--- /dev/null
+/*---------------------------- fmatrix.h ---------------------------*/
+// $Id$
+#ifndef __lac_fullmatrix_H
+#define __lac_fullmatrix_H
+/*---------------------------- fmatrix.h ---------------------------*/
+
+// This file is part of the DEAL Library
+// DEAL is Copyright(1995) by
+// Roland Becker, Guido Kanschat, Franz-Theo Suttmeier
+// Revised by Wolfgang Bangerth
+
+
+#include <base/exceptions.h>
+
+
+// forward declarations
+
+template<typename number> class Vector;
+
+class iVector;
+
+
+
+/**
+ * Rectangular/quadratic full matrix.
+ *
+ * Memory for Components is supplied explicitly <p>
+ * ( ! Amount of memory needs not to comply with actual dimension due to reinitializations ! ) <p>
+ * - all necessary methods for matrices are supplied <p>
+ * - operators available are '=' and '( )' <p>
+ * CONVENTIONS for used 'equations' : <p>
+ * - THIS matrix is always named 'A' <p>
+ * - matrices are always uppercase , vectors and scalars are lowercase <p>
+ * - Transp(A) used for transpose of matrix A
+ *
+ */
+template<typename number>
+class FullMatrix
+{
+ private:
+ /**
+ * Component-array.
+ */
+ number* val;
+ /**
+ * Dimension. Actual number of Columns
+ */
+ unsigned int dim_range;
+ /**
+ * Dimension. Actual number of Rows
+ */
+ unsigned int dim_image;
+ /**
+ * Dimension. Determines amount of reserved memory
+ */
+ unsigned int val_size;
+
+ /**
+ * Initialization . initialize memory for Matrix <p>
+ * ( m rows , n columns )
+ */
+ void init (const unsigned int m, const unsigned int n);
+
+ /**
+ * Return a read-write reference to the
+ * element #(i,j)#.
+ *
+ * This function does no bounds checking.
+ */
+ number& el (const unsigned int i, const unsigned int j);
+
+ /**
+ * Return the value of the element #(i,j)#.
+ *
+ * This function does no bounds checking.
+ */
+ number el (const unsigned int i, const unsigned int j) const;
+
+
+ public:
+ /**
+ * Constructor. Initialize the matrix as
+ * a square matrix with dimension #n#.
+ */
+ explicit FullMatrix (const unsigned int n = 1);
+
+ /**
+ * Constructor. Initialize the matrix as
+ * a rectangular #m# times #n# matrix.
+ */
+ FullMatrix (const unsigned int m, const unsigned int n);
+
+ /**
+ * Copy constructor. Be very careful with
+ * this constructor, since it may take a
+ * huge amount of computing time for large
+ * matrices!!
+ */
+ explicit FullMatrix (const FullMatrix&);
+
+ /**
+ * Destructor. Release all memory.
+ */
+ ~FullMatrix();
+
+ /**
+ * Comparison operator. Be careful with
+ * this thing, it may eat up huge amounts
+ * of computing time! It is most commonly
+ * used for internal consistency checks
+ * of programs.
+ */
+ bool operator == (const FullMatrix<number> &) const;
+
+ /**
+ * A = B . Copy all elements
+ */
+ template<typename number2>
+ FullMatrix<number>& operator = (const FullMatrix<number2>& B);
+
+
+ /**
+ * U(0-m,0-n) = s . Fill all elements
+ */
+ template<typename number2>
+ void fill (const FullMatrix<number2>& src,
+ const unsigned int i=0, const unsigned int j=0);
+
+ /**
+ * Change Dimension.
+ * Set dimension to (m,n) <p>
+ * ( reinit rectangular matrix )
+ */
+ void reinit (const unsigned int m, const unsigned int n);
+
+ /**
+ * Change Dimension.
+ * Set dimension to (n,n) <p>
+ * ( reinit quadratic matrix )
+ */
+ void reinit (const unsigned int n);
+
+ /**
+ * Adjust Dimension.
+ * Set dimension to ( m(B),n(B) ) <p>
+ * ( adjust to dimensions of another matrix B )
+ */
+ template<typename number2>
+ void reinit (const FullMatrix<number2> &B);
+
+ /**
+ * Return number of rows of this matrix.
+ * To remember: this matrix is an
+ * $m \times n$-matrix.
+ */
+ unsigned int m () const;
+
+ /**
+ * Return number of columns of this matrix.
+ * To remember: this matrix is an
+ * $m \times n$-matrix.
+ */
+ unsigned int n () const;
+
+ /**
+ * Return whether the matrix contains only
+ * elements with value zero. This function
+ * is mainly for internal consistency
+ * check and should seldomly be used when
+ * not in debug mode since it uses quite
+ * some time.
+ */
+ bool all_zero () const;
+
+ //@}
+
+
+ /**@name 2: Data-Access
+ */
+ //@{
+ /**
+ * Access Elements. returns element at relative 'address' i <p>
+ * ( -> access to A(i/n , i mod n) )
+ */
+ number el (const unsigned int i) const;
+
+ /**
+ * Return the value of the element #(i,j)#.
+ * Does the same as the #el(i,j)# function
+ * but does bounds checking.
+ */
+ number operator() (const unsigned int i, const unsigned int j) const;
+
+ /**
+ * Return a read-write reference to
+ * the element #(i,j)#.
+ * Does the same as the #el(i,j)# function
+ * but does bounds checking.
+ */
+ number& operator() (const unsigned int i, const unsigned int j);
+
+ /**
+ * Set all entries in the matrix to
+ * zero.
+ */
+ void clear ();
+ //@}
+
+
+ /**@name 3: Basic applications on matrices
+ */
+ //@{
+ /**
+ * A+=B . Simple addition
+ */
+ template<typename number2>
+ void add (const number s, const FullMatrix<number2>& B);
+
+ /**
+ * A+=Transp(B).
+ * Simple addition of the transpose of B to this
+ */
+ template<typename number2>
+ void Tadd (const number s, const FullMatrix<number2>& B);
+
+ /**
+ * C=A*B.
+ * Matrix-matrix-multiplication
+ */
+
+ template<typename number2>
+ void mmult (FullMatrix<number2>& C, const FullMatrix<number2>& B) const;
+
+ /**
+ * C=Transp(A)*B.
+ * Matrix-matrix-multiplication using
+ * transpose of this
+ */
+ template<typename number2>
+ void Tmmult (FullMatrix<number2>& C, const FullMatrix<number2>& B) const;
+
+ /**
+ * w (+)= A*v.
+ * Matrix-vector-multiplication ; <p>
+ * ( application of this to a vector v )
+ * flag adding=true : w+=A*v
+ */
+ template<typename number2>
+ void vmult (Vector<number2>& w, const Vector<number2>& v, const bool adding=false) const;
+
+ /**
+ * w (+)= Transp(A)*v.
+ * Matrix-vector-multiplication ; <p>
+ * (application of transpose of this to a vector v)
+ * flag adding=true : w+=A*v
+ */
+ template<typename number2>
+ void Tvmult (Vector<number2>& w, const Vector<number2>& v, const bool adding=false) const;
+
+ /**
+ * Return the norm of the vector #v# with
+ * respect to the norm induced by this
+ * matrix, i.e. $\left<v,Mv\right>$. This
+ * is useful, e.g. in the finite element
+ * context, where the $L_2$ norm of a
+ * function equals the matrix norm with
+ * respect to the mass matrix of the vector
+ * representing the nodal values of the
+ * finite element function.
+ *
+ * Note the order in which the matrix
+ * appears. For non-symmetric matrices
+ * there is a difference whether the
+ * matrix operates on the first
+ * or on the second operand of the
+ * scalar product.
+ *
+ * Obviously, the matrix needs to be square
+ * for this operation.
+ */
+ template<typename number2>
+ double matrix_norm (const Vector<number2> &v) const;
+
+ /**
+ * Build the matrix scalar product
+ * #u^T M v#. This function is mostly
+ * useful when building the cellwise
+ * scalar product of two functions in
+ * the finite element context.
+ */
+ template<typename number2>
+ double matrix_scalar_product (const Vector<number2> &u, const Vector<number2> &v) const;
+
+ /**
+ * A=Inverse(A). Inversion of this by
+ * Gauss-Jordan-algorithm
+ */
+ void gauss_jordan ();
+
+ /**
+ * Computes the determinant of a matrix.
+ * This is only implemented for one two and
+ * three dimensions, since for higher
+ * dimensions the numerical work explodes.
+ * Obviously, the matrix needs to be square
+ * for this function.
+ */
+ double determinant () const;
+
+ /**
+ * Compute the quadratic matrix norm.
+ * Return value is the root of the square
+ * sum of all matrix entries.
+ */
+ double norm2 () const;
+ /**
+ * Assign the inverse of the given
+ * matrix to #*this#. This function is
+ * only implemented (hardcoded) for
+ * square matrices of dimension one,
+ * two and three.
+ */
+ void invert (const FullMatrix<number> &M);
+ //@}
+
+
+ /**@name 4: Basic applications on Rows or Columns
+ */
+ //@{
+ /**
+ * A(i,1-n)+=s*A(j,1-n).
+ * Simple addition of rows of this
+ */
+ void add_row (const unsigned int i, const number s, const unsigned int j);
+
+ /**
+ * A(i,1-n)+=s*A(j,1-n)+t*A(k,1-n).
+ * Multiple addition of rows of this
+ */
+ void add_row (const unsigned int i,
+ const number s, const unsigned int j,
+ const number t, const unsigned int k);
+
+ /**
+ * A(1-n,i)+=s*A(1-n,j).
+ * Simple addition of columns of this
+ */
+ void add_col (const unsigned int i, const number s, const unsigned int j);
+
+ /**
+ * A(1-n,i)+=s*A(1-n,j)+t*A(1-n,k).
+ * Multiple addition of columns of this
+ */
+ void add_col (const unsigned int i,
+ const number s, const unsigned int j,
+ const number t, const unsigned int k);
+
+ /**
+ * Swap A(i,1-n) <-> A(j,1-n).
+ * Swap rows i and j of this
+ */
+ void swap_row (const unsigned int i, const unsigned int j);
+
+ /**
+ * Swap A(1-n,i) <-> A(1-n,j).
+ * Swap columns i and j of this
+ */
+ void swap_col (const unsigned int i, const unsigned int j);
+ //@}
+
+
+ /**@name 5: Mixed stuff. Including more
+ * applications on matrices
+ */
+ //@{
+ /**
+ * w=b-A*v.
+ * Residual calculation , returns |w|
+ */
+ template<typename number2, typename number3>
+ double residual (Vector<number2>& w, const Vector<number2>& v, const Vector<number3>& b) const;
+
+ /**
+ * Inversion of lower triangle .
+ */
+ template<typename number2>
+ void forward (Vector<number2>& dst, const Vector<number2>& src) const;
+
+ /**
+ * Inversion of upper triangle .
+ */
+ template<typename number2>
+ void backward (Vector<number2>& dst, const Vector<number2>& src) const;
+
+ /**
+ * QR - factorization of a matrix.
+ * The orthogonal transformation Q is
+ * applied to the vector y and this matrix. <p>
+ * After execution of householder, the upper
+ * triangle contains the resulting matrix R, <p>
+ * the lower the incomplete factorization matrices.
+ */
+ template<typename number2>
+ void householder (Vector<number2>& y);
+
+ /**
+ * Least - Squares - Approximation by QR-factorization.
+ */
+ template<typename number2>
+ double least_squares (Vector<number2>& dst, Vector<number2>& src);
+
+ /**
+ * A(i,i)+=B(i,1-n). Addition of complete
+ * rows of B to diagonal-elements of this ; <p>
+ * ( i = 1 ... m )
+ */
+ template<typename number2>
+ void add_diag (const number s, const FullMatrix<number2>& B);
+
+ /**
+ * A(i,i)+=s i=1-m.
+ * Add constant to diagonal elements of this
+ */
+ void diagadd (const number s);
+
+ /**
+ * w+=part(A)*v. Conditional partial
+ * Matrix-vector-multiplication <p>
+ * (used elements of v determined by x)
+ */
+ template<typename number2>
+ void gsmult (Vector<number2>& w, const Vector<number2>& v, const iVector& x) const;
+
+
+ /**
+ * Output of the matrix in user-defined format.
+ */
+ void print (ostream& s, int width=5, int precision=2) const;
+
+ /**
+ * Print the matrix in the usual format,
+ * i.e. as a matrix and not as a list of
+ * nonzero elements. For better
+ * readability, zero elements
+ * are displayed as empty space.
+ *
+ * Each entry is printed in scientific
+ * format, with one pre-comma digit and
+ * the number of digits given by
+ * #precision# after the comma, with one
+ * space following.
+ * The precision defaults to four, which
+ * suffices for most cases. The precision
+ * and output format are {\it not}
+ * properly reset to the old values
+ * when the function exits.
+ *
+ * You should be aware that this function
+ * may produce {\bf large} amounts of
+ * output if applied to a large matrix!
+ * Be careful with it.
