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AGG_CMATCMAT

typedef AGG_CMATCMAT

symbol type
typedef
declaration 
typedef aggregate _AGG_CMATCMAT {
  COMPLEX_MATRIX Q;  /* bzw. L, L */
  COMPLEX_MATRIX R;  /* bzw. U, D */
} AGG_CMATCMAT;
description

AGG_CMATCMATMAT

typedef AGG_CMATCMATMAT

symbol type
typedef
declaration 
typedef aggregate _AGG_CMATCMATMAT {
  COMPLEX_MATRIX L;
  COMPLEX_MATRIX U;
  MATRIX P;
} AGG_CMATCMATMAT;
description
Ergebnistyp von lu

AGG_CMATCVEC

typedef AGG_CMATCVEC

symbol type
typedef
declaration 
typedef aggregate _AGG_CMATCVEC {
  COMPLEX_MATRIX A;
  COMPLEX_VECTOR b;
} AGG_CMATCVEC;
description

AGG_CMATVEC

typedef AGG_CMATVEC

symbol type
typedef
declaration 
typedef aggregate _AGG_CMATVEC {
  COMPLEX_MATRIX A;
  VECTOR b;
} AGG_CMATVEC;
description

AGG_CMATVECCMAT

typedef AGG_CMATVECCMAT

symbol type
typedef
declaration 
typedef aggregate _AGG_CMATVECCMAT {
  COMPLEX_MATRIX U;
  VECTOR S;
  COMPLEX_MATRIX V;
} AGG_CMATVECCMAT;
description

AGG_MATMAT

typedef AGG_MATMAT

symbol type
typedef
declaration 
typedef aggregate _AGG_MATMAT {
  MATRIX Q;  /* bzw. L, L */
  MATRIX R;  /* bzw. U, D */
} AGG_MATMAT;
description
Ergebnistyp von qr und lu

AGG_MATMATMAT

typedef AGG_MATMATMAT

symbol type
typedef
declaration 
typedef aggregate _AGG_MATMATMAT {
  MATRIX L;
  MATRIX U;
  MATRIX P;
} AGG_MATMATMAT;
description
Ergebnistyp von lu

AGG_MATVEC

typedef AGG_MATVEC

symbol type
typedef
declaration 
typedef aggregate _AGG_MATVEC {
  MATRIX A;
  VECTOR b;
} AGG_MATVEC;
description
Ergebnistyp von eig

AGG_MATVECMAT

typedef AGG_MATVECMAT

symbol type
typedef
declaration 
typedef aggregate _AGG_MATVECMAT {
  MATRIX U;
  VECTOR S;
  MATRIX V;
} AGG_MATVECMAT;
description
Ergebnistyp von svd

Chol

MATRIX prefix operator Chol(const MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
MATRIX prefix operator Chol(const MATRIX & A ) precedence 28;
description
Computes the Cholesky factorization of a real symmetric
positive definite matrix A.
example 
   print Chol A;
remarks
The LAPACK routine dpotrf is used.
location
"lapfront.h", line 662
related topics
See section ldlt.

COMPLEX_MATRIX prefix operator Chol(const COMPLEX_MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
COMPLEX_MATRIX prefix operator Chol(const COMPLEX_MATRIX & A ) precedence 28;
description
Computes the Cholesky factorization of a complex hermitian
positive definite matrix A.
example 
   print Chol cA;
remarks
The LAPACK routine zpotrf is used.
location
"lapfront.h", line 673
related topics
See section ldlt.

Compan

MATRIX prefix operator Compan(VECTOR v) precedence 28;

symbol type
prefix operator (prototype)
declaration 
MATRIX prefix operator Compan(VECTOR v) precedence 28;
description
return the companion matrix of the polynom represented by v
remarks
v[1] may not be zero!
location
"lapfront.h", line 798
related topics
See section Roots.

COMPLEX_MATRIX prefix operator Compan(COMPLEX_VECTOR v);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_MATRIX prefix operator Compan(COMPLEX_VECTOR v);
description
return the companion matrix of the polynom represented by v.
remarks
v[1] may not be zero!
location
"lapfront.h", line 806
related topics
See section Roots.

