 

Indicator for transpose operations.

Enumeration values:
Transpose  Transpose the matrix.
NoTranspose  Do not transpose the matrix.

Definition at line 74 of file APPSPACK_Matrix.hpp.

Constructor & Destructor Documentation

APPSPACK::Matrix::Matrix (   ) 
 

Constructor. Creates an empty matrix.

Definition at line 43 of file APPSPACK_Matrix.cpp.

APPSPACK::Matrix::Matrix (  const Matrix &  B,
TransposeType  ttype = NoTranspose
) 
 

Copy constructor.

Sets A = B (or A = B' if ttype = Transpose).

Definition at line 49 of file APPSPACK_Matrix.cpp.

References operator=(), and transpose().

APPSPACK::Matrix::Matrix (  const Matrix &  B,
const Vector &  s,
TransposeType  ttype = NoTranspose
) 
 

Copy constructor with scaling.

Copies B into A and scales column j by s[j]. In other words,

\[ A_{ij} = s_j B_{ij}. \]

If ttype = Transpose, the

\[ A_{ij} = s_j B_{ji}. \]

Definition at line 59 of file APPSPACK_Matrix.cpp.

References operator=(), scale(), and transpose().

APPSPACK::Matrix::Matrix (  double **  Aptr,
int  nrows,
int  ncols
) 
 

Resizes A to be nrows by ncols. Sets A(i,j) = Aptr[i][j].

Definition at line 70 of file APPSPACK_Matrix.cpp.

References matrix, and resize().

APPSPACK::Matrix::~Matrix (   ) 
 

Destructor.

Definition at line 80 of file APPSPACK_Matrix.cpp.

Member Function Documentation

bool APPSPACK::Matrix::empty (   )  const
 

Returns true if A is empty, i.e., the number of rows is zero.

Definition at line 84 of file APPSPACK_Matrix.cpp.

References matrix.

Referenced by APPSPACK::Directions::addCompassDirections(), APPSPACK::Directions::addNormalDirections(), APPSPACK::Directions::buildTangentCone(), APPSPACK::Directions::buildWithLapack(), APPSPACK::Directions::computeNewDirections(), constrainedLSQR(), APPSPACK::Directions::empty(), APPSPACK::Constraints::Linear::errorCheck(), APPSPACK::Constraints::Linear::formSnapSystem(), APPSPACK::Directions::generateForLinear(), APPSPACK::Constraints::Linear::isBoundsOnly(), APPSPACK::Constraints::Linear::maxStep(), APPSPACK::Constraints::Linear::print(), APPSPACK::Constraints::Linear::setupMatrix(), and APPSPACK::Constraints::Linear::setupScaledSystem().

int APPSPACK::Matrix::getNrows (   )  const
 

Returns number of rows in A.

Definition at line 89 of file APPSPACK_Matrix.cpp.

References matrix.

Referenced by addMatrix(), addUniqueRows(), APPSPACK::Directions::buildWithCddlib(), constrainedLSQR(), copySubMatrix(), copyToFortranVector(), deleteRow(), APPSPACK::Constraints::Linear::errorCheck(), APPSPACK::Constraints::Linear::formDistanceVector(), APPSPACK::Constraints::Linear::formSnapSystem(), APPSPACK::Constraints::Linear::getActiveIndex(), getRighInvAndNullBasis(), getRow(), getRowPointers(), APPSPACK::Constraints::Linear::isEqualityFeasible(), APPSPACK::Constraints::Linear::isInequalityFeasible(), leftshift(), APPSPACK::Constraints::Linear::maxStep(), multMat(), multMatWithBlas(), multMatWithoutBlas(), multVec(), multVecWithBlas(), multVecWithoutBlas(), normalize(), nullSpace(), pruneDependentRows(), scale(), APPSPACK::Constraints::Linear::setupRhs(), APPSPACK::Constraints::Linear::setupScaledSystem(), svd(), transpose(), and APPSPACK::Directions::updateDirectionInfo().

int APPSPACK::Matrix::getNcols (   )  const
 

Returns number of columns in A.

Definition at line 94 of file APPSPACK_Matrix.cpp.

References matrix.