+ */
+ void print_formatted (ostream &out,
+ const unsigned int presicion=3) const;
+ //@}
+
+ /**
+ * Exception
+ */
+ DeclException2 (ExcInvalidIndex,
+ int, int,
+ << "The given index " << arg1
+ << " should be less than " << arg2 << ".");
+ /**
+ * Exception
+ */
+ DeclException2 (ExcDimensionMismatch,
+ int, int,
+ << "The two dimensions " << arg1 << " and " << arg2
+ << " do not match here.");
+ /**
+ * Exception
+ */
+ DeclException0 (ExcNotQuadratic);
+ /**
+ * Exception
+ */
+ DeclException0 (ExcNotRegular);
+ /**
+ * Exception
+ */
+ DeclException3 (ExcInvalidDestination,
+ int, int, int,
+ << "Target region not in matrix: size in this direction="
+ << arg1 << ", size of new matrix=" << arg2
+ << ", offset=" << arg3);
+ /**
+ * Exception
+ */
+ DeclException1 (ExcNotImplemented,
+ int,
+ << "This function is not implemented for the given"
+ << " matrix dimension " << arg1);
+ /**
+ * Exception
+ */
+ DeclException0 (ExcIO);
+};
+
+
+
+
+
+/*-------------------------Inline functions -------------------------------*/
+
+template <typename number>
+inline number &
+FullMatrix<number>::el (const unsigned int i, const unsigned int j)
+{
+ return val[i*dim_range+j];
+};
+
+
+template <typename number>
+inline number
+FullMatrix<number>::el (const unsigned int i, const unsigned int j) const
+{
+ return val[i*dim_range+j];
+};
+
+
+template <typename number>
+inline unsigned int
+FullMatrix<number>::m() const
+{
+ return dim_image;
+};
+
+
+template <typename number>
+inline unsigned int
+FullMatrix<number>::n() const
+{
+ return dim_range;
+};
+
+
+template <typename number>
+inline number
+FullMatrix<number>::el (const unsigned int i) const
+{
+ return val[i];
+};
+
+
+template <typename number>
+inline number
+FullMatrix<number>::operator() (const unsigned int i, const unsigned int j) const
+{
+ Assert (i<dim_image, ExcInvalidIndex (i, dim_image));
+ Assert (j<dim_range, ExcInvalidIndex (i, dim_range));
+ return el(i,j);
+};
+
+
+template <typename number>
+inline number &
+FullMatrix<number>::operator() (const unsigned int i, const unsigned int j)
+{
+ Assert (i<dim_image, ExcInvalidIndex (i, dim_image));
+ Assert (j<dim_range, ExcInvalidIndex (j, dim_range));
+ return el(i,j);
+}
+
+
+
+
+/*---------------------------- fullmatrix.h ---------------------------*/
+/* end of #ifndef __lac_fullmatrix_H */
+#endif
+/*---------------------------- fullmatrix.h ---------------------------*/
--- /dev/null
+// $Id$
+
+#include <lac/vector.h>
+#include <lac/ivector.h>
+#include <lac/fullmatrix.h>
+
+#include <cmath>
+#include <cstdlib>
+#include <cstdio>
+#include <iomanip>
+
+
+template <typename number>
+FullMatrix<number>::FullMatrix (const unsigned int n)
+{
+ init (n,n);
+};
+
+
+template <typename number>
+FullMatrix<number>::FullMatrix (const unsigned int m, const unsigned int n)
+{
+ init (m,n);
+};
+
+
+template <typename number>
+FullMatrix<number>::FullMatrix (const FullMatrix &m)
+{
+ init (m.dim_image, m.dim_range);
+ number * p = &val[0];
+ const number * vp = &m.val[0];
+ const number * const e = &val[dim_image*dim_range];
+
+ while (p!=e)
+ *p++ = *vp++;
+};
+
+
+template <typename number>
+void
+FullMatrix<number>::init (const unsigned int mm, const unsigned int nn)
+{
+ val_size = nn*mm;
+ val = new number[val_size];
+ dim_range = nn;
+ dim_image = mm;
+ clear ();
+};
+
+
+template <typename number>
+FullMatrix<number>::~FullMatrix ()
+{
+ delete[] val;
+};
+
+
+template <typename number>
+bool
+FullMatrix<number>::all_zero () const
+{
+ const number *p = &val[0],
+ *e = &val[n()*m()];
+ while (p!=e)
+ if (*p++ != 0.0)
+ return false;
+
+ return true;
+};
+
+
+template <typename number>
+void
+FullMatrix<number>::reinit (const unsigned int mm, const unsigned int nn)
+{
+ if (val_size<nn*mm)
+ {
+ delete[] val;
+ init(mm, nn);
+ }
+ else
+ {
+ dim_range = nn;
+ dim_image = mm;
+ clear ();
+ }
+}
+
+
+template <typename number>
+void
+FullMatrix<number>::reinit (const unsigned int n)
+{
+ reinit (n, n);
+};
+
+
+template <typename number>
+template <typename number2>
+void
+FullMatrix<number>::reinit (const FullMatrix<number2> &B)
+{
+ reinit (B.m(), B.n());
+};
+
+
+template <typename number>
+template <typename number2>
+void
+FullMatrix<number>::vmult (Vector<number2>& dst,
+ const Vector<number2>& src,
+ const bool adding) const
+{
+ Assert(dst.size() == m(), ExcDimensionMismatch(dst.size(), m()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+
+ double s;
+ if ((n()==3) && (m()==3))
+ {
+ double s0,s1,s2;
+ s = src(0);
+ s0 = s*val[0]; s1 = s*val[3]; s2 = s*val[6];
+ s = src(1);
+ s0 += s*val[1]; s1 += s*val[4]; s2 += s*val[7];
+ s = src(2);
+ s0 += s*val[2]; s1 += s*val[5]; s2 += s*val[8];
+
+ if (!adding)
+ {
+ dst(0) = s0;
+ dst(1) = s1;
+ dst(2) = s2;
+ }
+ else
+ {
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ }
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ double s0,s1,s2,s3;
+ s = src(0);
+ s0 = s*val[0]; s1 = s*val[4]; s2 = s*val[8]; s3 = s*val[12];
+ s = src(1);
+ s0 += s*val[1]; s1 += s*val[5]; s2 += s*val[9]; s3 += s*val[13];
+ s = src(2);
+ s0 += s*val[2]; s1 += s*val[6]; s2 += s*val[10]; s3 += s*val[14];
+ s = src(3);
+ s0 += s*val[3]; s1 += s*val[7]; s2 += s*val[11]; s3 += s*val[15];
+
+ if (!adding)
+ {
+ dst(0) = s0;
+ dst(1) = s1;
+ dst(2) = s2;
+ dst(3) = s3;
+ }
+ else
+ {
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ dst(3) += s3;
+ }
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ double s0,s1,s2,s3,s4,s5,s6,s7;
+ s = src(0);
+ s0 = s*val[0]; s1 = s*val[8]; s2 = s*val[16]; s3 = s*val[24];
+ s4 = s*val[32]; s5 = s*val[40]; s6 = s*val[48]; s7 = s*val[56];
+ s = src(1);
+ s0 += s*val[1]; s1 += s*val[9]; s2 += s*val[17]; s3 += s*val[25];
+ s4 += s*val[33]; s5 += s*val[41]; s6 += s*val[49]; s7 += s*val[57];
+ s = src(2);
+ s0 += s*val[2]; s1 += s*val[10]; s2 += s*val[18]; s3 += s*val[26];
+ s4 += s*val[34]; s5 += s*val[42]; s6 += s*val[50]; s7 += s*val[58];
+ s = src(3);
+ s0 += s*val[3]; s1 += s*val[11]; s2 += s*val[19]; s3 += s*val[27];
+ s4 += s*val[35]; s5 += s*val[43]; s6 += s*val[51]; s7 += s*val[59];
+ s = src(4);
+ s0 += s*val[4]; s1 += s*val[12]; s2 += s*val[20]; s3 += s*val[28];
+ s4 += s*val[36]; s5 += s*val[44]; s6 += s*val[52]; s7 += s*val[60];
+ s = src(5);
+ s0 += s*val[5]; s1 += s*val[13]; s2 += s*val[21]; s3 += s*val[29];
+ s4 += s*val[37]; s5 += s*val[45]; s6 += s*val[53]; s7 += s*val[61];
+ s = src(6);
+ s0 += s*val[6]; s1 += s*val[14]; s2 += s*val[22]; s3 += s*val[30];
+ s4 += s*val[38]; s5 += s*val[46]; s6 += s*val[54]; s7 += s*val[62];
+ s = src(7);
+ s0 += s*val[7]; s1 += s*val[15]; s2 += s*val[23]; s3 += s*val[31];
+ s4 += s*val[39]; s5 += s*val[47]; s6 += s*val[55]; s7 += s*val[63];
+
+ if (!adding)
+ {
+ dst(0) = s0;
+ dst(1) = s1;
+ dst(2) = s2;
+ dst(3) = s3;
+ dst(4) = s4;
+ dst(5) = s5;
+ dst(6) = s6;
+ dst(7) = s7;
+ }
+ else
+ {
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ dst(3) += s3;
+ dst(4) += s4;
+ dst(5) += s5;
+ dst(6) += s6;
+ dst(7) += s7;
+ }
+ }
+ else
+ {
+ number* e = val;
+ const unsigned int size_m = m(),
+ size_n = n();
+ for (unsigned int i=0; i<size_m; ++i)
+ {
+ s = 0.;
+ for (unsigned int j=0; j<size_n; ++j)
+ s += src(j) * *(e++);
+ if (!adding) dst(i) = s;
+ else dst(i) += s;
+ }
+ }
+}
+
+
+template <typename number>
+template <typename number2>
+void FullMatrix<number>::gsmult (Vector<number2>& dst, const Vector<number2>& src, const iVector& gl) const
+{
+ Assert(n() == m(), ExcNotQuadratic());
+ Assert(dst.size() == n(), ExcDimensionMismatch(dst.size(), n()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+ Assert(gl.n() == n(), ExcDimensionMismatch(gl.n(), n()));
+
+ double s;
+ if ((n()==3) && (m()==3))
+ {
+ double s0=0.,s1=0.,s2=0.;
+ s = src(0);
+ if(gl(1)<gl(0)) s1 = s*val[3]; if(gl(2)<gl(0)) s2 = s*val[6];
+ s = src(1);
+ if(gl(0)<gl(1)) s0 += s*val[1]; if(gl(2)<gl(1)) s2 += s*val[7];
+ s = src(2);
+ if(gl(0)<gl(2)) s0 += s*val[2]; if(gl(1)<gl(2)) s1 += s*val[5];
+
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ double s0=0.,s1=0.,s2=0.,s3=0.;
+ s = src(0);
+ if(gl(1)<gl(0)) s1 = s*val[4]; if(gl(2)<gl(0)) s2 = s*val[8]; if(gl(3)<gl(0)) s3 = s*val[12];
+ s = src(1);
+ if(gl(0)<gl(1)) s0 += s*val[1]; if(gl(2)<gl(1)) s2 += s*val[9]; if(gl(3)<gl(1)) s3 += s*val[13];
+ s = src(2);
+ if(gl(0)<gl(2)) s0 += s*val[2]; if(gl(1)<gl(2)) s1 += s*val[6]; if(gl(3)<gl(2)) s3 += s*val[14];
+ s = src(3);
+ if(gl(0)<gl(3)) s0 += s*val[3]; if(gl(1)<gl(3)) s1 += s*val[7]; if(gl(2)<gl(3)) s2 += s*val[11];
+
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ dst(3) += s3;
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ double s0=0.,s1=0.,s2=0.,s3=0.,s4=0.,s5=0.,s6=0.,s7=0.;
+ s = src(0);
+ if(gl(1)<gl(0)) s1 = s*val[8];
+ if(gl(2)<gl(0)) s2 = s*val[16];
+ if(gl(3)<gl(0)) s3 = s*val[24];
+ if(gl(4)<gl(0)) s4 = s*val[32];
+ if(gl(5)<gl(0)) s5 = s*val[40];
+ if(gl(6)<gl(0)) s6 = s*val[48];
+ if(gl(7)<gl(0)) s7 = s*val[56];
+ s = src(1);
+ if(gl(0)<gl(1)) s0 += s*val[1];
+ if(gl(2)<gl(1)) s2 += s*val[17];
+ if(gl(3)<gl(1)) s3 += s*val[25];
+ if(gl(4)<gl(1)) s4 += s*val[33];
+ if(gl(5)<gl(1)) s5 += s*val[41];
+ if(gl(6)<gl(1)) s6 += s*val[49];
+ if(gl(7)<gl(1)) s7 += s*val[57];
+ s = src(2);
+ if(gl(0)<gl(2)) s0 += s*val[2];
+ if(gl(1)<gl(2)) s1 += s*val[10];
+ if(gl(3)<gl(2)) s3 += s*val[26];
+ if(gl(4)<gl(2)) s4 += s*val[34];
+ if(gl(5)<gl(2)) s5 += s*val[42];
+ if(gl(6)<gl(2)) s6 += s*val[50];
+ if(gl(7)<gl(2)) s7 += s*val[58];
+ s = src(3);
+ if(gl(0)<gl(3)) s0 += s*val[3];
+ if(gl(1)<gl(3)) s1 += s*val[11];
+ if(gl(2)<gl(3)) s2 += s*val[19];
+ if(gl(4)<gl(3)) s4 += s*val[35];
+ if(gl(5)<gl(3)) s5 += s*val[43];
+ if(gl(6)<gl(3)) s6 += s*val[51];
+ if(gl(7)<gl(3)) s7 += s*val[59];
+ s = src(4);
+ if(gl(0)<gl(4)) s0 += s*val[4];
+ if(gl(1)<gl(4)) s1 += s*val[12];
+ if(gl(2)<gl(4)) s2 += s*val[20];
+ if(gl(3)<gl(4)) s3 += s*val[28];
+ if(gl(5)<gl(4)) s5 += s*val[44];
+ if(gl(6)<gl(4)) s6 += s*val[52];
+ if(gl(7)<gl(4)) s7 += s*val[60];
+ s = src(5);
+ if(gl(0)<gl(5)) s0 += s*val[5];
+ if(gl(1)<gl(5)) s1 += s*val[13];
+ if(gl(2)<gl(5)) s2 += s*val[21];
+ if(gl(3)<gl(5)) s3 += s*val[29];
+ if(gl(4)<gl(5)) s4 += s*val[37];
+ if(gl(6)<gl(5)) s6 += s*val[53];
+ if(gl(7)<gl(5)) s7 += s*val[61];
+ s = src(6);
+ if(gl(0)<gl(6)) s0 += s*val[6];
+ if(gl(1)<gl(6)) s1 += s*val[14];
+ if(gl(2)<gl(6)) s2 += s*val[22];
+ if(gl(3)<gl(6)) s3 += s*val[30];
+ if(gl(4)<gl(6)) s4 += s*val[38];
+ if(gl(5)<gl(6)) s5 += s*val[46];
+ if(gl(7)<gl(6)) s7 += s*val[62];
+ s = src(7);
+ if(gl(0)<gl(7)) s0 += s*val[7];
+ if(gl(1)<gl(7)) s1 += s*val[15];
+ if(gl(2)<gl(7)) s2 += s*val[23];
+ if(gl(3)<gl(7)) s3 += s*val[31];
+ if(gl(4)<gl(7)) s4 += s*val[39];
+ if(gl(5)<gl(7)) s5 += s*val[47];
+ if(gl(6)<gl(7)) s6 += s*val[55];
+
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ dst(3) += s3;
+ dst(4) += s4;
+ dst(5) += s5;
+ dst(6) += s6;
+ dst(7) += s7;
+ }
+ else
+ {
+ number* e = val;
+ const unsigned int size_m = m(),
+ size_n = n();
+ for (unsigned int i=0; i<size_m; ++i)
+ {
+ s = 0.;
+ for (unsigned int j=0; j<size_n; ++j)
+ if(gl(i)<gl(j)) s += src(j) * *(e++);
+ dst(i) += s;
+ }
+ }
+}
+
+template <typename number>
+template <typename number2>
+void FullMatrix<number>::Tvmult (Vector<number2>& dst, const Vector<number2>& src, const bool adding) const
+{
+ Assert(dst.size() == n(), ExcDimensionMismatch(dst.size(), n()));
+ Assert(src.size() == m(), ExcDimensionMismatch(src.size(), m()));
+
+ unsigned int i,j;
+ double s;
+ const unsigned int size_m = m(),
+ size_n = n();
+ for (i=0; i<size_m; ++i)
+ {
+ s = 0.;
+ for (j=0; j<size_n; ++j)
+ s += src(j) * el(j,i);
+ if(!adding) dst(i) = s;
+ else dst(i) += s;
+ }
+}
+
+template <typename number>
+template <typename number2, typename number3>
+double FullMatrix<number>::residual (Vector<number2>& dst, const Vector<number2>& src,
+ const Vector<number3>& right) const
+{
+ Assert(dst.size() == m(), ExcDimensionMismatch(dst.size(), m()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+ Assert(right.size() == m(), ExcDimensionMismatch(right.size(), m()));
+
+ unsigned int i,j;
+ double s, res = 0.;
+ const unsigned int size_m = m(),
+ size_n = n();
+ for (i=0; i<size_n; ++i)
+ {
+ s = right(i);
+ for (j=0; j<size_m; ++j)
+ s -= src(j) * el(i,j);
+ dst(i) = s;
+ res += s*s;
+ }
+ return sqrt(res);
+}
+
+template <typename number>
+template <typename number2>
+void FullMatrix<number>::forward (Vector<number2>& dst, const Vector<number2>& src) const
+{
+ Assert(n() == m(), ExcNotQuadratic());
+ Assert(dst.size() == n(), ExcDimensionMismatch(dst.size(), n()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+
+ unsigned int i,j;
+ unsigned int nu = (m()<n() ? m() : n());
+ double s;
+ for (i=0; i<nu; ++i)
+ {
+ s = src(i);
+ for (j=0; j<i; ++j) s -= dst(j) * el(i,j);
+ dst(i) = s/el(i,i);
+ }
+}
+
+template <typename number>
+template <typename number2>
+void FullMatrix<number>::backward (Vector<number2>& dst, const Vector<number2>& src) const
+{
+ Assert(n() == m(), ExcNotQuadratic());
+ Assert(dst.size() == n(), ExcDimensionMismatch(dst.size(), n()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+
+ unsigned int j;
+ unsigned int nu = (m()<n() ? m() : n());
+ double s;
+ for (int i=nu-1; i>=0; --i)
+ {
+ s = src(i);
+ for (j=i+1; j<nu; ++j) s -= dst(j) * el(i,j);
+ dst(i) = s/el(i,i);
+ }
+}
+
+template <typename number>
+template <typename number2>
+FullMatrix<number>&
+FullMatrix<number>::operator = (const FullMatrix<number2>& m)
