Annotation of OpenXM_contrib/PHC/Ada/Continuation/vlprs_tables.ads, Revision 1.1.1.1
1.1 maekawa 1: with Standard_Floating_Numbers; use Standard_Floating_Numbers;
2: with Standard_Floating_Vectors; use Standard_Floating_Vectors;
3: with Standard_Floating_Matrices; use Standard_Floating_Matrices;
4:
5: package vLpRs_Tables is
6:
7: -- DESCRIPTION :
8: -- This package implements the tables for an r-order extrapolation method.
9: -- For all tables, there is a full and a pipe-lining version.
10: -- For efficiency reasons the full v- and L-table are combined.
11:
12: -- I. The v-table : extrapolated values of log(|x_i(s_k)|).
13:
14: procedure v_pipe ( v : in out Vector; p : in Vector; vr : in double_float );
15: procedure v_pipe ( v,p : in Vector; vr : in double_float;
16: vrp : in out Vector );
17:
18: -- DESCRIPTION : computes one additional row of the v-table.
19:
20: -- REQUIRED : v'range = vrp'range = 0..r, p'range = 0..r-1.
21:
22: -- ON ENTRY :
23: -- v previous row of the v-table;
24: -- p current vector of p-factors;
25: -- vr equals log(|x_i(s_r)|).
26:
27: -- ON RETURN :
28: -- v or vrp last row in the v-table: vrp(r) should have error O(s^r).
29:
30: -- II. The L-table : linear combinations of the logarithms log(s_k).
31:
32: procedure L_pipe ( l : in out Vector; p : in Vector; lr : in double_float );
33: procedure L_pipe ( l,p : in Vector; lr : in double_float;
34: lrp : in out Vector );
35:
36: -- DESCRIPTION : computes one additional row of the L-table.
37:
38: -- REQUIRED : l'range = lrp'range = 0..r, p'range = 0..r-1.
39:
40: -- ON ENTRY :
41: -- l previous row of the v-table;
42: -- p current vector of p'factors;
43: -- lr equals log(s_r).
44:
45: -- ON RETURN :
46: -- l or lrp last row in the L-table, vrp(r)/lpr(r) = w_i + O(s^r).
47:
48: -- The full computation of both v- and L-table :
49:
50: procedure vL_full ( s,l,v : in Vector; srp,dsp,p,lrp,vrp : out Vector;
51: rt1,rt2 : in out Matrix );
52:
53: -- DESCRIPTION : computes the last row of v- and L-table from s-values.
54:
55: -- REQUIRED :
56: -- s'range = l'range = v'range = 0..r = lrp'range = vrp'range,
57: -- srp'range = dsp'range = 1..r-1, p'range = 0..r-1,
58: -- rt1'range(*) = 1..r-1 = rt2'range(*).
59:
60: -- ON ENTRY :
61: -- s consecutive s-values: s(0) > s(1) > .. > s(r) > 0;
62: -- l logs of the s-values: l(k) = log(s(k));
63: -- v points at the s-values: v(k) = log(|x_i(s(k))|).
64:
65: -- ON RETURN :
66: -- srp consecutive powers of s(r): srp(l) = s(r)**l;
67: -- dsp differences of powers: dsp(l) = srp(l) - s(r-1)**l.
68: -- p last row used in the p-table;
69: -- vrp last row in the v-table;
70: -- lrp last row in the L-table, vrp(r)/lpr(r) = w_i + O(s^r);
71: -- rt1 previous instance of the r-table;
72: -- rt2 last instance of the r-table.
73:
74: -- III. The p-table : extrapolation factors needed for v-table and L-table.
75:
76: procedure p_full ( s : in Vector; srp,dsp,p : out Vector;
77: rt1,rt2 : in out Matrix );
78:
79: -- DESCRIPTION : computes the last row of p-table from s-values.