Referenced by addRow(), addUniqueRows(), APPSPACK::Directions::buildWithLapack(), constrainedLSQR(), copyToFortranVector(), APPSPACK::Constraints::Linear::formSnapSystem(), getRighInvAndNullBasis(), leftshift(), multMat(), multMatWithBlas(), multMatWithoutBlas(), multVec(), multVecWithBlas(), multVecWithoutBlas(), nullSpace(), pruneDependentRows(), scale(), APPSPACK::Constraints::Linear::setupMatrix(), APPSPACK::Constraints::Linear::setupScaledSystem(), svd(), and transpose().

const APPSPACK::Vector & APPSPACK::Matrix::getRow (  int  i  )  const
 

Return ith row of A.

Definition at line 102 of file APPSPACK_Matrix.cpp.

References getNrows(), and matrix.

Referenced by addMatrix(), addUniqueRows(), APPSPACK::Directions::buildNormalCone(), copySubMatrix(), APPSPACK::Constraints::Linear::formSnapSystem(), APPSPACK::Directions::getDirection(), APPSPACK::Constraints::Linear::getEqState(), APPSPACK::Constraints::Linear::getIneqState(), APPSPACK::Directions::print(), and APPSPACK::Constraints::Linear::setupScaledSystem().

void APPSPACK::Matrix::getRowPointers (  vector< double * > &  Aptr  ) 
 

On exit Aptr[i] points to row i of A.

Definition at line 114 of file APPSPACK_Matrix.cpp.

References getNrows(), matrix, matrixChanged(), and APPSPACK::Vector::push_back().

void APPSPACK::Matrix::clear (   ) 
 

Empty the matrix A.

Definition at line 121 of file APPSPACK_Matrix.cpp.

References matrixChanged(), and resize().

Referenced by APPSPACK::Directions::buildWithCddlib(), APPSPACK::Directions::buildWithLapack(), APPSPACK::Directions::buildWithNothing(), copySubMatrix(), APPSPACK::Constraints::Linear::formSnapSystem(), APPSPACK::Directions::generateForLinear(), APPSPACK::Directions::generateUnconstrained(), and getRighInvAndNullBasis().

void APPSPACK::Matrix::addRow (  const Vector &  r  ) 
 

Append a copy of r to the bottom of A.

Definition at line 127 of file APPSPACK_Matrix.cpp.

References getNcols(), matrix, matrixChanged(), APPSPACK::Vector::push_back(), and APPSPACK::Vector::size().

Referenced by addMatrix(), addRow(), addUniqueRows(), APPSPACK::Directions::buildNormalCone(), APPSPACK::Directions::buildWithNothing(), copySubMatrix(), APPSPACK::Constraints::Linear::formSnapSystem(), APPSPACK::Directions::generateUnconstrained(), and APPSPACK::processTextInputFileLine().

void APPSPACK::Matrix::deleteRow (  int  i  ) 
 

Deletes the ith row of A.

Definition at line 140 of file APPSPACK_Matrix.cpp.

References APPSPACK::Vector::erase(), getNrows(), matrix, and matrixChanged().

Referenced by normalize(), and pruneDependentRows().

void APPSPACK::Matrix::addRow (  const Vector &  r,
double  alpha
) 
 

Append alpha * r (i.e., a scaled copy of r) to the bottom of A.

Definition at line 153 of file APPSPACK_Matrix.cpp.

References addRow(), matrix, matrixChanged(), and APPSPACK::Vector::scale().

void APPSPACK::Matrix::addMatrix (  const Matrix &  B  ) 
 

Append copies of the rows of matrix B to the bottom of A.

Definition at line 160 of file APPSPACK_Matrix.cpp.

References addRow(), getNrows(), getRow(), and matrixChanged().

Referenced by APPSPACK::Directions::addNormalDirections(), APPSPACK::Directions::buildNormalCone(), APPSPACK::Directions::buildWithCddlib(), APPSPACK::Directions::buildWithLapack(), and APPSPACK::Constraints::Linear::setupScaledSystem().

void APPSPACK::Matrix::addMatrix (  const Matrix &  B,
double  alpha
) 
 

Append the matrix alpha * B (i.e., a scaled copy of B) to the bottom of A.

Definition at line 167 of file APPSPACK_Matrix.cpp.

References addRow(), getNrows(), getRow(), and matrixChanged().

void APPSPACK::Matrix::addMatrix (  const Matrix &  B,
const Vector &  s
) 
 

Append matrix B scaled columnwise to the bottom of A.

In other words the matrix $\hat{B}$ is added to the bottom of A, where

\[ \hat{B}_{ij} = s_j B_{ij}. \]

Definition at line 174 of file APPSPACK_Matrix.cpp.

