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
|
#include "rb_lapack.h"
extern VOID zlaqr2_(logical* wantt, logical* wantz, integer* n, integer* ktop, integer* kbot, integer* nw, doublecomplex* h, integer* ldh, integer* iloz, integer* ihiz, doublecomplex* z, integer* ldz, integer* ns, integer* nd, doublecomplex* sh, doublecomplex* v, integer* ldv, integer* nh, doublecomplex* t, integer* ldt, integer* nv, doublecomplex* wv, integer* ldwv, doublecomplex* work, integer* lwork);
static VALUE
rblapack_zlaqr2(int argc, VALUE *argv, VALUE self){
VALUE rblapack_wantt;
logical wantt;
VALUE rblapack_wantz;
logical wantz;
VALUE rblapack_ktop;
integer ktop;
VALUE rblapack_kbot;
integer kbot;
VALUE rblapack_nw;
integer nw;
VALUE rblapack_h;
doublecomplex *h;
VALUE rblapack_iloz;
integer iloz;
VALUE rblapack_ihiz;
integer ihiz;
VALUE rblapack_z;
doublecomplex *z;
VALUE rblapack_nh;
integer nh;
VALUE rblapack_nv;
integer nv;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_ns;
integer ns;
VALUE rblapack_nd;
integer nd;
VALUE rblapack_sh;
doublecomplex *sh;
VALUE rblapack_h_out__;
doublecomplex *h_out__;
VALUE rblapack_z_out__;
doublecomplex *z_out__;
doublecomplex *v;
doublecomplex *t;
doublecomplex *wv;
doublecomplex *work;
integer ldh;
integer n;
integer ldz;
integer ldv;
integer ldwv;
integer ldt;
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 ns, nd, sh, h, z = NumRu::Lapack.zlaqr2( wantt, wantz, ktop, kbot, nw, h, iloz, ihiz, z, nh, nv, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK )\n\n* This subroutine is identical to ZLAQR3 except that it avoids\n* recursion by calling ZLAHQR instead of ZLAQR4.\n*\n*\n* ******************************************************************\n* Aggressive early deflation:\n*\n* This subroutine accepts as input an upper Hessenberg matrix\n* H and performs an unitary similarity transformation\n* designed to detect and deflate fully converged eigenvalues from\n* a trailing principal submatrix. On output H has been over-\n* written by a new Hessenberg matrix that is a perturbation of\n* an unitary similarity transformation of H. It is to be\n* hoped that the final version of H has many zero subdiagonal\n* entries.\n*\n* ******************************************************************\n\n* WANTT (input) LOGICAL\n* If .TRUE., then the Hessenberg matrix H is fully updated\n* so that the triangular Schur factor may be\n* computed (in cooperation with the calling subroutine).\n* If .FALSE., then only enough of H is updated to preserve\n* the eigenvalues.\n*\n* WANTZ (input) LOGICAL\n* If .TRUE., then the unitary matrix Z is updated so\n* so that the unitary Schur factor may be computed\n* (in cooperation with the calling subroutine).\n* If .FALSE., then Z is not referenced.\n*\n* N (input) INTEGER\n* The order of the matrix H and (if WANTZ is .TRUE.) the\n* order of the unitary matrix Z.\n*\n* KTOP (input) INTEGER\n* It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.\n* KBOT and KTOP together determine an isolated block\n* along the diagonal of the Hessenberg matrix.\n*\n* KBOT (input) INTEGER\n* It is assumed without a check that either\n* KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together\n* determine an isolated block along the diagonal of the\n* Hessenberg matrix.\n*\n* NW (input) INTEGER\n* Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1).\n*\n* H (input/output) COMPLEX*16 array, dimension (LDH,N)\n* On input the initial N-by-N section of H stores the\n* Hessenberg matrix undergoing aggressive early deflation.\n* On output H has been transformed by a unitary\n* similarity transformation, perturbed, and the returned\n* to Hessenberg form that (it is to be hoped) has some\n* zero subdiagonal entries.\n*\n* LDH (input) integer\n* Leading dimension of H just as declared in the calling\n* subroutine. N .LE. LDH\n*\n* ILOZ (input) INTEGER\n* IHIZ (input) INTEGER\n* Specify the rows of Z to which transformations must be\n* applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.\n*\n* Z (input/output) COMPLEX*16 array, dimension (LDZ,N)\n* IF WANTZ is .TRUE., then on output, the unitary\n* similarity transformation mentioned above has been\n* accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.\n* If WANTZ is .FALSE., then Z is unreferenced.\n*\n* LDZ (input) integer\n* The leading dimension of Z just as declared in the\n* calling subroutine. 1 .LE. LDZ.\n*\n* NS (output) integer\n* The number of unconverged (ie approximate) eigenvalues\n* returned in SR and SI that may be used as shifts by the\n* calling subroutine.\n*\n* ND (output) integer\n* The number of converged eigenvalues uncovered by this\n* subroutine.\n*\n* SH (output) COMPLEX*16 array, dimension KBOT\n* On output, approximate eigenvalues that may\n* be used for shifts are stored in SH(KBOT-ND-NS+1)\n* through SR(KBOT-ND). Converged eigenvalues are\n* stored in SH(KBOT-ND+1) through SH(KBOT).