R port of the Scilab optimbase module

Description

The goal of this package is to provide a building block for a large class of specialized optimization methods. This packages manages:

• the number of variables,

• the minimum and maximum bounds,

• the number of non linear inequality constraints,

• the cost function,

• the logging system,

• various termination criteria,

• etc...

Features The following is a list of features the optimbase toolbox currently provided:

• Manage cost function

  • optionnal additionnal argument

  • direct communication of the task to perform: cost function or inequality constraints

• Manage various termination criteria, including:

  • maximum number of iterations,

  • tolerance on function value (relative or absolute),

  • tolerance on the vector of estimated parameter x (relative or absolute),

  • maximum number of evaluations of the cost function,

• Manage the history of the convergence, including:

  • history of function values,

  • history of optimum point.

• Provide query features for

  • the status of the optimization process,

  • the number of iterations,

  • the number of function evaluations,

  • function value at initial point,

  • function value at optimal point,

  • the optimum parameters,

  • etc...

Details

See vignette('optimbase',package='optimbase') for more information.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Point Estimate Comparison with Bounds and Constraints

Description

optimbase.isinbounds checks that given parameter estimates are within the defined minimum and maximum boundaries, while optimbase.isinnonlincons checks that the given point estimate satisfies the defined nonlinear constraints.

Usage

  optimbase.isinbounds(this = NULL, x = NULL)
  optimbase.isinnonlincons(this=NULL,x=NULL)

Arguments

Value

Both functions return a list with the following elements:

this

The optimization object.

isfeasible

TRUE if the parameter estimates satisfy the constraints, FALSE otherwise.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Query for Bounds and Constraints

Description

optimbase.hasbounds and optimbase.hascons query an optimization object and determine whether bounds and nonlinear constraints have been specified. Bounds are defined in the boundsmin and boundsmax elements of the optimization object. The number of nonlinear constraints is defined in the nbineqconst element.

optimbase.hasconstraints determine whether any bound or constraint has been specified.

Usage

  optimbase.hasbounds(this = NULL)
  optimbase.hasnlcons(this = NULL)
  optimbase.hasconstraints(this = NULL)

Arguments

Value

Return TRUE if bounds or constraints are found, FALSE otherwise.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Optimbase Log functions

Description

optimbase.logstartup initializes logging if verbose logging is enabled (via the verbose element of the optimization object). If the logging has already been initialized, it generates an error and stops the optimization.

If verbose logging is enabled, optimbase.log prints the given message in the console. If verbose logging is disabled, it does nothing. If the logfile element of the optimization object has been set, it writes the message into the file instead of writing to the console.

optimbase.stoplog prints the given stopping rule message if verbose termination is enabled (via the verbosetermination element of the optimization object). If verbose termination is disabled, it does nothing.

optimbase.logshutdown turns verbose logging off.

Usage

  optimbase.logstartup(this = NULL)
  optimbase.log(this = NULL, msg = NULL)
  optimbase.stoplog(this = NULL, msg = NULL)
  optimbase.logshutdown(this = NULL)

Arguments

Value

All functions return the unchanged optimization object.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Check of Variable Class

Description

Utility functions in optimbase meant to check variable class. Stop the algorithm if the variable is not of the expected class.

assert.classboolean

for logical variables

assert.classfunction

for functions

assert.classreal

for numeric variables

assert.classinteger

for integer variables

assert.classstring

for character variables

unknownValueForOption stops the algorithm and returns an error message, when some checks in optimbase are not successful.

Usage

  assert.classboolean(var = NULL, varname = NULL, ivar = NULL)
  assert.classfunction(var = NULL, varname = NULL, ivar = NULL)
  assert.classreal(var = NULL, varname = NULL, ivar = NULL)
  assert.classinteger(var = NULL, varname = NULL, ivar = NULL)
  assert.classstring(var = NULL, varname = NULL, ivar = NULL)
  unknownValueForOption(value = NULL, optionname = NULL)

Arguments

Value

Return an error message through the stop function.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

S3 optimbase classes

Description

These functions support the S3 class 'optimbase' and related S3 classes 'optimbase.outputargs' and 'optimbase.functionargs'. They are intended to either create objects of these classes, check if an object is of these classes, or coerce it to one of these classes.

