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
|
#include "rb_lapack.h"
extern VOID cuncsd_(char* jobu1, char* jobu2, char* jobv1t, char* jobv2t, char* trans, char* signs, integer* m, integer* p, integer* q, complex* x11, integer* ldx11, complex* x12, integer* ldx12, complex* x21, integer* ldx21, complex* x22, integer* ldx22, real* theta, complex* u1, integer* ldu1, complex* u2, integer* ldu2, complex* v1t, integer* ldv1t, complex* v2t, integer* ldv2t, complex* work, integer* lwork, real* rwork, integer* lrwork, integer* iwork, integer* info);
static VALUE
rblapack_cuncsd(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobu1;
char jobu1;
VALUE rblapack_jobu2;
char jobu2;
VALUE rblapack_jobv1t;
char jobv1t;
VALUE rblapack_jobv2t;
char jobv2t;
VALUE rblapack_trans;
char trans;
VALUE rblapack_signs;
char signs;
VALUE rblapack_m;
integer m;
VALUE rblapack_x11;
complex *x11;
VALUE rblapack_x12;
complex *x12;
VALUE rblapack_x21;
complex *x21;
VALUE rblapack_x22;
complex *x22;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_lrwork;
integer lrwork;
VALUE rblapack_theta;
real *theta;
VALUE rblapack_u1;
complex *u1;
VALUE rblapack_u2;
complex *u2;
VALUE rblapack_v1t;
complex *v1t;
VALUE rblapack_v2t;
complex *v2t;
VALUE rblapack_info;
integer info;
complex *work;
real *rwork;
integer *iwork;
integer p;
integer q;
integer ldv2t;
integer ldv1t;
integer ldu1;
integer ldu2;
integer ldx11;
integer ldx12;
integer ldx21;
integer ldx22;
VALUE rblapack_options;
if (argc > 0 && TYPE(argv[argc-1]) == T_HASH) {
argc--;
rblapack_options = argv[argc];
if (rb_hash_aref(rblapack_options, sHelp) == Qtrue) {
printf("%s\n", "USAGE:\n theta, u1, u2, v1t, v2t, info = NumRu::Lapack.cuncsd( jobu1, jobu2, jobv1t, jobv2t, trans, signs, m, x11, x12, x21, x22, lwork, lrwork, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n RECURSIVE SUBROUTINE CUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* CUNCSD computes the CS decomposition of an M-by-M partitioned\n* unitary matrix X:\n*\n* [ I 0 0 | 0 0 0 ]\n* [ 0 C 0 | 0 -S 0 ]\n* [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**H\n* X = [-----------] = [---------] [---------------------] [---------] .\n* [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ]\n* [ 0 S 0 | 0 C 0 ]\n* [ 0 0 I | 0 0 0 ]\n*\n* X11 is P-by-Q. The unitary matrices U1, U2, V1, and V2 are P-by-P,\n* (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are\n* R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in\n* which R = MIN(P,M-P,Q,M-Q).\n*\n\n* Arguments\n* =========\n*\n* JOBU1 (input) CHARACTER\n* = 'Y': U1 is computed;\n* otherwise: U1 is not computed.\n*\n* JOBU2 (input) CHARACTER\n* = 'Y': U2 is computed;\n* otherwise: U2 is not computed.\n*\n* JOBV1T (input) CHARACTER\n* = 'Y': V1T is computed;\n* otherwise: V1T is not computed.\n*\n* JOBV2T (input) CHARACTER\n* = 'Y': V2T is computed;\n* otherwise: V2T is not computed.\n*\n* TRANS (input) CHARACTER\n* = 'T': X, U1, U2, V1T, and V2T are stored in row-major\n* order;\n* otherwise: X, U1, U2, V1T, and V2T are stored in column-\n* major order.\n*\n* SIGNS (input) CHARACTER\n* = 'O': The lower-left block is made nonpositive (the\n* \"other\" convention);\n* otherwise: The upper-right block is made nonpositive (the\n* \"default\" convention).\n*\n* M (input) INTEGER\n* The number of rows and columns in X.\n*\n* P (input) INTEGER\n* The number of rows in X11 and X12. 0 <= P <= M.\n*\n* Q (input) INTEGER\n* The number of columns in X11 and X21. 0 <= Q <= M.\n*\n* X (input/workspace) COMPLEX array, dimension (LDX,M)\n* On entry, the unitary matrix whose CSD is desired.\n*\n* LDX (input) INTEGER\n* The leading dimension of X. LDX >= MAX(1,M).