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
//
// GENERATED FILE
//
use super::*;
use crate::SpiceContext;
use f2rust_std::*;
/// Matrix transpose times matrix, 3x3
///
/// Multiply the transpose of a 3x3 matrix and a 3x3 matrix.
///
/// # Brief I/O
///
/// ```text
/// VARIABLE I/O DESCRIPTION
/// -------- --- --------------------------------------------------
/// M1 I 3x3 double precision matrix.
/// M2 I 3x3 double precision matrix.
/// MOUT O 3x3 double precision matrix which is the product
/// (M1**T) * M2.
/// ```
///
/// # Detailed Input
///
/// ```text
/// M1 is any 3x3 double precision matrix. Typically,
/// M1 will be a rotation matrix since then its
/// transpose is its inverse (but this is NOT a
/// requirement).
///
/// M2 is any 3x3 double precision matrix.
/// ```
///
/// # Detailed Output
///
/// ```text
/// MOUT is s 3x3 double precision matrix. MOUT is the
/// product MOUT = (M1**T) x M2.
/// ```
///
/// # Exceptions
///
/// ```text
/// Error free.
/// ```
///
/// # Particulars
///
/// ```text
/// The code reflects precisely the following mathematical expression
///
/// For each value of the subscripts I and J from 1 to 3:
///
/// MOUT(I,J) = Summation from K=1 to 3 of ( M1(K,I) * M2(K,J) )
///
/// Note that the reversal of the K and I subscripts in the left-hand
/// matrix M1 is what makes MOUT the product of the TRANSPOSE of M1
/// and not simply of M1 itself.
/// ```
///
/// # 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 two 3x3 matrices, multiply the transpose of the first
/// matrix by the second one.
///
///
/// Example code begins here.
///
///
/// PROGRAM MTXM_EX1
/// IMPLICIT NONE
///
/// C
/// C Local variables.
/// C
/// DOUBLE PRECISION M1 ( 3, 3 )
/// DOUBLE PRECISION M2 ( 3, 3 )
/// DOUBLE PRECISION MOUT ( 3, 3 )
///
/// INTEGER I
/// INTEGER J
///
/// C
/// C Define M1 and M2.
/// C
/// DATA M1 / 1.0D0, 4.0D0, 7.0D0,
/// . 2.0D0, 5.0D0, 8.0D0,
/// . 3.0D0, 6.0D0, 9.0D0 /
///
/// DATA M2 / 1.0D0, -1.0D0, 0.0D0,
/// . 1.0D0, 1.0D0, 0.0D0,
/// . 0.0D0, 0.0D0, 1.0D0 /
///
/// C
/// C Multiply the transpose of M1 by M2.
/// C
/// CALL MTXM ( M1, M2, MOUT )
///
/// WRITE(*,'(A)') 'Transpose of M1 times M2:'
/// DO I = 1, 3
///
/// WRITE(*,'(3F10.3)') ( MOUT(I,J), J=1,3)
///
/// END DO
///
/// END
///
///
/// When this program was executed on a Mac/Intel/gfortran/64-bit
/// platform, the output was:
///
///
/// Transpose of M1 times M2:
/// -3.000 5.000 7.000
/// -3.000 7.000 8.000
/// -3.000 9.000 9.000
/// ```
///
/// # Restrictions
///
/// ```text
/// 1) The user is responsible for checking the magnitudes of the
/// elements of M1 and M2 so that a floating point overflow does
/// not occur. (In the typical use where M1 and M2 are rotation
/// matrices, this not a risk at all.)
/// ```
///
/// # Author and Institution
///
/// ```text
/// N.J. Bachman (JPL)
/// 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 1.0.2, 23-APR-2010 (NJB)
///
/// Header correction: assertions that the output
/// can overwrite the input have been removed.
///
/// - 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 mtxm(m1: &[[f64; 3]; 3], m2: &[[f64; 3]; 3], mout: &mut [[f64; 3]; 3]) {
MTXM(
m1.as_flattened(),
m2.as_flattened(),
mout.as_flattened_mut(),
);
}
//$Procedure MTXM ( Matrix transpose times matrix, 3x3 )
pub fn MTXM(M1: &[f64], M2: &[f64], MOUT: &mut [f64]) {
let M1 = DummyArray2D::new(M1, 1..=3, 1..=3);
let M2 = DummyArray2D::new(M2, 1..=3, 1..=3);
let mut MOUT = DummyArrayMut2D::new(MOUT, 1..=3, 1..=3);
let mut PRODM = StackArray2D::<f64, 9>::new(1..=3, 1..=3);
//
// Local variables
//
//
// Perform the matrix multiplication
//
for I in 1..=3 {
for J in 1..=3 {
PRODM[[I, J]] = (((M1[[1, I]] * M2[[1, J]]) + (M1[[2, I]] * M2[[2, J]]))
+ (M1[[3, I]] * M2[[3, J]]));
}
}
//
// Move the result into MOUT
//
MOVED(PRODM.as_slice(), 9, MOUT.as_slice_mut());
}