References addRow(), getNrows(), getRow(), matrix, matrixChanged(), and APPSPACK::Vector::scale().

void APPSPACK::Matrix::addUniqueRows (  const Matrix &  B,
double  epsilon
) 
 

Selectivly appends the rows which are unique to B to the bottom of A.

In other words, the ith row $ b_i $ is added to the end of A if

\[ \|a_j - b_i\|_2 \le \epsilon \;\;\forall\;\; a_j \in A. \]

Here $ a_j $ is used to denote the jth row of A.

Note:
It is assumed that there is no repitition amongst the rows of B.

Definition at line 184 of file APPSPACK_Matrix.cpp.

References addRow(), getNcols(), getNrows(), getRow(), matrixChanged(), and APPSPACK::Vector::norm().

Referenced by APPSPACK::Directions::addCompassDirections(), and APPSPACK::Directions::appendNewDirections().

void APPSPACK::Matrix::operator= (  const Matrix &  B  ) 
 

Copy matrix (A = B).

Definition at line 213 of file APPSPACK_Matrix.cpp.

References matrix, and matrixChanged().

Referenced by Matrix().

void APPSPACK::Matrix::transpose (  const Matrix &  B  ) 
 

Copy transposed matrix (A = B').

Definition at line 219 of file APPSPACK_Matrix.cpp.

References getNcols(), getNrows(), matrix, matrixChanged(), and resize().

Referenced by Matrix().

void APPSPACK::Matrix::scale (  const Matrix &  B,
const Vector &  s
) 
 

Copy and scale matrix.

Copies B into A and scales column j by s[j]. In other words,

\[ A_{ij} = s_j B_{ij}. \]

Definition at line 232 of file APPSPACK_Matrix.cpp.

References matrix, and matrixChanged().

Referenced by APPSPACK::Directions::addCompassDirections(), APPSPACK::Directions::addNormalDirections(), APPSPACK::Directions::buildWithCddlib(), APPSPACK::Directions::buildWithLapack(), getRighInvAndNullBasis(), Matrix(), and APPSPACK::Constraints::Linear::setupScaledSystem().

void APPSPACK::Matrix::scale (  const Vector &  s  ) 
 

Scale matrix.

Scales column j by s[j]. In other words,

\[ A_{ij} = s_j A_{ij}. \]

Definition at line 242 of file APPSPACK_Matrix.cpp.

References getNcols(), getNrows(), matrix, and matrixChanged().

void APPSPACK::Matrix::setToIdentity (  int  n  ) 
 

Sets A = I, an n by n identity matrix.

Definition at line 253 of file APPSPACK_Matrix.cpp.

References matrix, matrixChanged(), resize(), and APPSPACK::Vector::zero().

Referenced by APPSPACK::Directions::buildWithLapack(), and APPSPACK::Constraints::Linear::setupScaledSystem().

void APPSPACK::Matrix::normalize (   ) 
 

Normalizes the rows of A.

Warning:
All rows of A with norm equal to zero are deleted from A.

Definition at line 264 of file APPSPACK_Matrix.cpp.

References deleteRow(), getNrows(), matrix, matrixChanged(), APPSPACK::Vector::norm(), and APPSPACK::Vector::scale().

Referenced by APPSPACK::Directions::addCompassDirections(), APPSPACK::Directions::addNormalDirections(), APPSPACK::Directions::buildWithCddlib(), and APPSPACK::Directions::buildWithLapack().

void APPSPACK::Matrix::multVec (  const Vector &  x,
Vector &  y,
TransposeType  ttype = NoTranspose
)  const
 

Compute y = Ax (or y = A'x if ttype = Transpose).

Definition at line 277 of file APPSPACK_Matrix.cpp.

References getNcols(), getNrows(), multVecWithBlas(), multVecWithoutBlas(), and APPSPACK::Vector::size().

Referenced by APPSPACK::Constraints::Linear::formDistanceVector(), APPSPACK::Constraints::Linear::formSnapSystem(), APPSPACK::Constraints::Linear::maxStep(), and APPSPACK::Constraints::Linear::setupScaledSystem().

void APPSPACK::Matrix::svd (  Matrix &  U,
Vector &  s,
Matrix &  VT
)  const
 

Compute the singular value decomposition (SVD) of A.