+{
+ reinit(m);
+
+ number * p = &val[0];
+ const number2 * vp = &m.val[0];
+ const number * const e = &val[dim_image*dim_range];
+
+ while (p!=e)
+ *p++ = *vp++;
+
+ return *this;
+}
+
+template <typename number>
+template <typename number2>
+void FullMatrix<number>::fill (const FullMatrix<number2>& src,
+ const unsigned int i, const unsigned int j)
+{
+ Assert (n() >= src.n() + j, ExcInvalidDestination(n(), src.n(), j));
+ Assert (m() >= src.m() + i, ExcInvalidDestination(m(), src.m(), i));
+
+ for (unsigned int ii=0; ii<src.m() ; ++ii)
+ for (unsigned int jj=0; jj<src.n() ; ++jj)
+ el(ii+i,jj+j) = src.el(ii,jj);
+}
+
+template <typename number>
+void FullMatrix<number>::add_row (const unsigned int i,
+ const number s, const unsigned int j)
+{
+ for (unsigned int k=0; k<m(); ++k)
+ el(i,k) += s*el(j,k);
+}
+
+template <typename number>
+void FullMatrix<number>::add_row (const unsigned int i, const number s,
+ const unsigned int j, const number t,
+ const unsigned int k)
+{
+ const unsigned int size_m = m();
+ for (unsigned l=0; l<size_m; ++l)
+ el(i,l) += s*el(j,l) + t*el(k,l);
+}
+
+template <typename number>
+void FullMatrix<number>::add_col (const unsigned int i, const number s,
+ const unsigned int j)
+{
+ for (unsigned int k=0; k<n(); ++k)
+ el(k,i) += s*el(k,j);
+}
+
+template <typename number>
+void FullMatrix<number>::add_col (const unsigned int i, const number s,
+ const unsigned int j, const number t,
+ const unsigned int k)
+{
+ for (unsigned int l=0; l<n(); ++l)
+ el(l,i) += s*el(l,j) + t*el(l,k);
+}
+
+template <typename number>
+void FullMatrix<number>::swap_row (const unsigned int i, const unsigned int j)
+{
+ number s;
+ for (unsigned int k=0; k<m(); ++k)
+ {
+ s = el(i,k); el(i,k) = el(j,k); el(j,k) = s;
+ }
+}
+
+template <typename number>
+void FullMatrix<number>::swap_col (const unsigned int i, const unsigned int j)
+{
+ number s;
+ for (unsigned int k=0; k<n(); ++k)
+ {
+ s = el(k,i); el(k,i) = el(k,j); el(k,j) = s;
+ }
+}
+
+template <typename number>
+void FullMatrix<number>::diagadd (const number src)
+{
+ Assert (m() == n(), ExcDimensionMismatch(m(),n()));
+ for (unsigned int i=0; i<n(); ++i)
+ el(i,i) += src;
+}
+
+template <typename number>
+template <typename number2>
+void FullMatrix<number>::mmult (FullMatrix<number2>& dst, const FullMatrix<number2>& src) const
+{
+ Assert (n() == src.m(), ExcDimensionMismatch(n(), src.m()));
+ unsigned int i,j,k;
+ double s = 1.;
+ dst.reinit(m(), src.n());
+
+ for (i=0;i<m();i++)
+ for (j=0; j<src.n(); ++j)
+ {
+ s = 0.;
+ for (k=0;k<n();k++) s+= el(i,k) * src.el(k,j);
+ dst.el(i,j) = s;
+ }
+}
+
+/*void FullMatrix<number>::mmult (FullMatrix& dst, const FullMatrix& src) const
+{
+ Assert (m() == src.n(), ExcDimensionMismatch(m(), src.n()));
+
+ unsigned int i,j,k;
+ double s = 1.;
+
+ dst.reinit(n(), src.m());
+
+ for (i=0;i<n();i++)
+ for (j=0;j<src.m();j++)
+ {
+ s = 0.;
+ for (k=0;k<m();k++) s+= el(i,k) * src.el(k,j);
+ dst.el(i,j) = s;
+ }
+}*/
+
+template <typename number>
+template <typename number2>
+void FullMatrix<number>::Tmmult (FullMatrix<number2>& dst, const FullMatrix<number2>& src) const
+{
+ Assert (n() == src.n(), ExcDimensionMismatch(n(), src.n()));
+
+ unsigned int i,j,k;
+ double s = 1.;
+ dst.reinit(m(), src.m());
+
+ for (i=0;i<m();i++)
+ for (j=0;j<src.m();j++)
+ {
+ s = 0.;
+ for (k=0;k<n();k++) s+= el(k,i) * src.el(k,j);
+ dst.el(i,j) = s;
+ }
+}
+
+/*void FullMatrix<number>::Tmmult(FullMatrix& dst, const FullMatrix& src) const
+{
+ Assert (m() == src.n(), ExcDimensionMismatch(m(), src.n()));
+
+ unsigned int i,j,k;
+ double s = 1.;
+
+ dst.reinit(n(), src.m());
+
+ for (i=0;i<n();i++)
+ for (j=0;j<src.m();j++)
+ {
+ s = 0.;
+ for (k=0;k<m();k++) s+= el(k,i) * src.el(k,j);
+ dst.el(i,j) = s;
+ }
+}*/
+
+
+
+template <typename number>
+template <typename number2>
+double FullMatrix<number>::matrix_norm (const Vector<number2> &v) const
+{
+ Assert(m() == v.size(), ExcDimensionMismatch(m(),v.size()));
+ Assert(n() == v.size(), ExcDimensionMismatch(n(),v.size()));
+
+ double sum = 0.;
+ const unsigned int n_rows = m();
+ const number *val_ptr = &val[0];
+ const number2 *v_ptr;
+
+ for (unsigned int row=0; row<n_rows; ++row)
+ {
+ double s = 0.;
+ const number * const val_end_of_row = val_ptr+n_rows;
+ v_ptr = v.begin();
+ while (val_ptr != val_end_of_row)
+ s += *val_ptr++ * *v_ptr++;
+
+ sum += s* v(row);
+ };
+
+ return sum;
+};
+
+
+
+template <typename number>
+template <typename number2>
+double FullMatrix<number>::matrix_scalar_product (const Vector<number2> &u, const Vector<number2> &v) const
+{
+ Assert(m() == u.size(), ExcDimensionMismatch(m(),v.size()));
+ Assert(n() == v.size(), ExcDimensionMismatch(n(),v.size()));
+
+ double sum = 0.;
+ const unsigned int n_rows = m();
+ const unsigned int n_cols = n();
+ const number *val_ptr = &val[0];
+ const number2 *v_ptr;
+
+ for (unsigned int row=0; row<n_rows; ++row)
+ {
+ double s = 0.;
+ const number * const val_end_of_row = val_ptr+n_cols;
+ v_ptr = v.begin();
+ while (val_ptr != val_end_of_row)
+ s += *val_ptr++ * *v_ptr++;
+
+ sum += s* u(row);
+ };
+
+ return sum;
+};
+
+
+
+template <typename number>
+void
+FullMatrix<number>::print (ostream& s, int w, int p) const
+{
+ unsigned int i,j;
+ for (i=0;i<m();i++)
+ {
+ for (j=0;j<n();j++) s << setw(w) << setprecision(p) << el(i,j);
+ s << endl;
+ }
+}
+
+template <typename number>
+template <typename number2>
+void
+FullMatrix<number>::add (const number s,const FullMatrix<number2>& src)
+{
+ Assert (m() == src.m(), ExcDimensionMismatch(m(), src.m()));
+ Assert (n() == src.n(), ExcDimensionMismatch(n(), src.n()));
+ if ((n()==3) && (m()==3))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(1);
+ val[2] += s * src.el(2);
+ val[3] += s * src.el(3);
+ val[4] += s * src.el(4);
+ val[5] += s * src.el(5);
+ val[6] += s * src.el(6);
+ val[7] += s * src.el(7);
+ val[8] += s * src.el(8);
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(1);
+ val[2] += s * src.el(2);
+ val[3] += s * src.el(3);
+ val[4] += s * src.el(4);
+ val[5] += s * src.el(5);
+ val[6] += s * src.el(6);
+ val[7] += s * src.el(7);
+ val[8] += s * src.el(8);
+ val[9] += s * src.el(9);
+ val[10] += s * src.el(10);
+ val[11] += s * src.el(11);
+ val[12] += s * src.el(12);
+ val[13] += s * src.el(13);
+ val[14] += s * src.el(14);
+ val[15] += s * src.el(15);
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(1);
+ val[2] += s * src.el(2);
+ val[3] += s * src.el(3);
+ val[4] += s * src.el(4);
+ val[5] += s * src.el(5);
+ val[6] += s * src.el(6);
+ val[7] += s * src.el(7);
+ val[8] += s * src.el(8);
+ val[9] += s * src.el(9);
+ val[10] += s * src.el(10);
+ val[11] += s * src.el(11);
+ val[12] += s * src.el(12);
+ val[13] += s * src.el(13);
+ val[14] += s * src.el(14);
+ val[15] += s * src.el(15);
+ val[16] += s * src.el(16);
+ val[17] += s * src.el(17);
+ val[18] += s * src.el(18);
+ val[19] += s * src.el(19);
+
+ val[20] += s * src.el(20);
+ val[21] += s * src.el(21);
+ val[22] += s * src.el(22);
+ val[23] += s * src.el(23);
+ val[24] += s * src.el(24);
+ val[25] += s * src.el(25);
+ val[26] += s * src.el(26);
+ val[27] += s * src.el(27);
+ val[28] += s * src.el(28);
+ val[29] += s * src.el(29);
+
+ val[30] += s * src.el(30);
+ val[31] += s * src.el(31);
+ val[32] += s * src.el(32);
+ val[33] += s * src.el(33);
+ val[34] += s * src.el(34);
+ val[35] += s * src.el(35);
+ val[36] += s * src.el(36);
+ val[37] += s * src.el(37);
+ val[38] += s * src.el(38);
+ val[39] += s * src.el(39);
+
+ val[40] += s * src.el(40);
+ val[41] += s * src.el(41);
+ val[42] += s * src.el(42);
+ val[43] += s * src.el(43);
+ val[44] += s * src.el(44);
+ val[45] += s * src.el(45);
+ val[46] += s * src.el(46);
+ val[47] += s * src.el(47);
+ val[48] += s * src.el(48);
+ val[49] += s * src.el(49);
+
+ val[50] += s * src.el(50);
+ val[51] += s * src.el(51);
+ val[52] += s * src.el(52);
+ val[53] += s * src.el(53);
+ val[54] += s * src.el(54);
+ val[55] += s * src.el(55);
+ val[56] += s * src.el(56);
+ val[57] += s * src.el(57);
+ val[58] += s * src.el(58);
+ val[59] += s * src.el(59);
+
+ val[60] += s * src.el(60);
+ val[61] += s * src.el(61);
+ val[62] += s * src.el(62);
+ val[63] += s * src.el(63);
+ }
+ else
+ {
+ const unsigned int size = n()*m();
+ for (unsigned int i=0; i<size; i++)
+ val[i] += s * src.el(i);
+ }
+}
+
+
+
+template <typename number>
+template <typename number2>
+void
+FullMatrix<number>::add_diag (const number s, const FullMatrix<number2>& src)
+{
+ Assert (m() == src.m(), ExcDimensionMismatch(m(), src.m()));
+ Assert (n() == src.n(), ExcDimensionMismatch(n(), src.n()));
+
+ if ((n()==3) && (m()==3))
+ {
+ val[0] += s * src.el(0);
+ val[0] += s * src.el(1);
+ val[0] += s * src.el(2);
+ val[3] += s * src.el(3);
+ val[3] += s * src.el(4);
+ val[3] += s * src.el(5);
+ val[6] += s * src.el(6);
+ val[6] += s * src.el(7);
+ val[6] += s * src.el(8);
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ val[0] += s * src.el(0);
+ val[0] += s * src.el(1);
+ val[0] += s * src.el(2);
+ val[0] += s * src.el(3);
+ val[4] += s * src.el(4);
+ val[4] += s * src.el(5);
+ val[4] += s * src.el(6);
+ val[4] += s * src.el(7);
+ val[8] += s * src.el(8);
+ val[8] += s * src.el(9);
+ val[8] += s * src.el(10);
+ val[8] += s * src.el(11);
+ val[12] += s * src.el(12);
+ val[12] += s * src.el(13);
+ val[12] += s * src.el(14);
+ val[12] += s * src.el(15);
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ val[0] += s * src.el(0);
+ val[0] += s * src.el(1);
+ val[0] += s * src.el(2);
+ val[0] += s * src.el(3);
+ val[0] += s * src.el(4);
+ val[0] += s * src.el(5);
+ val[0] += s * src.el(6);
+ val[0] += s * src.el(7);
+ val[8] += s * src.el(8);
+ val[8] += s * src.el(9);
+ val[8] += s * src.el(10);
+ val[8] += s * src.el(11);
+ val[8] += s * src.el(12);
+ val[8] += s * src.el(13);
+ val[8] += s * src.el(14);
+ val[8] += s * src.el(15);
+ val[16] += s * src.el(16);
+ val[16] += s * src.el(17);
+ val[16] += s * src.el(18);
+ val[16] += s * src.el(19);
+
+ val[16] += s * src.el(20);
+ val[16] += s * src.el(21);
+ val[16] += s * src.el(22);
+ val[16] += s * src.el(23);
+ val[24] += s * src.el(24);
+ val[24] += s * src.el(25);
+ val[24] += s * src.el(26);
+ val[24] += s * src.el(27);
+ val[24] += s * src.el(28);
+ val[24] += s * src.el(29);
+
+ val[24] += s * src.el(30);
+ val[24] += s * src.el(31);
+ val[32] += s * src.el(32);
+ val[32] += s * src.el(33);
+ val[32] += s * src.el(34);
+ val[32] += s * src.el(35);
+ val[32] += s * src.el(36);
+ val[32] += s * src.el(37);
+ val[32] += s * src.el(38);
+ val[32] += s * src.el(39);
+
+ val[40] += s * src.el(40);
+ val[40] += s * src.el(41);
+ val[40] += s * src.el(42);
+ val[40] += s * src.el(43);
+ val[40] += s * src.el(44);
+ val[40] += s * src.el(45);
+ val[40] += s * src.el(46);
+ val[40] += s * src.el(47);
+ val[48] += s * src.el(48);
+ val[48] += s * src.el(49);
+
+ val[48] += s * src.el(50);
+ val[48] += s * src.el(51);
+ val[48] += s * src.el(52);
+ val[48] += s * src.el(53);
+ val[48] += s * src.el(54);
+ val[48] += s * src.el(55);
+ val[56] += s * src.el(56);
+ val[56] += s * src.el(57);
+ val[56] += s * src.el(58);
+ val[56] += s * src.el(59);
+
+ val[56] += s * src.el(60);
+ val[56] += s * src.el(61);
+ val[56] += s * src.el(62);
+ val[56] += s * src.el(63);
+ }
+ else
+ {
+ const unsigned int size = n()*m();
+ for (unsigned int i=0; i<size; i++)
+ val[i] += s * src.el(i);
+ }
+}
+
+template <typename number>
+template <typename number2>
+void
+FullMatrix<number>::Tadd (const number s, const FullMatrix<number2>& src)
+{
+ Assert (m() == n(), ExcNotQuadratic());
+ Assert (m() == src.m(), ExcDimensionMismatch(m(), src.m()));
+ Assert (n() == src.n(), ExcDimensionMismatch(n(), src.n()));
+
+ if ((n()==3) && (m()==3))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(3);
+ val[2] += s * src.el(6);
+
+ val[3] += s * src.el(1);
+ val[4] += s * src.el(4);
+ val[5] += s * src.el(7);
+
+ val[6] += s * src.el(2);
+ val[7] += s * src.el(5);
+ val[8] += s * src.el(8);
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(4);
+ val[2] += s * src.el(8);
+ val[3] += s * src.el(12);
+
+ val[4] += s * src.el(1);
+ val[5] += s * src.el(5);
+ val[6] += s * src.el(9);
+ val[7] += s * src.el(13);
+
+ val[8] += s * src.el(2);
+ val[9] += s * src.el(6);
+ val[10] += s * src.el(10);
+ val[11] += s * src.el(14);
+
+ val[12] += s * src.el(3);
+ val[13] += s * src.el(7);
+ val[14] += s * src.el(11);
+ val[15] += s * src.el(15);
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(8);
+ val[2] += s * src.el(16);
+ val[3] += s * src.el(24);
+ val[4] += s * src.el(32);
+ val[5] += s * src.el(40);
+ val[6] += s * src.el(48);
+ val[7] += s * src.el(56);
+
+ val[8] += s * src.el(1);
+ val[9] += s * src.el(9);
+ val[10] += s * src.el(17);
+ val[11] += s * src.el(25);
+ val[12] += s * src.el(33);
+ val[13] += s * src.el(41);
+ val[14] += s * src.el(49);
+ val[15] += s * src.el(57);
+
+ val[16] += s * src.el(2);
+ val[17] += s * src.el(10);
+ val[18] += s * src.el(18);
+ val[19] += s * src.el(26);
+ val[20] += s * src.el(34);
+ val[21] += s * src.el(42);
+ val[22] += s * src.el(50);
+ val[23] += s * src.el(58);
+
+ val[24] += s * src.el(3);
+ val[25] += s * src.el(11);
+ val[26] += s * src.el(19);
+ val[27] += s * src.el(27);
+ val[28] += s * src.el(35);
+ val[29] += s * src.el(43);
+ val[30] += s * src.el(51);
+ val[31] += s * src.el(59);
+
+ val[32] += s * src.el(4);
+ val[33] += s * src.el(12);
+ val[34] += s * src.el(20);
