COX Library lapfrt2.cox

file lapfrt2

LAPACK FrontEnd
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Section 2: interval-algorithms

AGG_IMATIVEC

typedef AGG_IMATIVEC

symbol type
typedef
declaration 
typedef aggregate _AGG_IMATIVEC {
  INTERVAL_MATRIX A;
  INTERVAL_VECTOR b;
} AGG_IMATIVEC;
description

IInv

INTERVAL_MATRIX prefix operator IInv (const MATRIX & A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_MATRIX prefix operator IInv (const MATRIX & A) precedence 28;
description
Returns an enclosure of the inverse of A.
example 
    print IInv Pascal 3;
location
"lapfrt2.h", line 41

IPolyVal

INTERVAL prefix operator IPolyVal (const VECTOR &p, const double x0) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL prefix operator IPolyVal (const VECTOR &p, const double x0) precedence 28;
description
Polynomial evaluation.
If p is a vector of length n+1 of polynomial coefficients,
then PolyVal(p,x0) is the value of the polynomial evaluated at x0.
y = p[1]*x0^n + p[2]*x0^(n-1) + ... + p[n]*x0 + p[n+1]
remarks
This function returns an inclusion of the polynomial evaluated at x0.
location
"lapfrt2.h", line 79
related topics
See section IPolyValM. @xref{ PolyVal}.

INTERVAL_VECTOR prefix operator IPolyVal (const VECTOR &p, const VECTOR & x0);

symbol type
prefix operator (prototype)
declaration 
INTERVAL_VECTOR prefix operator IPolyVal (const VECTOR &p, const VECTOR & x0);
description
Polynomial evaluation.
If p is a vector of length n+1 of polynomial coefficients,
then PolyVal(p,x0) is the value of the polynomial evaluated at x0.
y = p[1]*x0^n + p[2]*x0^(n-1) + ... + p[n]*x0 + p[n+1]
remarks
This function returns an inclusion of the polynomial evaluated at x0.
location
"lapfrt2.h", line 90
related topics
See section IPolyValM. @xref{ PolyVal}.

INTERVAL_MATRIX prefix operator IPolyVal (const VECTOR &p, const MATRIX & x0) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_MATRIX prefix operator IPolyVal (const VECTOR &p, const MATRIX & x0) precedence 28;
description
Polynomial evaluation.
If p is a vector of length n+1 of polynomial coefficients,
then PolyVal(p,x0) is the value of the polynomial evaluated at x0.
y = p[1]*x0^n + p[2]*x0^(n-1) + ... + p[n]*x0 + p[n+1]
remarks
This function returns an inclusion of the polynomial evaluated at x0.
location
"lapfrt2.h", line 101
related topics
See section IPolyValM. @xref{ PolyVal}.

IPolyValM

INTERVAL_MATRIX prefix operator IPolyValM (const VECTOR &p, const MATRIX & x0) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_MATRIX prefix operator IPolyValM (const VECTOR &p, const MATRIX & x0) precedence 28;
description
Matrix polynomial evaluation.
If p is a vector of length n+1 of polynomial coefficients,
then PolyValM(p,x0) is the value of the polynomial evaluated at matrix x0.
y = p[1]*x0^n + p[2]*x0^(n-1) + ... + p[n]*x0 + p[n+1]
remarks
This function returns an inclusion of the polynomial evaluated at x0.
location
"lapfrt2.h", line 142
related topics
See section IPolyVal. @xref{ PolyVal}.

ISolve

INTERVAL_VECTOR prefix operator ISolve (const MATRIX & A, const VECTOR & b) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_VECTOR prefix operator ISolve (const MATRIX & A, const VECTOR & b) precedence 28;
description
Returns an enclosure of the solution set x of
the linear system A*x=b.
example 
    iv = ISolve(A,b);
remarks
Requires the explicit inverse of the system matrix A.
location
"lapfrt2.h", line 18

IeigS

INTERVAL_VECTOR prefix operator IeigS(const MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_VECTOR prefix operator IeigS(const MATRIX &m ) precedence 28;
description
computes an inclusion of all (real) eigenvalues of the symmetric argument.
example 
   print IeigS Hilbert 4;
location
"lapfrt2.h", line 55
related topics
@xref{eig,,,lapfront}. @xref{ eig2,,,lapfront}.