Cond

REAL prefix operator Cond(const MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator Cond(const MATRIX & A ) precedence 28;
description
returns the condition number in 2-norm, that is the ratio of the
largest singular value of A to the smallest.
example 
   print Cond Hilbert 5;
location
"lapfront.h", line 370
related topics
See section CondEst. @xref{ Norm}.

REAL prefix operator Cond(const COMPLEX_MATRIX & A );

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator Cond(const COMPLEX_MATRIX & A );
description
returns the condition number in 2-norm, that is the ratio of the
largest singular value of A to the smallest.
location
"lapfront.h", line 410
related topics
See section CondEst. @xref{ Norm}.

CondEst

REAL prefix operator CondEst(const MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator CondEst(const MATRIX & A ) precedence 28;
description
returns an estimate for the condition number in 1-norm.
example 
   print CondEst Hilbert 5;
remarks
The LAPACK routine dgecon or dsycon is used.
location
"lapfront.h", line 379
related topics
See section Cond. @xref{ CondEstS}. @xref{ CondEstH}.

REAL prefix operator CondEst(const COMPLEX_MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator CondEst(const COMPLEX_MATRIX & A ) precedence 28;
description
returns an estimate for the condition number in 1-norm.
remarks
The LAPACK routine zgecon or zsycon or zhecon is used.
location
"lapfront.h", line 417
related topics
See section Cond. @xref{ CondEstS}. @xref{ CondEstH}.

CondEstG

REAL prefix operator CondEstG(const MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator CondEstG(const MATRIX & A ) precedence 28;
description
returns an estimate for the condition number in 1-norm.
example 
   print CondEstG Random 4;
remarks
The LAPACK routine dgecon is used.
location
"lapfront.h", line 389
related topics
See section Cond. @xref{ CondEstS}. @xref{ CondEstH}.

REAL prefix operator CondEstG(const COMPLEX_MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator CondEstG(const COMPLEX_MATRIX & A ) precedence 28;
description
returns an estimate for the condition number in 1-norm.
remarks
The LAPACK routine zgecon is used.
location
"lapfront.h", line 425
related topics
See section Cond. @xref{ CondEstS}. @xref{ CondEstH}.

CondEstH

REAL prefix operator CondEstH(const COMPLEX_MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator CondEstH(const COMPLEX_MATRIX & A ) precedence 28;
description
returns an estimate for the condition number in 1-norm for complex
hermitian matrices.
remarks
The LAPACK routine zhecon is used.
location
"lapfront.h", line 442
related topics
See section Cond. @xref{ CondEst}. @xref{ CondEstS}.

CondEstS

REAL prefix operator CondEstS(const MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator CondEstS(const MATRIX & A ) precedence 28;
description
returns an estimate for the condition number in 1-norm for real
symmetric matrices.
example 
   print CondEstS Hilbert 5;
remarks
The LAPACK routine dsycon is used.
location
"lapfront.h", line 399
related topics
See section Cond. @xref{ CondEst}. @xref{ CondEstH}.

REAL prefix operator CondEstS(const COMPLEX_MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator CondEstS(const COMPLEX_MATRIX & A ) precedence 28;
description
returns an estimate for the condition number in 1-norm for complex
symmetric matrices.
remarks
The LAPACK routine zsycon is used.
location
"lapfront.h", line 433
related topics
See section Cond. @xref{ CondEst}. @xref{ CondEstH}.

Det

REAL prefix operator Det(const MATRIX &A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator Det(const MATRIX &A) precedence 28;
description
Computes the Det
example 
    print Det Random 3;
remarks
The LAPACK routine dgetrf is used.
location
"lapfront.h", line 786

Inv

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

symbol type
prefix operator (prototype)
declaration 
MATRIX prefix operator Inv(const MATRIX &A) precedence 28;
description
computes the explicit representation of the inverse of A.
example 
   print Inv Hilbert 3;
location
"lapfront.h", line 545
related topics
See section InvG. @xref{ InvS}.

COMPLEX_MATRIX prefix operator Inv(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_MATRIX prefix operator Inv(const COMPLEX_MATRIX &A);
description
computes the explicit representation of the inverse of A.
location
"lapfront.h", line 553
related topics
See section InvG. @xref{ InvS}.

