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Annotation of OpenXM_contrib/PHC/Ada/Continuation/vlprs_algorithm.ads, Revision 1.1.1.1

1.1       maekawa     1: with text_io;                            use text_io;
                      2: with Standard_Floating_Numbers;          use Standard_Floating_Numbers;
                      3: with Standard_Floating_Vectors;          use Standard_Floating_Vectors;
                      4: with Standard_Floating_Matrices;         use Standard_Floating_Matrices;
                      5:
                      6: package vLpRs_Algorithm is
                      7:
                      8: -- DESCRIPTION :
                      9: --   This package provides several routines for an extrapolation method on
                     10: --   the power series x(s) = a s^w ( 1 + O(s) ).
                     11: --   Because the aim is to estimate the leading power w, the algorithm
                     12: --   takes the logs as input.  So it considers the sequence
                     13: --     log(|x(s_k)|) = log(|a|) + w log(s_k) + log(1 + O(s_k)),
                     14: --   for a sequence s_0 > s_1 > .. > s_m > 0, with m >= the order r.
                     15:
                     16: -- USAGE :
                     17: --   The first two routines are interesting to fill up the pipe, until
                     18: --   sufficient data points are available to match the order.
                     19: --   From then on, the fully incremental version can be used.
                     20:
                     21: -- START UP FROM SCRATCH :
                     22:
                     23:   procedure vLpRs_full
                     24:                 ( r : in natural; s,logs,logx : in Vector;
                     25:                   srp,dsp,p,l,v : in out Vector; rt1,rt2 : in out Matrix );
                     26:
                     27:   -- DESCRIPTION :
                     28:   --   Calls the full version of the vLpRs-Algorithm.
                     29:
                     30:   -- REQUIRED :
                     31:   --   s'range = logs'range = logx'range, s'last >= r,
                     32:   --   srp'range = dsp'range = 1..r-1 = rt1'range(*) = rt2'range(*),
                     33:   --   p'range = 0..r-1, l'range = v'range = 0..r.
                     34:
                     35:   -- ON ENTRY :
                     36:   --   r          order of the extrapolation method;
                     37:   --   s          strictly decreasing sequence of positive numbers;
                     38:   --   logs       logarithms of the s-values;
                     39:   --   logx       logarithms of |x(s_k)|.
                     40:
                     41:   -- ON RETURN :
                     42:   --   srp        last row of powers of consecutive s-values;
                     43:   --   dsp        last row of differences of consecutive s-powers;
                     44:   --   p          last row of p-factors;
                     45:   --   l          last row in the L-table, with error O(s^r).
                     46:   --   v          last row in the v-table, with error O(s^r).
                     47:   --   rt1,rt2    last consecutive R-tables.
                     48:
                     49:   procedure vLpRs_pipe
                     50:                 ( file : in file_type;
                     51:                   r : in natural; s,logs,logx : in Vector;
                     52:                   srp,dsp,p,l,v : in out Vector; rt1,rt2 : in out Matrix );
                     53:
                     54:   -- DESCRIPTION :
                     55:   --   Constructs the extrapolation table in an incremental way.
                     56:
                     57:   -- REQUIRED :
                     58:   --   s'range = logs'range = logx'range, s'last >= r,
                     59:   --   srp'range = dsp'range = 1..r-1 = rt1'range(*) = rt2'range(*),
                     60:   --   p'range = 0..r-1, l'range = v'range = 0..r.
                     61:
                     62:   -- ON ENTRY :
                     63:   --   file       to write error table on;
                     64:   --   r          order of the extrapolation method;
                     65:   --   s          strictly decreasing sequence of positive numbers;
                     66:   --   logs       logarithms of the s-values;
                     67:   --   logx       logarithms of |x(s_k)|.
                     68:
                     69:   -- ON RETURN :
                     70:   --   srp        last row of powers of consecutive s-values;
                     71:   --   dsp        last row of differences of consecutive s-powers;
                     72:   --   p          last row of p-factors;
                     73:   --   l          last row in the L-table, with error O(s^r).
                     74:   --   v          last row in the v-table, with error O(s^r).
                     75:   --   rt1,rt2    last consecutive R-tables.
                     76:
                     77: -- INCREMENTAL UPDATE :
                     78:
                     79:   procedure vLpRs_pipe
                     80:                 ( s,logs,logx : in double_float;
                     81:                   srp,dsp,p,l,v : in out Vector; rt1,rt2 : in out Matrix );
                     82:
                     83:   procedure vLpRs_pipe
                     84:                 ( file : in file_type; s,logs,logx : in double_float;
                     85:                   srp,dsp,p,l,v : in out Vector; rt1,rt2 : in out Matrix );
                     86:
                     87:   -- DESCRIPTION :
                     88:   --   One additional row of every table is computed.
                     89:
                     90:   -- REQUIRED :
                     91:   --   srp'range = dsp'range = 1..r-1 = rt1'range(*) = rt2'range(*),
                     92:   --   p'range = 0..r-1, l'range = v'range = 0..r.
                     93:
                     94:   -- ON ENTRY :
                     95:   --   file       to write table with errors on;
                     96:   --   s          new s-value, must be smaller than latest one and nonzero;
                     97:   --   logs       logarithm of s;
                     98:   --   logx       logarithm of the absolute value of |x(s)|;
                     99:   --   srp        last row of powers of consecutive s-values;
                    100:   --   dsp        last row of differences of consecutive s-powers;
                    101:   --   p          last row of p-factors;
                    102:   --   l          last row of extrapolated logarithms of s-values;
                    103:   --   v          last row of extrapolated logarithms of data points;
                    104:   --   rt1,rt2    last consecutive R-tables.
                    105:
                    106:   -- ON RETURN :
                    107:   --   srp        updated row of powers of consecutive s-values;
                    108:   --   dsp        updated row of differences of consecutive s-powers;
                    109:   --   p          updated row of p-factors;
                    110:   --   l          updated row of extrapolated logarithms of s-values;
                    111:   --   v          updated row of extrapolated logarithms of data points;
                    112:   --   rt1,rt2    updated consecutive R-tables.
                    113:
                    114: end vLpRs_Algorithm;