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
|
#include "rb_lapack.h"
extern VOID claed8_(integer* k, integer* n, integer* qsiz, complex* q, integer* ldq, real* d, real* rho, integer* cutpnt, real* z, real* dlamda, complex* q2, integer* ldq2, real* w, integer* indxp, integer* indx, integer* indxq, integer* perm, integer* givptr, integer* givcol, real* givnum, integer* info);
static VALUE
rblapack_claed8(int argc, VALUE *argv, VALUE self){
VALUE rblapack_qsiz;
integer qsiz;
VALUE rblapack_q;
complex *q;
VALUE rblapack_d;
real *d;
VALUE rblapack_rho;
real rho;
VALUE rblapack_cutpnt;
integer cutpnt;
VALUE rblapack_z;
real *z;
VALUE rblapack_indxq;
integer *indxq;
VALUE rblapack_k;
integer k;
VALUE rblapack_dlamda;
real *dlamda;
VALUE rblapack_q2;
complex *q2;
VALUE rblapack_w;
real *w;
VALUE rblapack_perm;
integer *perm;
VALUE rblapack_givptr;
integer givptr;
VALUE rblapack_givcol;
integer *givcol;
VALUE rblapack_givnum;
real *givnum;
VALUE rblapack_info;
integer info;
VALUE rblapack_q_out__;
complex *q_out__;
VALUE rblapack_d_out__;
real *d_out__;
integer *indxp;
integer *indx;
integer ldq;
integer n;
integer ldq2;
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 k, dlamda, q2, w, perm, givptr, givcol, givnum, info, q, d, rho = NumRu::Lapack.claed8( qsiz, q, d, rho, cutpnt, z, indxq, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO )\n\n* Purpose\n* =======\n*\n* CLAED8 merges the two sets of eigenvalues together into a single\n* sorted set. Then it tries to deflate the size of the problem.\n* There are two ways in which deflation can occur: when two or more\n* eigenvalues are close together or if there is a tiny element in the\n* Z vector. For each such occurrence the order of the related secular\n* equation problem is reduced by one.\n*\n\n* Arguments\n* =========\n*\n* K (output) INTEGER\n* Contains the number of non-deflated eigenvalues.\n* This is the order of the related secular equation.\n*\n* N (input) INTEGER\n* The dimension of the symmetric tridiagonal matrix. N >= 0.\n*\n* QSIZ (input) INTEGER\n* The dimension of the unitary matrix used to reduce\n* the dense or band matrix to tridiagonal form.\n* QSIZ >= N if ICOMPQ = 1.\n*\n* Q (input/output) COMPLEX array, dimension (LDQ,N)\n* On entry, Q contains the eigenvectors of the partially solved\n* system which has been previously updated in matrix\n* multiplies with other partially solved eigensystems.\n* On exit, Q contains the trailing (N-K) updated eigenvectors\n* (those which were deflated) in its last N-K columns.\n*\n* LDQ (input) INTEGER\n* The leading dimension of the array Q. LDQ >= max( 1, N ).\n*\n* D (input/output) REAL array, dimension (N)\n* On entry, D contains the eigenvalues of the two submatrices to\n* be combined. On exit, D contains the trailing (N-K) updated\n* eigenvalues (those which were deflated) sorted into increasing\n* order.\n*\n* RHO (input/output) REAL\n* Contains the off diagonal element associated with the rank-1\n* cut which originally split the two submatrices which are now\n* being recombined. RHO is modified during the computation to\n* the value required by SLAED3.\n*\n* CUTPNT (input) INTEGER\n* Contains the location of the last eigenvalue in the leading\n* sub-matrix. MIN(1,N) <= CUTPNT <= N.\n*\n* Z (input) REAL array, dimension (N)\n* On input this vector contains the updating vector (the last\n* row of the first sub-eigenvector matrix and the first row of\n* the second sub-eigenvector matrix). The contents of Z are\n* destroyed during the updating process.\n*\n* DLAMDA (output) REAL array, dimension (N)\n* Contains a copy of the first K eigenvalues which will be used\n* by SLAED3 to form the secular equation.\n*\n* Q2 (output) COMPLEX array, dimension (LDQ2,N)\n* If ICOMPQ = 0, Q2 is not referenced. Otherwise,\n* Contains a copy of the first K eigenvectors which will be used\n* by SLAED7 in a matrix multiply (SGEMM) to update the new\n* eigenvectors.\n*\n* LDQ2 (input) INTEGER\n* The leading dimension of the array Q2. LDQ2 >= max( 1, N ).\n*\n* W (output) REAL array, dimension (N)\n* This will hold the first k values of the final\n* deflation-altered z-vector and will be passed to SLAED3.\n*\n* INDXP (workspace) INTEGER array, dimension (N)\n* This will contain the permutation used to place deflated\n* values of D at the end of the array. On output INDXP(1:K)\n* points to the nondeflated D-values and INDXP(K+1:N)\n* points to the deflated eigenvalues.\n*\n* INDX (workspace) INTEGER array, dimension (N)\n* This will contain the permutation used to sort the contents of\n* D into ascending order.\n*\n* INDXQ (input) INTEGER array, dimension (N)\n* This contains the permutation which separately sorts the two\n* sub-problems in D into ascending order. Note that elements in\n* the second half of this permutation must first have CUTPNT\n* added to their values in order to be accurate.