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Provides a time grid consisting of vector-valued optimization variables at each grid point. More...

#include <variables_grid.hpp>

Inheritance diagram for VariablesGrid:
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List of all members.

Public Member Functions

returnValue addVector (const DVector &newVector, double newTime=-INFTY)
returnValue appendTimes (const VariablesGrid &arg, MergeMethod _mergeMethod=MM_DUPLICATE)
returnValue appendTimes (const DMatrix &arg, MergeMethod _mergeMethod=MM_DUPLICATE)
returnValue appendValues (const VariablesGrid &arg)
DVector getFirstVector () const
returnValue getIntegral (InterpolationMode mode, DVector &value) const
DVector getLastVector () const
returnValue getSum (DVector &sum) const
VariablesGrid getTimeSubGrid (uint startIdx, uint endIdx) const
VariablesGrid getTimeSubGrid (double startTime, double endTime) const
VariablesGrid getValuesSubGrid (uint startIdx, uint endIdx) const
DVector getVector (uint pointIdx) const
returnValue init ()
returnValue init (uint _dim, const Grid &_grid, VariableType _type=VT_UNKNOWN, const char **const _names=0, const char **const _units=0, const DVector *const _scaling=0, const DVector *const _lb=0, const DVector *const _ub=0, const BooleanType *const _autoInit=0)
returnValue init (uint _dim, uint _nPoints, VariableType _type=VT_UNKNOWN, const char **const _names=0, const char **const _units=0, const DVector *const _scaling=0, const DVector *const _lb=0, const DVector *const _ub=0, const BooleanType *const _autoInit=0)
returnValue init (uint _dim, double _firstTime, double _lastTime, uint _nPoints, VariableType _type=VT_UNKNOWN, const char **const _names=0, const char **const _units=0, const DVector *const _scaling=0, const DVector *const _lb=0, const DVector *const _ub=0, const BooleanType *const _autoInit=0)
returnValue init (const DVector &arg, const Grid &_grid=trivialGrid, VariableType _type=VT_UNKNOWN)
returnValue merge (const VariablesGrid &arg, MergeMethod _mergeMethod=MM_DUPLICATE, BooleanType keepOverlap=BT_TRUE)
 operator DMatrix () const
double & operator() (uint pointIdx, uint rowIdx)
double operator() (uint pointIdx, uint rowIdx) const
VariablesGrid operator() (const uint rowIdx) const
VariablesGrid operator+ (const VariablesGrid &arg) const
VariablesGridoperator+= (const VariablesGrid &arg)
VariablesGrid operator- (const VariablesGrid &arg) const
VariablesGridoperator-= (const VariablesGrid &arg)
VariablesGridoperator= (const VariablesGrid &rhs)
VariablesGridoperator= (const MatrixVariablesGrid &rhs)
VariablesGridoperator= (const DMatrix &rhs)
BooleanType operator== (const VariablesGrid &arg) const
VariablesGrid operator[] (const uint pointIdx) const
returnValue setAllVectors (const DVector &_values)
returnValue setVector (uint pointIdx, const DVector &_values)
VariablesGridshiftBackwards (DVector lastValue=emptyVector)
VariablesGridshiftTimes (double timeShift)
 VariablesGrid ()
 VariablesGrid (uint _dim, const Grid &_grid, VariableType _type=VT_UNKNOWN, const char **const _names=0, const char **const _units=0, const DVector *const _scaling=0, const DVector *const _lb=0, const DVector *const _ub=0, const BooleanType *const _autoInit=0)
 VariablesGrid (uint _dim, uint _nPoints, VariableType _type=VT_UNKNOWN, const char **const _names=0, const char **const _units=0, const DVector *const _scaling=0, const DVector *const _lb=0, const DVector *const _ub=0, const BooleanType *const _autoInit=0)
 VariablesGrid (uint _dim, double _firstTime, double _lastTime, uint _nPoints, VariableType _type=VT_UNKNOWN, const char **const _names=0, const char **const _units=0, const DVector *const _scaling=0, const DVector *const _lb=0, const DVector *const _ub=0, const BooleanType *const _autoInit=0)
 VariablesGrid (const DVector &arg, const Grid &_grid=trivialGrid, VariableType _type=VT_UNKNOWN)
 VariablesGrid (const DMatrix &arg, VariableType _type=VT_UNKNOWN)
 VariablesGrid (const VariablesGrid &rhs)
 VariablesGrid (const MatrixVariablesGrid &rhs)
 ~VariablesGrid ()

Protected Member Functions

returnValue initializeFromBounds ()

Friends

class OptimizationAlgorithm
class OptimizationAlgorithmBase
class RealTimeAlgorithm

Detailed Description

Provides a time grid consisting of vector-valued optimization variables at each grid point.

