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"
static logical
rblapack_selctg(real *arg0, real *arg1, real *arg2){
VALUE rblapack_arg0, rblapack_arg1, rblapack_arg2;
VALUE rblapack_ret;
logical ret;
rblapack_arg0 = rb_float_new((double)(*arg0));
rblapack_arg1 = rb_float_new((double)(*arg1));
rblapack_arg2 = rb_float_new((double)(*arg2));
rblapack_ret = rb_yield_values(3, rblapack_arg0, rblapack_arg1, rblapack_arg2);
ret = (rblapack_ret == Qtrue);
return ret;
}
extern VOID sgges_(char* jobvsl, char* jobvsr, char* sort, L_fp selctg, integer* n, real* a, integer* lda, real* b, integer* ldb, integer* sdim, real* alphar, real* alphai, real* beta, real* vsl, integer* ldvsl, real* vsr, integer* ldvsr, real* work, integer* lwork, logical* bwork, integer* info);
static VALUE
rblapack_sgges(int argc, VALUE *argv, VALUE self){
VALUE rblapack_jobvsl;
char jobvsl;
VALUE rblapack_jobvsr;
char jobvsr;
VALUE rblapack_sort;
char sort;
VALUE rblapack_a;
real *a;
VALUE rblapack_b;
real *b;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_sdim;
integer sdim;
VALUE rblapack_alphar;
real *alphar;
VALUE rblapack_alphai;
real *alphai;
VALUE rblapack_beta;
real *beta;
VALUE rblapack_vsl;
real *vsl;
VALUE rblapack_vsr;
real *vsr;
VALUE rblapack_work;
real *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
real *a_out__;
VALUE rblapack_b_out__;
real *b_out__;
logical *bwork;
integer lda;
integer n;
integer ldb;
integer ldvsl;
integer ldvsr;
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 sdim, alphar, alphai, beta, vsl, vsr, work, info, a, b = NumRu::Lapack.sgges( jobvsl, jobvsr, sort, a, b, [:lwork => lwork, :usage => usage, :help => help]){|a,b,c| ... }\n\n\nFORTRAN MANUAL\n SUBROUTINE SGGES( JOBVSL, JOBVSR, SORT, SELCTG, N, A, LDA, B, LDB, SDIM, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, BWORK, INFO )\n\n* Purpose\n* =======\n*\n* SGGES computes for a pair of N-by-N real nonsymmetric matrices (A,B),\n* the generalized eigenvalues, the generalized real Schur form (S,T),\n* optionally, the left and/or right matrices of Schur vectors (VSL and\n* VSR). This gives the generalized Schur factorization\n*\n* (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T )\n*\n* Optionally, it also orders the eigenvalues so that a selected cluster\n* of eigenvalues appears in the leading diagonal blocks of the upper\n* quasi-triangular matrix S and the upper triangular matrix T.The\n* leading columns of VSL and VSR then form an orthonormal basis for the\n* corresponding left and right eigenspaces (deflating subspaces).\n*\n* (If only the generalized eigenvalues are needed, use the driver\n* SGGEV instead, which is faster.)\n*\n* A generalized eigenvalue for a pair of matrices (A,B) is a scalar w\n* or a ratio alpha/beta = w, such that A - w*B is singular. It is\n* usually represented as the pair (alpha,beta), as there is a\n* reasonable interpretation for beta=0 or both being zero.\n*\n* A pair of matrices (S,T) is in generalized real Schur form if T is\n* upper triangular with non-negative diagonal and S is block upper\n* triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond\n* to real generalized eigenvalues, while 2-by-2 blocks of S will be\n* \"standardized\" by making the corresponding elements of T have the\n* form:\n* [ a 0 ]\n* [ 0 b ]\n*\n* and the pair of corresponding 2-by-2 blocks in S and T will have a\n* complex conjugate pair of generalized eigenvalues.\n*\n*\n\n* Arguments\n* =========\n*\n* JOBVSL (input) CHARACTER*1\n* = 'N': do not compute the left Schur vectors;\n* = 'V': compute the left Schur vectors.\n*\n* JOBVSR (input) CHARACTER*1\n* = 'N': do not compute the right Schur vectors;\n* = 'V': compute the right Schur vectors.\n*\n* SORT (input) CHARACTER*1\n* Specifies whether or not to order the eigenvalues on the\n* diagonal of the generalized Schur form.