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
|
#include "rb_lapack.h"
extern VOID chpsv_(char* uplo, integer* n, integer* nrhs, complex* ap, integer* ipiv, complex* b, integer* ldb, integer* info);
static VALUE
rblapack_chpsv(int argc, VALUE *argv, VALUE self){
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_ap;
complex *ap;
VALUE rblapack_b;
complex *b;
VALUE rblapack_ipiv;
integer *ipiv;
VALUE rblapack_info;
integer info;
VALUE rblapack_ap_out__;
complex *ap_out__;
VALUE rblapack_b_out__;
complex *b_out__;
integer ldb;
integer nrhs;
integer n;
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, info, ap, b = NumRu::Lapack.chpsv( uplo, ap, b, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE CHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )\n\n* Purpose\n* =======\n*\n* CHPSV computes the solution to a complex system of linear equations\n* A * X = B,\n* where A is an N-by-N Hermitian matrix stored in packed format and X\n* and B are N-by-NRHS matrices.\n*\n* The diagonal pivoting method is used to factor A as\n* A = U * D * U**H, if UPLO = 'U', or\n* A = L * D * L**H, if UPLO = 'L',\n* where U (or L) is a product of permutation and unit upper (lower)\n* triangular matrices, D is Hermitian and block diagonal with 1-by-1\n* and 2-by-2 diagonal blocks. The factored form of A is then used to\n* solve the system of equations A * X = B.\n*\n\n* Arguments\n* =========\n*\n* UPLO (input) CHARACTER*1\n* = 'U': Upper triangle of A is stored;\n* = 'L': Lower triangle of A is stored.\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* AP (input/output) COMPLEX array, dimension (N*(N+1)/2)\n* On entry, the upper or lower triangle of the Hermitian matrix\n* A, packed columnwise in a linear array. The j-th column of A\n* is stored in the array AP as follows:\n* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.\n* See below for further details.\n*\n* On exit, the block diagonal matrix D and the multipliers used\n* to obtain the factor U or L from the factorization\n* A = U*D*U**H or A = L*D*L**H as computed by CHPTRF, stored as\n* a packed triangular matrix in the same storage format as A.\n*\n* IPIV (output) INTEGER array, dimension (N)\n* Details of the interchanges and the block structure of D, as\n* determined by CHPTRF. If IPIV(k) > 0, then rows and columns\n* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1\n* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,\n* then rows and columns k-1 and -IPIV(k) were interchanged and\n* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and\n* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and\n* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2\n* diagonal block.\n*\n* B (input/output) COMPLEX array, dimension (LDB,NRHS)\n* On entry, the N-by-NRHS right hand side matrix B.\n* On exit, if INFO = 0, the N-by-NRHS solution matrix X.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,N).\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, D(i,i) is exactly zero. The factorization\n* has been completed, but the block diagonal matrix D is\n* exactly singular, so the solution could not be\n* computed.\n*\n\n* Further Details\n* ===============\n*\n* The packed storage scheme is illustrated by the following example\n* when N = 4, UPLO = 'U':\n*\n* Two-dimensional storage of the Hermitian matrix A:\n*\n* a11 a12 a13 a14\n* a22 a23 a24\n* a33 a34 (aij = conjg(aji))\n* a44\n*\n* Packed storage of the upper triangle of A:\n*\n* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]\n*\n* =====================================================================\n*\n* .. External Functions ..\n LOGICAL LSAME\n EXTERNAL LSAME\n* ..\n* .. External Subroutines ..\n EXTERNAL CHPTRF, CHPTRS, XERBLA\n* ..\n* .. Intrinsic Functions ..\n INTRINSIC MAX\n* ..\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n ipiv, info, ap, b = NumRu::Lapack.chpsv( uplo, ap, b, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 3 && argc != 3)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 3)", argc);
rblapack_uplo = argv[0];
rblapack_ap = argv[1];
rblapack_b = argv[2];
if (argc == 3) {
} else if (rblapack_options != Qnil) {
} else {
}
uplo = StringValueCStr(rblapack_uplo)[0];
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (3th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (3th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
nrhs = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_SCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_SCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, complex*);
n = ldb;
if (!NA_IsNArray(rblapack_ap))
rb_raise(rb_eArgError, "ap (2th argument) must be NArray");
if (NA_RANK(rblapack_ap) != 1)
rb_raise(rb_eArgError, "rank of ap (2th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_ap) != (n*(n+1)/2))
rb_raise(rb_eRuntimeError, "shape 0 of ap must be %d", n*(n+1)/2);
if (NA_TYPE(rblapack_ap) != NA_SCOMPLEX)
rblapack_ap = na_change_type(rblapack_ap, NA_SCOMPLEX);
ap = NA_PTR_TYPE(rblapack_ap, complex*);
{
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[1];
shape[0] = n*(n+1)/2;
rblapack_ap_out__ = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
ap_out__ = NA_PTR_TYPE(rblapack_ap_out__, complex*);
MEMCPY(ap_out__, ap, complex, NA_TOTAL(rblapack_ap));
rblapack_ap = rblapack_ap_out__;
ap = ap_out__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = nrhs;
rblapack_b_out__ = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, complex*);
MEMCPY(b_out__, b, complex, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
chpsv_(&uplo, &n, &nrhs, ap, ipiv, b, &ldb, &info);
rblapack_info = INT2NUM(info);
return rb_ary_new3(4, rblapack_ipiv, rblapack_info, rblapack_ap, rblapack_b);
}
void
init_lapack_chpsv(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "chpsv", rblapack_chpsv, -1);
}
|