The class VariablesGrid provides a time grid consisting of vector-valued optimization variables at each grid point, as they usually occur when discretizing optimal control problems.

The class specalizes the MatrixVariablesGrid class to vectors represented internally as matrices with exactly one column.

Author:
Hans Joachim Ferreau, Boris Houska

Definition at line 56 of file variables_grid.hpp.


Constructor & Destructor Documentation

Default constructor.

Definition at line 46 of file variables_grid.cpp.

VariablesGrid::VariablesGrid ( uint  _dim,
const Grid _grid,
VariableType  _type = VT_UNKNOWN,
const char **const  _names = 0,
const char **const  _units = 0,
const DVector *const  _scaling = 0,
const DVector *const  _lb = 0,
const DVector *const  _ub = 0,
const BooleanType *const  _autoInit = 0 
)

Constructor that takes the dimension of each vector-valued MatrixVariable as well as the grid on which they are defined. Further information can optionally be specified.

Parameters:
[in]_dimDimension of each vector.
[in]_gridGrid on which the vector-valued MatrixVariable(s) are defined.
[in]_typeType of the variable(s).
[in]_namesArray containing names (labels) for each component of the variable(s).
[in]_unitsArray containing units for each component of the variable(s).
[in]_scalingArray containing the scaling for each component of the variable(s).
[in]_lbArray containing lower bounds for each component of the variable(s).
[in]_ubArray containing upper bounds for each component of the variable(s).
[in]_autoInitArray defining if each component of the variable(s) is to be automatically initialized.

Definition at line 51 of file variables_grid.cpp.

VariablesGrid::VariablesGrid ( uint  _dim,
uint  _nPoints,
VariableType  _type = VT_UNKNOWN,
const char **const  _names = 0,
const char **const  _units = 0,
const DVector *const  _scaling = 0,
const DVector *const  _lb = 0,
const DVector *const  _ub = 0,
const BooleanType *const  _autoInit = 0 
)

Constructor that takes the dimension of each vector-valued MatrixVariable as well as the number of grid points on which they are defined. Further information can optionally be specified.

Parameters:
[in]_dimDimension of each vector.
[in]_nPointsNumber of grid points on which the vector-valued MatrixVariable(s) are defined.
[in]_typeType of the variable(s).
[in]_namesArray containing names (labels) for each component of the variable(s).
[in]_unitsArray containing units for each component of the variable(s).
[in]_scalingArray containing the scaling for each component of the variable(s).
[in]_lbArray containing lower bounds for each component of the variable(s).
[in]_ubArray containing upper bounds for each component of the variable(s).
[in]_autoInitArray defining if each component of the variable(s) is to be automatically initialized.

Definition at line 65 of file variables_grid.cpp.

VariablesGrid::VariablesGrid ( uint  _dim,
double  _firstTime,
double  _lastTime,
uint  _nPoints,
VariableType  _type = VT_UNKNOWN,
const char **const  _names = 0,
const char **const  _units = 0,
const DVector *const  _scaling = 0,
const DVector *const  _lb = 0,
const DVector *const  _ub = 0,
const BooleanType *const  _autoInit = 0 
)

Constructor that takes the dimensions of each vector-valued MatrixVariable as well as the number of grid points on which they are defined. Moreover, it takes the time of the first and the last grid point; all intermediate grid points are setup to form a equidistant grid of time points. Further information can optionally be specified.

Parameters:
[in]_dimDimension of each vector.
[in]_firstTimeTime of first grid point.
[in]_lastTimeTime of last grid point.
[in]_nPointsNumber of grid points on which the vector-valued MatrixVariable(s) are defined.
[in]_typeType of the variable(s).
[in]_namesArray containing names (labels) for each component of the variable(s).
[in]_unitsArray containing units for each component of the variable(s).
[in]_scalingArray containing the scaling for each component of the variable(s).
[in]_lbArray containing lower bounds for each component of the variable(s).
[in]_ubArray containing upper bounds for each component of the variable(s).
[in]_autoInitArray defining if each component of the variable(s) is to be automatically initialized.

