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VectorCalculus

  

Hessian

  

computes the Hessian Matrix of a function from R^n to R

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Hessian(f, v, det, opts)

Hessian(f, v=p, det, opts)

Parameters

f

-

algebraic expression

v

-

(optional) list(name); specify the variables of differentiation

p

-

(optional) list(algebraic); point at which the Hessian is evaluated

det

-

(optional); equation of the form determinant = true or false; specify whether to return the determinant (default: determinant = false)

opts

-

(optional) equation(s) of the form option=value; options passed on to the constructed Matrix

Description

• 

The Hessian(f, v) command computes the Hessian Matrix of the function f with respect to the variables in v. This is the Matrix with an (i,j)th entry of diff(f, v[i], v[j]).

• 

If v is not provided, the differentiation variables are determined from the ambient coordinate system (see SetCoordinates), if possible.

• 

If p is supplied, the computed Hessian matrix will be evaluated at the corresponding point.  The dimension of the point must equal the number of differentiation variables.

• 

The det option specifies whether the determinant of the Hessian matrix is also returned.  If given as determinant = true, or just determinant, then an expression sequence containing the Hessian matrix and its determinant is returned.

• 

If any options are given in opts, they will be passed on to the construction of the returned Matrix. For details on available options, see Matrix.

Examples

withVectorCalculus:

Hessiancosxy,x,y

y2cosxysinxyyxcosxysinxyyxcosxyx2cosxy

(1)

HHessian1x2+y2+z2,x,y,z

H:=8x2x2+y2+z232x2+y2+z228xyx2+y2+z238xzx2+y2+z238xyx2+y2+z238y2x2+y2+z232x2+y2+z228yzx2+y2+z238xzx2+y2+z238yzx2+y2+z238z2x2+y2+z232x2+y2+z22

(2)

SetCoordinatespolarr,t:

Hessianrcost,shape=symmetric,determinant

0sintsintrcost,sint2

(3)

Hessianrcost,r,t=1,π3

012312312

(4)

Compatibility

• 

The determinant option was introduced in Maple 16.

• 

For more information on Maple 16 changes, see Updates in Maple 16.

See Also

VectorCalculus

VectorCalculus[diff]

VectorCalculus[Jacobian]

VectorCalculus[SetCoordinates]

VectorCalculus[Wronskian]

 


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