-
Notifications
You must be signed in to change notification settings - Fork 184
/
Copy pathstdlib_intrinsics_matmul.fypp
226 lines (195 loc) · 7.63 KB
/
stdlib_intrinsics_matmul.fypp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
#:include "common.fypp"
#:set I_KINDS_TYPES = list(zip(INT_KINDS, INT_TYPES, INT_KINDS))
#:set R_KINDS_TYPES = list(zip(REAL_KINDS, REAL_TYPES, REAL_SUFFIX))
#:set C_KINDS_TYPES = list(zip(CMPLX_KINDS, CMPLX_TYPES, CMPLX_SUFFIX))
submodule (stdlib_intrinsics) stdlib_intrinsics_matmul
use stdlib_linalg_blas, only: gemm
use stdlib_constants
implicit none
contains
! Algorithm for the optimal parenthesization of matrices
! Reference: Cormen, "Introduction to Algorithms", 4ed, ch-14, section-2
! Internal use only!
pure function matmul_chain_order(p) result(s)
integer, intent(in) :: p(:)
integer :: s(1:size(p) - 2, 2:size(p) - 1), m(1:size(p) - 1, 1:size(p) - 1)
integer :: n, l, i, j, k, q
n = size(p) - 1
m(:,:) = 0
s(:,:) = 0
do l = 2, n
do i = 1, n - l + 1
j = i + l - 1
m(i,j) = huge(1)
do k = i, j - 1
q = m(i,k) + m(k+1,j) + p(i)*p(k+1)*p(j+1)
if (q < m(i, j)) then
m(i,j) = q
s(i,j) = k
end if
end do
end do
end do
end function matmul_chain_order
#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
pure function matmul_chain_mult_${s}$_3 (m1, m2, m3, start, s, p) result(r)
${t}$, intent(in) :: m1(:,:), m2(:,:), m3(:,:)
integer, intent(in) :: start, s(:,2:), p(:)
${t}$, allocatable :: r(:,:), temp(:,:)
integer :: ord, m, n, k
ord = s(start, start + 2)
allocate(r(p(start), p(start + 3)))
if (ord == start) then
! m1*(m2*m3)
m = p(start + 1)
n = p(start + 3)
k = p(start + 2)
allocate(temp(m,n))
call gemm('N', 'N', m, n, k, one_${s}$, m2, m, m3, k, zero_${s}$, temp, m)
m = p(start)
n = p(start + 3)
k = p(start + 1)
call gemm('N', 'N', m, n, k, one_${s}$, m1, m, temp, k, zero_${s}$, r, m)
else if (ord == start + 1) then
! (m1*m2)*m3
m = p(start)
n = p(start + 2)
k = p(start + 1)
allocate(temp(m, n))
call gemm('N', 'N', m, n, k, one_${s}$, m1, m, m2, k, zero_${s}$, temp, m)
m = p(start)
n = p(start + 3)
k = p(start + 1)
call gemm('N', 'N', m, n, k, one_${s}$, temp, m, m3, k, zero_${s}$, r, m)
else
error stop "stdlib_matmul: error: unexpected s(i,j)"
end if
end function matmul_chain_mult_${s}$_3
pure function matmul_chain_mult_${s}$_4 (m1, m2, m3, m4, start, s, p) result(r)
${t}$, intent(in) :: m1(:,:), m2(:,:), m3(:,:), m4(:,:)
integer, intent(in) :: start, s(:,2:), p(:)
${t}$, allocatable :: r(:,:), temp(:,:), temp1(:,:)
integer :: ord, m, n, k
ord = s(start, start + 3)
allocate(r(p(start), p(start + 4)))
if (ord == start) then
! m1*(m2*m3*m4)
temp = matmul_chain_mult_${s}$_3(m2, m3, m4, start + 1, s, p)
m = p(start)
n = p(start + 4)
k = p(start + 1)
call gemm('N', 'N', m, n, k, one_${s}$, m1, m, temp, k, zero_${s}$, r, m)
else if (ord == start + 1) then
! (m1*m2)*(m3*m4)
m = p(start)
n = p(start + 2)
k = p(start + 1)
allocate(temp(m,n))
call gemm('N', 'N', m, n, k, one_${s}$, m1, m, m2, k, zero_${s}$, temp, m)