+ val[35] += s * src.el(28);
+ val[36] += s * src.el(36);
+ val[37] += s * src.el(44);
+ val[38] += s * src.el(52);
+ val[39] += s * src.el(60);
+
+ val[40] += s * src.el(5);
+ val[41] += s * src.el(13);
+ val[42] += s * src.el(21);
+ val[43] += s * src.el(29);
+ val[44] += s * src.el(37);
+ val[45] += s * src.el(45);
+ val[46] += s * src.el(53);
+ val[47] += s * src.el(61);
+
+ val[48] += s * src.el(6);
+ val[49] += s * src.el(14);
+ val[50] += s * src.el(22);
+ val[51] += s * src.el(30);
+ val[52] += s * src.el(38);
+ val[53] += s * src.el(46);
+ val[54] += s * src.el(54);
+ val[55] += s * src.el(62);
+
+ val[56] += s * src.el(7);
+ val[57] += s * src.el(15);
+ val[58] += s * src.el(23);
+ val[59] += s * src.el(31);
+ val[60] += s * src.el(39);
+ val[61] += s * src.el(47);
+ val[62] += s * src.el(55);
+ val[63] += s * src.el(63);
+ }
+ else
+ Assert (false, ExcNotImplemented(n()));
+}
+
+
+template <typename number>
+bool
+FullMatrix<number>::operator == (const FullMatrix<number> &m) const
+{
+ bool q = (dim_range==m.dim_range) && (dim_image==m.dim_image);
+ if (!q) return false;
+
+ for (unsigned int i=0; i<dim_image; ++i)
+ for (unsigned int j=0; j<dim_range; ++j)
+ if (el(i,j) != m.el(i,j)) return false;
+ return true;
+};
+
+
+template <typename number>
+double
+FullMatrix<number>::determinant () const
+{
+ Assert (dim_range == dim_image,
+ ExcDimensionMismatch(dim_range, dim_image));
+ Assert ((dim_range>=1) && (dim_range<=3), ExcNotImplemented(dim_range));
+
+ switch (dim_range)
+ {
+ case 1:
+ return el(0,0);
+ case 2:
+ return el(0,0)*el(1,1) - el(1,0)*el(0,1);
+ case 3:
+ return (el(0,0)*el(1,1)*el(2,2)
+ -el(0,0)*el(1,2)*el(2,1)
+ -el(1,0)*el(0,1)*el(2,2)
+ +el(1,0)*el(0,2)*el(2,1)
+ +el(2,0)*el(0,1)*el(1,2)
+ -el(2,0)*el(0,2)*el(1,1));
+ default:
+ return 0;
+ };
+};
+
+template <typename number>
+double
+FullMatrix<number>::norm2 () const
+{
+ double s = 0.;
+ for (unsigned int i=0;i<dim_image*dim_range;++i)
+ s += val[i]*val[i];
+ return s;
+}
+
+
+template <typename number>
+void FullMatrix<number>::clear ()
+{
+ number *val_ptr = &val[0];
+ const number *end_ptr = &val[n()*m()];
+ while (val_ptr != end_ptr)
+ *val_ptr++ = 0.;
+};
+
+
+
+template <typename number>
+void
+FullMatrix<number>::invert (const FullMatrix<number> &M)
+{
+ Assert (dim_range == dim_image, ExcNotQuadratic());
+ Assert ((dim_range>=1) && (dim_range<=4), ExcNotImplemented(dim_range));
+ Assert (dim_range == M.dim_range,
+ ExcDimensionMismatch(dim_range,M.dim_range));
+ Assert (dim_image == M.dim_image,
+ ExcDimensionMismatch(dim_image,M.dim_image));
+
+ switch (dim_range)
+ {
+ case 1:
+ val[0] = 1.0/M.val[0];
+ return;
+ case 2:
+ // this is Maple output,
+ // thus a bit unstructured
+ {
+ const double t4 = 1.0/(M.el(0,0)*M.el(1,1)-M.el(0,1)*M.el(1,0));
+ el(0,0) = M.el(1,1)*t4;
+ el(0,1) = -M.el(0,1)*t4;
+ el(1,0) = -M.el(1,0)*t4;
+ el(1,1) = M.el(0,0)*t4;
+ return;
+ };
+
+ case 3:
+ {
+ const double t4 = M.el(0,0)*M.el(1,1),
+ t6 = M.el(0,0)*M.el(1,2),
+ t8 = M.el(0,1)*M.el(1,0),
+ t00 = M.el(0,2)*M.el(1,0),
+ t01 = M.el(0,1)*M.el(2,0),
+ t04 = M.el(0,2)*M.el(2,0),
+ t07 = 1.0/(t4*M.el(2,2)-t6*M.el(2,1)-t8*M.el(2,2)+
+ t00*M.el(2,1)+t01*M.el(1,2)-t04*M.el(1,1));
+ el(0,0) = (M.el(1,1)*M.el(2,2)-M.el(1,2)*M.el(2,1))*t07;
+ el(0,1) = -(M.el(0,1)*M.el(2,2)-M.el(0,2)*M.el(2,1))*t07;
+ el(0,2) = -(-M.el(0,1)*M.el(1,2)+M.el(0,2)*M.el(1,1))*t07;
+ el(1,0) = -(M.el(1,0)*M.el(2,2)-M.el(1,2)*M.el(2,0))*t07;
+ el(1,1) = (M.el(0,0)*M.el(2,2)-t04)*t07;
+ el(1,2) = -(t6-t00)*t07;
+ el(2,0) = -(-M.el(1,0)*M.el(2,1)+M.el(1,1)*M.el(2,0))*t07;
+ el(2,1) = -(M.el(0,0)*M.el(2,1)-t01)*t07;
+ el(2,2) = (t4-t8)*t07;
+ return;
+ };
+
+ case 4:
+ {
+ // with (linalg);
+ // a:=matrix(4,4);
+ // evalm(a);
+ // ai:=inverse(a);
+ // readlib(C);
+ // C(ai,optimized,filename=x4);
+
+ const double t14 = M.el(0,0)*M.el(1,1);
+ const double t15 = M.el(2,2)*M.el(3,3);
+ const double t17 = M.el(2,3)*M.el(3,2);
+ const double t19 = M.el(0,0)*M.el(2,1);
+ const double t20 = M.el(1,2)*M.el(3,3);
+ const double t22 = M.el(1,3)*M.el(3,2);
+ const double t24 = M.el(0,0)*M.el(3,1);
+ const double t25 = M.el(1,2)*M.el(2,3);
+ const double t27 = M.el(1,3)*M.el(2,2);
+ const double t29 = M.el(1,0)*M.el(0,1);
+ const double t32 = M.el(1,0)*M.el(2,1);
+ const double t33 = M.el(0,2)*M.el(3,3);
+ const double t35 = M.el(0,3)*M.el(3,2);
+ const double t37 = M.el(1,0)*M.el(3,1);
+ const double t38 = M.el(0,2)*M.el(2,3);
+ const double t40 = M.el(0,3)*M.el(2,2);
+ const double t42 = t14*t15-t14*t17-t19*t20+t19*t22+
+ t24*t25-t24*t27-t29*t15+t29*t17+
+ t32*t33-t32*t35-t37*t38+t37*t40;
+ const double t43 = M.el(2,0)*M.el(0,1);
+ const double t46 = M.el(2,0)*M.el(1,1);
+ const double t49 = M.el(2,0)*M.el(3,1);
+ const double t50 = M.el(0,2)*M.el(1,3);
+ const double t52 = M.el(0,3)*M.el(1,2);
+ const double t54 = M.el(3,0)*M.el(0,1);
+ const double t57 = M.el(3,0)*M.el(1,1);
+ const double t60 = M.el(3,0)*M.el(2,1);
+ const double t63 = t43*t20-t43*t22-t46*t33+t46*t35+
+ t49*t50-t49*t52-t54*t25+t54*t27+
+ t57*t38-t57*t40-t60*t50+t60*t52;
+ const double t65 = 1/(t42+t63);
+ const double t71 = M.el(0,2)*M.el(2,1);
+ const double t73 = M.el(0,3)*M.el(2,1);
+ const double t75 = M.el(0,2)*M.el(3,1);
+ const double t77 = M.el(0,3)*M.el(3,1);
+ const double t81 = M.el(0,1)*M.el(1,2);
+ const double t83 = M.el(0,1)*M.el(1,3);
+ const double t85 = M.el(0,2)*M.el(1,1);
+ const double t87 = M.el(0,3)*M.el(1,1);
+ const double t101 = M.el(1,0)*M.el(2,2);
+ const double t103 = M.el(1,0)*M.el(2,3);
+ const double t105 = M.el(2,0)*M.el(1,2);
+ const double t107 = M.el(2,0)*M.el(1,3);
+ const double t109 = M.el(3,0)*M.el(1,2);
+ const double t111 = M.el(3,0)*M.el(1,3);
+ const double t115 = M.el(0,0)*M.el(2,2);
+ const double t117 = M.el(0,0)*M.el(2,3);
+ const double t119 = M.el(2,0)*M.el(0,2);
+ const double t121 = M.el(2,0)*M.el(0,3);
+ const double t123 = M.el(3,0)*M.el(0,2);
+ const double t125 = M.el(3,0)*M.el(0,3);
+ const double t129 = M.el(0,0)*M.el(1,2);
+ const double t131 = M.el(0,0)*M.el(1,3);
+ const double t133 = M.el(1,0)*M.el(0,2);
+ const double t135 = M.el(1,0)*M.el(0,3);
+ el(0,0) = (M.el(1,1)*M.el(2,2)*M.el(3,3)-M.el(1,1)*M.el(2,3)*M.el(3,2)-
+ M.el(2,1)*M.el(1,2)*M.el(3,3)+M.el(2,1)*M.el(1,3)*M.el(3,2)+
+ M.el(3,1)*M.el(1,2)*M.el(2,3)-M.el(3,1)*M.el(1,3)*M.el(2,2))*t65;
+ el(0,1) = -(M.el(0,1)*M.el(2,2)*M.el(3,3)-M.el(0,1)*M.el(2,3)*M.el(3,2)-
+ t71*M.el(3,3)+t73*M.el(3,2)+t75*M.el(2,3)-t77*M.el(2,2))*t65;
+ el(0,2) = (t81*M.el(3,3)-t83*M.el(3,2)-t85*M.el(3,3)+t87*M.el(3,2)+
+ t75*M.el(1,3)-t77*M.el(1,2))*t65;
+ el(0,3) = -(t81*M.el(2,3)-t83*M.el(2,2)-t85*M.el(2,3)+t87*M.el(2,2)+
+ t71*M.el(1,3)-t73*M.el(1,2))*t65;
+ el(1,0) = -(t101*M.el(3,3)-t103*M.el(3,2)-t105*M.el(3,3)+t107*M.el(3,2)+
+ t109*M.el(2,3)-t111*M.el(2,2))*t65;
+ el(1,1) = (t115*M.el(3,3)-t117*M.el(3,2)-t119*M.el(3,3)+t121*M.el(3,2)+
+ t123*M.el(2,3)-t125*M.el(2,2))*t65;
+ el(1,2) = -(t129*M.el(3,3)-t131*M.el(3,2)-t133*M.el(3,3)+t135*M.el(3,2)+
+ t123*M.el(1,3)-t125*M.el(1,2))*t65;
+ el(1,3) = (t129*M.el(2,3)-t131*M.el(2,2)-t133*M.el(2,3)+t135*M.el(2,2)+
+ t119*M.el(1,3)-t121*M.el(1,2))*t65;
+ el(2,0) = (t32*M.el(3,3)-t103*M.el(3,1)-t46*M.el(3,3)+t107*M.el(3,1)+
+ t57*M.el(2,3)-t111*M.el(2,1))*t65;
+ el(2,1) = -(t19*M.el(3,3)-t117*M.el(3,1)-t43*M.el(3,3)+t121*M.el(3,1)+
+ t54*M.el(2,3)-t125*M.el(2,1))*t65;
+ el(2,2) = (t14*M.el(3,3)-t131*M.el(3,1)-t29*M.el(3,3)+t135*M.el(3,1)+
+ t54*M.el(1,3)-t125*M.el(1,1))*t65;
+ el(2,3) = -(t14*M.el(2,3)-t131*M.el(2,1)-t29*M.el(2,3)+t135*M.el(2,1)+
+ t43*M.el(1,3)-t121*M.el(1,1))*t65;
+ el(3,0) = -(t32*M.el(3,2)-t101*M.el(3,1)-t46*M.el(3,2)+t105*M.el(3,1)+
+ t57*M.el(2,2)-t109*M.el(2,1))*t65;
+ el(3,1) = (t19*M.el(3,2)-t115*M.el(3,1)-t43*M.el(3,2)+t119*M.el(3,1)+
+ t54*M.el(2,2)-t123*M.el(2,1))*t65;
+ el(3,2) = -(t14*M.el(3,2)-t129*M.el(3,1)-t29*M.el(3,2)+t133*M.el(3,1)+
+ t54*M.el(1,2)-t123*M.el(1,1))*t65;
+ el(3,3) = (t14*M.el(2,2)-t129*M.el(2,1)-t29*M.el(2,2)+t133*M.el(2,1)+
+ t43*M.el(1,2)-t119*M.el(1,1))*t65;
+ }
+ };
+};
+
+
+
+template <typename number>
+void
+FullMatrix<number>::print_formatted (ostream &out, const unsigned int precision) const
+{
+ out.precision (precision);
+ out.setf (ios::scientific, ios::floatfield); // set output format
+
+ for (unsigned int i=0; i<m(); ++i)
+ {
+ for (unsigned int j=0; j<n(); ++j)
+ if (el(i,j) != 0)
+ out << setw(precision+7)
+ << el(i,j) << ' ';
+ else
+ out << setw(precision+8) << " ";
+ out << endl;
+ };
+
+ AssertThrow (out, ExcIO());
+
+ out.setf (0, ios::floatfield); // reset output format
+};
+
+
+// Gauss-Jordan-Algorithmus
+// cf. Stoer I (4th Edition) p. 153
+
+template <typename number>
+void
+FullMatrix<number>::gauss_jordan()
+{
+ Assert (dim_range == dim_image, ExcNotQuadratic());
+ iVector p(n());
+
+ unsigned int i,j,k,r;
+ double max, hr;
+
+ for (i=0; i<n(); ++i) p(i) = i;
+
+ for (j=0; j<n(); ++j)
+ {
+ // pivotsearch
+ max = fabs(el(j,j));
+ r = j;
+ for (i=j+1; i<n(); ++i)
+ {
+ if (fabs(el(i,j)) > max)
+ {
+ max = fabs(el(i,j));
+ r = i;
+ }
+ }
+ Assert(max>1.e-16, ExcNotRegular());
+ // rowinterchange
+ if (r>j)
+ {
+ for (k=0; k<n(); ++k)
+ {
+ hr = el(j,k) ; el(j,k) = el(r,k) ; el(r,k) = hr;
+ }
+ i = p(j) ; p(j) = p(r) ; p(r) = i;
+ }
+
+ // transformation
+ hr = 1./el(j,j);
+ el(j,j) = hr;
+ for (k=0; k<n(); ++k)
+ {
+ if (k==j) continue;
+ for (i=0; i<n(); ++i)
+ {
+ if (i==j) continue;
+ el(i,k) -= el(i,j)*el(j,k)*hr;
+ }
+ }
+ for (i=0; i<n(); ++i)
+ {
+ el(i,j) *= hr;
+ el(j,i) *= -hr;
+ }
+ el(j,j) = hr;
+ }
+ // columninterchange
+ Vector<number> hv(n());
+ for (i=0; i<n(); ++i)
+ {
+ for (k=0; k<n(); ++k) hv(p(k)) = el(i,k);
+ for (k=0; k<n(); ++k) el(i,k) = hv(k);
+ }
+}
+
+// QR-transformation cf. Stoer 1 4.8.2 (p. 191)
+
+template <typename number>
+template <typename number2>
+void
+FullMatrix<number>::householder(Vector<number2>& src)
+{
+ // m > n, src.n() = m
+ Assert (dim_range <= dim_image, ExcDimensionMismatch(dim_range, dim_image));
+ Assert (src.size() == dim_range, ExcDimensionMismatch(src.size(), dim_range));
+
+ for (unsigned int j=0 ; j<n() ; ++j)
+ {
+ double sigma = 0;
+ unsigned int i;
+ for (i=j ; i<m() ; ++i) sigma += el(i,j)*el(i,j);
+ if (fabs(sigma) < 1.e-15) return;
+ double s = el(j,j);
+ s = (s<0) ? sqrt(sigma) : -sqrt(sigma);
+ double dj = s;
+
+ double beta = 1./(s*el(j,j)-sigma);
+ el(j,j) -= s;
+
+ for (unsigned int k=j+1 ; k<n() ; ++k)
+ {
+ double sum = 0.;
+ for (i=j ; i<m() ; ++i) sum += el(i,j)*el(i,k);
+ sum *= beta;
+
+ for (i=j ; i<m() ; ++i) el(i,k) += sum*el(i,j);
+ }
+
+ double sum = 0.;
+ for (i=j ; i<m() ; ++i) sum += el(i,j)*src(i);
+ sum *= beta;
+
+ for (i=j ; i<m() ; ++i) src(i) += sum*el(i,j);
+ el(j,j) = dj;
+ }
+}
+
+template <typename number>
+template <typename number2>
+double
+FullMatrix<number>::least_squares(Vector<number2>& dst, Vector<number2>& src)
+{
+ // m > n, m = src.n, n = dst.n
+
+ householder(src);
+ backward(dst, src);
+
+ double sum = 0.;
+ for (unsigned int i=n() ; i<m() ; ++i) sum += src(i) * src(i);
+ return sqrt(sum);
+}
--- /dev/null
+/*---------------------------- fmatrix.h ---------------------------*/
+/* $Id$ */
+#ifndef __lac_fullmatrix_H
+#define __lac_fullmatrix_H
+/*---------------------------- fmatrix.h ---------------------------*/
+
+// This file is part of the DEAL Library
+// DEAL is Copyright(1995) by
+// Roland Becker, Guido Kanschat, Franz-Theo Suttmeier
+// Revised by Wolfgang Bangerth
+
+
+#include <base/exceptions.h>
+
+
+// forward declarations
+class iVector;
+
+
+
+/**
+ * Rectangular/quadratic full matrix.
+ *
+ * Memory for Components is supplied explicitly <p>
+ * ( ! Amount of memory needs not to comply with actual dimension due to reinitializations ! ) <p>
+ * - all necessary methods for matrices are supplied <p>
+ * - operators available are '=' and '( )' <p>
+ * CONVENTIONS for used 'equations' : <p>
+ * - THIS matrix is always named 'A' <p>
+ * - matrices are always uppercase , vectors and scalars are lowercase <p>
+ * - Transp(A) used for transpose of matrix A
+ *
+ */
+template<typename number>
+class FullMatrix
+{
+ private:
+ /**
+ * Component-array.
+ */
+ number* val;
+ /**
+ * Dimension. Actual number of Columns
+ */
+ unsigned int dim_range;
+ /**
+ * Dimension. Actual number of Rows
+ */
+ unsigned int dim_image;
+ /**
+ * Dimension. Determines amount of reserved memory
+ */
+ unsigned int val_size;
+
+ /**
+ * Initialization . initialize memory for Matrix <p>
+ * ( m rows , n columns )
+ */
+ void init (const unsigned int m, const unsigned int n);
+
+ /**
+ * Return a read-write reference to the
+ * element #(i,j)#.
+ *
+ * This function does no bounds checking.
+ */
+ number& el (const unsigned int i, const unsigned int j);
+
+ /**
+ * Return the value of the element #(i,j)#.
+ *
+ * This function does no bounds checking.
+ */
+ number el (const unsigned int i, const unsigned int j) const;
+
+
+ public:
+ /**
+ * Constructor. Initialize the matrix as
+ * a square matrix with dimension #n#.
+ */
+ explicit FMatrix (const unsigned int n = 1);
+
+ /**
+ * Constructor. Initialize the matrix as
+ * a rectangular #m# times #n# matrix.
+ */
+ FMatrix (const unsigned int m, const unsigned int n);
+
+ /**
+ * Copy constructor. Be very careful with
+ * this constructor, since it may take a
+ * huge amount of computing time for large
+ * matrices!!
+ */
+ explicit FMatrix (const FMatrix&);
+
+ /**
+ * Destructor. Release all memory.
