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Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Matrices/multprec_complex_linear_solvers.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Natural_Vectors;
        !             2: with Multprec_Floating_Numbers;          use Multprec_Floating_Numbers;
        !             3: with Multprec_Complex_Vectors;           use Multprec_Complex_Vectors;
        !             4: with Multprec_Complex_Matrices;          use Multprec_Complex_Matrices;
        !             5:
        !             6: package Multprec_Complex_Linear_Solvers is
        !             7:
        !             8: -- DESCRIPTION :
        !             9: --   This package offers a few routines to solve linear systems of equations.
        !            10: --   The code for lufac, lufco and lusolve is a literal translation from the
        !            11: --   f77-linpack code.
        !            12:
        !            13:   procedure Scale ( a : in out Matrix; b : in out Vector );
        !            14:
        !            15:   -- DESCRIPTION :
        !            16:   --   Divides the ith equation in the system a*x = b by the largest
        !            17:   --   element on the ith row of a, for i in a'range(1).
        !            18:
        !            19:   -- REQUIRED : a'range(1) = b'range(1).
        !            20:
        !            21:   procedure lufac ( a : in out Matrix; n : in integer;
        !            22:                     ipvt : out Standard_Natural_Vectors.Vector;
        !            23:                     info : out natural );
        !            24:
        !            25:   -- DESCRIPTION :
        !            26:   --   lufac factors a complex matrix by gaussian elimination
        !            27:
        !            28:   --   lufac is usually called by lufco, but it can be called
        !            29:   --   directly with a saving of time if rcond is not needed.
        !            30:   --   (time for lufco) = (1 + 9/n)*(time for lufac).
        !            31:
        !            32:   -- ON ENTRY :
        !            33:   --   a       complex matrix(1..n,1..n) to be factored
        !            34:   --   n       the dimension of the matrix a
        !            35:
        !            36:   -- ON RETURN :
        !            37:   --   a       an upper triangular matrix and the multipliers
        !            38:   --           which were used to obtain it.
        !            39:   --           The factorization can be written a = l*u where
        !            40:   --           l is a product of permutation and unit lower
        !            41:   --           triangular matrices and u is upper triangular.
        !            42:   --   ipvt    an integer vector of pivot indices
        !            43:   --   info    = 0  normal value
        !            44:   --           = k  if u(k,k) = 0.0.
        !            45:   --                This is not an error for this routine,
        !            46:   --                but it does indicate that lusolve will
        !            47:   --                divide by zero if called.  Use rcond in
        !            48:   --                lufco for a reliable indication of singularity.
        !            49:
        !            50:   procedure lufco ( a : in out Matrix; n : in integer;
        !            51:                     ipvt : out Standard_Natural_Vectors.Vector;
        !            52:                     rcond : out Floating_Number );
        !            53:
        !            54:   -- DESCRIPTION :
        !            55:   --   lufco factors a complex matrix by gaussian elimination
        !            56:   --   and estimates the condition of the matrix.
        !            57:
        !            58:   -- If rcond is not needed, lufac is slightly faster.
        !            59:   -- To solve a*x = b, follow lufco by lusolve.
        !            60:
        !            61:   -- ON ENTRY :
        !            62:   --   a       complex matrix(1..n,1..n) to be factored
        !            63:   --   n       the dimension of the matrix a
        !            64:
        !            65:   -- ON RETURN :
        !            66:   --   a       an upper triangular matrix and the multipliers
        !            67:   --           which are used to obtain it.
        !            68:   --           The factorization can be written a = l*u, where
        !            69:   --           l is a product of permutation and unit lower triangular
        !            70:   --           matrices and u is upper triangular.
        !            71:   --   ipvt    an integer vector of pivot indices
        !            72:   --   rcond   an estimate of the reciprocal condition of a.
        !            73:   --           For the system a*x = b, relative perturbations
        !            74:   --           in a and b of size epsilon may cause relative
        !            75:   --           perturbations in x of size epsilon/rcond.
        !            76:   --           If rcond is so small that the logical expression
        !            77:   --                  1.0 + rcond = 1.0
        !            78:   --           is true, than a may be singular to working precision.
        !            79:   --           In particular, rcond is zero if exact singularity is
        !            80:   --           detected or the estimate underflows.
        !            81:
        !            82:   procedure lusolve ( a : in Matrix; n : in integer;
        !            83:                       ipvt : in Standard_Natural_Vectors.Vector;
        !            84:                       b : in out Vector );
        !            85:
        !            86:   -- DESCRIPTION :
        !            87:   --   lusolve solves the complex system a*x = b using the factors
        !            88:   --   computed by lufac or lufco
        !            89:
        !            90:   -- ON ENTRY :
        !            91:   --   a       a complex matrix(1..n,1..n), the output from
        !            92:   --           lufac or lufco
        !            93:   --   n       the dimension of the matrix a
        !            94:   --   ipvt    the pivot vector from lufac or lufco
        !            95:   --   b       the right hand side vector
        !            96:
        !            97:   -- ON RETURN :
        !            98:   --   b       the solution vector x
        !            99:
        !           100:   procedure Triangulate ( a : in out Matrix; n,m : in integer );
        !           101:
        !           102:   -- DESCRIPTION :
        !           103:   --   triangulate makes the n*m complex matrix a triangular using
        !           104:   --   Gaussian elimination.
        !           105:
        !           106:   -- ON ENTRY :
        !           107:   --   a       a complex matrix(1..n,1..m)
        !           108:   --   n       the number of rows of a
        !           109:   --   m       the number of columns of a
        !           110:
        !           111:   -- ON RETURN :
        !           112:   --   a       the triangulated matrix
        !           113:
        !           114:   procedure Diagonalize ( a : in out Matrix; n,m : in integer );
        !           115:
        !           116:   -- DESCRIPTION :
        !           117:   --   diagonalize makes the n*m complex matrix a diagonal using
        !           118:   --   Gauss-Jordan.
        !           119:
        !           120:   -- ON ENTRY :
        !           121:   --   a       a complex matrix(1..n,1..m)
        !           122:   --   n       the number of rows of a
        !           123:   --   m       the number of columns of a
        !           124:
        !           125:   -- ON RETURN :
        !           126:   --   a       the diagonalized matrix
        !           127:
        !           128: end Multprec_Complex_Linear_Solvers;