InvG

MATRIX prefix operator InvG(const MATRIX &A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
MATRIX prefix operator InvG(const MATRIX &A) precedence 28;
description
computes the explicit representation of the inverse of A, using the lu factorization.
example 
   print Inv Hilbert 3;
remarks
The LAPACK routines dgetrf and dgetri are used.
location
"lapfront.h", line 559
related topics
See section Inv. @xref{ InvS}. @xref{ InvH}.

COMPLEX_MATRIX prefix operator InvG(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_MATRIX prefix operator InvG(const COMPLEX_MATRIX &A);
description
computes the explicit representation of the inverse of A, using the lu factorization.
remarks
The LAPACK routines zgetrf and zgetri are used.
location
"lapfront.h", line 569
related topics
See section Inv. @xref{ InvS}. @xref{ InvH}.

InvH

COMPLEX_MATRIX prefix operator InvH(const COMPLEX_MATRIX &A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
COMPLEX_MATRIX prefix operator InvH(const COMPLEX_MATRIX &A) precedence 28;
description
computes the explicit representation of the inverse of the hermitian matrix A,
using the ldlt factorization.
remarks
The LAPACK routines zhetrf and zhetri are used.
location
"lapfront.h", line 588
related topics
See section InvS. @xref{ InvG}. @xref{ Inv}.

InvS

MATRIX prefix operator InvS(const MATRIX &A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
MATRIX prefix operator InvS(const MATRIX &A) precedence 28;
description
computes the explicit representation of the inverse of the symmetric matrix A,
using the ldlt factorization.
example 
   print InvS Hilbert 3;
remarks
The LAPACK routines dsytrf and dsytri are used.
location
"lapfront.h", line 577
related topics
See section InvH. @xref{ InvG}. @xref{ Inv}.

COMPLEX_MATRIX prefix operator InvS(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_MATRIX prefix operator InvS(const COMPLEX_MATRIX &A);
description
computes the explicit representation of the inverse of the complex symmetric matrix A,
using the ldlt factorization.
remarks
The LAPACK routines zsytrf and zsytri are used.
location
"lapfront.h", line 597
related topics
See section InvH. @xref{ InvG}. @xref{ Inv}.

IsHermitian

int prefix operator IsHermitian(const COMPLEX_MATRIX & A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
int prefix operator IsHermitian(const COMPLEX_MATRIX & A) precedence 28;
description
return 1, if A is hermitian, 0 otherwise.
location
"lapfront.h", line 54
related topics
See section IsSymmetric.

IsSymmetric

int prefix operator IsSymmetric(const MATRIX & A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
int prefix operator IsSymmetric(const MATRIX & A) precedence 28;
description
return 1, if A is symmetric, 0 otherwise.
location
"lapfront.h", line 42
related topics
See section IsHermitian.

int prefix operator IsSymmetric(const COMPLEX_MATRIX & A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
int prefix operator IsSymmetric(const COMPLEX_MATRIX & A) precedence 28;
description
return 1, if A is complex symmetric, 0 otherwise.
location
"lapfront.h", line 48
related topics
See section IsHermitian.

Norm

REAL prefix operator Norm(const MATRIX & A, int type ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator Norm(const MATRIX & A, int type ) precedence 28;
description
The parameter type may have the following values:
Norm_1, Norm_2, Norm_Infinity, which results in
calculating the column sum, the largest singular value
and the row sum (Norm), respectively.
example 
   print Norm( Hilbert 3, Norm_1 );
remarks
For calculating the singular values, the LAPACK linear routine dgesvd is used.
location
"lapfront.h", line 322

REAL prefix operator Norm(const MATRIX & A );

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator Norm(const MATRIX & A );
description
computes the norm of the specified matrix. The default is the 2 norm.
example 
   print Norm Hilbert 3;
remarks
For calculating the singular values, the LAPACK linear routine dgesvd is used.
location
"lapfront.h", line 333

REAL prefix operator Norm(const COMPLEX_MATRIX & A, int type );

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator Norm(const COMPLEX_MATRIX & A, int type );
description
The parameter type may have the following values:
Norm_1, Norm_2, Norm_Infinity, which results in
calculating the column sum, the largest singular value
and the row sum (Norm), respectively.
example 
   print Norm( Hilbert 3, Norm_1 );
remarks
For calculating the singular values, the LAPACK linear routine dgesvd is used.
location
"lapfront.h", line 341

REAL prefix operator Norm(const COMPLEX_MATRIX & A );

