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
|
#include "rb_lapack.h"
extern VOID zptrfs_(char* uplo, integer* n, integer* nrhs, doublereal* d, doublecomplex* e, doublereal* df, doublecomplex* ef, doublecomplex* b, integer* ldb, doublecomplex* x, integer* ldx, doublereal* ferr, doublereal* berr, doublecomplex* work, doublereal* rwork, integer* info);
static VALUE
rblapack_zptrfs(int argc, VALUE *argv, VALUE self){
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_d;
doublereal *d;
VALUE rblapack_e;
doublecomplex *e;
VALUE rblapack_df;
doublereal *df;
VALUE rblapack_ef;
doublecomplex *ef;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_x;
doublecomplex *x;
VALUE rblapack_ferr;
doublereal *ferr;
VALUE rblapack_berr;
doublereal *berr;
VALUE rblapack_info;
integer info;
VALUE rblapack_x_out__;
doublecomplex *x_out__;
doublecomplex *work;
doublereal *rwork;
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 ferr, berr, info, x = NumRu::Lapack.zptrfs( uplo, d, e, df, ef, b, x, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZPTRFS improves the computed solution to a system of linear\n* equations when the coefficient matrix is Hermitian positive definite\n* and tridiagonal, and provides error bounds and backward error\n* estimates for the solution.\n*\n\n* Arguments\n* =========\n*\n* UPLO (input) CHARACTER*1\n* Specifies whether the superdiagonal or the subdiagonal of the\n* tridiagonal matrix A is stored and the form of the\n* factorization:\n* = 'U': E is the superdiagonal of A, and A = U**H*D*U;\n* = 'L': E is the subdiagonal of A, and A = L*D*L**H.\n* (The two forms are equivalent if A is real.)\n*\n* N (input) INTEGER\n* The order of the 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* D (input) DOUBLE PRECISION array, dimension (N)\n* The n real diagonal elements of the tridiagonal matrix A.\n*\n* E (input) COMPLEX*16 array, dimension (N-1)\n* The (n-1) off-diagonal elements of the tridiagonal matrix A\n* (see UPLO).\n*\n* DF (input) DOUBLE PRECISION array, dimension (N)\n* The n diagonal elements of the diagonal matrix D from\n* the factorization computed by ZPTTRF.\n*\n* EF (input) COMPLEX*16 array, dimension (N-1)\n* The (n-1) off-diagonal elements of the unit bidiagonal\n* factor U or L from the factorization computed by ZPTTRF\n* (see UPLO).\n*\n* B (input) COMPLEX*16 array, dimension (LDB,NRHS)\n* The 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 (input/output) COMPLEX*16 array, dimension (LDX,NRHS)\n* On entry, the solution matrix X, as computed by ZPTTRS.\n* On exit, the improved solution matrix X.\n*\n* LDX (input) INTEGER\n* The leading dimension of the array X. LDX >= max(1,N).\n*\n* FERR (output) DOUBLE PRECISION array, dimension (NRHS)\n* The forward error bound for each solution vector\n* X(j) (the j-th column of the solution matrix X).\n* If XTRUE is the true solution corresponding to X(j), FERR(j)\n* is an estimated upper bound for the magnitude of the largest\n* element in (X(j) - XTRUE) divided by the magnitude of the\n* largest element in X(j).\n*\n* BERR (output) DOUBLE PRECISION array, dimension (NRHS)\n* The componentwise relative backward error of each solution\n* vector X(j) (i.e., the smallest relative change in\n* any element of A or B that makes X(j) an exact solution).\n*\n* WORK (workspace) COMPLEX*16 array, dimension (N)\n*\n* RWORK (workspace) DOUBLE PRECISION array, dimension (N)\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value\n*\n* Internal Parameters\n* ===================\n*\n* ITMAX is the maximum number of steps of iterative refinement.\n*\n\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n ferr, berr, info, x = NumRu::Lapack.zptrfs( uplo, d, e, df, ef, b, x, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 7 && argc != 7)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 7)", argc);
