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
|
#include "rb_lapack.h"
extern VOID dsgesv_(integer* n, integer* nrhs, doublereal* a, integer* lda, integer* ipiv, doublereal* b, integer* ldb, doublereal* x, integer* ldx, doublereal* work, real* swork, integer* iter, integer* info);
static VALUE
rblapack_dsgesv(int argc, VALUE *argv, VALUE self){
VALUE rblapack_a;
doublereal *a;
VALUE rblapack_b;
doublereal *b;
VALUE rblapack_ipiv;
integer *ipiv;
VALUE rblapack_x;
doublereal *x;
VALUE rblapack_iter;
integer iter;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublereal *a_out__;
doublereal *work;
real *swork;
integer lda;
integer n;
integer ldb;
integer nrhs;
integer ldx;
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 ipiv, x, iter, info, a = NumRu::Lapack.dsgesv( a, b, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DSGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, ITER, INFO )\n\n* Purpose\n* =======\n*\n* DSGESV computes the solution to a real system of linear equations\n* A * X = B,\n* where A is an N-by-N matrix and X and B are N-by-NRHS matrices.\n*\n* DSGESV first attempts to factorize the matrix in SINGLE PRECISION\n* and use this factorization within an iterative refinement procedure\n* to produce a solution with DOUBLE PRECISION normwise backward error\n* quality (see below). If the approach fails the method switches to a\n* DOUBLE PRECISION factorization and solve.\n*\n* The iterative refinement is not going to be a winning strategy if\n* the ratio SINGLE PRECISION performance over DOUBLE PRECISION\n* performance is too small. A reasonable strategy should take the\n* number of right-hand sides and the size of the matrix into account.\n* This might be done with a call to ILAENV in the future. Up to now, we\n* always try iterative refinement.\n*\n* The iterative refinement process is stopped if\n* ITER > ITERMAX\n* or for all the RHS we have:\n* RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX\n* where\n* o ITER is the number of the current iteration in the iterative\n* refinement process\n* o RNRM is the infinity-norm of the residual\n* o XNRM is the infinity-norm of the solution\n* o ANRM is the infinity-operator-norm of the matrix A\n* o EPS is the machine epsilon returned by DLAMCH('Epsilon')\n* The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00\n* respectively.\n*\n\n* Arguments\n* =========\n*\n* N (input) INTEGER\n* The number of linear equations, i.e., the order of the\n* matrix A. N >= 0.\n*\n* NRHS (input) INTEGER\n* The number of right hand sides, i.e., the number of columns\n* of the matrix B. NRHS >= 0.\n*\n* A (input/output) DOUBLE PRECISION array,\n* dimension (LDA,N)\n* On entry, the N-by-N coefficient matrix A.\n* On exit, if iterative refinement has been successfully used\n* (INFO.EQ.0 and ITER.GE.0, see description below), then A is\n* unchanged, if double precision factorization has been used\n* (INFO.EQ.0 and ITER.LT.0, see description below), then the\n* array A contains the factors L and U from the factorization\n* A = P*L*U; the unit diagonal elements of L are not stored.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,N).\n*\n* IPIV (output) INTEGER array, dimension (N)\n* The pivot indices that define the permutation matrix P;\n* row i of the matrix was interchanged with row IPIV(i).\n* Corresponds either to the single precision factorization\n* (if INFO.EQ.0 and ITER.GE.0) or the double precision\n* factorization (if INFO.EQ.0 and ITER.LT.0).\n*\n* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)\n* The N-by-NRHS right hand side matrix B.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,N).\n*\n* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)\n* If INFO = 0, the N-by-NRHS solution matrix X.\n*\n* LDX (input) INTEGER\n* The leading dimension of the array X. LDX >= max(1,N).\n*\n* WORK (workspace) DOUBLE PRECISION array, dimension (N,NRHS)\n* This array is used to hold the residual vectors.\n*\n* SWORK (workspace) REAL array, dimension (N*(N+NRHS))\n* This array is used to use the single precision matrix and the\n* right-hand sides or solutions in single precision.\n*\n* ITER (output) INTEGER\n* < 0: iterative refinement has failed, double precision\n* factorization has been performed\n* -1 : the routine fell back to full precision for\n* implementation- or machine-specific reasons\n* -2 : narrowing the precision induced an overflow,\n* the routine fell back to full precision\n* -3 : failure of SGETRF\n* -31: stop the iterative refinement after the 30th\n* iterations\n* > 0: iterative refinement has been successfully used.\n* Returns the number of iterations\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value\n* > 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is\n* exactly zero. The factorization has been completed,\n* but the factor U is exactly singular, so the solution\n* could not be computed.\n*\n* =========\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n ipiv, x, iter, info, a = NumRu::Lapack.dsgesv( 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);
n = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_DFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_DFLOAT);
a = NA_PTR_TYPE(rblapack_a, doublereal*);
ldx = MAX(1,n);
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);
nrhs = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_DFLOAT)
rblapack_b = na_change_type(rblapack_b, NA_DFLOAT);
b = NA_PTR_TYPE(rblapack_b, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_ipiv = na_make_object(NA_LINT, 1, shape, cNArray);
}
ipiv = NA_PTR_TYPE(rblapack_ipiv, integer*);
{
na_shape_t shape[2];
shape[0] = ldx;
shape[1] = nrhs;
rblapack_x = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
x = NA_PTR_TYPE(rblapack_x, doublereal*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = n;
rblapack_a_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, doublereal*);
MEMCPY(a_out__, a, doublereal, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
work = ALLOC_N(doublereal, (n)*(nrhs));
swork = ALLOC_N(real, (n*(n+nrhs)));
dsgesv_(&n, &nrhs, a, &lda, ipiv, b, &ldb, x, &ldx, work, swork, &iter, &info);
free(work);
free(swork);
rblapack_iter = INT2NUM(iter);
rblapack_info = INT2NUM(info);
return rb_ary_new3(5, rblapack_ipiv, rblapack_x, rblapack_iter, rblapack_info, rblapack_a);
}
void
init_lapack_dsgesv(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dsgesv", rblapack_dsgesv, -1);
}
|