Definition at line 79 of file variables_grid.cpp.

VariablesGrid::VariablesGrid ( const DVector arg,
const Grid _grid = trivialGrid,
VariableType  _type = VT_UNKNOWN 
)

Constructor that creates a VariablesGrid on a given grid with given type. At each grid point, the vector-valued MatrixVariable is constructed from the vector passed.

Parameters:
[in]argDVector to be assign at each point of the grid.
[in]_gridGrid on which the vector-valued MatrixVariable(s) are defined.
[in]_typeType of the variable(s).

Definition at line 95 of file variables_grid.cpp.

Constructor which reads data from a matrix. The data is expected to be in matrix format and is interpreted as follows: the first entry of each row is taken as time of the grid point to be added, all remaining entries of each row are taken as numerical values of a vector-valued MatrixVariable with exactly one column. In effect, a MatrixVariablesGrid consisting of <number of columns - 1>-by-1 MatrixVariables defined on <number of="" rows>=""> grid points is setup. Note that all rows are expected to have equal number of columns.

Parameters:
[in]fileFile to be read.
Note:
The file is closed at the end of routine.

Definition at line 103 of file variables_grid.cpp.

Copy constructor (deep copy).

Parameters:
[in]rhsRight-hand side object.

Definition at line 119 of file variables_grid.cpp.

Copy constructor (deep copy).

Parameters:
[in]rhsRight-hand side object.

Definition at line 125 of file variables_grid.cpp.

Destructor.

Definition at line 133 of file variables_grid.cpp.


Member Function Documentation

returnValue VariablesGrid::addVector ( const DVector newVector,
double  newTime = -INFTY 
)

Adds a new grid point with given vector and time to grid.

Parameters:
[in]newVectorDVector of grid point to be added.
[in]newTimeTime of grid point to be added.
Returns:
SUCCESSFUL_RETURN,
RET_INVALID_ARGUMENTS

Definition at line 271 of file variables_grid.cpp.

Appends grid point of given grid to object. A merge method defines the way duplicate entries are handled.

Parameters:
[in]argGrid to append.
[in]_mergeMethodMerge method, see documentation of MergeMethod for details.
Returns:
SUCCESSFUL_RETURN,
RET_INVALID_ARGUMENTS

Definition at line 362 of file variables_grid.cpp.

Appends grid point of given grid to object. A merge method defines the way duplicate entries are handled.

Parameters:
[in]argGrid to append in matrix form.
[in]_mergeMethodMerge method, see documentation of MergeMethod for details.
Returns:
SUCCESSFUL_RETURN,
RET_INVALID_ARGUMENTS

Definition at line 412 of file variables_grid.cpp.

Appends values at all grid points of given grid to object. Both grids need to be defined over identical grid points.

Parameters:
[in]argGrid whose values are to appended.
Returns:
SUCCESSFUL_RETURN,
RET_INVALID_ARGUMENTS

Definition at line 421 of file variables_grid.cpp.

Returns vector at first grid point.

Returns:
DVector at first grid point

Definition at line 316 of file variables_grid.cpp.

Returns a component-wise approximation of the integral over all vectors at all grid points.

Parameters:
[in]modeSpecifies how the vector-values are interpolated for approximating the integral, see documentation of InterpolationMode for details.
[out]valueComponent-wise approximation of the integral over all vectors at all grid points.
Returns:
SUCCESSFUL_RETURN

Definition at line 625 of file variables_grid.cpp.

Returns vector at first grid point.

Returns:
DVector at first grid point

Definition at line 325 of file variables_grid.cpp.

Returns the component-wise sum over all vectors at all grid points.

Parameters:
[out]sumComponent-wise sum over all vectors at all grid points.
Returns:
SUCCESSFUL_RETURN

Definition at line 613 of file variables_grid.cpp.

VariablesGrid VariablesGrid::getTimeSubGrid ( uint  startIdx,
uint  endIdx 
) const

Returns the sub grid in time starting and ending at given indices.

Parameters:
[in]startIdxIndex of first grid point to be included in sub grid.
[in]endIdxIndex of last grid point to be included in sub grid.
Returns:
Sub grid in time

Reimplemented from MatrixVariablesGrid.