\n* = 'N': Eigenvalues are not ordered;\n* = 'S': Eigenvalues are ordered (see SELCTG);\n*\n* SELCTG (external procedure) LOGICAL FUNCTION of three REAL arguments\n* SELCTG must be declared EXTERNAL in the calling subroutine.\n* If SORT = 'N', SELCTG is not referenced.\n* If SORT = 'S', SELCTG is used to select eigenvalues to sort\n* to the top left of the Schur form.\n* An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if\n* SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either\n* one of a complex conjugate pair of eigenvalues is selected,\n* then both complex eigenvalues are selected.\n*\n* Note that in the ill-conditioned case, a selected complex\n* eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j),\n* BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2\n* in this case.\n*\n* N (input) INTEGER\n* The order of the matrices A, B, VSL, and VSR. N >= 0.\n*\n* A (input/output) REAL array, dimension (LDA, N)\n* On entry, the first of the pair of matrices.\n* On exit, A has been overwritten by its generalized Schur\n* form S.\n*\n* LDA (input) INTEGER\n* The leading dimension of A. LDA >= max(1,N).\n*\n* B (input/output) REAL array, dimension (LDB, N)\n* On entry, the second of the pair of matrices.\n* On exit, B has been overwritten by its generalized Schur\n* form T.\n*\n* LDB (input) INTEGER\n* The leading dimension of B. LDB >= max(1,N).\n*\n* SDIM (output) INTEGER\n* If SORT = 'N', SDIM = 0.\n* If SORT = 'S', SDIM = number of eigenvalues (after sorting)\n* for which SELCTG is true. (Complex conjugate pairs for which\n* SELCTG is true for either eigenvalue count as 2.)\n*\n* ALPHAR (output) REAL array, dimension (N)\n* ALPHAI (output) REAL array, dimension (N)\n* BETA (output) REAL array, dimension (N)\n* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will\n* be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i,\n* and BETA(j),j=1,...,N are the diagonals of the complex Schur\n* form (S,T) that would result if the 2-by-2 diagonal blocks of\n* the real Schur form of (A,B) were further reduced to\n* triangular form using 2-by-2 complex unitary transformations.\n* If ALPHAI(j) is zero, then the j-th eigenvalue is real; if\n* positive, then the j-th and (j+1)-st eigenvalues are a\n* complex conjugate pair, with ALPHAI(j+1) negative.\n*\n* Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)\n* may easily over- or underflow, and BETA(j) may even be zero.\n* Thus, the user should avoid naively computing the ratio.\n* However, ALPHAR and ALPHAI will be always less than and\n* usually comparable with norm(A) in magnitude, and BETA always\n* less than and usually comparable with norm(B).\n*\n* VSL (output) REAL array, dimension (LDVSL,N)\n* If JOBVSL = 'V', VSL will contain the left Schur vectors.\n* Not referenced if JOBVSL = 'N'.\n*\n* LDVSL (input) INTEGER\n* The leading dimension of the matrix VSL. LDVSL >=1, and\n* if JOBVSL = 'V', LDVSL >= N.\n*\n* VSR (output) REAL array, dimension (LDVSR,N)\n* If JOBVSR = 'V', VSR will contain the right Schur vectors.\n* Not referenced if JOBVSR = 'N'.\n*\n* LDVSR (input) INTEGER\n* The leading dimension of the matrix VSR. LDVSR >= 1, and\n* if JOBVSR = 'V', LDVSR >= N.\n*\n* WORK (workspace/output) REAL 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* If N = 0, LWORK >= 1, else LWORK >= max(8*N,6*N+16).\n* For good performance , LWORK must generally be larger.\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* BWORK (workspace) LOGICAL array, dimension (N)\n* Not referenced if SORT = 'N'.\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value.\n* = 1,...,N:\n* The QZ iteration failed. (A,B) are not in Schur\n* form, but ALPHAR(j), ALPHAI(j), and BETA(j) should\n* be correct for j=INFO+1,...,N.