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
|
#include "rb_lapack.h"
extern VOID sgelsy_(integer* m, integer* n, integer* nrhs, real* a, integer* lda, real* b, integer* ldb, integer* jpvt, real* rcond, integer* rank, real* work, integer* lwork, integer* info);
static VALUE
rblapack_sgelsy(int argc, VALUE *argv, VALUE self){
VALUE rblapack_a;
real *a;
VALUE rblapack_b;
real *b;
VALUE rblapack_jpvt;
integer *jpvt;
VALUE rblapack_rcond;
real rcond;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_rank;
integer rank;
VALUE rblapack_work;
real *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
real *a_out__;
VALUE rblapack_b_out__;
real *b_out__;
VALUE rblapack_jpvt_out__;
integer *jpvt_out__;
integer lda;
integer n;
integer m;
integer nrhs;
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 rank, work, info, a, b, jpvt = NumRu::Lapack.sgelsy( a, b, jpvt, rcond, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, LWORK, INFO )\n\n* Purpose\n* =======\n*\n* SGELSY computes the minimum-norm solution to a real linear least\n* squares problem:\n* minimize || A * X - B ||\n* using a complete orthogonal factorization of A. A is an M-by-N\n* matrix which may be rank-deficient.\n*\n* Several right hand side vectors b and solution vectors x can be\n* handled in a single call; they are stored as the columns of the\n* M-by-NRHS right hand side matrix B and the N-by-NRHS solution\n* matrix X.\n*\n* The routine first computes a QR factorization with column pivoting:\n* A * P = Q * [ R11 R12 ]\n* [ 0 R22 ]\n* with R11 defined as the largest leading submatrix whose estimated\n* condition number is less than 1/RCOND. The order of R11, RANK,\n* is the effective rank of A.\n*\n* Then, R22 is considered to be negligible, and R12 is annihilated\n* by orthogonal transformations from the right, arriving at the\n* complete orthogonal factorization:\n* A * P = Q * [ T11 0 ] * Z\n* [ 0 0 ]\n* The minimum-norm solution is then\n* X = P * Z' [ inv(T11)*Q1'*B ]\n* [ 0 ]\n* where Q1 consists of the first RANK columns of Q.\n*\n* This routine is basically identical to the original xGELSX except\n* three differences:\n* o The call to the subroutine xGEQPF has been substituted by the\n* the call to the subroutine xGEQP3. This subroutine is a Blas-3\n* version of the QR factorization with column pivoting.\n* o Matrix B (the right hand side) is updated with Blas-3.\n* o The permutation of matrix B (the right hand side) is faster and\n* more simple.\n*\n\n* Arguments\n* =========\n*\n* M (input) INTEGER\n* The number of rows of the matrix A. M >= 0.\n*\n* N (input) INTEGER\n* The number of columns of the matrix A. N >= 0.\n*\n* NRHS (input) INTEGER\n* The number of right hand sides, i.e., the number of\n* columns of matrices B and X. NRHS >= 0.\n*\n* A (input/output) REAL array, dimension (LDA,N)\n* On entry, the M-by-N matrix A.\n* On exit, A has been overwritten by details of its\n* complete orthogonal factorization.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,M).\n*\n* B (input/output) REAL array, dimension (LDB,NRHS)\n* On entry, the M-by-NRHS right hand side matrix B.\n* On exit, the N-by-NRHS solution matrix X.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,M,N).\n*\n* JPVT (input/output) INTEGER array, dimension (N)\n* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted\n* to the front of AP, otherwise column i is a free column.\n* On exit, if JPVT(i) = k, then the i-th column of AP\n* was the k-th column of A.\n*\n* RCOND (input) REAL\n* RCOND is used to determine the effective rank of A, which\n* is defined as the order of the largest leading triangular\n* submatrix R11 in the QR factorization with pivoting of A,\n* whose estimated condition number < 1/RCOND.