Return to givens_rotations.ads CVS log

Up to [local] / OpenXM_contrib / PHC / Ada / Math_Lib / Supports

Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Supports/givens_rotations.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Floating_Numbers;          use Standard_Floating_Numbers;
        !             2: with Standard_Integer_Vectors;
        !             3: with Standard_Floating_Vectors;          use Standard_Floating_Vectors;
        !             4: with Standard_Floating_Matrices;         use Standard_Floating_Matrices;
        !             5:
        !             6: package Givens_Rotations is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   This package contains operations to construct and perform
        !            10: --   Given rotations on vectors and matrices.
        !            11: --   The procedures in this package are listed in order like
        !            12: --   they have to be applied to write a right hand side vector
        !            13: --   as a linear combination of the column vectors of a matrix.
        !            14:
        !            15:   procedure Givens_Factors ( v : in Vector; i,j : in integer;
        !            16:                              cosi,sine : out double_float );
        !            17:   -- DESCRIPTION :
        !            18:   --   Computes the cosine and sine of the angle to be used in the
        !            19:   --   Givens rotation on the vector.
        !            20:
        !            21:   -- REQUIRED : v(i) /= 0 and v(j) /= 0, with i<j.
        !            22:
        !            23:   procedure Givens_Factors ( mat : in Matrix; i,j : in integer;
        !            24:                              cosi,sine : out double_float );
        !            25:   -- DESCRIPTION :
        !            26:   --   Computes the cosine and sine of the angle to be used in the
        !            27:   --   Givens rotation on the matrix.
        !            28:
        !            29:   -- REQUIRED : mat(i,i) /= 0 and mat(j,i) /= 0, with i<j.
        !            30:
        !            31:   procedure Givens_Rotation ( v : in out Vector; i,j : in integer;
        !            32:                               cosi,sine : in double_float );
        !            33:   -- DESCRIPTION :
        !            34:   --   Performs one Givens rotation on the vector
        !            35:   --   with given cosine and sine of the angle.
        !            36:
        !            37:   -- REQUIRED : v(i) /= 0 and v(j) /= 0, with i<j.
        !            38:
        !            39:   procedure Givens_Rotation ( mat : in out Matrix; lastcol,i,j : in integer;
        !            40:                               cosi,sine : in double_float );
        !            41:   procedure Givens_Rotation ( mat : in out Matrix; i,j : in integer;
        !            42:                               cosi,sine : in double_float );
        !            43:
        !            44:   -- DESCRIPTION :
        !            45:   --   Performs one Givens rotation on the matrix,
        !            46:   --   with given cosine and sine of the angle.
        !            47:   --   The parameter lastcol is the index of the last column of interest
        !            48:   --   in the matrix.
        !            49:
        !            50:   -- REQUIRED :
        !            51:   --   mat(i,i) /= 0 and mat(j,i) /= 0, with i<j.
        !            52:   --   It will be assumed that mat is already upper triangular up
        !            53:   --   to the ith row and colum, i.e. mat(k,l) = 0, l<i, k>l.
        !            54:
        !            55:   procedure Givens_Rotation ( v : in out Vector; i,j : in integer );
        !            56:
        !            57:   -- DESCRIPTION :
        !            58:   --   Performs one Givens rotation on the vector v.
        !            59:
        !            60:   -- REQUIRED : v(i) /= 0 and v(j) /= 0, with i<j.
        !            61:
        !            62:   procedure Givens_Rotation ( mat : in out Matrix; i,j : in integer );
        !            63:   procedure Givens_Rotation ( mat : in out Matrix; lastcol,i,j : in integer );
        !            64:
        !            65:   -- DESCRIPTION :
        !            66:   --   Performs one Givens rotation on the matrix.
        !            67:   --   The parameter lastcol is the index of the last column of interest
        !            68:   --   in the matrix.
        !            69:
        !            70:   -- REQUIRED :
        !            71:   --   mat(i,i) /= 0 and mat(i,j) /= 0, with i<j.
        !            72:   --   It will be assumed that mat is already upper triangular up
        !            73:   --   to the ith row and colum, i.e. mat(k,l) = 0, l<i, k>l.