\n*\n* THETA (output) REAL array, dimension (R), in which R =\n* MIN(P,M-P,Q,M-Q).\n* C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and\n* S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).\n*\n* U1 (output) COMPLEX array, dimension (P)\n* If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.\n*\n* LDU1 (input) INTEGER\n* The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=\n* MAX(1,P).\n*\n* U2 (output) COMPLEX array, dimension (M-P)\n* If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary\n* matrix U2.\n*\n* LDU2 (input) INTEGER\n* The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=\n* MAX(1,M-P).\n*\n* V1T (output) COMPLEX array, dimension (Q)\n* If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary\n* matrix V1**H.\n*\n* LDV1T (input) INTEGER\n* The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=\n* MAX(1,Q).\n*\n* V2T (output) COMPLEX array, dimension (M-Q)\n* If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary\n* matrix V2**H.\n*\n* LDV2T (input) INTEGER\n* The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=\n* MAX(1,M-Q).\n*\n* WORK (workspace) COMPLEX array, dimension (MAX(1,LWORK))\n* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n*\n* LWORK (input) INTEGER\n* The dimension of the array WORK.\n*\n* If LWORK = -1, then a workspace query is assumed; the routine\n* only calculates the optimal size of the WORK array, returns\n* this value as the first entry of the work array, and no error\n* message related to LWORK is issued by XERBLA.\n*\n* RWORK (workspace) REAL array, dimension MAX(1,LRWORK)\n* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.\n* If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1),\n* ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),\n* define the matrix in intermediate bidiagonal-block form\n* remaining after nonconvergence. INFO specifies the number\n* of nonzero PHI's.\n*\n* LRWORK (input) INTEGER\n* The dimension of the array RWORK.\n*\n* If LRWORK = -1, then a workspace query is assumed; the routine\n* only calculates the optimal size of the RWORK array, returns\n* this value as the first entry of the work array, and no error\n* message related to LRWORK is issued by XERBLA.\n*\n* IWORK (workspace) INTEGER array, dimension (M-Q)\n*\n* INFO (output) INTEGER\n* = 0: successful exit.\n* < 0: if INFO = -i, the i-th argument had an illegal value.\n* > 0: CBBCSD did not converge. See the description of RWORK\n* above for details.\n*\n* Reference\n* =========\n*\n* [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.\n* Algorithms, 50(1):33-65, 2009.\n*\n\n* ===================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n theta, u1, u2, v1t, v2t, info = NumRu::Lapack.cuncsd( jobu1, jobu2, jobv1t, jobv2t, trans, signs, m, x11, x12, x21, x22, lwork, lrwork, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 13 && argc != 13)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 13)", argc);
rblapack_jobu1 = argv[0];
rblapack_jobu2 = argv[1];
rblapack_jobv1t = argv[2];
rblapack_jobv2t = argv[3];
rblapack_trans = argv[4];
rblapack_signs = argv[5];
rblapack_m = argv[6];
rblapack_x11 = argv[7];
rblapack_x12 = argv[8];
rblapack_x21 = argv[9];
rblapack_x22 = argv[10];
rblapack_lwork = argv[11];
rblapack_lrwork = argv[12];
if (argc == 13) {
} else if (rblapack_options != Qnil) {
} else {
}
jobu1 = StringValueCStr(rblapack_jobu1)[0];
jobv1t = StringValueCStr(rblapack_jobv1t)[0];
trans = StringValueCStr(rblapack_trans)[0];
m = NUM2INT(rblapack_m);
if (!NA_IsNArray(rblapack_x21))
rb_raise(rb_eArgError, "x21 (10th argument) must be NArray");
if (NA_RANK(rblapack_x21) != 2)
rb_raise(rb_eArgError, "rank of x21 (10th argument) must be %d", 2);