\n*\n* RANK (output) INTEGER\n* The effective rank of A, i.e., the order of the submatrix\n* R11. This is the same as the order of the submatrix T11\n* in the complete orthogonal factorization of A.\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* The unblocked strategy requires that:\n* LWORK >= MAX( MN+3*N+1, 2*MN+NRHS ),\n* where MN = min( M, N ).\n* The block algorithm requires that:\n* LWORK >= MAX( MN+2*N+NB*(N+1), 2*MN+NB*NRHS ),\n* where NB is an upper bound on the blocksize returned\n* by ILAENV for the routines SGEQP3, STZRZF, STZRQF, SORMQR,\n* and SORMRZ.\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* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: If INFO = -i, the i-th argument had an illegal value.\n*\n\n* Further Details\n* ===============\n*\n* Based on contributions by\n* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA\n* E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain\n* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n rank, work, info, a, b, jpvt = NumRu::Lapack.sgelsy( a, b, jpvt, rcond, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 4 && argc != 5)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 4)", argc);
rblapack_a = argv[0];
rblapack_b = argv[1];
rblapack_jpvt = argv[2];
rblapack_rcond = argv[3];
if (argc == 5) {
rblapack_lwork = argv[4];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
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);
n = NA_SHAPE1(rblapack_a);
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_jpvt))
rb_raise(rb_eArgError, "jpvt (3th argument) must be NArray");
if (NA_RANK(rblapack_jpvt) != 1)
rb_raise(rb_eArgError, "rank of jpvt (3th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_jpvt) != n)
rb_raise(rb_eRuntimeError, "shape 0 of jpvt must be the same as shape 1 of a");
if (NA_TYPE(rblapack_jpvt) != NA_LINT)
rblapack_jpvt = na_change_type(rblapack_jpvt, NA_LINT);
jpvt = NA_PTR_TYPE(rblapack_jpvt, integer*);
m = lda;
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);
if (NA_SHAPE0(rblapack_b) != m)
rb_raise(rb_eRuntimeError, "shape 0 of b must be lda");
nrhs = 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*);
if (rblapack_lwork == Qnil)
lwork = MAX(MIN(m,n)+3*n+1, 2*MIN(m,n)+nrhs);
else {
lwork = NUM2INT(rblapack_lwork);
}
rcond = (real)NUM2DBL(rblapack_rcond);
ldb = MAX(m,n);
{
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] = MAX(m, n);
shape[1] = nrhs;
rblapack_b_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, real*);
{
VALUE __shape__[3];
__shape__[0] = m < n ? rb_range_new(rblapack_ZERO, INT2NUM(m), Qtrue) : Qtrue;
__shape__[1] = Qtrue;
__shape__[2] = rblapack_b;
na_aset(3, __shape__, rblapack_b_out__);
}
rblapack_b = rblapack_b_out__;
b = b_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_jpvt_out__ = na_make_object(NA_LINT, 1, shape, cNArray);
}
jpvt_out__ = NA_PTR_TYPE(rblapack_jpvt_out__, integer*);
MEMCPY(jpvt_out__, jpvt, integer, NA_TOTAL(rblapack_jpvt));
rblapack_jpvt = rblapack_jpvt_out__;
jpvt = jpvt_out__;
sgelsy_(&m, &n, &nrhs, a, &lda, b, &ldb, jpvt, &rcond, &rank, work, &lwork, &info);
rblapack_rank = INT2NUM(rank);
rblapack_info = INT2NUM(info);
{
VALUE __shape__[2];
__shape__[0] = m < n ? Qtrue : rb_range_new(rblapack_ZERO, INT2NUM(n), Qtrue);
__shape__[1] = Qtrue;
rblapack_b = na_aref(2, __shape__, rblapack_b);
}
return rb_ary_new3(6, rblapack_rank, rblapack_work, rblapack_info, rblapack_a, rblapack_b, rblapack_jpvt);
}
void
init_lapack_sgelsy(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sgelsy", rblapack_sgelsy, -1);
}
|
