newmatap.h
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00001 
00002 
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00006 
00007 // Copyright (C) 1991,2,3,4,8: R B Davies
00008 
00009 #ifndef NEWMATAP_LIB
00010 #define NEWMATAP_LIB 0
00011 
00012 #include "newmat.h"
00013 
00014 #ifdef use_namespace
00015 namespace NEWMAT {
00016 #endif
00017 
00018 
00019 // ************************** applications *****************************/
00020 
00021 
00022 void QRZT(Matrix&, LowerTriangularMatrix&);
00023 
00024 void QRZT(const Matrix&, Matrix&, Matrix&);
00025 
00026 void QRZ(Matrix&, UpperTriangularMatrix&);
00027 
00028 void QRZ(const Matrix&, Matrix&, Matrix&);
00029 
00030 inline void HHDecompose(Matrix& X, LowerTriangularMatrix& L)
00031 { QRZT(X,L); }
00032 
00033 inline void HHDecompose(const Matrix& X, Matrix& Y, Matrix& M)
00034 { QRZT(X, Y, M); }
00035 
00036 void updateQRZT(Matrix& X, LowerTriangularMatrix& L);
00037 
00038 void updateQRZ(Matrix& X, UpperTriangularMatrix& U);
00039 
00040 inline void UpdateQRZT(Matrix& X, LowerTriangularMatrix& L)
00041    { updateQRZT(X, L); }
00042 
00043 inline void UpdateQRZ(Matrix& X, UpperTriangularMatrix& U)
00044    { updateQRZ(X, U); }
00045 
00046 // Matrix A's first n columns are orthonormal
00047 // so A.Columns(1,n).t() * A.Columns(1,n) is the identity matrix.
00048 // Fill out the remaining columns of A to make them orthonormal
00049 // so A.t() * A is the identity matrix 
00050 void extend_orthonormal(Matrix& A, int n);
00051 
00052 
00053 ReturnMatrix Cholesky(const SymmetricMatrix&);
00054 
00055 ReturnMatrix Cholesky(const SymmetricBandMatrix&);
00056 
00057 
00058 // produces the Cholesky decomposition of A + x.t() * x where A = chol.t() * chol
00059 // and x is a RowVector
00060 void update_Cholesky(UpperTriangularMatrix& chol, RowVector x);
00061 inline void UpdateCholesky(UpperTriangularMatrix& chol, const RowVector& x)
00062    { update_Cholesky(chol, x); }
00063 
00064 // produces the Cholesky decomposition of A - x.t() * x where A = chol.t() * chol
00065 // and x is a RowVector
00066 void downdate_Cholesky(UpperTriangularMatrix &chol, RowVector x);
00067 inline void DowndateCholesky(UpperTriangularMatrix &chol, const RowVector& x)
00068    { downdate_Cholesky(chol, x); }
00069 
00070 // a RIGHT circular shift of the rows and columns from
00071 // 1,...,k-1,k,k+1,...l,l+1,...,p to
00072 // 1,...,k-1,l,k,k+1,...l-1,l+1,...p
00073 void right_circular_update_Cholesky(UpperTriangularMatrix &chol, int k, int l);
00074 inline void RightCircularUpdateCholesky(UpperTriangularMatrix &chol,
00075   int k, int l) { right_circular_update_Cholesky(chol, k, l); }
00076 
00077 // a LEFT circular shift of the rows and columns from
00078 // 1,...,k-1,k,k+1,...l,l+1,...,p to
00079 // 1,...,k-1,k+1,...l,k,l+1,...,p to
00080 void left_circular_update_Cholesky(UpperTriangularMatrix &chol, int k, int l); 
00081 inline void LeftCircularUpdateCholesky(UpperTriangularMatrix &chol,
00082    int k, int l) { left_circular_update_Cholesky(chol, k, l); } 
00083 
00084 
00085 void SVD(const Matrix&, DiagonalMatrix&, Matrix&, Matrix&,
00086     bool=true, bool=true);
00087 
00088 void SVD(const Matrix&, DiagonalMatrix&);
00089 
00090 inline void SVD(const Matrix& A, DiagonalMatrix& D, Matrix& U,
00091    bool withU = true) { SVD(A, D, U, U, withU, false); }
00092 
00093 void SortSV(DiagonalMatrix& D, Matrix& U, bool ascending = false);
00094 
00095 void SortSV(DiagonalMatrix& D, Matrix& U, Matrix& V, bool ascending = false);
00096 
00097 void Jacobi(const SymmetricMatrix&, DiagonalMatrix&);
00098 
00099 void Jacobi(const SymmetricMatrix&, DiagonalMatrix&, SymmetricMatrix&);
00100 
00101 void Jacobi(const SymmetricMatrix&, DiagonalMatrix&, Matrix&);
00102 
00103 void Jacobi(const SymmetricMatrix&, DiagonalMatrix&, SymmetricMatrix&,
00104    Matrix&, bool=true);
00105 
00106 void eigenvalues(const SymmetricMatrix&, DiagonalMatrix&);
00107 
00108 void eigenvalues(const SymmetricMatrix&, DiagonalMatrix&, SymmetricMatrix&);
00109 
00110 void eigenvalues(const SymmetricMatrix&, DiagonalMatrix&, Matrix&);
00111 
00112 inline void EigenValues(const SymmetricMatrix& A, DiagonalMatrix& D)
00113    { eigenvalues(A, D); }
00114 
00115 inline void EigenValues(const SymmetricMatrix& A, DiagonalMatrix& D,
00116    SymmetricMatrix& S) { eigenvalues(A, D, S); }
00117 
00118 inline void EigenValues(const SymmetricMatrix& A, DiagonalMatrix& D, Matrix& V)
00119    { eigenvalues(A, D, V); }
00120 
00121 class SymmetricEigenAnalysis