Usage

  optimbase(verbose, x0, fx0, xopt, fopt, tolfunabsolute, 
    tolfunrelative, tolfunmethod, tolxabsolute, tolxrelative, tolxmethod, 
    maxfunevals, funevals, maxiter, iterations, fun, status, historyxopt,
    historyfopt, verbosetermination, outputcommand, outputcommandarg,
    numberofvariables, storehistory, costfargument, boundsmin, boundsmax,
    nbineqconst, logfile, logfilehandle, logstartup, withderivatives)
  
  optimbase.outputargs(...)
  
  optimbase.functionargs(...)
  
  ## S3 method for class 'optimbase'
print(x,verbose=FALSE,...)
  
  ## S3 method for class 'optimbase'
is(x=NULL)
  
  ## S3 method for class 'optimbase'
summary(object,showhistory,...)
  
  ## S3 method for class 'optimbase.outputargs'
is(x=NULL)
  
  ## S3 method for class 'optimbase.outputargs'
as(x=NULL)
  
  ## S3 method for class 'optimbase.functionargs'
is(x=NULL)
  
  ## S3 method for class 'optimbase.functionargs'
as(x=NULL)
  

Arguments

Value

The optimbase function returns a new object of class 'optimbase', i.e. a list containing the following elements:

verbose

Default is FALSE.

x0

Default is NULL.

fx0

Default is NULL.

xopt

Default is 0.

fopt

Default is 0.

tolfunabsolute

Default is 0.

tolfunrelative

Default is .Machine$double.eps.

tolfunmethod

Default is FALSE.

tolxabsolute

Default is 0.

tolxrelative

Default is .Machine$double.eps.

tolxmethod

Default is TRUE.

maxfunevals

Default is 100.

funevals

Default is 0.

maxiter

Default is 100.

iterations

Default is 0.

fun

Default is ”.

status

Default is ”.

historyfopt

Default is NULL.

historyxopt

Default is NULL.

verbosetermination

Default is FALSE.

outputcommand

Default is ”.

outputcommandarg

Default is ”. If the user configures this element, it is expected to be an object of class 'optimbase.outputargs' or will be coerced to an object of class 'optimbase.outputargs'.

numberofvariables

Default is 0.

storehistory

Default is FALSE.

costfargument

Default is ”. If the user configures this element, it is expected to be an object of class 'optimbase.functionargs' or will be coerced to an object of class 'optimbase.functionargs'.

boundsmin

Default is NULL.

boundsmax

Default is NULL.

nbineqconst

Default is 0.

logfile

Default is ”.

logfilehandle

Default is 0.

logstartup

Default is FALSE.

withderivatives

Default is FALSE.

The print.optimbase and is.optimbase functions are S3 method for objects of class 'optimbase'. The showhistory argument can be provided to the print.optimbase function to indicate whether or not the history of optimization should be printed.

The optimbase.outputargs function returns a new object of class 'optimbase.outputargs', i.e. a list of all arguments provided by the user. The is.optimbase.outputargs functions are S3 method for objects of class 'optimbase.outputargs'.

The optimbase.functionargs function returns a new object of class 'optimbase.functionargs', i.e. a list of all arguments provided by the user. The is.optimbase.functionargs functions are S3 method for objects of class 'optimbase.functionargs'.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Check bounds.

Description

This function checks if the bounds defined in the optimization object are consistent (same number of minimal and maximal bounds as the number of variables, minimal bounds lower than maximal bounds) and puts an error message in the returned object if not.

Usage

  optimbase.checkbounds(this = NULL)

Arguments

Value

Return a list with the following list:

this

The optimization object.

isok

TRUE if the bounds are consistent, FALSE otherwise.

errmsg

An error message if the bounds are not consistent.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Check Cost Function

Description

This function checks that the cost function is correctly specified in the optimization object, including that the elements of this used by the cost function are consistent.

Usage

  optimbase.checkcostfun(this = NULL)

Arguments

Details

Depending on the definition of nonlinear constraints (nbineqconst element > 0) and the use of derivatives (withderivatives element set to TRUE), this function makes several cost function calls with different index value (see vignette('optimbase',package='optimbase') for more details about index). If at least one call fails, the function stops the search algorithm.

Following every successful cost function call, optimbase.checkcostfun calls optimbase.checkshape to check the dimensions of the matrix returned by the cost function against some expectations.

Value

Return the optimization object or an error message if one check is not successful.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase.checkshape

Check the Dimensions of the Cost Function Output

Description

This function is called by optimbase.checkcostfun to check whether the dimensions of a cost function output match the expectations.

Usage

  optimbase.checkshape(this = NULL, varname = NULL, data = NULL, index = NULL,
                       expectednrows = NULL, expectedncols = NULL)

Arguments

Value

Return the optimization object or an error message if the dimensions are inconsistent.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase.checkcostfun

Check Consistency of Initial Guesses

Description

This function checks that the initial guesses defined in the optimization object are consistent with the defined bounds and the non linear inequality constraints. The actual work is delegated to optimbase.isfeasible.