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator Norm(const COMPLEX_MATRIX & A );
description
computes the norm of the specified matrix. The default is the 2 norm.
example 
   print Norm Hilbert 3;
remarks
For calculating the singular values, the LAPACK linear routine dgesvd is used.
location
"lapfront.h", line 352

NormEst

REAL prefix operator NormEst(const MATRIX & A ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
REAL prefix operator NormEst(const MATRIX & A ) precedence 28;
description
estimates the 2-norm of the MATRIX A using the power iteration.
example 
   print NormEst A;
location
"lapfront.h", line 360

Roots

COMPLEX_VECTOR prefix operator Roots(const VECTOR &v) precedence 28;

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator Roots(const VECTOR &v) precedence 28;
description
returns the roots of the polynomial represented by v)
remarks
computes the eigenvalues of the companion matrix
location
"lapfront.h", line 814
related topics
See section Compan.

COMPLEX_VECTOR prefix operator Roots(const COMPLEX_VECTOR &v);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator Roots(const COMPLEX_VECTOR &v);
description
returns the roots of the polynomial represented by v)
remarks
computes the eigenvalues of the companion matrix
location
"lapfront.h", line 822
related topics
See section Compan.

Solve

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

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator Solve( const MATRIX &A, const VECTOR &b ) precedence 28;
description
Solves the linear equation A * x = b, where x and b are VECTORs and A is a MATRIX.
example 
    A = Hilbert 3;
    VECTOR b="1;2;3";
    print Solve(A,b);
location
"lapfront.h", line 84

COMPLEX_VECTOR prefix operator Solve( const COMPLEX_MATRIX & A, const COMPLEX_VECTOR & b );

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator Solve( const COMPLEX_MATRIX & A, const COMPLEX_VECTOR & b );
description
Solves the linear equation A * x = b, where x and b are COMPLEX_VECTORs and
A is a COMPLEX_MATRIX.
example 
    print Solve(cA,cb);
location
"lapfront.h", line 119

SolveG

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

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator SolveG( const MATRIX &A, const VECTOR &b ) precedence 28;
description
Solves the linear equation A * x = b, where x and b are VECTORs and A is a MATRIX.
example 
    A = Random 3;
    VECTOR b="1;2;3";
    print SolveG(A,b);
remarks
The LAPACK linear system solver dgesvx is used.
location
"lapfront.h", line 64

COMPLEX_VECTOR prefix operator SolveG( const COMPLEX_MATRIX & A, const COMPLEX_VECTOR & b );

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator SolveG( const COMPLEX_MATRIX & A, const COMPLEX_VECTOR & b );
description
Solves the linear equation A * x = b, where x and b are COMPLEX_VECTORs and
A is a COMPLEX_MATRIX.
example 
    print SolveG(cA,cb);
remarks
The LAPACK linear system solver zgesvx is used (no equilibration is done).
location
"lapfront.h", line 92

SolveH

COMPLEX_VECTOR prefix operator SolveH( const COMPLEX_MATRIX & A, const COMPLEX_VECTOR & b ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator SolveH( const COMPLEX_MATRIX & A, const COMPLEX_VECTOR & b ) precedence 28;
description
Solves the linear equation A * x = b, where x and b are COMPLEX_VECTORs and
A is a hermitian COMPLEX_MATRIX.
example 
    print SolveH(cA,cb);
remarks
The LAPACK linear system solver zhesvx is used.
location
"lapfront.h", line 101

SolveS

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

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator SolveS( const MATRIX &A, const VECTOR &b ) precedence 28;
description
Solves the linear equation A * x = b, where x and b are VECTORs and A is a symmetric MATRIX.
example 
    A = Hilbert 3;
    VECTOR b="1;2;3";
    print SolveS(A,b);
remarks
The LAPACK linear system solver dsysvx is used.
location
"lapfront.h", line 74

COMPLEX_VECTOR prefix operator SolveS( const COMPLEX_MATRIX & A, const COMPLEX_VECTOR & b );