+ */
+ ~FMatrix();
+
+ /**
+ * Comparison operator. Be careful with
+ * this thing, it may eat up huge amounts
+ * of computing time! It is most commonly
+ * used for internal consistency checks
+ * of programs.
+ */
+ bool operator == (const FMatrix<number> &) const;
+
+ /**
+ * A = B . Copy all elements
+ */
+ template<typename number2>
+ FMatrix& operator = (const<number2> FMatrix& B);
+
+
+ /**
+ * U(0-m,0-n) = s . Fill all elements
+ */
+ template<typename number2>
+ void fill (const FMatrix<number2>& src,
+ const unsigned int i=0, const unsigned int j=0);
+
+ /**
+ * Change Dimension.
+ * Set dimension to (m,n) <p>
+ * ( reinit rectangular matrix )
+ */
+ void reinit (const unsigned int m, const unsigned int n);
+
+ /**
+ * Change Dimension.
+ * Set dimension to (n,n) <p>
+ * ( reinit quadratic matrix )
+ */
+ void reinit (const unsigned int n);
+
+ /**
+ * Adjust Dimension.
+ * Set dimension to ( m(B),n(B) ) <p>
+ * ( adjust to dimensions of another matrix B )
+ */
+ void reinit (const FMatrix<number2> &B);
+
+ /**
+ * Return number of rows of this matrix.
+ * To remember: this matrix is an
+ * $m \times n$-matrix.
+ */
+ unsigned int m () const;
+
+ /**
+ * Return number of columns of this matrix.
+ * To remember: this matrix is an
+ * $m \times n$-matrix.
+ */
+ unsigned int n () const;
+
+ /**
+ * Return whether the matrix contains only
+ * elements with value zero. This function
+ * is mainly for internal consistency
+ * check and should seldomly be used when
+ * not in debug mode since it uses quite
+ * some time.
+ */
+ bool all_zero () const;
+
+ //@}
+
+
+ /**@name 2: Data-Access
+ */
+ //@{
+ /**
+ * Access Elements. returns element at relative 'address' i <p>
+ * ( -> access to A(i/n , i mod n) )
+ */
+ number el (const unsigned int i) const;
+
+ /**
+ * Return the value of the element #(i,j)#.
+ * Does the same as the #el(i,j)# function
+ * but does bounds checking.
+ */
+ number operator() (const unsigned int i, const unsigned int j) const;
+
+ /**
+ * Return a read-write reference to
+ * the element #(i,j)#.
+ * Does the same as the #el(i,j)# function
+ * but does bounds checking.
+ */
+ number& operator() (const unsigned int i, const unsigned int j);
+
+ /**
+ * Set all entries in the matrix to
+ * zero.
+ */
+ void clear ();
+ //@}
+
+
+ /**@name 3: Basic applications on matrices
+ */
+ //@{
+ /**
+ * A+=B . Simple addition
+ */
+ template<typename number2>
+ void add (const number s, const FMatrix<number2>& B);
+
+ /**
+ * A+=Transp(B).
+ * Simple addition of the transpose of B to this
+ */
+ template<typename number2>
+ void Tadd (const number s, const FMatrix<number2>& B);
+
+ /**
+ * C=A*B.
+ * Matrix-matrix-multiplication
+ */
+
+ template<typename number2>
+ void mmult (FMatrix<number2>& C, const FMatrix<number2>& B) const;
+
+ /**
+ * C=Transp(A)*B.
+ * Matrix-matrix-multiplication using
+ * transpose of this
+ */
+ template<typename number2>
+ void Tmmult (FMatrix<number2>& C, const FMatrix<number2>& B) const;
+
+ /**
+ * w (+)= A*v.
+ * Matrix-vector-multiplication ; <p>
+ * ( application of this to a vector v )
+ * flag adding=true : w+=A*v
+ */
+ template<typename number2>
+ void vmult (Vector<number2>& w, const Vector<number2>& v, const bool adding=false) const;
+
+ /**
+ * w (+)= Transp(A)*v.
+ * Matrix-vector-multiplication ; <p>
+ * (application of transpose of this to a vector v)
+ * flag adding=true : w+=A*v
+ */
+ template<typename number2>
+ void Tvmult (Vector<number2>& w, const Vector<number2>& v, const bool adding=false) const;
+
+ /**
+ * Return the norm of the vector #v# with
+ * respect to the norm induced by this
+ * matrix, i.e. $\left<v,Mv\right>$. This
+ * is useful, e.g. in the finite element
+ * context, where the $L_2$ norm of a
+ * function equals the matrix norm with
+ * respect to the mass matrix of the vector
+ * representing the nodal values of the
+ * finite element function.
+ *
+ * Note the order in which the matrix
+ * appears. For non-symmetric matrices
+ * there is a difference whether the
+ * matrix operates on the first
+ * or on the second operand of the
+ * scalar product.
+ *
+ * Obviously, the matrix needs to be square
+ * for this operation.
+ */
+ template<typename number2>
+ double matrix_norm (const Vector<number2> &v) const;
+
+ /**
+ * Build the matrix scalar product
+ * #u^T M v#. This function is mostly
+ * useful when building the cellwise
+ * scalar product of two functions in
+ * the finite element context.
+ */
+ template<typename number2>
+ double matrix_scalar_product (const Vector<number2> &u, const Vector<number2> &v) const;
+
+ /**
+ * A=Inverse(A). Inversion of this by
+ * Gauss-Jordan-algorithm
+ */
+ void gauss_jordan ();
+
+ /**
+ * Computes the determinant of a matrix.
+ * This is only implemented for one two and
+ * three dimensions, since for higher
+ * dimensions the numerical work explodes.
+ * Obviously, the matrix needs to be square
+ * for this function.
+ */
+ double determinant () const;
+
+ /**
+ * Compute the quadratic matrix norm.
+ * Return value is the root of the square
+ * sum of all matrix entries.
+ */
+ double norm2 () const;
+ /**
+ * Assign the inverse of the given
+ * matrix to #*this#. This function is
+ * only implemented (hardcoded) for
+ * square matrices of dimension one,
+ * two and three.
+ */
+ void invert (const FMatrix<number> &M);
+ //@}
+
+
+ /**@name 4: Basic applications on Rows or Columns
+ */
+ //@{
+ /**
+ * A(i,1-n)+=s*A(j,1-n).
+ * Simple addition of rows of this
+ */
+ void add_row (const unsigned int i, const number s, const unsigned int j);
+
+ /**
+ * A(i,1-n)+=s*A(j,1-n)+t*A(k,1-n).
+ * Multiple addition of rows of this
+ */
+ void add_row (const unsigned int i,
+ const number s, const unsigned int j,
+ const number t, const unsigned int k);
+
+ /**
+ * A(1-n,i)+=s*A(1-n,j).
+ * Simple addition of columns of this
+ */
+ void add_col (const unsigned int i, const number s, const unsigned int j);
+
+ /**
+ * A(1-n,i)+=s*A(1-n,j)+t*A(1-n,k).
+ * Multiple addition of columns of this
+ */
+ void add_col (const unsigned int i,
+ const number s, const unsigned int j,
+ const number t, const unsigned int k);
+
+ /**
+ * Swap A(i,1-n) <-> A(j,1-n).
+ * Swap rows i and j of this
+ */
+ void swap_row (const unsigned int i, const unsigned int j);
+
+ /**
+ * Swap A(1-n,i) <-> A(1-n,j).
+ * Swap columns i and j of this
+ */
+ void swap_col (const unsigned int i, const unsigned int j);
+ //@}
+
+
+ /**@name 5: Mixed stuff. Including more
+ * applications on matrices
+ */
+ //@{
+ /**
+ * w=b-A*v.
+ * Residual calculation , returns |w|
+ */
+ template<typename number2, typename number3>
+ double residual (Vector<number2>& w, const Vector<number2>& v, const Vector<number3>& b) const;
+
+ /**
+ * Inversion of lower triangle .
+ */
+ template<typename number2>
+ void forward (Vector<number2>& dst, const Vector<number2>& src) const;
+
+ /**
+ * Inversion of upper triangle .
+ */
+ template<typename number2>
+ void backward (Vector<number2>& dst, const Vector<number2>& src) const;
+
+ /**
+ * QR - factorization of a matrix.
+ * The orthogonal transformation Q is
+ * applied to the vector y and this matrix. <p>
+ * After execution of householder, the upper
+ * triangle contains the resulting matrix R, <p>
+ * the lower the incomplete factorization matrices.
+ */
+ template<typename number2>
+ void householder (Vector<number2>& y);
+
+ /**
+ * Least - Squares - Approximation by QR-factorization.
+ */
+ template<typename number2>
+ number least_squares (Vector<number2>& dst, Vector<number2>& src);
+
+ /**
+ * A(i,i)+=B(i,1-n). Addition of complete
+ * rows of B to diagonal-elements of this ; <p>
+ * ( i = 1 ... m )
+ */
+ template<typename number2>
+ void add_diag (const number s, const FMatrix& B);
+
+ /**
+ * A(i,i)+=s i=1-m.
+ * Add constant to diagonal elements of this
+ */
+ void diagadd (const number s);
+
+ /**
+ * w+=part(A)*v. Conditional partial
+ * Matrix-vector-multiplication <p>
+ * (used elements of v determined by x)
+ */
+ template<typename number2>
+ void gsmult (Vector<number2>& w, const Vector<number2>& v, const iVector& x) const;
+
+
+ /**
+ * Output of the matrix in user-defined format.
+ */
+ void print (ostream& s, int width=5, int precision=2) const;
+
+ /**
+ * Print the matrix in the usual format,
+ * i.e. as a matrix and not as a list of
+ * nonzero elements. For better
+ * readability, zero elements
+ * are displayed as empty space.
+ *
+ * Each entry is printed in scientific
+ * format, with one pre-comma digit and
+ * the number of digits given by
+ * #precision# after the comma, with one
+ * space following.
+ * The precision defaults to four, which
+ * suffices for most cases. The precision
+ * and output format are {\it not}
+ * properly reset to the old values
+ * when the function exits.
+ *
+ * You should be aware that this function
+ * may produce {\bf large} amounts of
+ * output if applied to a large matrix!
+ * Be careful with it.
+ */
+ void print_formatted (ostream &out,
+ const unsigned int presicion=3) const;
+ //@}
+
+ /**
+ * Exception
+ */
+ DeclException2 (ExcInvalidIndex,
+ int, int,
+ << "The given index " << arg1
+ << " should be less than " << arg2 << ".");
+ /**
+ * Exception
+ */
+ DeclException2 (ExcDimensionMismatch,
+ int, int,
+ << "The two dimensions " << arg1 << " and " << arg2
+ << " do not match here.");
+ /**
+ * Exception
+ */
+ DeclException0 (ExcNotQuadratic);
+ /**
+ * Exception
+ */
+ DeclException0 (ExcInternalError);
+ /**
+ * Exception
+ */
+ DeclException3 (ExcInvalidDestination,
+ int, int, int,
+ << "Target region not in matrix: size in this direction="
+ << arg1 << ", size of new matrix=" << arg2
+ << ", offset=" << arg3);
+ /**
+ * Exception
+ */
+ DeclException1 (ExcNotImplemented,
+ int,
+ << "This function is not implemented for the given"
+ << " matrix dimension " << arg1);
+ /**
+ * Exception
+ */
+ DeclException0 (ExcIO);
+};
+
+
+
+
+
+/*-------------------------Inline functions -------------------------------*/
+
+template <typename number>
+inline number &
+FMatrix::el (const unsigned int i, const unsigned int j)
+{
+ return val[i*dim_range+j];
+};
+
+
+template <typename number>
+inline number
+FMatrix::el (const unsigned int i, const unsigned int j) const
+{
+ return val[i*dim_range+j];
+};
+
+
+template <typename number>
+inline unsigned int
+FMatrix::m() const
+{
+ return dim_image;
+};
+
+
+template <typename number>
+inline unsigned int
+FMatrix::n() const
+{
+ return dim_range;
+};
+
+
+template <typename number>
+inline number
+FMatrix::el (const unsigned int i) const
+{
+ return val[i];
+};
+
+
+template <typename number>
+inline number
+FMatrix::operator() (const unsigned int i, const unsigned int j) const
+{
+ Assert (i<dim_image, ExcInvalidIndex (i, dim_image));
+ Assert (j<dim_range, ExcInvalidIndex (i, dim_range));
+ return el(i,j);
+};
+
+
+template <typename number>
+inline number &
+FMatrix::operator() (const unsigned int i, const unsigned int j)
+{
+ Assert (i<dim_image, ExcInvalidIndex (i, dim_image));
+ Assert (j<dim_range, ExcInvalidIndex (j, dim_range));
+ return el(i,j);
+}
+
+
+
+
+/*---------------------------- fmatrix.h ---------------------------*/
+/* end of #ifndef __fmatrix_H */
+#endif
+/*---------------------------- fmatrix.h ---------------------------*/
--- /dev/null
+// $Id$
+
+#include <lac/dvector.h>
+#include <lac/ivector.h>
+#include <lac/fullmatrix.h>
+
+#include <cmath>
+#include <cstdlib>
+#include <cstdio>
+#include <iomanip>
+
+
+template <typename number>
+dFMatrix::dFMatrix (const unsigned int n) {
+ init (n,n);
+};
+
+
+template <typename number>
+dFMatrix::dFMatrix (const unsigned int m, const unsigned int n) {
+ init (m,n);
+};
+
+
+template <typename number>
+dFMatrix::dFMatrix (const dFMatrix &m)
+{
+ init (m.dim_image, m.dim_range);
+ double * p = &val[0];
+ const double * vp = &m.val[0];
+ const double * const e = &val[dim_image*dim_range];
+
+ while (p!=e)
+ *p++ = *vp++;
+};
+
+
+template <typename number>
+void dFMatrix::init (const unsigned int mm, const unsigned int nn)
+{
+ val_size = nn*mm;
+ val = new double[val_size];
+ dim_range = nn;
+ dim_image = mm;
+ clear ();
+};
+
+
+template <typename number>
+dFMatrix::~dFMatrix () {
+ delete[] val;
+};
+
+
+template <typename number>
+bool dFMatrix::all_zero () const {
+ const double *p = &val[0],
+ *e = &val[n()*m()];
+ while (p!=e)
+ if (*p++ != 0.0)
+ return false;
+
+ return true;
+};
+
+
+template <typename number>
+void dFMatrix::reinit (const unsigned int mm, const unsigned int nn)
+{
+ if (val_size<nn*mm)
+ {
+ delete[] val;
+ init(mm, nn);
+ }
+ else
+ {
+ dim_range = nn;
+ dim_image = mm;
+// memset(val, 0, sizeof(double)*nn*mm);
+ clear ();
+ }
+}
+
+
+template <typename number>
+void dFMatrix::reinit (const unsigned int n) {
+ reinit (n, n);
+};
+
+
+template <typename number>
+void dFMatrix::reinit (const dFMatrix &B) {
+ reinit (B.m(), B.n());
+};
+
+
+template <typename number>
+void dFMatrix::vmult (dVector& dst, const dVector& src,