Usage

  optimbase.checkx0(this = NULL)

Arguments

Value

Return a list with the following elements:

this

The optimization object.

isok

TRUE if the initial guesses are consistent with the settings, FALSE otherwise.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase.isfeasible

Erase an optimization history.

Description

Erase the optimization history in an optimization object.

Usage

  optimbase.destroy(this = NULL)

Arguments

Details

This function erases the content of the historyfopt and historyxopt elements in this and call the optimbase.logshutdown function if the logstartup element in this is set to TRUE.

Value

Return an updated optimization object.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase.logshutdown

Call Cost Function

Description

This function calls the cost function defined in the fun element of the current object and returns the required results. If an additionnal argument for the cost function is defined in current object, it is passed to the function as the last argument. See vignette('optimbase',package='optimbase') for more details.

Usage

  optimbase.function(this = NULL, x = NULL, index = NULL)

Arguments

Value

Return a list with the following elements:

this

The updated optimization object.

f

The value of the cost function.

g

The gradient of the cost function.

c

The nonlinear, positive, inequality constraints.

gc

The gradient of the nonlinear, positive, inequality constraints.

index

An integer:

• if index > 0, everything went fine,

• if index == 0, interrupts the optimization,

• if index < 0, one of the function could not be evaluated.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Get the value for the given element

Description

Get the value for the given element in an optimization object.

Usage

  optimbase.get(this = NULL, key = NULL)
  optimbase.histget(this = NULL, iter = NULL, key = NULL)

Arguments

Details

While optimbase.get extracts the entire content of the object element, including historyxopt and historyfopt, optimbase.histget only extracts the content of the history at the iteration iter.

Value

Return the value of the list element key, or an error message if key does not exist.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase, optimbase.set

Grid evaluation of a constrained or unconstrained cost function

Description

Evaluate a constrained or unconstrained cost function on a grid of points around a given initial point estimate.

Usage

  optimbase.gridsearch(fun = NULL, x0 = NULL, xmin = NULL, 
                       xmax = NULL, npts = 3, alpha = 10)

Arguments

Details

optimbase.gridsearch evaluates the cost function at each point of a grid of npts^length(x0) points. If lower (xmin) and upper (xmax) bounds are provided, the range of evaluation points is limited by those bounds and alpha is not used. Otherwise, the range of evaluation points is defined as [x0/alpha,x0*alpha].

optimbase.gridsearch also determines if the cost function is feasible at each evaluation point by calling optimbase.isfeasible.

Value

Return a data.frame with the coordinates of the evaluation point, the value of the cost function and its feasibility. The data.frame is ordered by feasibility and increasing value of the cost function.

Author(s)

Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase.isfeasible

Examples

# Problem: find x and y that maximize 3.6*x - 0.4*x^2 + 1.6*y - 0.2*y^2 and
#          satisfy the constrains:
#            2*x - y <= 10
#            x >= 0
#            y >= 0
#

gridfun <- function(x=NULL,index=NULL,fmsfundata=NULL,...){

  f <- c()
  c <- c()
  if (index == 2 | index == 6)
    f <- -(3.6*x[1] - 0.4*x[1]*x[1] + 1.6*x[2] - 0.2*x[2]*x[2])
  if (index == 5 | index == 6)
    c <- c(10 - 2*x[1] - x[2],
           x[1],
           x[2])
  varargout <- list(f = f, g = c(), c = c, gc = c(), index = index)

  return(varargout)
}


x0 <- c(0.35,0.3)
npts <- 6
alpha <- 10

res <- optimbase.gridsearch(fun=gridfun,x0=x0,xmin=NULL,xmax=NULL,
                     npts=npts,alpha=alpha)

# 3.5 and 3 is the actual solution of the optimization problem
print(res)

Iteration Log Incrementation

Description

This function increments the number of iterations stored in the iterations element of the optimization object.

Usage

  optimbase.incriter(this = NULL)

Arguments

Value

Return the optimization object after increasing the content of the iterations element by 1 unit.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Check Point Estimate

Description

This function checks that the point estimate is consistent with the bounds and the non linear inequality constraints. It is usually called by optimbase.checkx0 to check initial guesses.

Usage

  optimbase.isfeasible(this = NULL, x = NULL)

Arguments

Details

Returns 1 if the given point satisfies bounds constraints and inequality constraints.