Compute $ A = U \Sigma V^{T}$ where U is an m x m orthogonal matrix, V is an n x n orthogonal matrix, and $\Sigma$ is an m x n diagonal matrix where

\[ \Sigma = \left[ \begin{array}{cccc} s_{1} & 0 & \cdots & 0 \\ 0 & s_2 & \cdots & 0 \\ \vdots &\vdots & \ddots &\vdots \\ 0 & 0 & 0 & s_{p}\\ \end{array} \right], \]

with $s_1 \geq s_2 \geq \cdots \geq s_p$ and p = min{m,n}.

Parameters:
U (output) Matrix U from the SVD
s (output) diagonal of $\Sigma$ from the SVD
VT (output) Matrix V' from the SVD (note that this is transposed!)
Note:
Method requires that APPSPACK be configured with LAPACK.

Definition at line 320 of file APPSPACK_Matrix.cpp.

References copyFromFortranVector(), APPSPACK::DGESVD_F77(), getMatrixVector(), getNcols(), getNrows(), and APPSPACK::Vector::resize().

Referenced by getRighInvAndNullBasis(), and nullSpace().

void APPSPACK::Matrix::multMat (  const Matrix &  B,
TransposeType  ttype = NoTranspose
) 
 

On exit A = A*B if ttype = NoTranspose, and A = A*B' otherwise.

Definition at line 363 of file APPSPACK_Matrix.cpp.

References matrix, and matrixChanged().

Referenced by APPSPACK::Directions::addCompassDirections(), APPSPACK::Directions::addNormalDirections(), APPSPACK::Directions::buildWithLapack(), getRighInvAndNullBasis(), and APPSPACK::Constraints::Linear::setupScaledSystem().

void APPSPACK::Matrix::multMat (  const Matrix &  B,
Matrix &  C,
TransposeType  ttype = NoTranspose
)  const
 

On exit C = A*B if ttype = NoTranspose, and C = A*B' otherwise.

Definition at line 372 of file APPSPACK_Matrix.cpp.

References getNcols(), getNrows(), multMatWithBlas(), and multMatWithoutBlas().

void APPSPACK::Matrix::nullSpace (  Matrix &  ZT,
double  tol
)  const
 

On exit the rows of ZT form an orthonormal basis for null(A).

Parameters:
ZT (output) ZT is a matrix of size $ n_z \times n $ where n is the number of columns in A and $ n_z = n - {\rm rank}(A) $ .
tol (input) Any singular value of A that is less than this value is considered to be zero for the purposes of determining the rank.
Note:
Method requires that APPSPACK be configured with LAPACK.

Definition at line 403 of file APPSPACK_Matrix.cpp.

References copySubMatrix(), getNcols(), getNrows(), APPSPACK::Vector::size(), and svd().

Referenced by APPSPACK::Directions::addCompassDirections(), APPSPACK::Directions::addNormalDirections(), APPSPACK::Directions::buildWithLapack(), and APPSPACK::Constraints::Linear::setupScaledSystem().

bool APPSPACK::Matrix::getRighInvAndNullBasis (  Matrix &  RT,
Matrix &  NT,
double  tol
)  const
 

Computes right inverse and null space basis matrix for A (if possible).

Let A be an $m \times n$ matrix. We assume $n < m$ and that A has full row rank (i.e., rank(A) = m); if not, the method returns false because a right inverse cannot be computed. Otherwise, matrices R and N are computed such that R is a right-inverse of A, i.e., $AR = I$, and the columns of N are an orthonormal basis for the null space of A so that $AN = 0$.

Parameters:
RT (output) The transpose of R, the right inverse of A
NT (output) The transpose N, whose columns span the null space of A
tol (input) Used in the rank determination, i.e., only singular values greater than or equal to tol are considered to be non-zero.
Returns:
True if the right inverse of A exists; false otherwise.
Note:
Method requires that APPSPACK be configured with LAPACK.

Definition at line 436 of file APPSPACK_Matrix.cpp.

References clear(), copySubMatrix(), getNcols(), getNrows(), multMat(), scale(), APPSPACK::Vector::size(), and svd().

Referenced by APPSPACK::Directions::buildWithLapack().

void APPSPACK::Matrix::pruneDependentRows (  Vector &  b,
double  epsilon
) 
 

Deletes dependent rows of A and corresponding entries in b. On exit, Ax = b forms a consistent system.

Parameters:
b Righthand-side vector in system Ax=b.
epsilon Error tolerance used when determining linearly independent subset.
A consistent system is returned on exit by deleting rows of A and entries of b corresponding to dependent rows.