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator SolveS( const COMPLEX_MATRIX & A, const COMPLEX_VECTOR & b );
description
Solves the linear equation A * x = b, where x and b are COMPLEX_VECTORs and
A is a symmetric (not hermitian!) COMPLEX_MATRIX.
example 
    print SolveS(cA,cb);
remarks
The LAPACK linear system solver zsysvx is used.
location
"lapfront.h", line 110

cg

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

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator cg(const MATRIX & A, const VECTOR &b) precedence 28;
description
Conjugate gradient method (GvL, Algorithm 10.3-1)
MATRIX A supposed to s.p.d.
example 
    x = cg(A,b);
remarks
x may not be identically with b
location
"lapfront.h", line 725

eig

COMPLEX_VECTOR prefix operator eig(const MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator eig(const MATRIX &m ) precedence 28;
description
calculates all eigenvalues of the argument.
example 
   print eig Hilbert 4;
remarks
The LAPACK routine dgeevx is used.
Permutations to make the matrix more nearly upper triangular are performed.
Diagonally scaling is done, ie. replace A by D*A*D**(-1), where D is a
diagonal matrix chosen to make the rows and columns of A more equal in
norm.
location
"lapfront.h", line 141
related topics
See section eig2. @xref{ eigS}.

AGG_CMATCVEC prefix operator eig(const MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCVEC prefix operator eig(const MATRIX &m ) precedence 28;
description
calculates all eigenvectors and eigenvalues of the argument.
example 
   (M,v) = eig Random 4;
remarks
The LAPACK routine dgeevx is used (no balancing is done).
Permutations to make the matrix more nearly upper triangular are performed.
Diagonally scaling is done, ie. replace A by D*A*D**(-1), where D is a
diagonal matrix chosen to make the rows and columns of A more equal in
norm.
location
"lapfront.h", line 178
related topics
See section eig2. @xref{ eigS}.

COMPLEX_VECTOR prefix operator eig(const COMPLEX_MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator eig(const COMPLEX_MATRIX &m ) precedence 28;
description
calculates all eigenvalues of the complex argument.
remarks
The LAPACK routine zgeevx is used.
Permutations to make the matrix more nearly upper triangular are performed.
Diagonally scaling is done, ie. replace A by D*A*D**(-1), where D is a
diagonal matrix chosen to make the rows and columns of A more equal in
norm.
location
"lapfront.h", line 213
related topics
See section eig2. @xref{ eigS}.

AGG_CMATCVEC prefix operator eig(const COMPLEX_MATRIX & cm ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCVEC prefix operator eig(const COMPLEX_MATRIX & cm ) precedence 28;
description
calculates all eigenvectors and eigenvalues of the complex argument.
example 
   (M,v) = eig CM;

   The LAPACK routine zgeevx is used.
   Permutations to make the matrix more nearly upper triangular are performed.
   Diagonally scaling is done, ie. replace A by D*A*D**(-1), where D is a 
   diagonal matrix chosen to make the rows and columns of A more equal in
   norm.
location
"lapfront.h", line 247
related topics
See section eig2. @xref{ eigS}.

eig2

COMPLEX_VECTOR prefix operator eig2(const MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator eig2(const MATRIX &m ) precedence 28;
description
calculates all eigenvalues of the argument.
example 
   print eig2 Hilbert 4;
remarks
The LAPACK routine dgeev is used (no balancing is done).
location
"lapfront.h", line 130
related topics
See section eig. @xref{ eigS}.

AGG_CMATCVEC prefix operator eig2(const MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCVEC prefix operator eig2(const MATRIX &m ) precedence 28;
description
calculates all eigenvectors and eigenvalues of the argument.
example 
   (M,v) = eig2 Random 4;
remarks
The LAPACK routine dgeev is used (no balancing is done).
location
"lapfront.h", line 167
related topics
See section eig. @xref{ eigS}.

COMPLEX_VECTOR prefix operator eig2(const COMPLEX_MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator eig2(const COMPLEX_MATRIX &m ) precedence 28;
description
calculates all eigenvalues of the complex argument.
remarks
The LAPACK routine zgeev is used (no balancing is done).
location
"lapfront.h", line 204
related topics
See section eig. @xref{ eigS}.

