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
|
#include "rb_lapack.h"
extern VOID dbdsdc_(char* uplo, char* compq, integer* n, doublereal* d, doublereal* e, doublereal* u, integer* ldu, doublereal* vt, integer* ldvt, doublereal* q, integer* iq, doublereal* work, integer* iwork, integer* info);
static VALUE
rblapack_dbdsdc(int argc, VALUE *argv, VALUE self){
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_compq;
char compq;
VALUE rblapack_d;
doublereal *d;
VALUE rblapack_e;
doublereal *e;
VALUE rblapack_u;
doublereal *u;
VALUE rblapack_vt;
doublereal *vt;
VALUE rblapack_q;
doublereal *q;
VALUE rblapack_iq;
integer *iq;
VALUE rblapack_info;
integer info;
VALUE rblapack_d_out__;
doublereal *d_out__;
VALUE rblapack_e_out__;
doublereal *e_out__;
integer c__0;
integer c__9;
real smlsiz;
doublereal *work;
integer *iwork;
integer n;
integer ldvt;
integer ldu;
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 u, vt, q, iq, info, d, e = NumRu::Lapack.dbdsdc( uplo, compq, d, e, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* DBDSDC computes the singular value decomposition (SVD) of a real\n* N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT,\n* using a divide and conquer method, where S is a diagonal matrix\n* with non-negative diagonal elements (the singular values of B), and\n* U and VT are orthogonal matrices of left and right singular vectors,\n* respectively. DBDSDC can be used to compute all singular values,\n* and optionally, singular vectors or singular vectors in compact form.\n*\n* This code makes very mild assumptions about floating point\n* arithmetic. It will work on machines with a guard digit in\n* add/subtract, or on those binary machines without guard digits\n* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.\n* It could conceivably fail on hexadecimal or decimal machines\n* without guard digits, but we know of none. See DLASD3 for details.\n*\n* The code currently calls DLASDQ if singular values only are desired.\n* However, it can be slightly modified to compute singular values\n* using the divide and conquer method.\n*\n\n* Arguments\n* =========\n*\n* UPLO (input) CHARACTER*1\n* = 'U': B is upper bidiagonal.\n* = 'L': B is lower bidiagonal.\n*\n* COMPQ (input) CHARACTER*1\n* Specifies whether singular vectors are to be computed\n* as follows:\n* = 'N': Compute singular values only;\n* = 'P': Compute singular values and compute singular\n* vectors in compact form;\n* = 'I': Compute singular values and singular vectors.\n*\n* N (input) INTEGER\n* The order of the matrix B. N >= 0.\n*\n* D (input/output) DOUBLE PRECISION array, dimension (N)\n* On entry, the n diagonal elements of the bidiagonal matrix B.\n* On exit, if INFO=0, the singular values of B.\n*\n* E (input/output) DOUBLE PRECISION array, dimension (N-1)\n* On entry, the elements of E contain the offdiagonal\n* elements of the bidiagonal matrix whose SVD is desired.\n* On exit, E has been destroyed.\n*\n* U (output) DOUBLE PRECISION array, dimension (LDU,N)\n* If COMPQ = 'I', then:\n* On exit, if INFO = 0, U contains the left singular vectors\n* of the bidiagonal matrix.\n* For other values of COMPQ, U is not referenced.\n*\n* LDU (input) INTEGER\n* The leading dimension of the array U. LDU >= 1.\n* If singular vectors are desired, then LDU >= max( 1, N ).\n*\n* VT (output) DOUBLE PRECISION array, dimension (LDVT,N)\n* If COMPQ = 'I', then:\n* On exit, if INFO = 0, VT' contains the right singular\n* vectors of the bidiagonal matrix.\n* For other values of COMPQ, VT is not referenced.\n*\n* LDVT (input) INTEGER\n* The leading dimension of the array VT. LDVT >= 1.\n* If singular vectors are desired, then LDVT >= max( 1, N ).\n*\n* Q (output) DOUBLE PRECISION array, dimension (LDQ)\n* If COMPQ = 'P', then:\n* On exit, if INFO = 0, Q and IQ contain the left\n* and right singular vectors in a compact form,\n* requiring O(N log N) space instead of 2*N**2.\n* In particular, Q contains all the DOUBLE PRECISION data in\n* LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1))))\n* words of memory, where SMLSIZ is returned by ILAENV and\n* is equal to the maximum size of the subproblems at the\n* bottom of the computation tree (usually about 25).\n* For other values of COMPQ, Q is not referenced.\n*\n* IQ (output) INTEGER array, dimension (LDIQ)\n* If COMPQ = 'P', then:\n* On exit, if INFO = 0, Q and IQ contain the left\n* and right singular vectors in a compact form,\n* requiring O(N log N) space instead of 2*N**2.