Actual source code: fsolvebaij.F90
1: !
2: !
3: ! Fortran kernel for sparse triangular solve in the BAIJ matrix format
4: ! This ONLY works for factorizations in the NATURAL ORDERING, i.e.
5: ! with MatSolve_SeqBAIJ_4_NaturalOrdering()
6: !
7: #include <petsc/finclude/petscsys.h>
8: !
10: subroutine FortranSolveBAIJ4Unroll(n,x,ai,aj,adiag,a,b)
11: implicit none
12: MatScalar a(0:*)
13: PetscScalar x(0:*)
14: PetscScalar b(0:*)
15: PetscInt n
16: PetscInt ai(0:*)
17: PetscInt aj(0:*)
18: PetscInt adiag(0:*)
20: PetscInt i,j,jstart,jend
21: PetscInt idx,ax,jdx
22: PetscScalar s1,s2,s3,s4
23: PetscScalar x1,x2,x3,x4
24: !
25: ! Forward Solve
26: !
27: PETSC_AssertAlignx(16,a(1))
28: PETSC_AssertAlignx(16,x(1))
29: PETSC_AssertAlignx(16,b(1))
30: PETSC_AssertAlignx(16,ai(1))
31: PETSC_AssertAlignx(16,aj(1))
32: PETSC_AssertAlignx(16,adiag(1))
34: x(0) = b(0)
35: x(1) = b(1)
36: x(2) = b(2)
37: x(3) = b(3)
38: idx = 0
39: do 20 i=1,n-1
40: jstart = ai(i)
41: jend = adiag(i) - 1
42: ax = 16*jstart
43: idx = idx + 4
44: s1 = b(idx)
45: s2 = b(idx+1)
46: s3 = b(idx+2)
47: s4 = b(idx+3)
48: do 30 j=jstart,jend
49: jdx = 4*aj(j)
51: x1 = x(jdx)
52: x2 = x(jdx+1)
53: x3 = x(jdx+2)
54: x4 = x(jdx+3)
55: s1 = s1-(a(ax)*x1 +a(ax+4)*x2+a(ax+8)*x3 +a(ax+12)*x4)
56: s2 = s2-(a(ax+1)*x1+a(ax+5)*x2+a(ax+9)*x3 +a(ax+13)*x4)
57: s3 = s3-(a(ax+2)*x1+a(ax+6)*x2+a(ax+10)*x3+a(ax+14)*x4)
58: s4 = s4-(a(ax+3)*x1+a(ax+7)*x2+a(ax+11)*x3+a(ax+15)*x4)
59: ax = ax + 16
60: 30 continue
61: x(idx) = s1
62: x(idx+1) = s2
63: x(idx+2) = s3
64: x(idx+3) = s4
65: 20 continue
67: !
68: ! Backward solve the upper triangular
69: !
70: do 40 i=n-1,0,-1
71: jstart = adiag(i) + 1
72: jend = ai(i+1) - 1
73: ax = 16*jstart
74: s1 = x(idx)
75: s2 = x(idx+1)
76: s3 = x(idx+2)
77: s4 = x(idx+3)
78: do 50 j=jstart,jend
79: jdx = 4*aj(j)
80: x1 = x(jdx)
81: x2 = x(jdx+1)
82: x3 = x(jdx+2)
83: x4 = x(jdx+3)
84: s1 = s1-(a(ax)*x1 +a(ax+4)*x2+a(ax+8)*x3 +a(ax+12)*x4)
85: s2 = s2-(a(ax+1)*x1+a(ax+5)*x2+a(ax+9)*x3 +a(ax+13)*x4)
86: s3 = s3-(a(ax+2)*x1+a(ax+6)*x2+a(ax+10)*x3+a(ax+14)*x4)
87: s4 = s4-(a(ax+3)*x1+a(ax+7)*x2+a(ax+11)*x3+a(ax+15)*x4)
88: ax = ax + 16
89: 50 continue
90: ax = 16*adiag(i)
91: x(idx) = a(ax)*s1 +a(ax+4)*s2+a(ax+8)*s3 +a(ax+12)*s4
92: x(idx+1) = a(ax+1)*s1+a(ax+5)*s2+a(ax+9)*s3 +a(ax+13)*s4
93: x(idx+2) = a(ax+2)*s1+a(ax+6)*s2+a(ax+10)*s3+a(ax+14)*s4
94: x(idx+3) = a(ax+3)*s1+a(ax+7)*s2+a(ax+11)*s3+a(ax+15)*s4
95: idx = idx - 4
96: 40 continue
97: return
98: end
100: ! version that does not call BLAS 2 operation for each row block
101: !