Definition at line 542 of file variables_grid.cpp.

VariablesGrid VariablesGrid::getTimeSubGrid ( double  startTime,
double  endTime 
) const

Returns the sub grid in time starting and ending at given times.

Parameters:
[in]startTimeTime of first grid point to be included in sub grid.
[in]endTimeTime of last grid point to be included in sub grid.
Returns:
Sub grid in time

Definition at line 561 of file variables_grid.cpp.

VariablesGrid VariablesGrid::getValuesSubGrid ( uint  startIdx,
uint  endIdx 
) const

Returns the sub grid of values. It comprises all grid points of the object, but comprises at each grid point only the compenents starting and ending at given indices.

Parameters:
[in]startIdxIndex of first compenent to be included in sub grid.
[in]endIdxIndex of last compenent to be included in sub grid.
Note:
This function implicitly assumes that vectors at all grid points have same number of components (or at least more than 'endIdx').
Returns:
Sub grid of values

Reimplemented from MatrixVariablesGrid.

Definition at line 593 of file variables_grid.cpp.

DVector VariablesGrid::getVector ( uint  pointIdx) const

Returns vector at grid point with given index.

Parameters:
[in]pointIdxIndex of grid point.
Returns:
DVector at grid point with given index (empty if index is out of bounds)

Definition at line 306 of file variables_grid.cpp.

Initializes an empty VariablesGrid.

Returns:
SUCCESSFUL_RETURN

Reimplemented from MatrixVariablesGrid.

Definition at line 208 of file variables_grid.cpp.

returnValue VariablesGrid::init ( uint  _dim,
const Grid _grid,
VariableType  _type = VT_UNKNOWN,
const char **const  _names = 0,
const char **const  _units = 0,
const DVector *const  _scaling = 0,
const DVector *const  _lb = 0,
const DVector *const  _ub = 0,
const BooleanType *const  _autoInit = 0 
)

Initializes the VariablesGrid on a given grid with given dimension of each vector-valued MatrixVariable. Further information can optionally be specified.

Parameters:
[in]_dimDimension of each vector.
[in]_gridGrid on which the vector-valued MatrixVariable(s) are defined.
[in]_typeType of the variable(s).
[in]_namesArray containing names (labels) for each component of the variable(s).
[in]_unitsArray containing units for each component of the variable(s).
[in]_scalingArray containing the scaling for each component of the variable(s).
[in]_lbArray containing lower bounds for each component of the variable(s).
[in]_ubArray containing upper bounds for each component of the variable(s).
[in]_autoInitArray defining if each component of the variable(s) is to be automatically initialized.
Returns:
SUCCESSFUL_RETURN

Definition at line 214 of file variables_grid.cpp.

returnValue VariablesGrid::init ( uint  _dim,
uint  _nPoints,
VariableType  _type = VT_UNKNOWN,
const char **const  _names = 0,
const char **const  _units = 0,
const DVector *const  _scaling = 0,
const DVector *const  _lb = 0,
const DVector *const  _ub = 0,
const BooleanType *const  _autoInit = 0 
)

Initializes the VariablesGrid taking the dimension of each vector-valued MatrixVariable as well as the number of grid points on which they are defined. Further information can optionally be specified.

Parameters:
[in]_dimDimension of each vector.
[in]_nPointsNumber of grid points on which the vector-valued MatrixVariable(s) are defined.
[in]_typeType of the variable(s).
[in]_namesArray containing names (labels) for each component of the variable(s).
[in]_unitsArray containing units for each component of the variable(s).
[in]_scalingArray containing the scaling for each component of the variable(s).
[in]_lbArray containing lower bounds for each component of the variable(s).
[in]_ubArray containing upper bounds for each component of the variable(s).
[in]_autoInitArray defining if each component of the variable(s) is to be automatically initialized.
Returns:
SUCCESSFUL_RETURN

Definition at line 229 of file variables_grid.cpp.

returnValue VariablesGrid::init ( uint  _dim,
double  _firstTime,
double  _lastTime,
uint  _nPoints,
VariableType  _type = VT_UNKNOWN,
const char **const  _names = 0,
const char **const  _units = 0,
const DVector *const  _scaling = 0,
const DVector *const  _lb = 0,
const DVector *const  _ub = 0,
const BooleanType *const  _autoInit = 0 
)

Initializes the MatrixVariablesGrid taking the dimension of each vector-valued MatrixVariable as well as the number of grid points on which they are defined. Moreover, it takes the time of the first and the last grid point; all intermediate grid points are setup to form a equidistant grid of time points. Further information can optionally be specified.

