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: end
99: ! version that does not call BLAS 2 operation for each row block
100: !
101: subroutine FortranSolveBAIJ4(n,x,ai,aj,adiag,a,b,w)
102: implicit none
103: MatScalar a(0:*)
104: PetscScalar x(0:*),b(0:*),w(0:*)
105: PetscInt n,ai(0:*),aj(0:*),adiag(0:*)
106: PetscInt ii,jj,i,j
108: PetscInt jstart,jend,idx,ax,jdx,kdx,nn
109: PetscScalar s(0:3)
111: !
112: ! Forward Solve
113: !
115: PETSC_AssertAlignx(16,a(1))
116: PETSC_AssertAlignx(16,w(1))
117: PETSC_AssertAlignx(16,x(1))
118: PETSC_AssertAlignx(16,b(1))
119: PETSC_AssertAlignx(16,ai(1))
120: PETSC_AssertAlignx(16,aj(1))
121: PETSC_AssertAlignx(16,adiag(1))
123: x(0) = b(0)
124: x(1) = b(1)
125: x(2) = b(2)
126: x(3) = b(3)
127: idx = 0
128: do 20 i=1,n-1
129: !
130: ! Pack required part of vector into work array
131: !
132: kdx = 0
133: jstart = ai(i)
134: jend = adiag(i) - 1
135: if (jend - jstart .ge. 500) then
136: write(6,*) 'Overflowing vector FortranSolveBAIJ4()'
137: endif
138: do 30 j=jstart,jend
140: jdx = 4*aj(j)
142: w(kdx) = x(jdx)
143: w(kdx+1) = x(jdx+1)
144: w(kdx+2) = x(jdx+2)
145: w(kdx+3) = x(jdx+3)
146: kdx = kdx + 4
147: 30 continue
149: ax = 16*jstart
150: idx = idx + 4
151: s(0) = b(idx)
152: s(1) = b(idx+1)
153: s(2) = b(idx+2)
154: s(3) = b(idx+3)
155: !
156: ! s = s - a(ax:)*w
157: !
158: nn = 4*(jend - jstart + 1) - 1
159: do 100, ii=0,3
160: do 110, jj=0,nn
161: s(ii) = s(ii) - a(ax+4*jj+ii)*w(jj)
162: 110 continue
163: 100 continue
165: x(idx) = s(0)
166: x(idx+1) = s(1)
167: x(idx+2) = s(2)
168: x(idx+3) = s(3)
169: 20 continue
171: !
172: ! Backward solve the upper triangular
173: !
174: do 40 i=n-1,0,-1
175: jstart = adiag(i) + 1
176: jend = ai(i+1) - 1
177: ax = 16*jstart
178: s(0) = x(idx)
179: s(1) = x(idx+1)
180: s(2) = x(idx+2)
181: s(3) = x(idx+3)
182: !
183: ! Pack each chunk of vector needed
184: !
185: kdx = 0
186: if (jend - jstart .ge. 500) then
187: write(6,*) 'Overflowing vector FortranSolveBAIJ4()'
188: endif
189: do 50 j=jstart,jend
190: jdx = 4*aj(j)
191: w(kdx) = x(jdx)
192: w(kdx+1) = x(jdx+1)
193: w(kdx+2) = x(jdx+2)
194: w(kdx+3) = x(jdx+3)
195: kdx = kdx + 4
196: 50 continue
197: nn = 4*(jend - jstart + 1) - 1
198: do 200, ii=0,3
199: do 210, jj=0,nn
200: s(ii) = s(ii) - a(ax+4*jj+ii)*w(jj)
201: 210 continue
202: 200 continue
204: ax = 16*adiag(i)
205: x(idx) = a(ax)*s(0) +a(ax+4)*s(1)+a(ax+8)*s(2) +a(ax+12)*s(3)
206: x(idx+1)= a(ax+1)*s(0)+a(ax+5)*s(1)+a(ax+9)*s(2) +a(ax+13)*s(3)
207: x(idx+2)= a(ax+2)*s(0)+a(ax+6)*s(1)+a(ax+10)*s(2)+a(ax+14)*s(3)
208: x(idx+3)= a(ax+3)*s(0)+a(ax+7)*s(1)+a(ax+11)*s(2)+a(ax+15)*s(3)
209: idx = idx - 4
210: 40 continue
212: end