00122 // not implemented yet
00123 {
00124 public:
00125    SymmetricEigenAnalysis(const SymmetricMatrix&);
00126 private:
00127    DiagonalMatrix diag;
00128    DiagonalMatrix offdiag;
00129    SymmetricMatrix backtransform;
00130    FREE_CHECK(SymmetricEigenAnalysis)
00131 };
00132 
00133 void sort_ascending(GeneralMatrix&);
00134 
00135 void sort_descending(GeneralMatrix&);
00136 
00137 inline void SortAscending(GeneralMatrix& gm) { sort_ascending(gm); }
00138 
00139 inline void SortDescending(GeneralMatrix& gm) { sort_descending(gm); }
00140 
00142 class FFT_Controller
00143 {
00144 public:
00145    static bool OnlyOldFFT;
00146    static bool ar_1d_ft (int PTS, Real* X, Real *Y);
00147    static bool CanFactor(int PTS);
00148 };
00149 
00150 void FFT(const ColumnVector&, const ColumnVector&,
00151    ColumnVector&, ColumnVector&);
00152 
00153 void FFTI(const ColumnVector&, const ColumnVector&,
00154    ColumnVector&, ColumnVector&);
00155 
00156 void RealFFT(const ColumnVector&, ColumnVector&, ColumnVector&);
00157 
00158 void RealFFTI(const ColumnVector&, const ColumnVector&, ColumnVector&);
00159 
00160 void DCT_II(const ColumnVector&, ColumnVector&);
00161 
00162 void DCT_II_inverse(const ColumnVector&, ColumnVector&);
00163 
00164 void DST_II(const ColumnVector&, ColumnVector&);
00165 
00166 void DST_II_inverse(const ColumnVector&, ColumnVector&);
00167 
00168 void DCT(const ColumnVector&, ColumnVector&);
00169 
00170 void DCT_inverse(const ColumnVector&, ColumnVector&);
00171 
00172 void DST(const ColumnVector&, ColumnVector&);
00173 
00174 void DST_inverse(const ColumnVector&, ColumnVector&);
00175 
00176 void FFT2(const Matrix& U, const Matrix& V, Matrix& X, Matrix& Y);
00177 
00178 void FFT2I(const Matrix& U, const Matrix& V, Matrix& X, Matrix& Y);
00179 
00180 
00181 // This class is used by the new FFT program
00182 
00183 // Suppose an integer is expressed as a sequence of digits with each
00184 // digit having a different radix.
00185 // This class supposes we are counting with this multi-radix number
00186 // but also keeps track of the number with the digits (and radices)
00187 // reversed.
00188 // The integer starts at zero
00189 // operator++() increases it by 1
00190 // Counter gives the number of increments
00191 // Reverse() gives the value with the digits in reverse order
00192 // Swap is true if reverse is less than counter
00193 // Finish is true when we have done a complete cycle and are back at zero
00194 
00195 class MultiRadixCounter
00196 {
00197    const SimpleIntArray& Radix;
00198                               // radix of each digit
00199                               // n-1 highest order, 0 lowest order
00200    SimpleIntArray& Value;     // value of each digit
00201    const int n;               // number of digits
00202    int reverse;               // value when order of digits is reversed
00203    int product;               // product of radices
00204    int counter;               // counter
00205    bool finish;               // true when we have gone over whole range
00206 public:
00207    MultiRadixCounter(int nx, const SimpleIntArray& rx,
00208       SimpleIntArray& vx);
00209    void operator++();         // increment the multi-radix counter
00210    bool Swap() const { return reverse < counter; }
00211    bool Finish() const { return finish; }
00212    int Reverse() const { return reverse; }
00213    int Counter() const { return counter; }
00214 };
00215 
00216 // multiplication by Helmert matrix
00217 ReturnMatrix Helmert(int n, bool full=false);
00218 ReturnMatrix Helmert(const ColumnVector& X, bool full=false);
00219 ReturnMatrix Helmert(int n, int j, bool full=false);
00220 ReturnMatrix Helmert_transpose(const ColumnVector& Y, bool full=false);
00221 Real Helmert_transpose(const ColumnVector& Y, int j, bool full=false);
00222 ReturnMatrix Helmert(const Matrix& X, bool full=false);
00223 ReturnMatrix Helmert_transpose(const Matrix& Y, bool full=false);
00224 
00225 
00226 
00227 
00228 #ifdef use_namespace
00229 }
00230 #endif
00231 
00232 
00233 
00234 #endif
00235 
00236 // body file: cholesky.cpp
00237 // body file: evalue.cpp
00238 // body file: fft.cpp
00239 // body file: hholder.cpp
00240 // body file: jacobi.cpp
00241 // body file: newfft.cpp
00242 // body file: sort.cpp
00243 // body file: svd.cpp
00244 // body file: nm_misc.cpp
00245 
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00247 
00249 
00250 


kni
Author(s): Martin Günther
autogenerated on Mon Aug 14 2017 02:44:13