Parameters:
[in]_dimDimension of each vector.
[in]_firstTimeTime of first grid point.
[in]_lastTimeTime of last grid point.
[in]_nPointsNumber of grid points on which the vector-valued MatrixVariable(s) are defined.
[in]_typeType of the variable(s).
[in]_namesArray containing names (labels) for each component of the variable(s).
[in]_unitsArray containing units for each component of the variable(s).
[in]_scalingArray containing the scaling for each component of the variable(s).
[in]_lbArray containing lower bounds for each component of the variable(s).
[in]_ubArray containing upper bounds for each component of the variable(s).
[in]_autoInitArray defining if each component of the variable(s) is to be automatically initialized.
Returns:
SUCCESSFUL_RETURN

Definition at line 244 of file variables_grid.cpp.

returnValue VariablesGrid::init ( const DVector arg,
const Grid _grid = trivialGrid,
VariableType  _type = VT_UNKNOWN 
)

Initializes the VariablesGrid on a given grid with given type. At each grid point, the vector-valued MatrixVariable is constructed from the matrix passed.

Parameters:
[in]argDVector to be assign at each point of the grid.
[in]_gridGrid on which the vector-valued MatrixVariable(s) are defined.
[in]_typeType of the variable(s).
Returns:
SUCCESSFUL_RETURN

Definition at line 261 of file variables_grid.cpp.

Initializes the grid vector by taking average between upper and lower bound. If one of these bounds is infinity it is initialized with the bound. If both bounds are infinity it is initialized with 0. This routine is only for internal use by the OptimizationAlgorithm, that is a friend of this class.

Returns:
SUCCESSFUL_RETURN

Definition at line 666 of file variables_grid.cpp.

returnValue VariablesGrid::merge ( const VariablesGrid arg,
MergeMethod  _mergeMethod = MM_DUPLICATE,
BooleanType  keepOverlap = BT_TRUE 
)

Constructs the set union in time of current and given grid. A merge method defines the way duplicate entries are handled. Moreover, it can be specified whether an overlap in time of both grids shall be kept or if only the entries of one of them shall be kept according to the merge method.

Parameters:
[in]argGrid to append.
[in]_mergeMethodMerge method, see documentation of MergeMethod for details.
[in]keepOverlapFlag indicating whether overlap shall be kept.
Returns:
SUCCESSFUL_RETURN,
RET_INVALID_ARGUMENTS

Definition at line 446 of file variables_grid.cpp.

VariablesGrid::operator DMatrix ( ) const

Definition at line 703 of file variables_grid.cpp.

double& VariablesGrid::operator() ( uint  pointIdx,
uint  rowIdx 
) [inline]

Returns the value of a certain component at a certain grid point.

Parameters:
[in]pointIdxIndex of grid point.
[in]rowIdxRow index of the component to be returned.
Returns:
Value of component 'rowIdx' at grid point 'pointIdx'
double VariablesGrid::operator() ( uint  pointIdx,
uint  rowIdx 
) const [inline]

Returns the value of a certain component at a certain grid point.

Parameters:
[in]pointIdxIndex of grid point.
[in]rowIdxRow index of the component to be returned.
Returns:
Value of component 'rowIdx' at grid point 'pointIdx'
VariablesGrid VariablesGrid::operator() ( const uint  rowIdx) const

Returns a VariablesGrid consisting only of the given row.

Parameters:
[in]rowIdxRow index of the component to be returned.
Returns:
VariablesGrid consisting only of the given row

Reimplemented from MatrixVariablesGrid.

Definition at line 169 of file variables_grid.cpp.

VariablesGrid VariablesGrid::operator+ ( const VariablesGrid arg) const [inline]

Adds (element-wise) two VariablesGrid into a temporary object.

Parameters:
[in]argSecond summand.
Returns:
Temporary object containing sum of VariablesGrids.
VariablesGrid& VariablesGrid::operator+= ( const VariablesGrid arg) [inline]

Adds (element-wise) a VariablesGrid to object.