AGG_IMATIVEC prefix operator IeigS(const MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
AGG_IMATIVEC prefix operator IeigS(const MATRIX &m ) precedence 28;
description
computes an inclusion of all (real) eigenvalues and (real) eigenvectors
of the symmetric argument.
example 
   (V,w) = IeigS Hilbert 4;
location
"lapfrt2.h", line 64
related topics
@xref{eig,,,lapfront}. @xref{ eig2,,,lapfront}.

Inv

INTERVAL_MATRIX prefix operator Inv (const INTERVAL_MATRIX & A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_MATRIX prefix operator Inv (const INTERVAL_MATRIX & A) precedence 28;
description
Returns an enclosure of the inverse of A.
location
"lapfrt2.h", line 47

PolyVal

INTERVAL prefix operator PolyVal (const INTERVAL_VECTOR &p, const INTERVAL& x0) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL prefix operator PolyVal (const INTERVAL_VECTOR &p, const INTERVAL& x0) precedence 28;
description
Polynomial evaluation.
If p is a vector of length n+1 of polynomial coefficients,
then PolyVal(p,x0) is the value of the polynomial evaluated at x0.
y = p[1]*x0^n + p[2]*x0^(n-1) + ... + p[n]*x0 + p[n+1]
location
"lapfrt2.h", line 113
related topics
See section PolyValM.

INTERVAL_VECTOR prefix operator PolyVal (const INTERVAL_VECTOR &p, const INTERVAL_VECTOR & x0) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_VECTOR prefix operator PolyVal (const INTERVAL_VECTOR &p, 
                                         const INTERVAL_VECTOR & x0) precedence 28;
description
Polynomial evaluation.
If p is a vector of length n+1 of polynomial coefficients,
then PolyVal(p,x0) is the value of the polynomial evaluated at x0.
y = p[1]*x0^n + p[2]*x0^(n-1) + ... + p[n]*x0 + p[n+1]
location
"lapfrt2.h", line 122
related topics
See section PolyValM.

INTERVAL_MATRIX prefix operator PolyVal (const INTERVAL_VECTOR &p, const INTERVAL_MATRIX & x0) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_MATRIX prefix operator PolyVal (const INTERVAL_VECTOR &p, 
                                         const INTERVAL_MATRIX & x0) precedence 28;
description
Polynomial evaluation.
If p is a vector of length n+1 of polynomial coefficients,
then PolyVal(p,x0) is the value of the polynomial evaluated at x0.
y = p[1]*x0^n + p[2]*x0^(n-1) + ... + p[n]*x0 + p[n+1]
location
"lapfrt2.h", line 132
related topics
See section PolyValM.

PolyValM

INTERVAL_MATRIX prefix operator PolyValM (const INTERVAL_VECTOR &p, const INTERVAL_MATRIX & x0) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_MATRIX prefix operator PolyValM (const INTERVAL_VECTOR &p, const INTERVAL_MATRIX & x0) precedence 28;
description
Matrix polynomial evaluation.
If p is a vector of length n+1 of polynomial coefficients,
then PolyValM(p,x0) is the value of the polynomial evaluated at matrix x0.
y = p[1]*x0^n + p[2]*x0^(n-1) + ... + p[n]*x0 + p[n+1]
location
"lapfrt2.h", line 153
related topics
See section PolyVal.

Solve

INTERVAL_VECTOR prefix operator Solve (const INTERVAL_MATRIX & A, const INTERVAL_VECTOR & b) precedence 28;

symbol type
prefix operator (prototype)
declaration 
INTERVAL_VECTOR prefix operator Solve (const INTERVAL_MATRIX & A, 
                                       const INTERVAL_VECTOR & b) precedence 28;
description
Returns an enclosure of the solution set x of
the linear system A*x=b.
example 
    iv = Solve(A,b);
remarks
Requires the explicit inverse of the midpoint of the system matrix A.
location
"lapfrt2.h", line 27

lapfrt2 Data Type Index

a

  • AGG_IMATIVEC, typedef

    • lapfrt2 Function Index

    i

  • IeigS, prefix operator
  • IInv, prefix operator
  • Inv, prefix operator
  • IPolyVal, prefix operator
  • IPolyValM, prefix operator
  • ISolve, prefix operator

    • p

  • PolyVal, prefix operator
  • PolyValM, prefix operator

    • s

  • Solve, prefix operator