+ const bool adding) const
+{
+ Assert(dst.size() == m(), ExcDimensionMismatch(dst.size(), m()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+
+ double s;
+ if ((n()==3) && (m()==3))
+ {
+ double s0,s1,s2;
+ s = src(0);
+ s0 = s*val[0]; s1 = s*val[3]; s2 = s*val[6];
+ s = src(1);
+ s0 += s*val[1]; s1 += s*val[4]; s2 += s*val[7];
+ s = src(2);
+ s0 += s*val[2]; s1 += s*val[5]; s2 += s*val[8];
+
+ if (!adding)
+ {
+ dst(0) = s0;
+ dst(1) = s1;
+ dst(2) = s2;
+ }
+ else
+ {
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ }
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ double s0,s1,s2,s3;
+ s = src(0);
+ s0 = s*val[0]; s1 = s*val[4]; s2 = s*val[8]; s3 = s*val[12];
+ s = src(1);
+ s0 += s*val[1]; s1 += s*val[5]; s2 += s*val[9]; s3 += s*val[13];
+ s = src(2);
+ s0 += s*val[2]; s1 += s*val[6]; s2 += s*val[10]; s3 += s*val[14];
+ s = src(3);
+ s0 += s*val[3]; s1 += s*val[7]; s2 += s*val[11]; s3 += s*val[15];
+
+ if (!adding)
+ {
+ dst(0) = s0;
+ dst(1) = s1;
+ dst(2) = s2;
+ dst(3) = s3;
+ }
+ else
+ {
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ dst(3) += s3;
+ }
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ double s0,s1,s2,s3,s4,s5,s6,s7;
+ s = src(0);
+ s0 = s*val[0]; s1 = s*val[8]; s2 = s*val[16]; s3 = s*val[24];
+ s4 = s*val[32]; s5 = s*val[40]; s6 = s*val[48]; s7 = s*val[56];
+ s = src(1);
+ s0 += s*val[1]; s1 += s*val[9]; s2 += s*val[17]; s3 += s*val[25];
+ s4 += s*val[33]; s5 += s*val[41]; s6 += s*val[49]; s7 += s*val[57];
+ s = src(2);
+ s0 += s*val[2]; s1 += s*val[10]; s2 += s*val[18]; s3 += s*val[26];
+ s4 += s*val[34]; s5 += s*val[42]; s6 += s*val[50]; s7 += s*val[58];
+ s = src(3);
+ s0 += s*val[3]; s1 += s*val[11]; s2 += s*val[19]; s3 += s*val[27];
+ s4 += s*val[35]; s5 += s*val[43]; s6 += s*val[51]; s7 += s*val[59];
+ s = src(4);
+ s0 += s*val[4]; s1 += s*val[12]; s2 += s*val[20]; s3 += s*val[28];
+ s4 += s*val[36]; s5 += s*val[44]; s6 += s*val[52]; s7 += s*val[60];
+ s = src(5);
+ s0 += s*val[5]; s1 += s*val[13]; s2 += s*val[21]; s3 += s*val[29];
+ s4 += s*val[37]; s5 += s*val[45]; s6 += s*val[53]; s7 += s*val[61];
+ s = src(6);
+ s0 += s*val[6]; s1 += s*val[14]; s2 += s*val[22]; s3 += s*val[30];
+ s4 += s*val[38]; s5 += s*val[46]; s6 += s*val[54]; s7 += s*val[62];
+ s = src(7);
+ s0 += s*val[7]; s1 += s*val[15]; s2 += s*val[23]; s3 += s*val[31];
+ s4 += s*val[39]; s5 += s*val[47]; s6 += s*val[55]; s7 += s*val[63];
+
+ if (!adding)
+ {
+ dst(0) = s0;
+ dst(1) = s1;
+ dst(2) = s2;
+ dst(3) = s3;
+ dst(4) = s4;
+ dst(5) = s5;
+ dst(6) = s6;
+ dst(7) = s7;
+ }
+ else
+ {
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ dst(3) += s3;
+ dst(4) += s4;
+ dst(5) += s5;
+ dst(6) += s6;
+ dst(7) += s7;
+ }
+ }
+ else
+ {
+ double* e = val;
+ const unsigned int size_m = m(),
+ size_n = n();
+ for (unsigned int i=0; i<size_m; ++i)
+ {
+ s = 0.;
+ for (unsigned int j=0; j<size_n; ++j)
+ s += src(j) * *(e++);
+ if (!adding) dst(i) = s;
+ else dst(i) += s;
+ }
+ }
+}
+
+
+template <typename number>
+void dFMatrix::gsmult (dVector& dst, const dVector& src, const iVector& gl) const
+{
+ Assert(n() == m(), ExcNotQuadratic());
+ Assert(dst.size() == n(), ExcDimensionMismatch(dst.size(), n()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+ Assert(gl.n() == n(), ExcDimensionMismatch(gl.n(), n()));
+
+ double s;
+ if ((n()==3) && (m()==3))
+ {
+ double s0=0.,s1=0.,s2=0.;
+ s = src(0);
+ if(gl(1)<gl(0)) s1 = s*val[3]; if(gl(2)<gl(0)) s2 = s*val[6];
+ s = src(1);
+ if(gl(0)<gl(1)) s0 += s*val[1]; if(gl(2)<gl(1)) s2 += s*val[7];
+ s = src(2);
+ if(gl(0)<gl(2)) s0 += s*val[2]; if(gl(1)<gl(2)) s1 += s*val[5];
+
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ double s0=0.,s1=0.,s2=0.,s3=0.;
+ s = src(0);
+ if(gl(1)<gl(0)) s1 = s*val[4]; if(gl(2)<gl(0)) s2 = s*val[8]; if(gl(3)<gl(0)) s3 = s*val[12];
+ s = src(1);
+ if(gl(0)<gl(1)) s0 += s*val[1]; if(gl(2)<gl(1)) s2 += s*val[9]; if(gl(3)<gl(1)) s3 += s*val[13];
+ s = src(2);
+ if(gl(0)<gl(2)) s0 += s*val[2]; if(gl(1)<gl(2)) s1 += s*val[6]; if(gl(3)<gl(2)) s3 += s*val[14];
+ s = src(3);
+ if(gl(0)<gl(3)) s0 += s*val[3]; if(gl(1)<gl(3)) s1 += s*val[7]; if(gl(2)<gl(3)) s2 += s*val[11];
+
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ dst(3) += s3;
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ double s0=0.,s1=0.,s2=0.,s3=0.,s4=0.,s5=0.,s6=0.,s7=0.;
+ s = src(0);
+ if(gl(1)<gl(0)) s1 = s*val[8];
+ if(gl(2)<gl(0)) s2 = s*val[16];
+ if(gl(3)<gl(0)) s3 = s*val[24];
+ if(gl(4)<gl(0)) s4 = s*val[32];
+ if(gl(5)<gl(0)) s5 = s*val[40];
+ if(gl(6)<gl(0)) s6 = s*val[48];
+ if(gl(7)<gl(0)) s7 = s*val[56];
+ s = src(1);
+ if(gl(0)<gl(1)) s0 += s*val[1];
+ if(gl(2)<gl(1)) s2 += s*val[17];
+ if(gl(3)<gl(1)) s3 += s*val[25];
+ if(gl(4)<gl(1)) s4 += s*val[33];
+ if(gl(5)<gl(1)) s5 += s*val[41];
+ if(gl(6)<gl(1)) s6 += s*val[49];
+ if(gl(7)<gl(1)) s7 += s*val[57];
+ s = src(2);
+ if(gl(0)<gl(2)) s0 += s*val[2];
+ if(gl(1)<gl(2)) s1 += s*val[10];
+ if(gl(3)<gl(2)) s3 += s*val[26];
+ if(gl(4)<gl(2)) s4 += s*val[34];
+ if(gl(5)<gl(2)) s5 += s*val[42];
+ if(gl(6)<gl(2)) s6 += s*val[50];
+ if(gl(7)<gl(2)) s7 += s*val[58];
+ s = src(3);
+ if(gl(0)<gl(3)) s0 += s*val[3];
+ if(gl(1)<gl(3)) s1 += s*val[11];
+ if(gl(2)<gl(3)) s2 += s*val[19];
+ if(gl(4)<gl(3)) s4 += s*val[35];
+ if(gl(5)<gl(3)) s5 += s*val[43];
+ if(gl(6)<gl(3)) s6 += s*val[51];
+ if(gl(7)<gl(3)) s7 += s*val[59];
+ s = src(4);
+ if(gl(0)<gl(4)) s0 += s*val[4];
+ if(gl(1)<gl(4)) s1 += s*val[12];
+ if(gl(2)<gl(4)) s2 += s*val[20];
+ if(gl(3)<gl(4)) s3 += s*val[28];
+ if(gl(5)<gl(4)) s5 += s*val[44];
+ if(gl(6)<gl(4)) s6 += s*val[52];
+ if(gl(7)<gl(4)) s7 += s*val[60];
+ s = src(5);
+ if(gl(0)<gl(5)) s0 += s*val[5];
+ if(gl(1)<gl(5)) s1 += s*val[13];
+ if(gl(2)<gl(5)) s2 += s*val[21];
+ if(gl(3)<gl(5)) s3 += s*val[29];
+ if(gl(4)<gl(5)) s4 += s*val[37];
+ if(gl(6)<gl(5)) s6 += s*val[53];
+ if(gl(7)<gl(5)) s7 += s*val[61];
+ s = src(6);
+ if(gl(0)<gl(6)) s0 += s*val[6];
+ if(gl(1)<gl(6)) s1 += s*val[14];
+ if(gl(2)<gl(6)) s2 += s*val[22];
+ if(gl(3)<gl(6)) s3 += s*val[30];
+ if(gl(4)<gl(6)) s4 += s*val[38];
+ if(gl(5)<gl(6)) s5 += s*val[46];
+ if(gl(7)<gl(6)) s7 += s*val[62];
+ s = src(7);
+ if(gl(0)<gl(7)) s0 += s*val[7];
+ if(gl(1)<gl(7)) s1 += s*val[15];
+ if(gl(2)<gl(7)) s2 += s*val[23];
+ if(gl(3)<gl(7)) s3 += s*val[31];
+ if(gl(4)<gl(7)) s4 += s*val[39];
+ if(gl(5)<gl(7)) s5 += s*val[47];
+ if(gl(6)<gl(7)) s6 += s*val[55];
+
+ dst(0) += s0;
+ dst(1) += s1;
+ dst(2) += s2;
+ dst(3) += s3;
+ dst(4) += s4;
+ dst(5) += s5;
+ dst(6) += s6;
+ dst(7) += s7;
+ }
+ else
+ {
+ double* e = val;
+ const unsigned int size_m = m(),
+ size_n = n();
+ for (unsigned int i=0; i<size_m; ++i)
+ {
+ s = 0.;
+ for (unsigned int j=0; j<size_n; ++j)
+ if(gl(i)<gl(j)) s += src(j) * *(e++);
+ dst(i) += s;
+ }
+ }
+}
+
+template <typename number>
+void dFMatrix::Tvmult (dVector& dst, const dVector& src, const bool adding) const
+{
+ Assert(dst.size() == n(), ExcDimensionMismatch(dst.size(), n()));
+ Assert(src.size() == m(), ExcDimensionMismatch(src.size(), m()));
+
+ unsigned int i,j;
+ double s;
+ const unsigned int size_m = m(),
+ size_n = n();
+ for (i=0; i<size_m; ++i)
+ {
+ s = 0.;
+ for (j=0; j<size_n; ++j)
+ s += src(j) * el(j,i);
+ if(!adding) dst(i) = s;
+ else dst(i) += s;
+ }
+}
+
+template <typename number>
+double dFMatrix::residual (dVector& dst, const dVector& src,
+ const dVector& right) const
+{
+ Assert(dst.size() == m(), ExcDimensionMismatch(dst.size(), m()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+ Assert(right.size() == m(), ExcDimensionMismatch(right.size(), m()));
+
+ unsigned int i,j;
+ double s, res = 0.;
+ const unsigned int size_m = m(),
+ size_n = n();
+ for (i=0; i<size_n; ++i)
+ {
+ s = right(i);
+ for (j=0; j<size_m; ++j)
+ s -= src(j) * el(i,j);
+ dst(i) = s;
+ res += s*s;
+ }
+ return sqrt(res);
+}
+
+template <typename number>
+void dFMatrix::forward (dVector& dst, const dVector& src) const
+{
+ Assert(n() == m(), ExcNotQuadratic());
+ Assert(dst.size() == n(), ExcDimensionMismatch(dst.size(), n()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+
+ unsigned int i,j;
+ unsigned int nu = (m()<n() ? m() : n());
+ double s;
+ for (i=0; i<nu; ++i)
+ {
+ s = src(i);
+ for (j=0; j<i; ++j) s -= dst(j) * el(i,j);
+ dst(i) = s/el(i,i);
+ }
+}
+
+template <typename number>
+void dFMatrix::backward (dVector& dst, const dVector& src) const
+{
+ Assert(n() == m(), ExcNotQuadratic());
+ Assert(dst.size() == n(), ExcDimensionMismatch(dst.size(), n()));
+ Assert(src.size() == n(), ExcDimensionMismatch(src.size(), n()));
+
+ unsigned int j;
+ unsigned int nu = (m()<n() ? m() : n());
+ double s;
+ for (int i=nu-1; i>=0; --i)
+ {
+ s = src(i);
+ for (j=i+1; j<nu; ++j) s -= dst(j) * el(i,j);
+ dst(i) = s/el(i,i);
+ }
+}
+
+template <typename number>
+dFMatrix&
+dFMatrix::operator = (const dFMatrix& m) {
+ reinit(m);
+
+ double * p = &val[0];
+ const double * vp = &m.val[0];
+ const double * const e = &val[dim_image*dim_range];
+
+ while (p!=e)
+ *p++ = *vp++;
+
+ return *this;
+}
+
+template <typename number>
+void dFMatrix::fill (const dFMatrix& src,
+ const unsigned int i, const unsigned int j)
+{
+ Assert (n() >= src.n() + j, ExcInvalidDestination(n(), src.n(), j));
+ Assert (m() >= src.m() + i, ExcInvalidDestination(m(), src.m(), i));
+
+ for (unsigned int ii=0; ii<src.m() ; ++ii)
+ for (unsigned int jj=0; jj<src.n() ; ++jj)
+ el(ii+i,jj+j) = src.el(ii,jj);
+}
+
+template <typename number>
+void dFMatrix::add_row (const unsigned int i,
+ const double s, const unsigned int j)
+{
+ for (unsigned int k=0; k<m(); ++k)
+ el(i,k) += s*el(j,k);
+}
+
+template <typename number>
+void dFMatrix::add_row (const unsigned int i, const double s,
+ const unsigned int j, const double t,
+ const unsigned int k)
+{
+ const unsigned int size_m = m();
+ for (unsigned l=0; l<size_m; ++l)
+ el(i,l) += s*el(j,l) + t*el(k,l);
+}
+
+template <typename number>
+void dFMatrix::add_col (const unsigned int i, const double s,
+ const unsigned int j)
+{
+ for (unsigned int k=0; k<n(); ++k)
+ el(k,i) += s*el(k,j);
+}
+
+template <typename number>
+void dFMatrix::add_col (const unsigned int i, const double s,
+ const unsigned int j, const double t,
+ const unsigned int k)
+{
+ for (unsigned int l=0; l<n(); ++l)
+ el(l,i) += s*el(l,j) + t*el(l,k);
+}
+
+template <typename number>
+void dFMatrix::swap_row (const unsigned int i, const unsigned int j)
+{
+ double s;
+ for (unsigned int k=0; k<m(); ++k)
+ {
+ s = el(i,k); el(i,k) = el(j,k); el(j,k) = s;
+ }
+}
+
+template <typename number>
+void dFMatrix::swap_col (const unsigned int i, const unsigned int j)
+{
+ double s;
+ for (unsigned int k=0; k<n(); ++k)
+ {
+ s = el(k,i); el(k,i) = el(k,j); el(k,j) = s;
+ }
+}
+
+template <typename number>
+void dFMatrix::diagadd (const double& src)
+{
+ Assert (m() == n(), ExcDimensionMismatch(m(),n()));
+ for (unsigned int i=0; i<n(); ++i)
+ el(i,i) += src;
+}
+
+template <typename number>
+void dFMatrix::mmult (dFMatrix& dst, const dFMatrix& src) const
+{
+ Assert (n() == src.m(), ExcDimensionMismatch(n(), src.m()));
+ unsigned int i,j,k;
+ double s = 1.;
+ dst.reinit(m(), src.n());
+
+ for (i=0;i<m();i++)
+ for (j=0; j<src.n(); ++j)
+ {
+ s = 0.;
+ for (k=0;k<n();k++) s+= el(i,k) * src.el(k,j);
+ dst.el(i,j) = s;
+ }
+}
+
+/*void dFMatrix::mmult (dFMatrix& dst, const dFMatrix& src) const
+{
+ Assert (m() == src.n(), ExcDimensionMismatch(m(), src.n()));
+
+ unsigned int i,j,k;
+ double s = 1.;
+
+ dst.reinit(n(), src.m());
+
+ for (i=0;i<n();i++)
+ for (j=0;j<src.m();j++)
+ {
+ s = 0.;
+ for (k=0;k<m();k++) s+= el(i,k) * src.el(k,j);
+ dst.el(i,j) = s;
+ }
+}*/
+
+template <typename number>
+void dFMatrix::Tmmult (dFMatrix& dst, const dFMatrix& src) const
+{
+ Assert (n() == src.n(), ExcDimensionMismatch(n(), src.n()));
+
+ unsigned int i,j,k;
+ double s = 1.;
+ dst.reinit(m(), src.m());
+
+ for (i=0;i<m();i++)
+ for (j=0;j<src.m();j++)
+ {
+ s = 0.;
+ for (k=0;k<n();k++) s+= el(k,i) * src.el(k,j);
+ dst.el(i,j) = s;
+ }
+}
+
+/*void dFMatrix::Tmmult(dFMatrix& dst, const dFMatrix& src) const
+{
+ Assert (m() == src.n(), ExcDimensionMismatch(m(), src.n()));
+
+ unsigned int i,j,k;
+ double s = 1.;
+
+ dst.reinit(n(), src.m());
+
+ for (i=0;i<n();i++)
+ for (j=0;j<src.m();j++)
+ {
+ s = 0.;
+ for (k=0;k<m();k++) s+= el(k,i) * src.el(k,j);
+ dst.el(i,j) = s;
+ }
+}*/
+
+
+
+template <typename number>
+double dFMatrix::matrix_norm (const dVector &v) const {
+ Assert(m() == v.size(), ExcDimensionMismatch(m(),v.size()));
+ Assert(n() == v.size(), ExcDimensionMismatch(n(),v.size()));
+
+ double sum = 0.;
+ const unsigned int n_rows = m();
+ const double *val_ptr = &val[0];
+ const double *v_ptr;
+
+ for (unsigned int row=0; row<n_rows; ++row)
+ {
+ double s = 0.;
+ const double * const val_end_of_row = val_ptr+n_rows;
+ v_ptr = v.begin();
+ while (val_ptr != val_end_of_row)
+ s += *val_ptr++ * *v_ptr++;
+
+ sum += s* v(row);
+ };
+
+ return sum;
+};
+
+
+
+template <typename number>
+double dFMatrix::matrix_scalar_product (const dVector &u, const dVector &v) const {
