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
|
#include "rb_lapack.h"
extern VOID slagv2_(real* a, integer* lda, real* b, integer* ldb, real* alphar, real* alphai, real* beta, real* csl, real* snl, real* csr, real* snr);
static VALUE
rblapack_slagv2(int argc, VALUE *argv, VALUE self){
VALUE rblapack_a;
real *a;
VALUE rblapack_b;
real *b;
VALUE rblapack_alphar;
real *alphar;
VALUE rblapack_alphai;
real *alphai;
VALUE rblapack_beta;
real *beta;
VALUE rblapack_csl;
real csl;
VALUE rblapack_snl;
real snl;
VALUE rblapack_csr;
real csr;
VALUE rblapack_snr;
real snr;
VALUE rblapack_a_out__;
real *a_out__;
VALUE rblapack_b_out__;
real *b_out__;
integer lda;
integer ldb;
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 alphar, alphai, beta, csl, snl, csr, snr, a, b = NumRu::Lapack.slagv2( a, b, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SLAGV2( A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR )\n\n* Purpose\n* =======\n*\n* SLAGV2 computes the Generalized Schur factorization of a real 2-by-2\n* matrix pencil (A,B) where B is upper triangular. This routine\n* computes orthogonal (rotation) matrices given by CSL, SNL and CSR,\n* SNR such that\n*\n* 1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0\n* types), then\n*\n* [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]\n* [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]\n*\n* [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]\n* [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ],\n*\n* 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues,\n* then\n*\n* [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ]\n* [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ]\n*\n* [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ]\n* [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ]\n*\n* where b11 >= b22 > 0.\n*\n*\n\n* Arguments\n* =========\n*\n* A (input/output) REAL array, dimension (LDA, 2)\n* On entry, the 2 x 2 matrix A.\n* On exit, A is overwritten by the ``A-part'' of the\n* generalized Schur form.\n*\n* LDA (input) INTEGER\n* THe leading dimension of the array A. LDA >= 2.\n*\n* B (input/output) REAL array, dimension (LDB, 2)\n* On entry, the upper triangular 2 x 2 matrix B.\n* On exit, B is overwritten by the ``B-part'' of the\n* generalized Schur form.\n*\n* LDB (input) INTEGER\n* THe leading dimension of the array B. LDB >= 2.\n*\n* ALPHAR (output) REAL array, dimension (2)\n* ALPHAI (output) REAL array, dimension (2)\n* BETA (output) REAL array, dimension (2)\n* (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the\n* pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may\n* be zero.\n*\n* CSL (output) REAL\n* The cosine of the left rotation matrix.\n*\n* SNL (output) REAL\n* The sine of the left rotation matrix.\n*\n* CSR (output) REAL\n* The cosine of the right rotation matrix.\n*\n* SNR (output) REAL\n* The sine of the right rotation matrix.\n*\n\n* Further Details\n* ===============\n*\n* Based on contributions by\n* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n alphar, alphai, beta, csl, snl, csr, snr, a, b = NumRu::Lapack.slagv2( a, b, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 2 && argc != 2)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 2)", argc);
rblapack_a = argv[0];
rblapack_b = argv[1];
if (argc == 2) {
} else if (rblapack_options != Qnil) {
} else {
}
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (1th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (1th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
if (NA_SHAPE1(rblapack_a) != (2))
rb_raise(rb_eRuntimeError, "shape 1 of a must be %d", 2);
if (NA_TYPE(rblapack_a) != NA_SFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_SFLOAT);
a = NA_PTR_TYPE(rblapack_a, real*);
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (2th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (2th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
if (NA_SHAPE1(rblapack_b) != (2))
rb_raise(rb_eRuntimeError, "shape 1 of b must be %d", 2);
if (NA_TYPE(rblapack_b) != NA_SFLOAT)
rblapack_b = na_change_type(rblapack_b, NA_SFLOAT);
b = NA_PTR_TYPE(rblapack_b, real*);
{
na_shape_t shape[1];
shape[0] = 2;
rblapack_alphar = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
alphar = NA_PTR_TYPE(rblapack_alphar, real*);
{
na_shape_t shape[1];
shape[0] = 2;
rblapack_alphai = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
alphai = NA_PTR_TYPE(rblapack_alphai, real*);
{
na_shape_t shape[1];
shape[0] = 2;
rblapack_beta = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
beta = NA_PTR_TYPE(rblapack_beta, real*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = 2;
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] = 2;
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__;
slagv2_(a, &lda, b, &ldb, alphar, alphai, beta, &csl, &snl, &csr, &snr);
rblapack_csl = rb_float_new((double)csl);
rblapack_snl = rb_float_new((double)snl);
rblapack_csr = rb_float_new((double)csr);
rblapack_snr = rb_float_new((double)snr);
return rb_ary_new3(9, rblapack_alphar, rblapack_alphai, rblapack_beta, rblapack_csl, rblapack_snl, rblapack_csr, rblapack_snr, rblapack_a, rblapack_b);
}
void
init_lapack_slagv2(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "slagv2", rblapack_slagv2, -1);
}
|
