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
|
#include "rb_lapack.h"
extern VOID zhesv_(char* uplo, integer* n, integer* nrhs, doublecomplex* a, integer* lda, integer* ipiv, doublecomplex* b, integer* ldb, doublecomplex* work, integer* lwork, integer* info);
static VALUE
rblapack_zhesv(int argc, VALUE *argv, VALUE self){
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_ipiv;
integer *ipiv;
VALUE rblapack_work;
doublecomplex *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublecomplex *a_out__;
VALUE rblapack_b_out__;
doublecomplex *b_out__;
integer lda;
integer n;
integer ldb;
integer nrhs;
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, work, info, a, b = NumRu::Lapack.zhesv( uplo, a, b, lwork, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZHESV computes the solution to a complex system of linear equations\n* A * X = B,\n* where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS\n* 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, and D is Hermitian and block diagonal with\n* 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then\n* used to 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* A (input/output) COMPLEX*16 array, dimension (LDA,N)\n* On entry, the Hermitian matrix A. If UPLO = 'U', the leading\n* N-by-N upper triangular part of A contains the upper\n* triangular part of the matrix A, and the strictly lower\n* triangular part of A is not referenced. If UPLO = 'L', the\n* leading N-by-N lower triangular part of A contains the lower\n* triangular part of the matrix A, and the strictly upper\n* triangular part of A is not referenced.\n*\n* On exit, if INFO = 0, the block diagonal matrix D and the\n* multipliers used to obtain the factor U or L from the\n* factorization A = U*D*U**H or A = L*D*L**H as computed by\n* ZHETRF.\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* Details of the interchanges and the block structure of D, as\n* determined by ZHETRF. 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*16 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* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))\n* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n*\n* LWORK (input) INTEGER\n* The length of WORK. LWORK >= 1, and for best performance\n* LWORK >= max(1,N*NB), where NB is the optimal blocksize for\n* ZHETRF.\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* > 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 computed.\n*\n\n* =====================================================================\n*\n* .. Local Scalars ..\n LOGICAL LQUERY\n INTEGER LWKOPT, NB\n* ..\n* .. External Functions ..\n LOGICAL LSAME\n INTEGER ILAENV\n EXTERNAL LSAME, ILAENV\n* ..\n* .. External Subroutines ..\n EXTERNAL XERBLA, ZHETRF, ZHETRS2\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, work, info, a, b = NumRu::Lapack.zhesv( uplo, a, b, lwork, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 4 && argc != 4)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 4)", argc);
rblapack_uplo = argv[0];
rblapack_a = argv[1];
rblapack_b = argv[2];
rblapack_lwork = argv[3];
if (argc == 4) {
} 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_DCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_DCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, doublecomplex*);
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (2th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (2th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
n = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_DCOMPLEX)
rblapack_a = na_change_type(rblapack_a, NA_DCOMPLEX);
a = NA_PTR_TYPE(rblapack_a, doublecomplex*);
lwork = NUM2INT(rblapack_lwork);
{
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] = MAX(1,lwork);
rblapack_work = na_make_object(NA_DCOMPLEX, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, doublecomplex*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = n;
rblapack_a_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, doublecomplex*);
MEMCPY(a_out__, a, doublecomplex, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = nrhs;
rblapack_b_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, doublecomplex*);
MEMCPY(b_out__, b, doublecomplex, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
zhesv_(&uplo, &n, &nrhs, a, &lda, ipiv, b, &ldb, work, &lwork, &info);
rblapack_info = INT2NUM(info);
return rb_ary_new3(5, rblapack_ipiv, rblapack_work, rblapack_info, rblapack_a, rblapack_b);
}
void
init_lapack_zhesv(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zhesv", rblapack_zhesv, -1);
}
|