+ Assert(m() == u.size(), ExcDimensionMismatch(m(),v.size()));
+ Assert(n() == v.size(), ExcDimensionMismatch(n(),v.size()));
+
+ double sum = 0.;
+ const unsigned int n_rows = m();
+ const unsigned int n_cols = n();
+ const double *val_ptr = &val[0];
+ const double *v_ptr;
+
+ for (unsigned int row=0; row<n_rows; ++row)
+ {
+ double s = 0.;
+ const double * const val_end_of_row = val_ptr+n_cols;
+ v_ptr = v.begin();
+ while (val_ptr != val_end_of_row)
+ s += *val_ptr++ * *v_ptr++;
+
+ sum += s* u(row);
+ };
+
+ return sum;
+};
+
+
+
+template <typename number>
+void dFMatrix::print (ostream& s, int w, int p) const
+{
+ unsigned int i,j;
+ for (i=0;i<m();i++)
+ {
+ for (j=0;j<n();j++) s << setw(w) << setprecision(p) << el(i,j);
+ s << endl;
+ }
+}
+
+template <typename number>
+void dFMatrix::add (const double s,const dFMatrix& src)
+{
+ Assert (m() == src.m(), ExcDimensionMismatch(m(), src.m()));
+ Assert (n() == src.n(), ExcDimensionMismatch(n(), src.n()));
+ if ((n()==3) && (m()==3))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(1);
+ val[2] += s * src.el(2);
+ val[3] += s * src.el(3);
+ val[4] += s * src.el(4);
+ val[5] += s * src.el(5);
+ val[6] += s * src.el(6);
+ val[7] += s * src.el(7);
+ val[8] += s * src.el(8);
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(1);
+ val[2] += s * src.el(2);
+ val[3] += s * src.el(3);
+ val[4] += s * src.el(4);
+ val[5] += s * src.el(5);
+ val[6] += s * src.el(6);
+ val[7] += s * src.el(7);
+ val[8] += s * src.el(8);
+ val[9] += s * src.el(9);
+ val[10] += s * src.el(10);
+ val[11] += s * src.el(11);
+ val[12] += s * src.el(12);
+ val[13] += s * src.el(13);
+ val[14] += s * src.el(14);
+ val[15] += s * src.el(15);
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(1);
+ val[2] += s * src.el(2);
+ val[3] += s * src.el(3);
+ val[4] += s * src.el(4);
+ val[5] += s * src.el(5);
+ val[6] += s * src.el(6);
+ val[7] += s * src.el(7);
+ val[8] += s * src.el(8);
+ val[9] += s * src.el(9);
+ val[10] += s * src.el(10);
+ val[11] += s * src.el(11);
+ val[12] += s * src.el(12);
+ val[13] += s * src.el(13);
+ val[14] += s * src.el(14);
+ val[15] += s * src.el(15);
+ val[16] += s * src.el(16);
+ val[17] += s * src.el(17);
+ val[18] += s * src.el(18);
+ val[19] += s * src.el(19);
+
+ val[20] += s * src.el(20);
+ val[21] += s * src.el(21);
+ val[22] += s * src.el(22);
+ val[23] += s * src.el(23);
+ val[24] += s * src.el(24);
+ val[25] += s * src.el(25);
+ val[26] += s * src.el(26);
+ val[27] += s * src.el(27);
+ val[28] += s * src.el(28);
+ val[29] += s * src.el(29);
+
+ val[30] += s * src.el(30);
+ val[31] += s * src.el(31);
+ val[32] += s * src.el(32);
+ val[33] += s * src.el(33);
+ val[34] += s * src.el(34);
+ val[35] += s * src.el(35);
+ val[36] += s * src.el(36);
+ val[37] += s * src.el(37);
+ val[38] += s * src.el(38);
+ val[39] += s * src.el(39);
+
+ val[40] += s * src.el(40);
+ val[41] += s * src.el(41);
+ val[42] += s * src.el(42);
+ val[43] += s * src.el(43);
+ val[44] += s * src.el(44);
+ val[45] += s * src.el(45);
+ val[46] += s * src.el(46);
+ val[47] += s * src.el(47);
+ val[48] += s * src.el(48);
+ val[49] += s * src.el(49);
+
+ val[50] += s * src.el(50);
+ val[51] += s * src.el(51);
+ val[52] += s * src.el(52);
+ val[53] += s * src.el(53);
+ val[54] += s * src.el(54);
+ val[55] += s * src.el(55);
+ val[56] += s * src.el(56);
+ val[57] += s * src.el(57);
+ val[58] += s * src.el(58);
+ val[59] += s * src.el(59);
+
+ val[60] += s * src.el(60);
+ val[61] += s * src.el(61);
+ val[62] += s * src.el(62);
+ val[63] += s * src.el(63);
+ }
+ else
+ {
+ const unsigned int size = n()*m();
+ for (unsigned int i=0; i<size; i++)
+ val[i] += s * src.el(i);
+ }
+}
+
+
+
+template <typename number>
+void dFMatrix::add_diag (const double s, const dFMatrix& src)
+{
+ Assert (m() == src.m(), ExcDimensionMismatch(m(), src.m()));
+ Assert (n() == src.n(), ExcDimensionMismatch(n(), src.n()));
+
+ if ((n()==3) && (m()==3))
+ {
+ val[0] += s * src.el(0);
+ val[0] += s * src.el(1);
+ val[0] += s * src.el(2);
+ val[3] += s * src.el(3);
+ val[3] += s * src.el(4);
+ val[3] += s * src.el(5);
+ val[6] += s * src.el(6);
+ val[6] += s * src.el(7);
+ val[6] += s * src.el(8);
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ val[0] += s * src.el(0);
+ val[0] += s * src.el(1);
+ val[0] += s * src.el(2);
+ val[0] += s * src.el(3);
+ val[4] += s * src.el(4);
+ val[4] += s * src.el(5);
+ val[4] += s * src.el(6);
+ val[4] += s * src.el(7);
+ val[8] += s * src.el(8);
+ val[8] += s * src.el(9);
+ val[8] += s * src.el(10);
+ val[8] += s * src.el(11);
+ val[12] += s * src.el(12);
+ val[12] += s * src.el(13);
+ val[12] += s * src.el(14);
+ val[12] += s * src.el(15);
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ val[0] += s * src.el(0);
+ val[0] += s * src.el(1);
+ val[0] += s * src.el(2);
+ val[0] += s * src.el(3);
+ val[0] += s * src.el(4);
+ val[0] += s * src.el(5);
+ val[0] += s * src.el(6);
+ val[0] += s * src.el(7);
+ val[8] += s * src.el(8);
+ val[8] += s * src.el(9);
+ val[8] += s * src.el(10);
+ val[8] += s * src.el(11);
+ val[8] += s * src.el(12);
+ val[8] += s * src.el(13);
+ val[8] += s * src.el(14);
+ val[8] += s * src.el(15);
+ val[16] += s * src.el(16);
+ val[16] += s * src.el(17);
+ val[16] += s * src.el(18);
+ val[16] += s * src.el(19);
+
+ val[16] += s * src.el(20);
+ val[16] += s * src.el(21);
+ val[16] += s * src.el(22);
+ val[16] += s * src.el(23);
+ val[24] += s * src.el(24);
+ val[24] += s * src.el(25);
+ val[24] += s * src.el(26);
+ val[24] += s * src.el(27);
+ val[24] += s * src.el(28);
+ val[24] += s * src.el(29);
+
+ val[24] += s * src.el(30);
+ val[24] += s * src.el(31);
+ val[32] += s * src.el(32);
+ val[32] += s * src.el(33);
+ val[32] += s * src.el(34);
+ val[32] += s * src.el(35);
+ val[32] += s * src.el(36);
+ val[32] += s * src.el(37);
+ val[32] += s * src.el(38);
+ val[32] += s * src.el(39);
+
+ val[40] += s * src.el(40);
+ val[40] += s * src.el(41);
+ val[40] += s * src.el(42);
+ val[40] += s * src.el(43);
+ val[40] += s * src.el(44);
+ val[40] += s * src.el(45);
+ val[40] += s * src.el(46);
+ val[40] += s * src.el(47);
+ val[48] += s * src.el(48);
+ val[48] += s * src.el(49);
+
+ val[48] += s * src.el(50);
+ val[48] += s * src.el(51);
+ val[48] += s * src.el(52);
+ val[48] += s * src.el(53);
+ val[48] += s * src.el(54);
+ val[48] += s * src.el(55);
+ val[56] += s * src.el(56);
+ val[56] += s * src.el(57);
+ val[56] += s * src.el(58);
+ val[56] += s * src.el(59);
+
+ val[56] += s * src.el(60);
+ val[56] += s * src.el(61);
+ val[56] += s * src.el(62);
+ val[56] += s * src.el(63);
+ }
+ else
+ {
+ const unsigned int size = n()*m();
+ for (unsigned int i=0; i<size; i++)
+ val[i] += s * src.el(i);
+ }
+}
+
+template <typename number>
+void dFMatrix::Tadd (const double s, const dFMatrix& src)
+{
+ Assert (m() == n(), ExcNotQuadratic());
+ Assert (m() == src.m(), ExcDimensionMismatch(m(), src.m()));
+ Assert (n() == src.n(), ExcDimensionMismatch(n(), src.n()));
+
+ if ((n()==3) && (m()==3))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(3);
+ val[2] += s * src.el(6);
+
+ val[3] += s * src.el(1);
+ val[4] += s * src.el(4);
+ val[5] += s * src.el(7);
+
+ val[6] += s * src.el(2);
+ val[7] += s * src.el(5);
+ val[8] += s * src.el(8);
+ }
+ else if ((n()==4) && (m()==4))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(4);
+ val[2] += s * src.el(8);
+ val[3] += s * src.el(12);
+
+ val[4] += s * src.el(1);
+ val[5] += s * src.el(5);
+ val[6] += s * src.el(9);
+ val[7] += s * src.el(13);
+
+ val[8] += s * src.el(2);
+ val[9] += s * src.el(6);
+ val[10] += s * src.el(10);
+ val[11] += s * src.el(14);
+
+ val[12] += s * src.el(3);
+ val[13] += s * src.el(7);
+ val[14] += s * src.el(11);
+ val[15] += s * src.el(15);
+ }
+ else if ((n()==8) && (m()==8))
+ {
+ val[0] += s * src.el(0);
+ val[1] += s * src.el(8);
+ val[2] += s * src.el(16);
+ val[3] += s * src.el(24);
+ val[4] += s * src.el(32);
+ val[5] += s * src.el(40);
+ val[6] += s * src.el(48);
+ val[7] += s * src.el(56);
+
+ val[8] += s * src.el(1);
+ val[9] += s * src.el(9);
+ val[10] += s * src.el(17);
+ val[11] += s * src.el(25);
+ val[12] += s * src.el(33);
+ val[13] += s * src.el(41);
+ val[14] += s * src.el(49);
+ val[15] += s * src.el(57);
+
+ val[16] += s * src.el(2);
+ val[17] += s * src.el(10);
+ val[18] += s * src.el(18);
+ val[19] += s * src.el(26);
+ val[20] += s * src.el(34);
+ val[21] += s * src.el(42);
+ val[22] += s * src.el(50);
+ val[23] += s * src.el(58);
+
+ val[24] += s * src.el(3);
+ val[25] += s * src.el(11);
+ val[26] += s * src.el(19);
+ val[27] += s * src.el(27);
+ val[28] += s * src.el(35);
+ val[29] += s * src.el(43);
+ val[30] += s * src.el(51);
+ val[31] += s * src.el(59);
+
+ val[32] += s * src.el(4);
+ val[33] += s * src.el(12);
+ val[34] += s * src.el(20);
+ val[35] += s * src.el(28);
+ val[36] += s * src.el(36);
+ val[37] += s * src.el(44);
+ val[38] += s * src.el(52);
+ val[39] += s * src.el(60);
+
+ val[40] += s * src.el(5);
+ val[41] += s * src.el(13);
+ val[42] += s * src.el(21);
+ val[43] += s * src.el(29);
+ val[44] += s * src.el(37);
+ val[45] += s * src.el(45);
+ val[46] += s * src.el(53);
+ val[47] += s * src.el(61);
+
+ val[48] += s * src.el(6);
+ val[49] += s * src.el(14);
+ val[50] += s * src.el(22);
+ val[51] += s * src.el(30);
+ val[52] += s * src.el(38);
+ val[53] += s * src.el(46);
+ val[54] += s * src.el(54);
+ val[55] += s * src.el(62);
+
+ val[56] += s * src.el(7);
+ val[57] += s * src.el(15);
+ val[58] += s * src.el(23);
+ val[59] += s * src.el(31);
+ val[60] += s * src.el(39);
+ val[61] += s * src.el(47);
+ val[62] += s * src.el(55);
+ val[63] += s * src.el(63);
+ }
+ else
+ Assert (false, ExcInternalError());
+}
+
+
+template <typename number>
+bool
+dFMatrix::operator == (const dFMatrix &m) const
+{
+ bool q = (dim_range==m.dim_range) && (dim_image==m.dim_image);
+ if (!q) return false;
+
+ for (unsigned int i=0; i<dim_image; ++i)
+ for (unsigned int j=0; j<dim_range; ++j)
+ if (el(i,j) != m.el(i,j)) return false;
+ return true;
+};
+
+
+template <typename number>
+double dFMatrix::determinant () const {
+ Assert (dim_range == dim_image,
+ ExcDimensionMismatch(dim_range, dim_image));
+ Assert ((dim_range>=1) && (dim_range<=3), ExcNotImplemented(dim_range));
+
+ switch (dim_range)
+ {
+ case 1:
+ return el(0,0);
+ case 2:
+ return el(0,0)*el(1,1) - el(1,0)*el(0,1);
+ case 3:
+ return (el(0,0)*el(1,1)*el(2,2)
+ -el(0,0)*el(1,2)*el(2,1)
+ -el(1,0)*el(0,1)*el(2,2)
+ +el(1,0)*el(0,2)*el(2,1)
+ +el(2,0)*el(0,1)*el(1,2)
+ -el(2,0)*el(0,2)*el(1,1));
+ default:
+ return 0;
+ };
+};
+
+template <typename number>
+double dFMatrix::norm2 () const
+{
+ double s = 0.;
+ for (unsigned int i=0;i<dim_image*dim_range;++i)
+ s += val[i]*val[i];
+ return s;
+}
+
+
+template <typename number>
+void dFMatrix::clear () {
+ double *val_ptr = &val[0];
+ const double *end_ptr = &val[n()*m()];
+ while (val_ptr != end_ptr)
+ *val_ptr++ = 0.;
+};
+
+
+
+template <typename number>
+void dFMatrix::invert (const dFMatrix &M) {
+ Assert (dim_range == dim_image, ExcNotQuadratic());
+ Assert ((dim_range>=1) && (dim_range<=4), ExcNotImplemented(dim_range));
+ Assert (dim_range == M.dim_range,
+ ExcDimensionMismatch(dim_range,M.dim_range));
+ Assert (dim_image == M.dim_image,
+ ExcDimensionMismatch(dim_image,M.dim_image));
+
+ switch (dim_range)
+ {
+ case 1:
+ val[0] = 1.0/M.val[0];
+ return;
+ case 2:
+ // this is Maple output,
+ // thus a bit unstructured
+ {
+ const double t4 = 1.0/(M.el(0,0)*M.el(1,1)-M.el(0,1)*M.el(1,0));
+ el(0,0) = M.el(1,1)*t4;
+ el(0,1) = -M.el(0,1)*t4;
+ el(1,0) = -M.el(1,0)*t4;
+ el(1,1) = M.el(0,0)*t4;
+ return;
+ };
+
+ case 3:
+ {
+ const double t4 = M.el(0,0)*M.el(1,1),
+ t6 = M.el(0,0)*M.el(1,2),
+ t8 = M.el(0,1)*M.el(1,0),
+ t00 = M.el(0,2)*M.el(1,0),
+ t01 = M.el(0,1)*M.el(2,0),
+ t04 = M.el(0,2)*M.el(2,0),
+ t07 = 1.0/(t4*M.el(2,2)-t6*M.el(2,1)-t8*M.el(2,2)+
+ t00*M.el(2,1)+t01*M.el(1,2)-t04*M.el(1,1));
+ el(0,0) = (M.el(1,1)*M.el(2,2)-M.el(1,2)*M.el(2,1))*t07;
+ el(0,1) = -(M.el(0,1)*M.el(2,2)-M.el(0,2)*M.el(2,1))*t07;
+ el(0,2) = -(-M.el(0,1)*M.el(1,2)+M.el(0,2)*M.el(1,1))*t07;
+ el(1,0) = -(M.el(1,0)*M.el(2,2)-M.el(1,2)*M.el(2,0))*t07;
+ el(1,1) = (M.el(0,0)*M.el(2,2)-t04)*t07;
+ el(1,2) = -(t6-t00)*t07;
+ el(2,0) = -(-M.el(1,0)*M.el(2,1)+M.el(1,1)*M.el(2,0))*t07;
+ el(2,1) = -(M.el(0,0)*M.el(2,1)-t01)*t07;
+ el(2,2) = (t4-t8)*t07;
+ return;
+ };
+
+ case 4:
+ {
+ // with (linalg);
+ // a:=matrix(4,4);
+ // evalm(a);
+ // ai:=inverse(a);
+ // readlib(C);
+ // C(ai,optimized,filename=x4);
+
+ const double t14 = M.el(0,0)*M.el(1,1);
+ const double t15 = M.el(2,2)*M.el(3,3);
+ const double t17 = M.el(2,3)*M.el(3,2);
+ const double t19 = M.el(0,0)*M.el(2,1);
+ const double t20 = M.el(1,2)*M.el(3,3);
+ const double t22 = M.el(1,3)*M.el(3,2);
+ const double t24 = M.el(0,0)*M.el(3,1);
+ const double t25 = M.el(1,2)*M.el(2,3);
+ const double t27 = M.el(1,3)*M.el(2,2);
+ const double t29 = M.el(1,0)*M.el(0,1);
+ const double t32 = M.el(1,0)*M.el(2,1);
+ const double t33 = M.el(0,2)*M.el(3,3);