\n* > N: =N+1: other than QZ iteration failed in SHGEQZ.\n* =N+2: after reordering, roundoff changed values of\n* some complex eigenvalues so that leading\n* eigenvalues in the Generalized Schur form no\n* longer satisfy SELCTG=.TRUE. This could also\n* be caused due to scaling.\n* =N+3: reordering failed in STGSEN.\n*\n\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n sdim, alphar, alphai, beta, vsl, vsr, work, info, a, b = NumRu::Lapack.sgges( jobvsl, jobvsr, sort, a, b, [:lwork => lwork, :usage => usage, :help => help]){|a,b,c| ... }\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 5 && argc != 6)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 5)", argc);
rblapack_jobvsl = argv[0];
rblapack_jobvsr = argv[1];
rblapack_sort = argv[2];
rblapack_a = argv[3];
rblapack_b = argv[4];
if (argc == 6) {
rblapack_lwork = argv[5];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
jobvsl = StringValueCStr(rblapack_jobvsl)[0];
sort = StringValueCStr(rblapack_sort)[0];
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (5th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (5th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
n = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_SFLOAT)
rblapack_b = na_change_type(rblapack_b, NA_SFLOAT);
b = NA_PTR_TYPE(rblapack_b, real*);
jobvsr = StringValueCStr(rblapack_jobvsr)[0];
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (4th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (4th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
if (NA_SHAPE1(rblapack_a) != n)
rb_raise(rb_eRuntimeError, "shape 1 of a must be the same as shape 1 of b");
if (NA_TYPE(rblapack_a) != NA_SFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_SFLOAT);
a = NA_PTR_TYPE(rblapack_a, real*);
ldvsl = lsame_(&jobvsl,"V") ? n : 1;
if (rblapack_lwork == Qnil)
lwork = MAX(8*n,6*n+16);
else {
lwork = NUM2INT(rblapack_lwork);
}
ldvsr = lsame_(&jobvsr,"V") ? n : 1;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_alphar = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
alphar = NA_PTR_TYPE(rblapack_alphar, real*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_alphai = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
alphai = NA_PTR_TYPE(rblapack_alphai, real*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_beta = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
beta = NA_PTR_TYPE(rblapack_beta, real*);
{
na_shape_t shape[2];
shape[0] = ldvsl;
shape[1] = n;
rblapack_vsl = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
vsl = NA_PTR_TYPE(rblapack_vsl, real*);
{
na_shape_t shape[2];
shape[0] = ldvsr;
shape[1] = n;
rblapack_vsr = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
vsr = NA_PTR_TYPE(rblapack_vsr, real*);
{
na_shape_t shape[1];
shape[0] = MAX(1,lwork);
rblapack_work = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, real*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = n;
rblapack_a_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, real*);
MEMCPY(a_out__, a, real, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = n;
rblapack_b_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, real*);
MEMCPY(b_out__, b, real, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
bwork = ALLOC_N(logical, (lsame_(&sort,"N") ? 0 : n));
sgges_(&jobvsl, &jobvsr, &sort, rblapack_selctg, &n, a, &lda, b, &ldb, &sdim, alphar, alphai, beta, vsl, &ldvsl, vsr, &ldvsr, work, &lwork, bwork, &info);
free(bwork);
rblapack_sdim = INT2NUM(sdim);
rblapack_info = INT2NUM(info);
return rb_ary_new3(10, rblapack_sdim, rblapack_alphar, rblapack_alphai, rblapack_beta, rblapack_vsl, rblapack_vsr, rblapack_work, rblapack_info, rblapack_a, rblapack_b);
}
void
init_lapack_sgges(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sgges", rblapack_sgges, -1);
}
|