Returns 0 if the given point is not in the bounds.

Returns -1 if the given point does not satisfies inequality constraints.

Value

Return a list with the following elements:

this

The optimization object.

isfeasible

The feasibility flag, either -1, 0 or 1.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase.checkx0

Call user-defined output function

Description

Call user-defined output function.

Usage

  optimbase.outputcmd(this = NULL, state = NULL, data = NULL)

Arguments

Details

The data list argument may contain more levels than those presented above. These additional levels may contain values which are specific to the specialized algorithm, such as the simplex in a Nelder-Mead method, the gradient of the cost function in a BFGS method, etc...

Value

Do not return any data, but execute the output function defined in the outputcommand element of this.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Create Basic Optimization Data Object

Description

This function creates a basic optimization data object by extracting the content of specific fields of an optimization object.

Usage

  optimbase.outstruct(this = NULL)

Arguments

Value

Return an object of class 'optimbase.data', i.e. a list with the following elements:

x

The current optimum point estimate (extracted from this$xopt).

fval

The value of the cost function at the current optimum point estimate (extracted from this$fopt).

iteration

The current number of iteration (extracted from this$iterations).

funccount

The current number of function evaluations (extracted from this$funevals).

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Projection of Point Estimate to Bounds

Description

This function determines if all elements of a point estimate are within the defined bounds. In the case one or more parameter estimates are not, the function projects those to their corresponding bounds.

Usage

  optimbase.proj2bnds(this = NULL, x = NULL)

Arguments

Value

Return a list with the following elements:

this

The optimization object.

p

A vector of updated paremeter estimes. The ith element of the vector is:

• x[i] if this$boundsmin[i] < x[i] < this$boundsmax[i],

• this$boundsmin[i] if x[i] <= this$boundsmin[i],

• this$boundsmax[i] if this$boundsmax[i] <= x[i].

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Optimization Object Configuration

Description

This functions configures the current optimization object with the given value for the given key.

Usage

  optimbase.set(this = NULL, key = NULL, value = NULL)
  optimbase.histset(this = NULL, iter = NULL, key = NULL, value = NULL)

Arguments

Details

optimbase.set set the content of the key element of the optimization object this to value.

The only available keys in optimbase.set are the following:

'verbose'

Set to 1 to enable verbose logging.

'x0'

The initial guesses, as a n x 1 column vector, where n is the number of variables.

'fx0'

The value of the cost function at the initial point estimate.

'xopt'

The optimum point estimate.

'fopt'

The value of the cost function at the optimum point estimate.

'tolfunabsolute'

The absolute tolerance for the function value.

'tolfunrelative'

The relative tolerance for the function value.

'tolfunmethod'

The method used for the tolerance on function value in the termination criteria. The following values are available: TRUE, FALSE. If this criteria is triggered, the status of the optimization is set to 'tolf'.

'tolxabsolute'

The absolute tolerance on x.

'tolxrelative'

The relative tolerance on x.

'tolxmethod'

The method used for the tolerance on x in the termination criteria. The following values are available: TRUE, FALSE. If this criteria is triggered during optimization, the status of the optimization is set to 'tolx'.

'maxfunevals'

The maximum number of function evaluations. If this criteria is triggered during optimization, the status of the optimization is set to 'maxfuneval' (see vignette('optimbase',package='optimbase') for more details).

'funevals'

The number of function evaluations.

'maxiter'

The maximum number of iterations. If this criteria is triggered during optimization, the status of the optimization is set to 'maxiter' (see vignette('optimbase',package='optimbase') for more details).

'iterations'

The number of iterations.

'function'

The objective function, which computes the value of the cost function and the non linear constraints, if any. See vignette('optimbase',package='optimbase') for the details of the communication between the optimization system and the cost function.

'status'

A string containing the status of the optimization.

'historyxopt'

A list, with nbiter element, containing the history of x during the iterations. This list is available after optimization if the history storing was enabled with the storehistory element.

'historyfopt'

An vector, with nbiter values, containing the history of the function value during the iterations. This vector is available after optimization if the history storing was enabled with the storehistory element.

'verbosetermination'

Set to 1 to enable verbose termination logging.

'outputcommand'

A command which is called back for output. Details of the communication between the optimization system and the output command function are provided in vignette('optimbase',package='optimbase').

'outputcommandarg'

An additionnal argument, passed to the output command.

'numberofvariables'

The number of variables to optimize.

'storehistory'

Set to TRUE to enable the history storing.

'costfargument'

An additionnal argument, passed to the cost function.