\n*\n* PERM (output) INTEGER array, dimension (N)\n* Contains the permutations (from deflation and sorting) to be\n* applied to each eigenblock.\n*\n* GIVPTR (output) INTEGER\n* Contains the number of Givens rotations which took place in\n* this subproblem.\n*\n* GIVCOL (output) INTEGER array, dimension (2, N)\n* Each pair of numbers indicates a pair of columns to take place\n* in a Givens rotation.\n*\n* GIVNUM (output) REAL array, dimension (2, N)\n* Each number indicates the S value to be used in the\n* corresponding Givens rotation.\n*\n* INFO (output) INTEGER\n* = 0: successful exit.\n* < 0: if INFO = -i, the i-th argument had an illegal value.\n*\n\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n k, dlamda, q2, w, perm, givptr, givcol, givnum, info, q, d, rho = NumRu::Lapack.claed8( qsiz, q, d, rho, cutpnt, z, indxq, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 7 && argc != 7)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 7)", argc);
rblapack_qsiz = argv[0];
rblapack_q = argv[1];
rblapack_d = argv[2];
rblapack_rho = argv[3];
rblapack_cutpnt = argv[4];
rblapack_z = argv[5];
rblapack_indxq = argv[6];
if (argc == 7) {
} else if (rblapack_options != Qnil) {
} else {
}
qsiz = NUM2INT(rblapack_qsiz);
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_SFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_SFLOAT);
d = NA_PTR_TYPE(rblapack_d, real*);
cutpnt = NUM2INT(rblapack_cutpnt);
if (!NA_IsNArray(rblapack_indxq))
rb_raise(rb_eArgError, "indxq (7th argument) must be NArray");
if (NA_RANK(rblapack_indxq) != 1)
rb_raise(rb_eArgError, "rank of indxq (7th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_indxq) != n)
rb_raise(rb_eRuntimeError, "shape 0 of indxq must be the same as shape 0 of d");
if (NA_TYPE(rblapack_indxq) != NA_LINT)
rblapack_indxq = na_change_type(rblapack_indxq, NA_LINT);
indxq = NA_PTR_TYPE(rblapack_indxq, integer*);
if (!NA_IsNArray(rblapack_q))
rb_raise(rb_eArgError, "q (2th argument) must be NArray");
if (NA_RANK(rblapack_q) != 2)
rb_raise(rb_eArgError, "rank of q (2th argument) must be %d", 2);
ldq = NA_SHAPE0(rblapack_q);
if (NA_SHAPE1(rblapack_q) != n)
rb_raise(rb_eRuntimeError, "shape 1 of q must be the same as shape 0 of d");
if (NA_TYPE(rblapack_q) != NA_SCOMPLEX)
rblapack_q = na_change_type(rblapack_q, NA_SCOMPLEX);
q = NA_PTR_TYPE(rblapack_q, complex*);
if (!NA_IsNArray(rblapack_z))
rb_raise(rb_eArgError, "z (6th argument) must be NArray");
if (NA_RANK(rblapack_z) != 1)
rb_raise(rb_eArgError, "rank of z (6th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_z) != n)
rb_raise(rb_eRuntimeError, "shape 0 of z must be the same as shape 0 of d");
if (NA_TYPE(rblapack_z) != NA_SFLOAT)
rblapack_z = na_change_type(rblapack_z, NA_SFLOAT);
z = NA_PTR_TYPE(rblapack_z, real*);
rho = (real)NUM2DBL(rblapack_rho);
ldq2 = MAX( 1, n );
{
na_shape_t shape[1];
shape[0] = n;
rblapack_dlamda = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
dlamda = NA_PTR_TYPE(rblapack_dlamda, real*);
{
na_shape_t shape[2];
shape[0] = ldq2;
shape[1] = n;
rblapack_q2 = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
}
q2 = NA_PTR_TYPE(rblapack_q2, complex*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_w = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
w = NA_PTR_TYPE(rblapack_w, real*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_perm = na_make_object(NA_LINT, 1, shape, cNArray);
}
perm = NA_PTR_TYPE(rblapack_perm, integer*);
{
na_shape_t shape[2];
shape[0] = 2;
shape[1] = n;
rblapack_givcol = na_make_object(NA_LINT, 2, shape, cNArray);
}
givcol = NA_PTR_TYPE(rblapack_givcol, integer*);
{
na_shape_t shape[2];
shape[0] = 2;
shape[1] = n;
rblapack_givnum = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
givnum = NA_PTR_TYPE(rblapack_givnum, real*);
{
na_shape_t shape[2];
shape[0] = ldq;
shape[1] = n;
rblapack_q_out__ = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
}
q_out__ = NA_PTR_TYPE(rblapack_q_out__, complex*);
MEMCPY(q_out__, q, complex, NA_TOTAL(rblapack_q));
rblapack_q = rblapack_q_out__;
q = q_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_d_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
d_out__ = NA_PTR_TYPE(rblapack_d_out__, real*);
MEMCPY(d_out__, d, real, NA_TOTAL(rblapack_d));
rblapack_d = rblapack_d_out__;
d = d_out__;
indxp = ALLOC_N(integer, (n));
indx = ALLOC_N(integer, (n));
claed8_(&k, &n, &qsiz, q, &ldq, d, &rho, &cutpnt, z, dlamda, q2, &ldq2, w, indxp, indx, indxq, perm, &givptr, givcol, givnum, &info);
free(indxp);
free(indx);
rblapack_k = INT2NUM(k);
rblapack_givptr = INT2NUM(givptr);
rblapack_info = INT2NUM(info);
rblapack_rho = rb_float_new((double)rho);
return rb_ary_new3(12, rblapack_k, rblapack_dlamda, rblapack_q2, rblapack_w, rblapack_perm, rblapack_givptr, rblapack_givcol, rblapack_givnum, rblapack_info, rblapack_q, rblapack_d, rblapack_rho);
}
void
init_lapack_claed8(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "claed8", rblapack_claed8, -1);
}
|