Dependent rows are determined as follows:

An LQ factorization of A is first computed, where L denotes a lower triangular matrix and Q an orthogonal matrix. In exact arithmetic, the nonzero diagonal entries of L correspond to a linearly independent subset of the rows of A. To allow for numerical round off, row $ a_i^T $ and entry $ b_i $ are deleted from A and b respectively if

\[ |L(i,i)| < \epsilon. \]

Note:
Method requires that APPSPACK be configured with LAPACK.

Definition at line 475 of file APPSPACK_Matrix.cpp.

References deleteRow(), APPSPACK::DGELQF_F77(), APPSPACK::Vector::erase(), getMatrixVector(), getNcols(), getNrows(), matrixChanged(), and NoTranspose.

Referenced by APPSPACK::Constraints::Linear::formSnapSystem().

void APPSPACK::Matrix::constrainedLSQR (  Vector &  x,
const Vector &  b
)  const
 

Solve a constrained least-squares problem for the case when A has full row rank.

Parameters:
x (input/output) On entry, x denotes current point. On exit, x equals the solution to the below constrained least-squares problem.
b (input) The right-hand side vector to system $ A \hat x = b.$
This method solves the following constrained least-squares problem:

\[ \begin{array}{ll} {\rm minimize} & \|\hat x - x\| \\ {\rm subject} & A \hat x = b, \end{array} \]

using LAPACK function DGGLSE_F77().

Note:
It is assumed that A has full row rank.

Method requires that APPSPACK be configured with LAPACK.

Definition at line 502 of file APPSPACK_Matrix.cpp.

References APPSPACK::DGGLSE_F77(), empty(), getMatrixVector(), getNcols(), and getNrows().

Referenced by APPSPACK::Constraints::Linear::snapToBoundary().

ostream & APPSPACK::Matrix::leftshift (  ostream &  stream  )  const
 

Print object to the given stream

Definition at line 528 of file APPSPACK_Matrix.cpp.

References APPSPACK::Print::formatDouble(), getNcols(), getNrows(), and matrix.

Referenced by operator<<().

void APPSPACK::Matrix::matrixChanged (   )  [private]
 

Sets fmatvecSet and fmatvecTSet to false.

Should be called inside ever non-const method.

Definition at line 542 of file APPSPACK_Matrix.cpp.

References fmatvecSet, and fmatvecTSet.

Referenced by addMatrix(), addRow(), addUniqueRows(), clear(), copyFromFortranVector(), copySubMatrix(), deleteRow(), getRowPointers(), multMat(), normalize(), operator=(), pruneDependentRows(), resize(), scale(), setToIdentity(), and transpose().

const APPSPACK::Vector & APPSPACK::Matrix::getMatrixVector (  TransposeType  ttype = NoTranspose  )  const [private]
 

Private member variables fmatvec and fmatvecTSet should never be access directly. Instead method getMatrixVector() should be called. If ttype equals NoTranspose, A is returns as a single vector stored column-wise. If ttype equals Transpose, A is returns as a single vector stored row-wise.

Definition at line 548 of file APPSPACK_Matrix.cpp.

References copyToFortranVector(), fmatvec, fmatvecSet, fmatvecT, and fmatvecTSet.

Referenced by constrainedLSQR(), multMatWithBlas(), multVecWithBlas(), pruneDependentRows(), and svd().

void APPSPACK::Matrix::copyToFortranVector (  Vector &  Avec,
TransposeType  ttype = NoTranspose
)  const [private]
 

Converts A to a Fortran-style vector.

Converts A to a vector stored columnwise so that the vector representation is

\[ \left[ \begin{array}{c} a_{11} \\ a_{21} \\ \vdots \\ a_{m1} \\ a_{12} \\ a_{22} \\ \vdots \\ a_{m2} \\ a_{13} \\ \vdots \\ \vdots \\ a_{mn} \end{array} \right] \]

The index mapping is:

\[ (i,j) \rightarrow (j * m) + i \]

Store A' instead if ttype = Transpose

Definition at line 570 of file APPSPACK_Matrix.cpp.

References APPSPACK::Vector::append(), getNcols(), getNrows(), matrix, APPSPACK::Vector::push_back(), APPSPACK::Vector::reserve(), and APPSPACK::Vector::resize().

Referenced by getMatrixVector().

void APPSPACK::Matrix::copyFromFortranVector (  const Vector &  Avec,
int  nrows,
int  ncols,
TransposeType  ttype = NoTranspose
)  [private]
 

Unpack A from a Fortran-style vector.