p = NA_SHAPE0(rblapack_x21);
q = NA_SHAPE1(rblapack_x21);
if (NA_TYPE(rblapack_x21) != NA_SCOMPLEX)
rblapack_x21 = na_change_type(rblapack_x21, NA_SCOMPLEX);
x21 = NA_PTR_TYPE(rblapack_x21, complex*);
lwork = NUM2INT(rblapack_lwork);
jobu2 = StringValueCStr(rblapack_jobu2)[0];
signs = StringValueCStr(rblapack_signs)[0];
lrwork = NUM2INT(rblapack_lrwork);
jobv2t = StringValueCStr(rblapack_jobv2t)[0];
if (!NA_IsNArray(rblapack_x11))
rb_raise(rb_eArgError, "x11 (8th argument) must be NArray");
if (NA_RANK(rblapack_x11) != 2)
rb_raise(rb_eArgError, "rank of x11 (8th argument) must be %d", 2);
if (NA_SHAPE0(rblapack_x11) != p)
rb_raise(rb_eRuntimeError, "shape 0 of x11 must be the same as shape 0 of x21");
if (NA_SHAPE1(rblapack_x11) != q)
rb_raise(rb_eRuntimeError, "shape 1 of x11 must be the same as shape 1 of x21");
if (NA_TYPE(rblapack_x11) != NA_SCOMPLEX)
rblapack_x11 = na_change_type(rblapack_x11, NA_SCOMPLEX);
x11 = NA_PTR_TYPE(rblapack_x11, complex*);
if (!NA_IsNArray(rblapack_x22))
rb_raise(rb_eArgError, "x22 (11th argument) must be NArray");
if (NA_RANK(rblapack_x22) != 2)
rb_raise(rb_eArgError, "rank of x22 (11th argument) must be %d", 2);
if (NA_SHAPE0(rblapack_x22) != p)
rb_raise(rb_eRuntimeError, "shape 0 of x22 must be the same as shape 0 of x21");
if (NA_SHAPE1(rblapack_x22) != (m-q))
rb_raise(rb_eRuntimeError, "shape 1 of x22 must be %d", m-q);
if (NA_TYPE(rblapack_x22) != NA_SCOMPLEX)
rblapack_x22 = na_change_type(rblapack_x22, NA_SCOMPLEX);
x22 = NA_PTR_TYPE(rblapack_x22, complex*);
ldv1t = lsame_(&jobv1t,"Y") ? MAX(1,q) : 0;
if (!NA_IsNArray(rblapack_x12))
rb_raise(rb_eArgError, "x12 (9th argument) must be NArray");
if (NA_RANK(rblapack_x12) != 2)
rb_raise(rb_eArgError, "rank of x12 (9th argument) must be %d", 2);
if (NA_SHAPE0(rblapack_x12) != p)
rb_raise(rb_eRuntimeError, "shape 0 of x12 must be the same as shape 0 of x21");
if (NA_SHAPE1(rblapack_x12) != (m-q))
rb_raise(rb_eRuntimeError, "shape 1 of x12 must be %d", m-q);
if (NA_TYPE(rblapack_x12) != NA_SCOMPLEX)
rblapack_x12 = na_change_type(rblapack_x12, NA_SCOMPLEX);
x12 = NA_PTR_TYPE(rblapack_x12, complex*);
ldu1 = lsame_(&jobu1,"Y") ? MAX(1,p) : 0;
ldx11 = p;
ldx21 = p;
ldv2t = lsame_(&jobv2t,"Y") ? MAX(1,m-q) : 0;
ldx12 = p;
ldu2 = lsame_(&jobu2,"Y") ? MAX(1,m-p) : 0;
ldx22 = p;
{
na_shape_t shape[1];
shape[0] = MIN(MIN(MIN(p,m-p),q),m-q);
rblapack_theta = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
theta = NA_PTR_TYPE(rblapack_theta, real*);
{
na_shape_t shape[1];
shape[0] = p;
rblapack_u1 = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
u1 = NA_PTR_TYPE(rblapack_u1, complex*);
{
na_shape_t shape[1];
shape[0] = m-p;
rblapack_u2 = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
u2 = NA_PTR_TYPE(rblapack_u2, complex*);
{
na_shape_t shape[1];
shape[0] = q;
rblapack_v1t = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
v1t = NA_PTR_TYPE(rblapack_v1t, complex*);
{
na_shape_t shape[1];
shape[0] = m-q;
rblapack_v2t = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
v2t = NA_PTR_TYPE(rblapack_v2t, complex*);
work = ALLOC_N(complex, (MAX(1,lwork)));
rwork = ALLOC_N(real, (MAX(1,lrwork)));
iwork = ALLOC_N(integer, (m-q));
cuncsd_(&jobu1, &jobu2, &jobv1t, &jobv2t, &trans, &signs, &m, &p, &q, x11, &ldx11, x12, &ldx12, x21, &ldx21, x22, &ldx22, theta, u1, &ldu1, u2, &ldu2, v1t, &ldv1t, v2t, &ldv2t, work, &lwork, rwork, &lrwork, iwork, &info);
free(work);
free(rwork);
free(iwork);
rblapack_info = INT2NUM(info);
return rb_ary_new3(6, rblapack_theta, rblapack_u1, rblapack_u2, rblapack_v1t, rblapack_v2t, rblapack_info);
}
void
init_lapack_cuncsd(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "cuncsd", rblapack_cuncsd, -1);
}
|