Parameters:
[in]argSecond summand.
Returns:
Reference to object after addition
VariablesGrid VariablesGrid::operator- ( const VariablesGrid arg) const [inline]

Subtracts (element-wise) a VariablesGrid from the object and stores result into a temporary object.

Parameters:
[in]argSubtrahend.
Returns:
Temporary object containing the difference of the VariablesGrids
VariablesGrid& VariablesGrid::operator-= ( const VariablesGrid arg) [inline]

Subtracts (element-wise) a VariablesGrid from the object.

Parameters:
[in]argSubtrahend.
Returns:
Reference to object after subtraction
VariablesGrid & VariablesGrid::operator= ( const VariablesGrid rhs)

Assignment operator (deep copy).

Parameters:
[in]rhsRight-hand side object.

Definition at line 138 of file variables_grid.cpp.

VariablesGrid & VariablesGrid::operator= ( const MatrixVariablesGrid rhs)

Assignment operator (deep copy).

Parameters:
[in]rhsRight-hand side object.

Reimplemented from MatrixVariablesGrid.

Definition at line 149 of file variables_grid.cpp.

VariablesGrid & VariablesGrid::operator= ( const DMatrix rhs)

Assignment operator which reads data from a matrix. The data is interpreted as follows: the first entry of each row is taken as time of the grid point to be added, all remaining entries of each row are taken as numerical values of a vector-valued MatrixVariable with exactly one column. In effect, a MatrixVariablesGrid consisting of <number of columns - 1>-by-1 MatrixVariables defined on <number of="" rows>=""> grid points is setup.

Parameters:
[in]rhsDMatrix to be read.
Note:
The file is closed at the end of routine.

Reimplemented from MatrixVariablesGrid.

Definition at line 162 of file variables_grid.cpp.

BooleanType VariablesGrid::operator== ( const VariablesGrid arg) const [inline]

Tests for equality,

Parameters:
[in]rhsObject of comparison.
Returns:
BT_TRUE iff both objects are equal,
BT_FALSE otherwise
VariablesGrid VariablesGrid::operator[] ( const uint  pointIdx) const

Returns a VariablesGrid consisting only of the values at given grid point.

Parameters:
[in]pointIdxIndex of grid point.
Returns:
VariablesGrid consisting only of the values at given grid point

Reimplemented from MatrixVariablesGrid.

Definition at line 191 of file variables_grid.cpp.

Assigns new vector to all grid points.

Parameters:
[in]_valueNew vector.
Returns:
SUCCESSFUL_RETURN,
RET_INDEX_OUT_OF_BOUNDS,
RET_VECTOR_DIMENSION_MISMATCH

Definition at line 296 of file variables_grid.cpp.

returnValue VariablesGrid::setVector ( uint  pointIdx,
const DVector _values 
)

Assigns new vector to grid point with given index.

Parameters:
[in]pointIdxIndex of grid point.
[in]_valueNew vector.
Returns:
SUCCESSFUL_RETURN,
RET_INDEX_OUT_OF_BOUNDS,
RET_VECTOR_DIMENSION_MISMATCH
Parameters:
pointIdxIndex of the grid point.
_valuesNew values of the sub-vector.

Definition at line 279 of file variables_grid.cpp.

Shifts all grid points backwards by one grid point, deleting the first one and doubling the value at last grid point.

Returns:
Reference to object with shifted points

Definition at line 343 of file variables_grid.cpp.

VariablesGrid & VariablesGrid::shiftTimes ( double  timeShift)

Shifts times at all grid points by a given offset.

Parameters:
[in]timeShiftTime offset for shifting.
Returns:
Reference to object with shifted times

Reimplemented from MatrixVariablesGrid.

Definition at line 335 of file variables_grid.cpp.


Friends And Related Function Documentation

friend class OptimizationAlgorithm [friend]

Definition at line 59 of file variables_grid.hpp.

friend class OptimizationAlgorithmBase [friend]

Definition at line 58 of file variables_grid.hpp.

friend class RealTimeAlgorithm [friend]

Definition at line 60 of file variables_grid.hpp.


The documentation for this class was generated from the following files:


acado
Author(s): Milan Vukov, Rien Quirynen
autogenerated on Thu Aug 27 2015 12:01:40