\n* In particular, IQ contains all INTEGER data in\n* LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1))))\n* words of memory, where SMLSIZ is returned by ILAENV and\n* is equal to the maximum size of the subproblems at the\n* bottom of the computation tree (usually about 25).\n* For other values of COMPQ, IQ is not referenced.\n*\n* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))\n* If COMPQ = 'N' then LWORK >= (4 * N).\n* If COMPQ = 'P' then LWORK >= (6 * N).\n* If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).\n*\n* IWORK (workspace) INTEGER array, dimension (8*N)\n*\n* INFO (output) INTEGER\n* = 0: successful exit.\n* < 0: if INFO = -i, the i-th argument had an illegal value.\n* > 0: The algorithm failed to compute a singular value.\n* The update process of divide and conquer failed.\n*\n\n* Further Details\n* ===============\n*\n* Based on contributions by\n* Ming Gu and Huan Ren, Computer Science Division, University of\n* California at Berkeley, USA\n*\n* =====================================================================\n* Changed dimension statement in comment describing E from (N) to\n* (N-1). Sven, 17 Feb 05.\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n u, vt, q, iq, info, d, e = NumRu::Lapack.dbdsdc( uplo, compq, d, e, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 4 && argc != 4)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 4)", argc);
rblapack_uplo = argv[0];
rblapack_compq = argv[1];
rblapack_d = argv[2];
rblapack_e = argv[3];
if (argc == 4) {
} else if (rblapack_options != Qnil) {
} else {
}
uplo = StringValueCStr(rblapack_uplo)[0];
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (3th argument) must be NArray");
if (NA_RANK(rblapack_d) != 1)
rb_raise(rb_eArgError, "rank of d (3th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_d);
if (NA_TYPE(rblapack_d) != NA_DFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_DFLOAT);
d = NA_PTR_TYPE(rblapack_d, doublereal*);
c__0 = 0;
compq = StringValueCStr(rblapack_compq)[0];
c__9 = 9;
ldu = lsame_(&compq,"I") ? MAX(1,n) : 0;
if (!NA_IsNArray(rblapack_e))
rb_raise(rb_eArgError, "e (4th argument) must be NArray");
if (NA_RANK(rblapack_e) != 1)
rb_raise(rb_eArgError, "rank of e (4th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_e) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of e must be %d", n-1);
if (NA_TYPE(rblapack_e) != NA_DFLOAT)
rblapack_e = na_change_type(rblapack_e, NA_DFLOAT);
e = NA_PTR_TYPE(rblapack_e, doublereal*);
smlsiz = ilaenv_(&c__9, "DBDSDC", " ", &c__0, &c__0, &c__0, &c__0);
ldvt = lsame_(&compq,"I") ? MAX(1,n) : 0;
{
na_shape_t shape[2];
shape[0] = lsame_(&compq,"I") ? ldu : 0;
shape[1] = lsame_(&compq,"I") ? n : 0;
rblapack_u = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
u = NA_PTR_TYPE(rblapack_u, doublereal*);
{
na_shape_t shape[2];
shape[0] = lsame_(&compq,"I") ? ldvt : 0;
shape[1] = lsame_(&compq,"I") ? n : 0;
rblapack_vt = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
vt = NA_PTR_TYPE(rblapack_vt, doublereal*);
{
na_shape_t shape[1];
shape[0] = lsame_(&compq,"I") ? (lsame_(&compq,"P") ? n*(11+2*smlsiz+8*(int)(log(((double)n)/(smlsiz+1))/log(2.0))) : 0) : 0;
rblapack_q = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
q = NA_PTR_TYPE(rblapack_q, doublereal*);
{
na_shape_t shape[1];
shape[0] = lsame_(&compq,"I") ? (lsame_(&compq,"P") ? n*(3+3*(int)(log(((double)n)/(smlsiz+1))/log(2.0))) : 0) : 0;
rblapack_iq = na_make_object(NA_LINT, 1, shape, cNArray);
}
iq = NA_PTR_TYPE(rblapack_iq, integer*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_d_out__ = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
d_out__ = NA_PTR_TYPE(rblapack_d_out__, doublereal*);
MEMCPY(d_out__, d, doublereal, NA_TOTAL(rblapack_d));
rblapack_d = rblapack_d_out__;
d = d_out__;
{
na_shape_t shape[1];
shape[0] = n-1;
rblapack_e_out__ = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
e_out__ = NA_PTR_TYPE(rblapack_e_out__, doublereal*);
MEMCPY(e_out__, e, doublereal, NA_TOTAL(rblapack_e));
rblapack_e = rblapack_e_out__;
e = e_out__;
work = ALLOC_N(doublereal, (MAX(1,lsame_(&compq,"N") ? 4*n : lsame_(&compq,"P") ? 6*n : lsame_(&compq,"I") ? 3*n*n+4*n : 0)));
iwork = ALLOC_N(integer, (8*n));
dbdsdc_(&uplo, &compq, &n, d, e, u, &ldu, vt, &ldvt, q, iq, work, iwork, &info);
free(work);
free(iwork);
rblapack_info = INT2NUM(info);
return rb_ary_new3(7, rblapack_u, rblapack_vt, rblapack_q, rblapack_iq, rblapack_info, rblapack_d, rblapack_e);
}
void
init_lapack_dbdsdc(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dbdsdc", rblapack_dbdsdc, -1);
}
|