80:
81: -- REQUIRED :
82: -- s'range = 0..r, srp'range = dsp'range = 1..r-1, p'range = 0..r-1,
83: -- rt1'range(*) = 1..r-1 = rt2'range(*).
84:
85: -- NOTE : p_full = R_full followed by p_pipe.
86:
87: procedure p_pipe ( rt1,rt2 : in Matrix; p : out Vector );
88:
89: -- DESCRIPTION : update of one row of the p-table.
90:
91: -- REQUIRED : rt1'range(*) = rt2'range(*) = 1..r-1, p'range = 0..r-1.
92:
93: -- ON ENTRY :
94: -- rt1 previous instance of the R-table;
95: -- rt2 last instance of the R-table.
96:
97: -- ON RETURN :
98: -- p p-factors, with p(0) = 1, p(i) = rt1(i,i)/rt2(i,i).
99:
100: -- IV. The R-table : propagated error factors.
101:
102: procedure R_full ( s : in Vector; srp,dsp,p : out Vector;
103: rt1,rt2 : in out Matrix );
104:
105: procedure RR_full ( s : in Vector; srp,dsp,p : out Vector;
106: rt1,rt2 : in out Matrix );
107:
108: -- DESCRIPTION : computation of the r-table from a sequence of s-values.
109: -- The RR_full computes the subdiagonal as well.
110:
111: -- REQUIRED :
112: -- s'range = 0..r, srp'range = dsp'range = 1..r-1, p'range = 0..r-1,
113: -- rt1'range(*) = 1..r-1 = rt2'range(*).
114:
115: -- ON ENTRY :
116: -- s sequence of consecutive s-values.
117:
118: -- ON RETURN :
119: -- srp,dsp see the output of s_full;
120: -- p last row used in the p-table;
121: -- rt1 previous instance of the r-table;
122: -- rt2 last instance of the r-table.
123:
124: procedure R_pipe ( rt1 : in Matrix; s,p : in Vector; rt2 : in out Matrix );
125: procedure RR_pipe ( rt1 : in Matrix; s,p : in Vector; rt2 : in out Matrix );
126:
127: -- DESCRIPTION : update of the r-table. RR_pipe updates also subdiagonal.
128:
129: -- REQUIRED :
130: -- rt1'range(*) = rt2'range(*) = s'range = 1..r-1, p'range = 0..r-1.
131:
132: -- ON ENTRY :
133: -- rt1 last instance of the R-table;
134: -- s current row of differences of powers of s-values;
135: -- p last row of the current p-table.
136:
137: -- ON RETURN :
138: -- rt2 new instance of the R-table.
139:
140: -- V. The s-table : consecutive s-values with differences of their powers.
141:
142: procedure s_full ( s : in Vector; srp,dsp : out Vector );
143:
144: -- DESCRIPTION : computes the s-table in full.
145:
146: -- REQUIRED : s'range = 0..r, srp'range = dsp'range = 1..r-1.
147:
148: -- ON ENTRY :
149: -- s the s-values, with s(0) > s(1) > .. > s(r) > 0.
150:
151: -- ON RETURN :
152: -- srp consecutive powers of s(r): srp(l) = s(r)**l;
153: -- dsp differences of powers: dsp(l) = srp(l) - s(r-1)**l.
154:
155: procedure s_pipe ( srp : in out Vector; sr : in double_float;
156: dsp : out Vector );
157: procedure s_pipe ( sr1 : in Vector; sr : in double_float;
158: srp,dsp : out Vector );
159:
160: -- DESCRIPTION : computes an additional row of the s-table.
161:
162: -- REQUIRED : sr1'range = srp'range = dsp'range = 1..r-1.
163:
164: -- ON ENTRY :
165: -- sr1 or srp consecutive powers of s(r-1): srp(l) = s(r-1)**l.
166: -- sr new last value for s(r).
167:
168: -- ON RETURN : same as s_full.
169:
170: end vLpRs_Tables;
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