        !            74:
        !            75:   procedure Upper_Triangulate
        !            76:                ( row : in integer; mat : in out Matrix; tol : in double_float;
        !            77:                  ipvt : in out Standard_Integer_Vectors.Vector;
        !            78:                  pivot : out integer );
        !            79:
        !            80:   -- DESCRIPTION :
        !            81:   --   Makes the matrix upper triangular by updating the current row of
        !            82:   --   the matrix.  If pivot = 0 on return, then the matrix is singular.
        !            83:
        !            84:   -- REQUIRED :
        !            85:   --   The matrix is upper triangular up to current row, which means that
        !            86:   --   abs(max(i,i)) > tol, for i in mat'first(1)..row-1.
        !            87:
        !            88:   procedure Upper_Triangulate ( mat : in out Matrix; tol : in double_float );
        !            89:   procedure Upper_Triangulate ( mat : in out Matrix; tol : in double_float;
        !            90:                                 ipvt : out Standard_Integer_Vectors.Vector );
        !            91:   -- DESCRIPTION :
        !            92:   --   Makes the matrix upper triangular by means of Givens rotations.
        !            93:   --   The parameter tol is used to determine whether an element is zero.
        !            94:   --   Column interchangements are performed when necessary.
        !            95:   --   The pivoting information will be returned in the vector ipvt.
        !            96:   --   Stops when a zero row is encountered.
        !            97:
        !            98:   -- REQUIRED : mat'first(1) = mat'first(2).
        !            99:
        !           100:   procedure Upper_Triangulate ( mat : in out Matrix; rhs : in out Vector;
        !           101:                                 tol : in double_float );
        !           102:   procedure Upper_Triangulate ( mat : in out Matrix; rhs : in out Vector;
        !           103:                                 tol : in double_float;
        !           104:                                 ipvt : out Standard_Integer_Vectors.Vector );
        !           105:   -- DESCRIPTION :
        !           106:   --   Makes the matrix upper triangular and
        !           107:   --   performs all Givens rotations as well on the right hand side vector.
        !           108:   --   The parameter tol is used to determine whether an element is zero.
        !           109:   --   Column interchangements are performed when necessary.
        !           110:   --   The pivoting information will be returned in the vector ipvt.
        !           111:   --   Stops when a zero row is encountered.
        !           112:
        !           113:   -- REQUIRED : mat'first(1) = mat(first(2).
        !           114:
        !           115:   procedure Solve ( mat : in Matrix; rhs : in Vector; tol : in double_float;
        !           116:                     x : out Vector );
        !           117:
        !           118:   -- DESCRIPTION :
        !           119:   --   Solves the system defined by mat*x = rhs.
        !           120:   --   In case rank(mat) < mat'length(1), then only
        !           121:   --   x(mat'first(1)..mat'first(1)+rank(mat)-1) will be meaningful.
        !           122:
        !           123:   -- REQUIRED :
        !           124:   --   mat is upper triangular and mat(i,i) /= 0, for i in 1..Rank(mat).
        !           125:
        !           126:   -- NOTE :
        !           127:   --   Eventually, when column interchangements where applied during
        !           128:   --   the triangulation of the matrix, then x is not the decomposition
        !           129:   --   of the right hand side vector in terms of the first column of
        !           130:   --   the matrix.
        !           131:
        !           132:   procedure Solve ( mat : in Matrix; rhs : in Vector; tol : in double_float;
        !           133:                     rank : in natural; x : out Vector );
        !           134:
        !           135:   -- DESCRIPTION :
        !           136:   --   Solves the system defined by mat*x = rhs.
        !           137:   --   Here only the first rows in columns up to the given rank are
        !           138:   --   considered.  So only x(mat'first(1)..mat'first(1)+rank-1) will
        !           139:   --   be meaningful.
        !           140:
        !           141:   -- REQUIRED :
        !           142:   --   The matrix is upper triangular up to its rank
        !           143:   --   and mat(i,i) /= 0, for i in 1..rank.
        !           144:
        !           145: end Givens_Rotations;