m = p(start + 2)
n = p(start + 4)
k = p(start + 3)
allocate(temp1(m,n))
call gemm('N', 'N', m, n, k, one_${s}$, m3, m, m4, k, zero_${s}$, temp1, m)
m = p(start)
n = p(start + 4)
k = p(start + 2)
call gemm('N', 'N', m, n, k, one_${s}$, temp, m, temp1, k, zero_${s}$, r, m)
else if (ord == start + 2) then
! (m1*m2*m3)*m4
temp = matmul_chain_mult_${s}$_3(m1, m2, m3, start, s, p)
m = p(start)
n = p(start + 4)
k = p(start + 3)
call gemm('N', 'N', m, n, k, one_${s}$, temp, m, m4, k, zero_${s}$, r, m)
else
error stop "stdlib_matmul: error: unexpected s(i,j)"
end if
end function matmul_chain_mult_${s}$_4
pure module function stdlib_matmul_${s}$ (m1, m2, m3, m4, m5) result(r)
${t}$, intent(in) :: m1(:,:), m2(:,:)
${t}$, intent(in), optional :: m3(:,:), m4(:,:), m5(:,:)
${t}$, allocatable :: r(:,:), temp(:,:), temp1(:,:)
integer :: p(6), num_present, m, n, k
integer, allocatable :: s(:,:)
p(1) = size(m1, 1)
p(2) = size(m2, 1)
p(3) = size(m2, 2)
num_present = 2
if (present(m3)) then
p(3) = size(m3, 1)
p(4) = size(m3, 2)
num_present = num_present + 1
end if
if (present(m4)) then
p(4) = size(m4, 1)
p(5) = size(m4, 2)
num_present = num_present + 1
end if
if (present(m5)) then
p(5) = size(m5, 1)
p(6) = size(m5, 2)
num_present = num_present + 1
end if
allocate(r(p(1), p(num_present + 1)))
if (num_present == 2) then
m = p(1)
n = p(3)
k = p(2)
call gemm('N', 'N', m, n, k, one_${s}$, m1, m, m2, k, zero_${s}$, r, m)
return
end if
! Now num_present >= 3
allocate(s(1:num_present - 1, 2:num_present))
s = matmul_chain_order(p(1: num_present + 1))
if (num_present == 3) then
r = matmul_chain_mult_${s}$_3(m1, m2, m3, 1, s, p(1:4))
return
else if (num_present == 4) then
r = matmul_chain_mult_${s}$_4(m1, m2, m3, m4, 1, s, p(1:5))
return
end if
! Now num_present is 5
select case (s(1, 5))
case (1)
! m1*(m2*m3*m4*m5)
temp = matmul_chain_mult_${s}$_4(m2, m3, m4, m5, 2, s, p)
m = p(1)
n = p(6)
k = p(2)
call gemm('N', 'N', m, n, k, one_${s}$, m1, m, temp, k, zero_${s}$, r, m)
case (2)
! (m1*m2)*(m3*m4*m5)
m = p(1)
n = p(3)
k = p(2)
allocate(temp(m,n))
call gemm('N', 'N', m, n, k, one_${s}$, m1, m, m2, k, zero_${s}$, temp, m)
temp1 = matmul_chain_mult_${s}$_3(m3, m4, m5, 3, s, p)
k = n
n = p(6)
call gemm('N', 'N', m, n, k, one_${s}$, temp, m, temp1, k, zero_${s}$, r, m)
case (3)
! (m1*m2*m3)*(m4*m5)
temp = matmul_chain_mult_${s}$_3(m1, m2, m3, 3, s, p)
m = p(4)
n = p(6)
k = p(5)
allocate(temp1(m,n))
call gemm('N', 'N', m, n, k, one_${s}$, m4, m, m5, k, zero_${s}$, temp1, m)
k = m
m = p(1)
call gemm('N', 'N', m, n, k, one_${s}$, temp, m, temp1, k, zero_${s}$, r, m)
case (4)
! (m1*m2*m3*m4)*m5
temp = matmul_chain_mult_${s}$_4(m1, m2, m3, m4, 1, s, p)
m = p(1)
n = p(6)
k = p(5)
call gemm('N', 'N', m, n, k, one_${s}$, temp, m, m5, k, zero_${s}$, r, m)
case default
error stop "stdlib_matmul: error: unexpected s(i,j)"
end select
end function stdlib_matmul_${s}$
#:endfor
end submodule stdlib_intrinsics_matmul