+ const double t35 = M.el(0,3)*M.el(3,2);
+ const double t37 = M.el(1,0)*M.el(3,1);
+ const double t38 = M.el(0,2)*M.el(2,3);
+ const double t40 = M.el(0,3)*M.el(2,2);
+ const double t42 = t14*t15-t14*t17-t19*t20+t19*t22+
+ t24*t25-t24*t27-t29*t15+t29*t17+
+ t32*t33-t32*t35-t37*t38+t37*t40;
+ const double t43 = M.el(2,0)*M.el(0,1);
+ const double t46 = M.el(2,0)*M.el(1,1);
+ const double t49 = M.el(2,0)*M.el(3,1);
+ const double t50 = M.el(0,2)*M.el(1,3);
+ const double t52 = M.el(0,3)*M.el(1,2);
+ const double t54 = M.el(3,0)*M.el(0,1);
+ const double t57 = M.el(3,0)*M.el(1,1);
+ const double t60 = M.el(3,0)*M.el(2,1);
+ const double t63 = t43*t20-t43*t22-t46*t33+t46*t35+
+ t49*t50-t49*t52-t54*t25+t54*t27+
+ t57*t38-t57*t40-t60*t50+t60*t52;
+ const double t65 = 1/(t42+t63);
+ const double t71 = M.el(0,2)*M.el(2,1);
+ const double t73 = M.el(0,3)*M.el(2,1);
+ const double t75 = M.el(0,2)*M.el(3,1);
+ const double t77 = M.el(0,3)*M.el(3,1);
+ const double t81 = M.el(0,1)*M.el(1,2);
+ const double t83 = M.el(0,1)*M.el(1,3);
+ const double t85 = M.el(0,2)*M.el(1,1);
+ const double t87 = M.el(0,3)*M.el(1,1);
+ const double t101 = M.el(1,0)*M.el(2,2);
+ const double t103 = M.el(1,0)*M.el(2,3);
+ const double t105 = M.el(2,0)*M.el(1,2);
+ const double t107 = M.el(2,0)*M.el(1,3);
+ const double t109 = M.el(3,0)*M.el(1,2);
+ const double t111 = M.el(3,0)*M.el(1,3);
+ const double t115 = M.el(0,0)*M.el(2,2);
+ const double t117 = M.el(0,0)*M.el(2,3);
+ const double t119 = M.el(2,0)*M.el(0,2);
+ const double t121 = M.el(2,0)*M.el(0,3);
+ const double t123 = M.el(3,0)*M.el(0,2);
+ const double t125 = M.el(3,0)*M.el(0,3);
+ const double t129 = M.el(0,0)*M.el(1,2);
+ const double t131 = M.el(0,0)*M.el(1,3);
+ const double t133 = M.el(1,0)*M.el(0,2);
+ const double t135 = M.el(1,0)*M.el(0,3);
+ el(0,0) = (M.el(1,1)*M.el(2,2)*M.el(3,3)-M.el(1,1)*M.el(2,3)*M.el(3,2)-
+ M.el(2,1)*M.el(1,2)*M.el(3,3)+M.el(2,1)*M.el(1,3)*M.el(3,2)+
+ M.el(3,1)*M.el(1,2)*M.el(2,3)-M.el(3,1)*M.el(1,3)*M.el(2,2))*t65;
+ el(0,1) = -(M.el(0,1)*M.el(2,2)*M.el(3,3)-M.el(0,1)*M.el(2,3)*M.el(3,2)-
+ t71*M.el(3,3)+t73*M.el(3,2)+t75*M.el(2,3)-t77*M.el(2,2))*t65;
+ el(0,2) = (t81*M.el(3,3)-t83*M.el(3,2)-t85*M.el(3,3)+t87*M.el(3,2)+
+ t75*M.el(1,3)-t77*M.el(1,2))*t65;
+ el(0,3) = -(t81*M.el(2,3)-t83*M.el(2,2)-t85*M.el(2,3)+t87*M.el(2,2)+
+ t71*M.el(1,3)-t73*M.el(1,2))*t65;
+ el(1,0) = -(t101*M.el(3,3)-t103*M.el(3,2)-t105*M.el(3,3)+t107*M.el(3,2)+
+ t109*M.el(2,3)-t111*M.el(2,2))*t65;
+ el(1,1) = (t115*M.el(3,3)-t117*M.el(3,2)-t119*M.el(3,3)+t121*M.el(3,2)+
+ t123*M.el(2,3)-t125*M.el(2,2))*t65;
+ el(1,2) = -(t129*M.el(3,3)-t131*M.el(3,2)-t133*M.el(3,3)+t135*M.el(3,2)+
+ t123*M.el(1,3)-t125*M.el(1,2))*t65;
+ el(1,3) = (t129*M.el(2,3)-t131*M.el(2,2)-t133*M.el(2,3)+t135*M.el(2,2)+
+ t119*M.el(1,3)-t121*M.el(1,2))*t65;
+ el(2,0) = (t32*M.el(3,3)-t103*M.el(3,1)-t46*M.el(3,3)+t107*M.el(3,1)+
+ t57*M.el(2,3)-t111*M.el(2,1))*t65;
+ el(2,1) = -(t19*M.el(3,3)-t117*M.el(3,1)-t43*M.el(3,3)+t121*M.el(3,1)+
+ t54*M.el(2,3)-t125*M.el(2,1))*t65;
+ el(2,2) = (t14*M.el(3,3)-t131*M.el(3,1)-t29*M.el(3,3)+t135*M.el(3,1)+
+ t54*M.el(1,3)-t125*M.el(1,1))*t65;
+ el(2,3) = -(t14*M.el(2,3)-t131*M.el(2,1)-t29*M.el(2,3)+t135*M.el(2,1)+
+ t43*M.el(1,3)-t121*M.el(1,1))*t65;
+ el(3,0) = -(t32*M.el(3,2)-t101*M.el(3,1)-t46*M.el(3,2)+t105*M.el(3,1)+
+ t57*M.el(2,2)-t109*M.el(2,1))*t65;
+ el(3,1) = (t19*M.el(3,2)-t115*M.el(3,1)-t43*M.el(3,2)+t119*M.el(3,1)+
+ t54*M.el(2,2)-t123*M.el(2,1))*t65;
+ el(3,2) = -(t14*M.el(3,2)-t129*M.el(3,1)-t29*M.el(3,2)+t133*M.el(3,1)+
+ t54*M.el(1,2)-t123*M.el(1,1))*t65;
+ el(3,3) = (t14*M.el(2,2)-t129*M.el(2,1)-t29*M.el(2,2)+t133*M.el(2,1)+
+ t43*M.el(1,2)-t119*M.el(1,1))*t65;
+ }
+ };
+};
+
+
+
+template <typename number>
+void dFMatrix::print_formatted (ostream &out, const unsigned int precision) const {
+ out.precision (precision);
+ out.setf (ios::scientific, ios::floatfield); // set output format
+
+ for (unsigned int i=0; i<m(); ++i)
+ {
+ for (unsigned int j=0; j<n(); ++j)
+ if (el(i,j) != 0)
+ out << setw(precision+7)
+ << el(i,j) << ' ';
+ else
+ out << setw(precision+8) << " ";
+ out << endl;
+ };
+
+ AssertThrow (out, ExcIO());
+
+ out.setf (0, ios::floatfield); // reset output format
+};
+
+
+// Gauss-Jordan-Algorithmus
+// cf. Stoer I (4th Edition) p. 153
+
+void dFMatrix::gauss_jordan()
+{
+ Assert (dim_range == dim_image, ExcNotQuadratic());
+ iVector p(n());
+
+ unsigned int i,j,k,r;
+ double max, hr;
+
+ for (i=0; i<n(); ++i) p(i) = i;
+
+ for (j=0; j<n(); ++j)
+ {
+ // pivotsearch
+ max = fabs(el(j,j));
+ r = j;
+ for (i=j+1; i<n(); ++i)
+ {
+ if (fabs(el(i,j)) > max)
+ {
+ max = fabs(el(i,j));
+ r = i;
+ }
+ }
+ Assert(max>1.e-16, ExcNotRegular());
+ // rowinterchange
+ if (r>j)
+ {
+ for (k=0; k<n(); ++k)
+ {
+ hr = el(j,k) ; el(j,k) = el(r,k) ; el(r,k) = hr;
+ }
+ i = p(j) ; p(j) = p(r) ; p(r) = i;
+ }
+
+ // transformation
+ hr = 1./el(j,j);
+ el(j,j) = hr;
+ for (k=0; k<n(); ++k)
+ {
+ if (k==j) continue;
+ for (i=0; i<n(); ++i)
+ {
+ if (i==j) continue;
+ el(i,k) -= el(i,j)*el(j,k)*hr;
+ }
+ }
+ for (i=0; i<n(); ++i)
+ {
+ el(i,j) *= hr;
+ el(j,i) *= -hr;
+ }
+ el(j,j) = hr;
+ }
+ // columninterchange
+ dVector hv(n());
+ for (i=0; i<n(); ++i)
+ {
+ for (k=0; k<n(); ++k) hv(p(k)) = el(i,k);
+ for (k=0; k<n(); ++k) el(i,k) = hv(k);
+ }
+}
+
+// QR-transformation cf. Stoer 1 4.8.2 (p. 191)
+
+template <typename number>
+void
+dFMatrix::householder(dVector& src)
+{
+ // m > n, src.n() = m
+ Assert (dim_range <= dim_image, ExcDimensionMismatch(dim_range, dim_image));
+ Assert (src.size() == dim_range, ExcDimensionMismatch(src.size(), dim_range));
+
+ for (unsigned int j=0 ; j<n() ; ++j)
+ {
+ double sigma = 0;
+ unsigned int i;
+ for (i=j ; i<m() ; ++i) sigma += el(i,j)*el(i,j);
+ if (fabs(sigma) < 1.e-15) return;
+ double s = el(j,j);
+ s = (s<0) ? sqrt(sigma) : -sqrt(sigma);
+ double dj = s;
+
+ double beta = 1./(s*el(j,j)-sigma);
+ el(j,j) -= s;
+
+ for (unsigned int k=j+1 ; k<n() ; ++k)
+ {
+ double sum = 0.;
+ for (i=j ; i<m() ; ++i) sum += el(i,j)*el(i,k);
+ sum *= beta;
+
+ for (i=j ; i<m() ; ++i) el(i,k) += sum*el(i,j);
+ }
+
+ double sum = 0.;
+ for (i=j ; i<m() ; ++i) sum += el(i,j)*src(i);
+ sum *= beta;
+
+ for (i=j ; i<m() ; ++i) src(i) += sum*el(i,j);
+ el(j,j) = dj;
+ }
+}
+
+template <typename number>
+double
+dFMatrix::least_squares(dVector& dst, dVector& src)
+{
+ // m > n, m = src.n, n = dst.n
+
+ householder(src);
+ backward(dst, src);
+
+ double sum = 0.;
+ for (unsigned int i=n() ; i<m() ; ++i) sum += src(i) * src(i);
+ return sqrt(sum);
+}
--- /dev/null
+// $Id$
+
+// Driver for FullMatrix template instantiation.
+
+/* Instantiation is controlled by preprocessor symbols:
+ *
+ * 1. TYPEMAT : numerical type used in the matrix
+ * 2. TYPEVEC : numerical type for vector entries
+ * 3. TYPERES : numerical type for entries in the right hand side vector
+ * 4. TYPEMAT2: numerical type for the second matrix
+ */
+
+#include <lac/fullmatrix.templates.h>
+
+#define TYPEMAT double
+
+template class FullMatrix<TYPEMAT>;
+
+#define TYPEMAT2 double
+
+//template FullMatrix<TYPEMAT>& FullMatrix<TYPEMAT>::operator =(const FullMatrix<TYPEMAT2>&);
+template void FullMatrix<TYPEMAT>::fill (const FullMatrix<TYPEMAT2>&, const unsigned, const unsigned);
+template void FullMatrix<TYPEMAT>::reinit (const FullMatrix<TYPEMAT2>&);
+template void FullMatrix<TYPEMAT>::add (const TYPEMAT, const FullMatrix<TYPEMAT2>&);
+template void FullMatrix<TYPEMAT>::Tadd (const TYPEMAT, const FullMatrix<TYPEMAT2>&);
+template void FullMatrix<TYPEMAT>::mmult (FullMatrix<TYPEMAT2>&, const FullMatrix<TYPEMAT2>&) const;
+template void FullMatrix<TYPEMAT>::Tmmult (FullMatrix<TYPEMAT2>&, const FullMatrix<TYPEMAT2>&) const;
+template void FullMatrix<TYPEMAT>::add_diag (const TYPEMAT, const FullMatrix<TYPEMAT2>&);
+
+
+#define TYPEVEC double
+#define TYPERES double
+
+template void FullMatrix<TYPEMAT>::vmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const bool) const;
+template void FullMatrix<TYPEMAT>::Tvmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const bool) const;
+template double FullMatrix<TYPEMAT>::residual(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const Vector<TYPERES>&) const;
+template double FullMatrix<TYPEMAT>::matrix_norm (const Vector<TYPEVEC> &) const;
+template double FullMatrix<TYPEMAT>::matrix_scalar_product(const Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::forward(Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::backward(Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::householder(Vector<TYPEVEC>&);
+template double FullMatrix<TYPEMAT>::least_squares(Vector<TYPEVEC>&, Vector<TYPEVEC>&);
+template void FullMatrix<TYPEMAT>::gsmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const iVector&) const;
+
+#undef TYPEVEC
+#define TYPEVEC float
+
+template void FullMatrix<TYPEMAT>::vmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const bool) const;
+template void FullMatrix<TYPEMAT>::Tvmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const bool) const;
+template double FullMatrix<TYPEMAT>::residual(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const Vector<TYPERES>&) const;
+template double FullMatrix<TYPEMAT>::matrix_norm (const Vector<TYPEVEC> &) const;
+template double FullMatrix<TYPEMAT>::matrix_scalar_product(const Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::forward(Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::backward(Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::householder(Vector<TYPEVEC>&);
+template double FullMatrix<TYPEMAT>::least_squares(Vector<TYPEVEC>&, Vector<TYPEVEC>&);
+template void FullMatrix<TYPEMAT>::gsmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const iVector&) const;
+
--- /dev/null
+// $Id$
+
+// Driver for FullMatrix template instantiation.
+
+/* Instantiation is controlled by preprocessor symbols:
+ *
+ * 1. TYPEMAT : numerical type used in the matrix
+ * 2. TYPEVEC : numerical type for vector entries
+ * 3. TYPERES : numerical type for entries in the right hand side vector
+ * 4. TYPEMAT2: numerical type for the second matrix
+ */
+
+#include <lac/fullmatrix.templates.h>
+
+#define TYPEMAT float
+
+template class FullMatrix<TYPEMAT>;
+
+#define TYPEMAT2 float
+
+//template FullMatrix<TYPEMAT>& FullMatrix<TYPEMAT>::operator =(const FullMatrix<TYPEMAT2>&);
+template void FullMatrix<TYPEMAT>::fill (const FullMatrix<TYPEMAT2>&, const unsigned, const unsigned);
+template void FullMatrix<TYPEMAT>::reinit (const FullMatrix<TYPEMAT2>&);
+template void FullMatrix<TYPEMAT>::add (const TYPEMAT, const FullMatrix<TYPEMAT2>&);
+template void FullMatrix<TYPEMAT>::Tadd (const TYPEMAT, const FullMatrix<TYPEMAT2>&);
+template void FullMatrix<TYPEMAT>::mmult (FullMatrix<TYPEMAT2>&, const FullMatrix<TYPEMAT2>&) const;
+template void FullMatrix<TYPEMAT>::Tmmult (FullMatrix<TYPEMAT2>&, const FullMatrix<TYPEMAT2>&) const;
+template void FullMatrix<TYPEMAT>::add_diag (const TYPEMAT, const FullMatrix<TYPEMAT2>&);
+
+
+#define TYPEVEC double
+#define TYPERES double
+
+template void FullMatrix<TYPEMAT>::vmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const bool) const;
+template void FullMatrix<TYPEMAT>::Tvmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const bool) const;
+template double FullMatrix<TYPEMAT>::residual(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const Vector<TYPERES>&) const;
+template double FullMatrix<TYPEMAT>::matrix_norm (const Vector<TYPEVEC> &) const;
+template double FullMatrix<TYPEMAT>::matrix_scalar_product(const Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::forward(Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::backward(Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::householder(Vector<TYPEVEC>&);
+template double FullMatrix<TYPEMAT>::least_squares(Vector<TYPEVEC>&, Vector<TYPEVEC>&);
+template void FullMatrix<TYPEMAT>::gsmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const iVector&) const;
+
+#undef TYPEVEC
+#define TYPEVEC float
+
+template void FullMatrix<TYPEMAT>::vmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const bool) const;
+template void FullMatrix<TYPEMAT>::Tvmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const bool) const;
+template double FullMatrix<TYPEMAT>::residual(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const Vector<TYPERES>&) const;
+template double FullMatrix<TYPEMAT>::matrix_norm (const Vector<TYPEVEC> &) const;
+template double FullMatrix<TYPEMAT>::matrix_scalar_product(const Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::forward(Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::backward(Vector<TYPEVEC>&, const Vector<TYPEVEC>&) const;
+template void FullMatrix<TYPEMAT>::householder(Vector<TYPEVEC>&);
+template double FullMatrix<TYPEMAT>::least_squares(Vector<TYPEVEC>&, Vector<TYPEVEC>&);
+template void FullMatrix<TYPEMAT>::gsmult(Vector<TYPEVEC>&, const Vector<TYPEVEC>&, const iVector&) const;
+
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