Assumes A' is stored in the vector if ttype = Transpose

Definition at line 595 of file APPSPACK_Matrix.cpp.

References matrix, matrixChanged(), and resize().

Referenced by multMatWithBlas(), and svd().

void APPSPACK::Matrix::resize (  int  m,
int  n
)  [private]
 

Resize A to have m rows and n columns.

Definition at line 624 of file APPSPACK_Matrix.cpp.

References matrix, matrixChanged(), and APPSPACK::Vector::resize().

Referenced by clear(), copyFromFortranVector(), APPSPACK::Constraints::Linear::getActiveIndex(), Matrix(), multMatWithoutBlas(), setToIdentity(), and transpose().

void APPSPACK::Matrix::copySubMatrix (  int  istart,
int  iextent,
const Matrix &  B
)  [private]
 

Sets A equal to the specified block-row submatrix of B.

Parameters:
istart Starting row of submatrix.
iextent Number of rows past istart to copy from B.
B Matrix to be copied from.
On exit A equals the block-row submatrix of B designated by rows istart through istart + iextent of B. Essentially,

\[ A(i,j) = B(istart+i, j), \; 0 \le i < iextent, \; 0 \le j < n_B \]

where $ n_B $ denotes the number of columns in $ B$. Hence $ A $ is an (iextent X $n_B$) matrix on exit.

Definition at line 633 of file APPSPACK_Matrix.cpp.

References addRow(), clear(), getNrows(), getRow(), and matrixChanged().

Referenced by getRighInvAndNullBasis(), and nullSpace().

void APPSPACK::Matrix::multMatWithBlas (  const APPSPACK::Matrix &  Bin,
APPSPACK::Matrix &  C,
TransposeType  ttype
)  const [private]
 

Performs a matrix multiply using Blas 3 routine DGEMM_F77().

On exit C = A*B if ttype = NoTranspose, and C = A*B' otherwise.

Note:
Method requires that APPSPACK be configured with LAPACK.

Definition at line 648 of file APPSPACK_Matrix.cpp.

References copyFromFortranVector(), APPSPACK::DGEMM_F77(), getMatrixVector(), getNcols(), getNrows(), and Transpose.

Referenced by multMat().

void APPSPACK::Matrix::multMatWithoutBlas (  const APPSPACK::Matrix &  Bin,
APPSPACK::Matrix &  C,
TransposeType  ttype
)  const [private]
 

Performs a matrix multiply by hand without blas subroutines.

On exit C = A*B if ttype = NoTranspose, and C = A*B' otherwise.

Definition at line 698 of file APPSPACK_Matrix.cpp.

References getNcols(), getNrows(), matrix, and resize().

Referenced by multMat().

void APPSPACK::Matrix::multVecWithBlas (  const Vector &  x,
Vector &  y,
TransposeType  ttype = NoTranspose
)  const [private]
 

Performs a matrix-vector multiply with Blas subroutine DGEMV_F77().

Computes y = Ax (or y = A'x if ttype = Transpose).

Note:
Method requires that APPSPACK be configured with LAPACK.

Definition at line 754 of file APPSPACK_Matrix.cpp.

References APPSPACK::DGEMV_F77(), getMatrixVector(), getNcols(), and getNrows().

Referenced by multVec().

void APPSPACK::Matrix::multVecWithoutBlas (  const Vector &  x,
Vector &  y,
TransposeType  ttype = NoTranspose
)  const [private]
 

Performs a matrix-vector multiply by hand without blas subroutines.

Computes y = Ax (or y = A'x if ttype = Transpose).

Definition at line 733 of file APPSPACK_Matrix.cpp.

References getNcols(), getNrows(), matrix, and APPSPACK::Vector::zero().

Referenced by multVec().

Member Data Documentation

vector<Vector> APPSPACK::Matrix::matrix [private]
 

The matrix A.

The matrix is stored rowwise, i.e., matrix[i] is row i of A. and matrix[i][j] is A_ij.

Definition at line 414 of file APPSPACK_Matrix.hpp.

Referenced by addMatrix(), addRow(), copyFromFortranVector(), copyToFortranVector(), deleteRow(), empty(), getNcols(), getNrows(), getRow(), getRowPointers(), leftshift(), Matrix(), multMat(), multMatWithoutBlas(), multVecWithoutBlas(), normalize(), o