AGG_CMATCVEC prefix operator eig2(const COMPLEX_MATRIX & cm ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCVEC prefix operator eig2(const COMPLEX_MATRIX & cm ) precedence 28;
description
calculates all eigenvectors and eigenvalues of the complex argument.
example 
   (M,v) = eig2 CM;
remarks
The LAPACK routine zgeev is used (no balancing is done).
location
"lapfront.h", line 235
related topics
See section eig. @xref{ eigS}.

eigH

VECTOR prefix operator eigH(const COMPLEX_MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator eigH(const COMPLEX_MATRIX &m ) precedence 28;
description
calculates all eigenvalues of the complex hermitian argument.
remarks
The LAPACK routine zheevx is used.
location
"lapfront.h", line 226
related topics
See section eig. @xref{ eig2}. @xref{ eigS}.

AGG_CMATVEC prefix operator eigH(const COMPLEX_MATRIX & cm ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
AGG_CMATVEC prefix operator eigH(const COMPLEX_MATRIX & cm ) precedence 28;
description
calculates all eigenvectors and eigenvalues of the complex hermitian argument.
example 
   (M,v) = eigH CM;

   The LAPACK routine zheevx is used.
location
"lapfront.h", line 262
related topics
See section eig. @xref{ eig2}. @xref{ eigS}.

eigS

VECTOR prefix operator eigS(const MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator eigS(const MATRIX &m ) precedence 28;
description
calculates all (real) eigenvalues of the symmetric argument.
example 
   print eigS Hilbert 4;
remarks
The LAPACK routine dsyevx is used.
location
"lapfront.h", line 156
related topics
See section eig. @xref{ eig2}.

AGG_MATVEC prefix operator eigS(const MATRIX &m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
AGG_MATVEC prefix operator eigS(const MATRIX &m ) precedence 28;
description
calculates all (real) eigenvalues an eigenvectors of the symmetric argument.
example 
   (M,v) = eigS RandS 3;
remarks
The LAPACK routine dsyevx is used.
location
"lapfront.h", line 193
related topics
See section eig. @xref{ eig2}.

ldlt

AGG_MATMAT prefix operator ldlt(const MATRIX &A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
AGG_MATMAT prefix operator ldlt(const MATRIX &A) precedence 28;
description
Computes the factorization of a real symmetric matrix A using
the Bunch-Kaufman diagonal pivoting method:
A = L*D*L'
example 
   (L,D) = ldlt A;
remarks
The LAPACK routine dsytrf is used.
location
"lapfront.h", line 610
related topics
See section Chol.

AGG_MATMATMAT prefix operator ldlt(const MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_MATMATMAT prefix operator ldlt(const MATRIX &A);
description
Computes the factorization of a real symmetric matrix A using
the Bunch-Kaufman diagonal pivoting method:
P*A*P' = L*D*L'
example 
   (L,D,P) = ldlt A;
remarks
The LAPACK routine dsytrf is used.
location
"lapfront.h", line 622
related topics
See section Chol.

AGG_CMATCMAT prefix operator ldlt(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCMAT prefix operator ldlt(const COMPLEX_MATRIX &A);
description
Computes the factorization of a complex hermitian matrix A using
the Bunch-Kaufman diagonal pivoting method:
A = L*D*L'
example 
   (L,D) = ldlt A;
remarks
The LAPACK routine zhetrf is used.
location
"lapfront.h", line 634
related topics
See section Chol.

AGG_CMATCMATMAT prefix operator ldlt(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCMATMAT prefix operator ldlt(const COMPLEX_MATRIX &A);
description
Computes the factorization of a complex hermitian matrix A using
the Bunch-Kaufman diagonal pivoting method:
P*A*P' = L*D*L'
example 
   (L,D,P) = ldlt A;
remarks
The LAPACK routine zhetrf is used.
location
"lapfront.h", line 646
related topics
See section Chol.

lls

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

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator lls(const MATRIX &A, const VECTOR &b) precedence 28;
description
Linear Least Squares.
lls(A,b) returns the vector x that solves A*x = b
in a least squares sense.
remarks
The LAPACK routine DGELS is used (using QR or LQ factorization).
The MATRIX A must have full rank (rank(A)=min(Rows,Cols)).
location
"lapfront.h", line 738
related topics
See section lls2.