\n*\n* V (workspace) COMPLEX*16 array, dimension (LDV,NW)\n* An NW-by-NW work array.\n*\n* LDV (input) integer scalar\n* The leading dimension of V just as declared in the\n* calling subroutine. NW .LE. LDV\n*\n* NH (input) integer scalar\n* The number of columns of T. NH.GE.NW.\n*\n* T (workspace) COMPLEX*16 array, dimension (LDT,NW)\n*\n* LDT (input) integer\n* The leading dimension of T just as declared in the\n* calling subroutine. NW .LE. LDT\n*\n* NV (input) integer\n* The number of rows of work array WV available for\n* workspace. NV.GE.NW.\n*\n* WV (workspace) COMPLEX*16 array, dimension (LDWV,NW)\n*\n* LDWV (input) integer\n* The leading dimension of W just as declared in the\n* calling subroutine. NW .LE. LDV\n*\n* WORK (workspace) COMPLEX*16 array, dimension LWORK.\n* On exit, WORK(1) is set to an estimate of the optimal value\n* of LWORK for the given values of N, NW, KTOP and KBOT.\n*\n* LWORK (input) integer\n* The dimension of the work array WORK. LWORK = 2*NW\n* suffices, but greater efficiency may result from larger\n* values of LWORK.\n*\n* If LWORK = -1, then a workspace query is assumed; ZLAQR2\n* only estimates the optimal workspace size for the given\n* values of N, NW, KTOP and KBOT. The estimate is returned\n* in WORK(1). No error message related to LWORK is issued\n* by XERBLA. Neither H nor Z are accessed.\n*\n\n* ================================================================\n* Based on contributions by\n* Karen Braman and Ralph Byers, Department of Mathematics,\n* University of Kansas, USA\n*\n* ================================================================\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n ns, nd, sh, h, z = NumRu::Lapack.zlaqr2( wantt, wantz, ktop, kbot, nw, h, iloz, ihiz, z, nh, nv, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 11 && argc != 12)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 11)", argc);
rblapack_wantt = argv[0];
rblapack_wantz = argv[1];
rblapack_ktop = argv[2];
rblapack_kbot = argv[3];
rblapack_nw = argv[4];
rblapack_h = argv[5];
rblapack_iloz = argv[6];
rblapack_ihiz = argv[7];
rblapack_z = argv[8];
rblapack_nh = argv[9];
rblapack_nv = argv[10];
if (argc == 12) {
rblapack_lwork = argv[11];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
wantt = (rblapack_wantt == Qtrue);
ktop = NUM2INT(rblapack_ktop);
nw = NUM2INT(rblapack_nw);
iloz = NUM2INT(rblapack_iloz);
if (!NA_IsNArray(rblapack_z))
rb_raise(rb_eArgError, "z (9th argument) must be NArray");
if (NA_RANK(rblapack_z) != 2)
rb_raise(rb_eArgError, "rank of z (9th argument) must be %d", 2);
ldz = NA_SHAPE0(rblapack_z);
n = NA_SHAPE1(rblapack_z);
if (NA_TYPE(rblapack_z) != NA_DCOMPLEX)
rblapack_z = na_change_type(rblapack_z, NA_DCOMPLEX);
z = NA_PTR_TYPE(rblapack_z, doublecomplex*);
nv = NUM2INT(rblapack_nv);
ldwv = nw;
ldv = nw;
wantz = (rblapack_wantz == Qtrue);
if (!NA_IsNArray(rblapack_h))
rb_raise(rb_eArgError, "h (6th argument) must be NArray");
if (NA_RANK(rblapack_h) != 2)
rb_raise(rb_eArgError, "rank of h (6th argument) must be %d", 2);
ldh = NA_SHAPE0(rblapack_h);
if (NA_SHAPE1(rblapack_h) != n)
rb_raise(rb_eRuntimeError, "shape 1 of h must be the same as shape 1 of z");
if (NA_TYPE(rblapack_h) != NA_DCOMPLEX)
rblapack_h = na_change_type(rblapack_h, NA_DCOMPLEX);
h = NA_PTR_TYPE(rblapack_h, doublecomplex*);
nh = NUM2INT(rblapack_nh);
ldt = nw;
kbot = NUM2INT(rblapack_kbot);
if (rblapack_lwork == Qnil)
lwork = 2*nw;
else {
lwork = NUM2INT(rblapack_lwork);
}
ihiz = NUM2INT(rblapack_ihiz);
{
na_shape_t shape[1];
shape[0] = MAX(1,kbot);
rblapack_sh = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
sh = NA_PTR_TYPE(rblapack_sh, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = ldh;
shape[1] = n;
rblapack_h_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
h_out__ = NA_PTR_TYPE(rblapack_h_out__, doublecomplex*);
MEMCPY(h_out__, h, doublecomplex, NA_TOTAL(rblapack_h));
rblapack_h = rblapack_h_out__;
h = h_out__;
{
na_shape_t shape[2];
shape[0] = ldz;
shape[1] = n;
rblapack_z_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
z_out__ = NA_PTR_TYPE(rblapack_z_out__, doublecomplex*);
MEMCPY(z_out__, z, doublecomplex, NA_TOTAL(rblapack_z));
rblapack_z = rblapack_z_out__;
z = z_out__;
v = ALLOC_N(doublecomplex, (ldv)*(MAX(1,nw)));
t = ALLOC_N(doublecomplex, (ldv)*(MAX(1,nw)));
wv = ALLOC_N(doublecomplex, (ldv)*(MAX(1,nw)));
work = ALLOC_N(doublecomplex, (MAX(1,lwork)));
zlaqr2_(&wantt, &wantz, &n, &ktop, &kbot, &nw, h, &ldh, &iloz, &ihiz, z, &ldz, &ns, &nd, sh, v, &ldv, &nh, t, &ldt, &nv, wv, &ldwv, work, &lwork);
free(v);
free(t);
free(wv);
free(work);
rblapack_ns = INT2NUM(ns);
rblapack_nd = INT2NUM(nd);
return rb_ary_new3(5, rblapack_ns, rblapack_nd, rblapack_sh, rblapack_h, rblapack_z);
}
void
init_lapack_zlaqr2(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zlaqr2", rblapack_zlaqr2, -1);
}
|
