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
//
// GENERATED FILE
//
use super::*;
use crate::SpiceContext;
use f2rust_std::*;
/// Matrix times matrix transpose, general dimension
///
/// Multiply a matrix and the transpose of a matrix, both of
/// arbitrary size.
///
/// # Brief I/O
///
/// ```text
/// VARIABLE I/O DESCRIPTION
/// -------- --- --------------------------------------------------
/// M1 I Left-hand matrix to be multiplied.
/// M2 I Right-hand matrix whose transpose is to be
/// multiplied.
/// NR1 I Row dimension of M1 and row dimension of MOUT.
/// NC1C2 I Column dimension of M1 and column dimension of M2.
/// NR2 I Row dimension of M2 and column dimension of MOUT.
/// MOUT O Product matrix M1 * M2**T.
/// ```
///
/// # Detailed Input
///
/// ```text
/// M1 is any double precision matrix of arbitrary size.
///
/// M2 is any double precision matrix of arbitrary size.
///
/// The number of columns in M2 must match the number of
/// columns in M1.
///
/// NR1 is the number of rows in both M1 and MOUT.
///
/// NC1C2 is the number of columns in M1 and (by necessity)
/// the number of columns of M2.
///
/// NR2 is the number of rows in both M2 and the number of
/// columns in MOUT.
/// ```
///
/// # Detailed Output
///
/// ```text
/// MOUT is a double precision matrix of dimension NR1 x NR2.
///
/// MOUT is the product matrix given by
///
/// T
/// MOUT = M1 x M2
///
/// where the superscript "T" denotes the transpose
/// matrix.
///
/// MOUT must not overwrite M1 or M2.
/// ```
///
/// # Exceptions
///
/// ```text
/// Error free.
/// ```
///
/// # Particulars
///
/// ```text
/// The code reflects precisely the following mathematical expression
///
/// For each value of the subscript I from 1 to NR1, and J from 1
/// to NR2:
///
/// MOUT(I,J) = Summation from K=1 to NC1C2 of ( M1(I,K) * M2(J,K) )
///
/// Notice that the order of the subscripts of M2 are reversed from
/// what they would be if this routine merely multiplied M1 and M2.
/// It is this transposition of subscripts that makes this routine
/// multiply M1 and the TRANPOSE of M2.
///
/// Since this subroutine operates on matrices of arbitrary size, it
/// is not feasible to buffer intermediate results. Thus, MOUT
/// should NOT overwrite either M1 or M2.
/// ```
///
/// # Examples
///
/// ```text
/// The numerical results shown for this example may differ across
/// platforms. The results depend on the SPICE kernels used as
/// input, the compiler and supporting libraries, and the machine
/// specific arithmetic implementation.
///
/// 1) Given a 2x3 and a 3x4 matrices, multiply the first matrix by
/// the transpose of the second one.
///
///
/// Example code begins here.
///
///
/// PROGRAM MXMTG_EX1
/// IMPLICIT NONE
///
/// C
/// C Local variables.
/// C
/// DOUBLE PRECISION M1 ( 2, 3 )
/// DOUBLE PRECISION M2 ( 4, 3 )
/// DOUBLE PRECISION MOUT ( 2, 4 )
///
/// INTEGER I
/// INTEGER J
///
/// C
/// C Define M1 and M2.
/// C
/// DATA M1 / 1.0D0, 3.0D0,
/// . 2.0D0, 2.0D0,
/// . 3.0D0, 1.0D0 /
///
/// DATA M2 / 1.0D0, 2.0D0, 1.0D0, 2.0D0,
/// . 2.0D0, 1.0D0, 2.0D0, 1.0D0,
/// . 0.0D0, 2.0D0, 0.0D0, 2.0D0 /
///
/// C
/// C Multiply M1 by the transpose of M2.
/// C
/// CALL MXMTG ( M1, M2, 2, 3, 4, MOUT )
///
/// WRITE(*,'(A)') 'M1 times transpose of M2:'
/// DO I = 1, 2
///
/// WRITE(*,'(4F10.3)') ( MOUT(I,J), J=1,4)
///
/// END DO
///
/// END
///
///
/// When this program was executed on a Mac/Intel/gfortran/64-bit
/// platform, the output was:
///
///
/// M1 times transpose of M2:
/// 5.000 10.000 5.000 10.000
/// 7.000 10.000 7.000 10.000
/// ```
///
/// # Restrictions
///
/// ```text
/// 1) No error checking is performed to prevent numeric overflow or
/// underflow.
///
/// The user is responsible for checking the magnitudes of the
/// elements of M1 and M2 so that a floating point overflow does
/// not occur.
///
/// 2) No error checking is performed to determine if the input and
/// output matrices have, in fact, been correctly dimensioned.
/// ```
///
/// # Author and Institution
///
/// ```text
/// J. Diaz del Rio (ODC Space)
/// W.M. Owen (JPL)
/// W.L. Taber (JPL)
/// ```
///
/// # Version
///
/// ```text
/// - SPICELIB Version 1.1.0, 04-JUL-2021 (JDR)
///
/// Added IMPLICIT NONE statement.
///
/// Edited the header to comply with NAIF standard.
/// Added complete code example based on the existing example.
///
/// - SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)
///
/// Comment section for permuted index source lines was added
/// following the header.
///
/// - SPICELIB Version 1.0.0, 31-JAN-1990 (WMO)
/// ```
pub fn mxmtg(m1: &[f64], m2: &[f64], nr1: i32, nc1c2: i32, nr2: i32, mout: &mut [f64]) {
MXMTG(m1, m2, nr1, nc1c2, nr2, mout);
}
//$Procedure MXMTG ( Matrix times matrix transpose, general dimension )
pub fn MXMTG(M1: &[f64], M2: &[f64], NR1: i32, NC1C2: i32, NR2: i32, MOUT: &mut [f64]) {
let M1 = DummyArray2D::new(M1, 1..=NR1, 1..=NC1C2);
let M2 = DummyArray2D::new(M2, 1..=NR2, 1..=NC1C2);
let mut MOUT = DummyArrayMut2D::new(MOUT, 1..=NR1, 1..=NR2);
let mut SUM: f64 = 0.0;
//
// Local variables
//
//
// Perform the matrix multiplication
//
for I in 1..=NR1 {
for J in 1..=NR2 {
SUM = 0.0;
for K in 1..=NC1C2 {
SUM = (SUM + (M1[[I, K]] * M2[[J, K]]));
}
MOUT[[I, J]] = SUM;
}
}
}