COMPLEX_VECTOR prefix operator lls(const COMPLEX_MATRIX &A, const COMPLEX_VECTOR &b);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator lls(const COMPLEX_MATRIX &A, const COMPLEX_VECTOR &b);
description
Linear Least Squares.
lls(A,b) returns the vector x that solves A*x = b
in a least squares sense.
remarks
The LAPACK routine ZGELS is used (using QR or LQ factorization).
The MATRIX A must have full rank (rank(A)=min(Rows,Cols)).
location
"lapfront.h", line 749
related topics
See section lls2.

lls2

VECTOR prefix operator lls2(const MATRIX &A, const VECTOR &b) precedence 28;

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator lls2(const MATRIX &A, const VECTOR &b) precedence 28;
description
Linear Least Squares.
lls2(A,b) returns the vector x that solves A*x = b
in a least squares sense.
remarks
The LAPACK routine DGELSS is used (using singular value decomposition).
The MATRIX A may be rankdeficient.
location
"lapfront.h", line 760
related topics
See section lls.

COMPLEX_VECTOR prefix operator lls2(const COMPLEX_MATRIX &A, const COMPLEX_VECTOR &b);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_VECTOR prefix operator lls2(const COMPLEX_MATRIX &A, const COMPLEX_VECTOR &b);
description
Linear Least Squares.
lls2(A,b) returns the vector x that solves A*x = b
in a least squares sense.
remarks
The LAPACK routine ZGELSS is used (using singular value decomposition).
The MATRIX A may be rankdeficient.
location
"lapfront.h", line 771
related topics
See section lls.

lu

MATRIX prefix operator lu(const MATRIX &A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
MATRIX prefix operator lu(const MATRIX &A) precedence 28;
description
Computes the LU factorization A = L * U. L is a lower triangular matrix and U an upper
triangular matrix.
example 
    A = Random 3;
    print lu A;
remarks
This routine returns the output of dgetrf (no equilibration is done).
location
"lapfront.h", line 481

AGG_MATMAT prefix operator lu(const MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_MATMAT prefix operator lu(const MATRIX &A);
description
Computes the LU factorization A = L * U. L is a lower triangular matrix and U is an upper
triangular matrix.
example 
    A = Random 3;
    (l,u) = lu A;
remarks
The LAPACK routine dgetrf is used (no equilibration is done).
location
"lapfront.h", line 491

AGG_MATMATMAT prefix operator lu(const MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_MATMATMAT prefix operator lu(const MATRIX &A);
description
Computes the LU factorization P*A = L * U. L is a lower triangular matrix, U is an upper
triangular matrix and P a permutation matrix.
example 
    A = Random 3;
    (l,u,p) = lu A;
remarks
The LAPACK routine dgetrf is used (no equilibration is done).
location
"lapfront.h", line 501

COMPLEX_MATRIX prefix operator lu(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_MATRIX prefix operator lu(const COMPLEX_MATRIX &A);
description
Computes the LU factorization A = L * U. L is a lower triangular matrix and U an upper
triangular matrix.
example 
    A = Random 3;
    print lu A;
remarks
This routine returns the output of zgetrf (no equilibration is done).
location
"lapfront.h", line 511

AGG_CMATCMAT prefix operator lu(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCMAT prefix operator lu(const COMPLEX_MATRIX &A);
description
Computes the LU factorization A = L * U. L is a lower triangular matrix and U is an upper
triangular matrix.
example 
    A = Random 3;
    (l,u) = lu A;
remarks
The LAPACK routine zgetrf is used (no equilibration is done).
location
"lapfront.h", line 521

AGG_CMATCMATMAT prefix operator lu(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCMATMAT prefix operator lu(const COMPLEX_MATRIX &A);
description
Computes the LU factorization P*A = L * U. L is a lower triangular matrix, U is an upper
triangular matrix and P a permutation matrix.
example 
    A = Random 3;
    (l,u,p) = lu A;
remarks
The LAPACK routine zgetrf is used (no equilibration is done).
location
"lapfront.h", line 531

qr

MATRIX prefix operator qr(const MATRIX &A) precedence 28;

symbol type
prefix operator (prototype)
declaration 
MATRIX prefix operator qr(const MATRIX &A) precedence 28;
description
Computes the QR factorization A = Q * R. Q is unitary and R is an upper
triangular matrix.
example 
    A = Random 3;
    print Triu qr A;
remarks
This routine returns the output of dgetrf (Triu qr A is R).
location
"lapfront.h", line 688