rblapack_uplo = argv[0];
rblapack_d = argv[1];
rblapack_e = argv[2];
rblapack_df = argv[3];
rblapack_ef = argv[4];
rblapack_b = argv[5];
rblapack_x = argv[6];
if (argc == 7) {
} else if (rblapack_options != Qnil) {
} else {
}
uplo = StringValueCStr(rblapack_uplo)[0];
if (!NA_IsNArray(rblapack_df))
rb_raise(rb_eArgError, "df (4th argument) must be NArray");
if (NA_RANK(rblapack_df) != 1)
rb_raise(rb_eArgError, "rank of df (4th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_df);
if (NA_TYPE(rblapack_df) != NA_DFLOAT)
rblapack_df = na_change_type(rblapack_df, NA_DFLOAT);
df = NA_PTR_TYPE(rblapack_df, doublereal*);
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (6th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (6th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
nrhs = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_DCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_DCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, doublecomplex*);
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (2th argument) must be NArray");
if (NA_RANK(rblapack_d) != 1)
rb_raise(rb_eArgError, "rank of d (2th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_d) != n)
rb_raise(rb_eRuntimeError, "shape 0 of d must be the same as shape 0 of df");
if (NA_TYPE(rblapack_d) != NA_DFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_DFLOAT);
d = NA_PTR_TYPE(rblapack_d, doublereal*);
if (!NA_IsNArray(rblapack_ef))
rb_raise(rb_eArgError, "ef (5th argument) must be NArray");
if (NA_RANK(rblapack_ef) != 1)
rb_raise(rb_eArgError, "rank of ef (5th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_ef) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of ef must be %d", n-1);
if (NA_TYPE(rblapack_ef) != NA_DCOMPLEX)
rblapack_ef = na_change_type(rblapack_ef, NA_DCOMPLEX);
ef = NA_PTR_TYPE(rblapack_ef, doublecomplex*);
if (!NA_IsNArray(rblapack_e))
rb_raise(rb_eArgError, "e (3th argument) must be NArray");
if (NA_RANK(rblapack_e) != 1)
rb_raise(rb_eArgError, "rank of e (3th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_e) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of e must be %d", n-1);
if (NA_TYPE(rblapack_e) != NA_DCOMPLEX)
rblapack_e = na_change_type(rblapack_e, NA_DCOMPLEX);
e = NA_PTR_TYPE(rblapack_e, doublecomplex*);
if (!NA_IsNArray(rblapack_x))
rb_raise(rb_eArgError, "x (7th argument) must be NArray");
if (NA_RANK(rblapack_x) != 2)
rb_raise(rb_eArgError, "rank of x (7th argument) must be %d", 2);
ldx = NA_SHAPE0(rblapack_x);
if (NA_SHAPE1(rblapack_x) != nrhs)
rb_raise(rb_eRuntimeError, "shape 1 of x must be the same as shape 1 of b");
if (NA_TYPE(rblapack_x) != NA_DCOMPLEX)
rblapack_x = na_change_type(rblapack_x, NA_DCOMPLEX);
x = NA_PTR_TYPE(rblapack_x, doublecomplex*);
{
na_shape_t shape[1];
shape[0] = nrhs;
rblapack_ferr = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
ferr = NA_PTR_TYPE(rblapack_ferr, doublereal*);
{
na_shape_t shape[1];
shape[0] = nrhs;
rblapack_berr = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
berr = NA_PTR_TYPE(rblapack_berr, doublereal*);
{
na_shape_t shape[2];
shape[0] = ldx;
shape[1] = nrhs;
rblapack_x_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
x_out__ = NA_PTR_TYPE(rblapack_x_out__, doublecomplex*);
MEMCPY(x_out__, x, doublecomplex, NA_TOTAL(rblapack_x));
rblapack_x = rblapack_x_out__;
x = x_out__;
work = ALLOC_N(doublecomplex, (n));
rwork = ALLOC_N(doublereal, (n));
zptrfs_(&uplo, &n, &nrhs, d, e, df, ef, b, &ldb, x, &ldx, ferr, berr, work, rwork, &info);
free(work);
free(rwork);
rblapack_info = INT2NUM(info);
return rb_ary_new3(4, rblapack_ferr, rblapack_berr, rblapack_info, rblapack_x);
}
void
init_lapack_zptrfs(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zptrfs", rblapack_zptrfs, -1);
}
|