'boundsmin'

The minimum bounds for the parameters.

'boundsmax'

The maximum bounds for the parameters.

'nbineqconst'

The number of inequality constraints.

'logfile'

The name of the log file.

'logfilehandle'

Set to 1 if logging has been started

'logstartup'

Set to 1 if logging has been started

'withderivatives'

Set to TRUE if the algorithm uses derivatives.

The only available keys in optimbase.histset are 'historyxopt' and 'historyfopt'. Contrary to optimbase.set, this function only alters the value of historyxopt and historyfopt at the specific iteration iter.

Value

An updated optimization object.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

optimbase

Evaluation of Termation Status

Description

This function determines whether the optimization must continue or terminate. If the verbosetermination element of the optimization object is enabled, messages are printed detailing the termination intermediate steps. The optimbase.terminate function takes into account the number of iterations, the number of evaluations of the cost function, the tolerance on x and the tolerance on f. See the section "Termination" in vignette('optimbase',package='optimbase') for more details.

Usage

  optimbase.terminate(this = NULL, previousfopt = NULL, currentfopt = NULL,
                      previousxopt = NULL, currentxopt = NULL)

Arguments

Value

Return a list with the following elements:

this

The updated optimization object.

terminate

TRUE if the algorithm terminates, FALSE if the algorithm must continue.

status

The termination status could be 'maxiter', 'maxfuneval', 'tolf' or 'tolx' if terminate is set to TRUE, 'continue' otherwise.

Author(s)

Author of Scilab optimbase module: Michael Baudin (INRIA - Digiteo)

Author of R adaptation: Sebastien Bihorel (sb.pmlab@gmail.com)

Vector, Matrix or Data.Frame Size

Description

size is a utility function which determines the dimensions of vectors (coerced to matrices), matrices, arrays, data.frames, and list elements.

Usage

  size(x = NULL, n = NULL)

Arguments

Details

size is a wrapper function around dim. It returns the n^th dimension of x if n is provided. If n is not provide, all dimensions will be determined. If x is a list, n is ignored and the dimensions of all elements of x are recursively determined.

Value

Returns a vector or list of dimensions.

Author(s)

Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

dim

Examples

  a <- 1
  b <- letters[1:6]
  c <- matrix(1:20,nrow=4,ncol=5)
  d <- array(1:40, dim=c(2,5,2,2))
  e <- data.frame(a,b)
  f <- list(a,b,c,d,e)

  size(NULL) # 0 0
  size(NA)   # 1 1
  size(a)    # 1 1
  size(b,2)  # 6
  size(c)    # 4 5
  size(d)    # 2 5 2 2
  size(e,3)  # NA
  size(f)

Auto-collapse of Vectors

Description

strvec is a utility function which collapses all elements of a vector into a character scalar.

Usage

  strvec(x = NULL)

Arguments

Value

A character scalar consisting of all the elements of x separated by a single white space.

Author(s)

Sebastien Bihorel (sb.pmlab@gmail.com)

Examples

  strvec(letters[1:10])
  strvec(1:10)

Vector and Matrix Transpose

Description

transpose is a wrapper function around the t function, which tranposes matrices. Contrary to t, transpose processes vectors as if they were row matrices.

Usage

  transpose(object = NULL)

Arguments

Value

Return a matrix which is the exact transpose of the vector or matrix x

Author(s)

Sebastien Bihorel (sb.pmlab@gmail.com)

See Also

t

Examples

  1:6
  t(1:6)
  transpose(1:6)
  mat <- matrix(1:15,nrow=5,ncol=3)
  mat
  transpose(mat)

Vector to Matrix Conversion

Description

This function converts a vector into a row matrix.

Usage

  vec2matrix(object = NULL)

Arguments

Details

If object is already a matrix, object is not modified. If object is not a matrix or a vector, the algorithm is stopped.

Value

Return a row matrix.

Author(s)

Sebastien Bihorel (sb.pmlab@gmail.com)

Matrix of zeros or ones.

Description

Creates a matrix of zeros or ones.

Usage

  zeros(nx = 1, ny = nx)
  ones(nx = 1, ny = nx)

Arguments

Details

zeros and ones create full matrices of zeros and ones. If the user only provides an input for nx, the produced matrices are nx x nx square matrices.

Value

Return of nx x ny matrix of zeros of ones.

Author(s)

Sebastien Bihorel (sb.pmlab@gmail.com)

Examples

  zeros()
  zeros(3)
  ones(4,5)
  # Will fail
  try(ones('3','3'))