AGG_MATMAT prefix operator qr(const MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_MATMAT prefix operator qr(const MATRIX &A);
description
Computes the QR factorization A = Q * R. Q is unitary and R is an upper
triangular matrix.
example 
    (Q,R) = Random 3;
remarks
The LAPACK routine dgeqrf is used (no pivoting is done).
location
"lapfront.h", line 698

COMPLEX_MATRIX prefix operator qr(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
COMPLEX_MATRIX prefix operator qr(const COMPLEX_MATRIX &A);
description
Computes the QR factorization A = Q * R. Q is unitary and R is an upper
triangular matrix.
remarks
This routine returns the output of zgetrf (Triu qr A is R).
location
"lapfront.h", line 707

AGG_CMATCMAT prefix operator qr(const COMPLEX_MATRIX &A);

symbol type
prefix operator (prototype)
declaration 
AGG_CMATCMAT prefix operator qr(const COMPLEX_MATRIX &A);
description
Computes the QR factorization A = Q * R. Q is unitary and R is an upper
triangular matrix.
remarks
The LAPACK routine zgeqrf is used (no pivoting is done).
location
"lapfront.h", line 714

svd

VECTOR prefix operator svd(const MATRIX& m ) precedence 28;

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator svd(const MATRIX& m ) precedence 28;
description
calculates all singuar values of the argument (A = U * Diag s * Transpose V).
example 
   print svd Hilbert 4;
remarks
The LAPACK routine dgesvd is used.
location
"lapfront.h", line 277

AGG_MATVECMAT prefix operator svd(const MATRIX& m );

symbol type
prefix operator (prototype)
declaration 
AGG_MATVECMAT prefix operator svd(const MATRIX& m );
description
calculates all singular vectors and values of the argument (A = U * Diag s * Transpose V).
example 
   (U,s,V) = svd Hilbert 4;
remarks
The LAPACK routine dgesvd is used.
location
"lapfront.h", line 286

VECTOR prefix operator svd(const COMPLEX_MATRIX& m );

symbol type
prefix operator (prototype)
declaration 
VECTOR prefix operator svd(const COMPLEX_MATRIX& m );
description
calculates all singuar values of the complex argument (cA = U * Diag s * Transpose V).
example 
   print svd cA;
remarks
The LAPACK routine zgesvd is used.
location
"lapfront.h", line 295

AGG_CMATVECCMAT prefix operator svd(const COMPLEX_MATRIX& m );

symbol type
prefix operator (prototype)
declaration 
AGG_CMATVECCMAT prefix operator svd(const COMPLEX_MATRIX& m );
description
calculates all singular vectors and values of the complex argument (cA = U * Diag s * Transpose V).
example 
   (U,s,V) = svd cA;
remarks
The LAPACK routine zgesvd is used.
location
"lapfront.h", line 304

lapfront Data Type Index

a

  • AGG_CMATCMAT, typedef
  • AGG_CMATCMATMAT, typedef
  • AGG_CMATCVEC, typedef
  • AGG_CMATVEC, typedef
  • AGG_CMATVECCMAT, typedef
  • AGG_MATMAT, typedef
  • AGG_MATMATMAT, typedef
  • AGG_MATVEC, typedef
  • AGG_MATVECMAT, typedef

    • lapfront Function Index

    c

  • cg, prefix operator
  • Chol, prefix operator
  • Compan, prefix operator
  • Cond, prefix operator
  • CondEst, prefix operator
  • CondEstG, prefix operator
  • CondEstH, prefix operator
  • CondEstS, prefix operator

    • d

  • Det, prefix operator

    • e

  • eig, prefix operator
  • eig2, prefix operator
  • eigH, prefix operator
  • eigS, prefix operator

    • i

  • Inv, prefix operator
  • InvG, prefix operator
  • InvH, prefix operator
  • InvS, prefix operator
  • IsHermitian, prefix operator
  • IsSymmetric, prefix operator

    • l

  • ldlt, prefix operator
  • lls, prefix operator
  • lls2, prefix operator
  • lu, prefix operator

    • n

  • Norm, prefix operator
  • NormEst, prefix operator

    • q

  • qr, prefix operator

    • r

  • Roots, prefix operator

    • s

  • Solve, prefix operator
  • SolveG, prefix operator
  • SolveH, prefix operator
  • SolveS, prefix operator
  • svd, prefix operator