102: subroutine FortranSolveBAIJ4(n,x,ai,aj,adiag,a,b,w)
103: implicit none
104: MatScalar a(0:*)
105: PetscScalar x(0:*),b(0:*),w(0:*)
106: PetscInt n,ai(0:*),aj(0:*),adiag(0:*)
107: PetscInt ii,jj,i,j
109: PetscInt jstart,jend,idx,ax,jdx,kdx,nn
110: PetscScalar s(0:3)
112: !
113: ! Forward Solve
114: !
116: PETSC_AssertAlignx(16,a(1))
117: PETSC_AssertAlignx(16,w(1))
118: PETSC_AssertAlignx(16,x(1))
119: PETSC_AssertAlignx(16,b(1))
120: PETSC_AssertAlignx(16,ai(1))
121: PETSC_AssertAlignx(16,aj(1))
122: PETSC_AssertAlignx(16,adiag(1))
124: x(0) = b(0)
125: x(1) = b(1)
126: x(2) = b(2)
127: x(3) = b(3)
128: idx = 0
129: do 20 i=1,n-1
130: !
131: ! Pack required part of vector into work array
132: !
133: kdx = 0
134: jstart = ai(i)
135: jend = adiag(i) - 1
136: if (jend - jstart .ge. 500) then
137: write(6,*) 'Overflowing vector FortranSolveBAIJ4()'
138: endif
139: do 30 j=jstart,jend
141: jdx = 4*aj(j)
143: w(kdx) = x(jdx)
144: w(kdx+1) = x(jdx+1)
145: w(kdx+2) = x(jdx+2)
146: w(kdx+3) = x(jdx+3)
147: kdx = kdx + 4
148: 30 continue
150: ax = 16*jstart
151: idx = idx + 4
152: s(0) = b(idx)
153: s(1) = b(idx+1)
154: s(2) = b(idx+2)
155: s(3) = b(idx+3)
156: !
157: ! s = s - a(ax:)*w
158: !
159: nn = 4*(jend - jstart + 1) - 1
160: do 100, ii=0,3
161: do 110, jj=0,nn
162: s(ii) = s(ii) - a(ax+4*jj+ii)*w(jj)
163: 110 continue
164: 100 continue
166: x(idx) = s(0)
167: x(idx+1) = s(1)
168: x(idx+2) = s(2)
169: x(idx+3) = s(3)
170: 20 continue
172: !
173: ! Backward solve the upper triangular
174: !
175: do 40 i=n-1,0,-1
176: jstart = adiag(i) + 1
177: jend = ai(i+1) - 1
178: ax = 16*jstart
179: s(0) = x(idx)
180: s(1) = x(idx+1)
181: s(2) = x(idx+2)
182: s(3) = x(idx+3)
183: !
184: ! Pack each chunk of vector needed
185: !
186: kdx = 0
187: if (jend - jstart .ge. 500) then
188: write(6,*) 'Overflowing vector FortranSolveBAIJ4()'
189: endif
190: do 50 j=jstart,jend
191: jdx = 4*aj(j)
192: w(kdx) = x(jdx)
193: w(kdx+1) = x(jdx+1)
194: w(kdx+2) = x(jdx+2)
195: w(kdx+3) = x(jdx+3)
196: kdx = kdx + 4
197: 50 continue
198: nn = 4*(jend - jstart + 1) - 1
199: do 200, ii=0,3
200: do 210, jj=0,nn
201: s(ii) = s(ii) - a(ax+4*jj+ii)*w(jj)
202: 210 continue
203: 200 continue
205: ax = 16*adiag(i)
206: x(idx) = a(ax)*s(0) +a(ax+4)*s(1)+a(ax+8)*s(2) +a(ax+12)*s(3)
207: x(idx+1)= a(ax+1)*s(0)+a(ax+5)*s(1)+a(ax+9)*s(2) +a(ax+13)*s(3)
208: x(idx+2)= a(ax+2)*s(0)+a(ax+6)*s(1)+a(ax+10)*s(2)+a(ax+14)*s(3)
209: x(idx+3)= a(ax+3)*s(0)+a(ax+7)*s(1)+a(ax+11)*s(2)+a(ax+15)*s(3)
210: idx = idx - 4
211: 40 continue
213: return
214: end