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
|
#include "rb_lapack.h"
extern VOID sspgvd_(integer* itype, char* jobz, char* uplo, integer* n, real* ap, real* bp, real* w, real* z, integer* ldz, real* work, integer* lwork, integer* iwork, integer* liwork, integer* info);
static VALUE
rblapack_sspgvd(int argc, VALUE *argv, VALUE self){
VALUE rblapack_itype;
integer itype;
VALUE rblapack_jobz;
char jobz;
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_ap;
real *ap;
VALUE rblapack_bp;
real *bp;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_liwork;
integer liwork;
VALUE rblapack_w;
real *w;
VALUE rblapack_z;
real *z;
VALUE rblapack_work;
real *work;
VALUE rblapack_iwork;
integer *iwork;
VALUE rblapack_info;
integer info;
VALUE rblapack_ap_out__;
real *ap_out__;
VALUE rblapack_bp_out__;
real *bp_out__;
integer ldap;
integer n;
integer ldz;
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 w, z, work, iwork, info, ap, bp = NumRu::Lapack.sspgvd( itype, jobz, uplo, ap, bp, [:lwork => lwork, :liwork => liwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )\n\n* Purpose\n* =======\n*\n* SSPGVD computes all the eigenvalues, and optionally, the eigenvectors\n* of a real generalized symmetric-definite eigenproblem, of the form\n* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and\n* B are assumed to be symmetric, stored in packed format, and B is also\n* positive definite.\n* If eigenvectors are desired, it uses a divide and conquer algorithm.\n*\n* The divide and conquer algorithm makes very mild assumptions about\n* floating point arithmetic. It will work on machines with a guard\n* digit in add/subtract, or on those binary machines without guard\n* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or\n* Cray-2. It could conceivably fail on hexadecimal or decimal machines\n* without guard digits, but we know of none.\n*\n\n* Arguments\n* =========\n*\n* ITYPE (input) INTEGER\n* Specifies the problem type to be solved:\n* = 1: A*x = (lambda)*B*x\n* = 2: A*B*x = (lambda)*x\n* = 3: B*A*x = (lambda)*x\n*\n* JOBZ (input) CHARACTER*1\n* = 'N': Compute eigenvalues only;\n* = 'V': Compute eigenvalues and eigenvectors.\n*\n* UPLO (input) CHARACTER*1\n* = 'U': Upper triangles of A and B are stored;\n* = 'L': Lower triangles of A and B are stored.\n*\n* N (input) INTEGER\n* The order of the matrices A and B. N >= 0.\n*\n* AP (input/output) REAL array, dimension (N*(N+1)/2)\n* On entry, the upper or lower triangle of the symmetric 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.\n*\n* On exit, the contents of AP are destroyed.\n*\n* BP (input/output) REAL array, dimension (N*(N+1)/2)\n* On entry, the upper or lower triangle of the symmetric matrix\n* B, packed columnwise in a linear array. The j-th column of B\n* is stored in the array BP as follows:\n* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;\n* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.\n*\n* On exit, the triangular factor U or L from the Cholesky\n* factorization B = U**T*U or B = L*L**T, in the same storage\n* format as B.\n*\n* W (output) REAL array, dimension (N)\n* If INFO = 0, the eigenvalues in ascending order.\n*\n* Z (output) REAL array, dimension (LDZ, N)\n* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of\n* eigenvectors. The eigenvectors are normalized as follows:\n* if ITYPE = 1 or 2, Z**T*B*Z = I;\n* if ITYPE = 3, Z**T*inv(B)*Z = I.\n* If JOBZ = 'N', then Z is not referenced.\n*\n* LDZ (input) INTEGER\n* The leading dimension of the array Z. LDZ >= 1, and if\n* JOBZ = 'V', LDZ >= max(1,N).\n*\n* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))\n* On exit, if INFO = 0, WORK(1) returns the required LWORK.\n*\n* LWORK (input) INTEGER\n* The dimension of the array WORK.\n* If N <= 1, LWORK >= 1.\n* If JOBZ = 'N' and N > 1, LWORK >= 2*N.\n* If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.\n*\n* If LWORK = -1, then a workspace query is assumed; the routine\n* only calculates the required sizes of the WORK and IWORK\n* arrays, returns these values as the first entries of the WORK\n* and IWORK arrays, and no error message related to LWORK or\n* LIWORK is issued by XERBLA.\n*\n* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))\n* On exit, if INFO = 0, IWORK(1) returns the required LIWORK.\n*\n* LIWORK (input) INTEGER\n* The dimension of the array IWORK.\n* If JOBZ = 'N' or N <= 1, LIWORK >= 1.\n* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.\n*\n* If LIWORK = -1, then a workspace query is assumed; the\n* routine only calculates the required sizes of the WORK and\n* IWORK arrays, returns these values as the first entries of\n* the WORK and IWORK arrays, and no error message related to\n* LWORK or LIWORK 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: SPPTRF or SSPEVD returned an error code:\n* <= N: if INFO = i, SSPEVD failed to converge;\n* i off-diagonal elements of an intermediate\n* tridiagonal form did not converge to zero;\n* > N: if INFO = N + i, for 1 <= i <= N, then the leading\n* minor of order i of B is not positive definite.\n* The factorization of B could not be completed and\n* no eigenvalues or eigenvectors were computed.\n*\n\n* Further Details\n* ===============\n*\n* Based on contributions by\n* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n w, z, work, iwork, info, ap, bp = NumRu::Lapack.sspgvd( itype, jobz, uplo, ap, bp, [:lwork => lwork, :liwork => liwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 5 && argc != 7)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 5)", argc);
rblapack_itype = argv[0];
rblapack_jobz = argv[1];
rblapack_uplo = argv[2];
rblapack_ap = argv[3];
rblapack_bp = argv[4];
if (argc == 7) {
rblapack_lwork = argv[5];
rblapack_liwork = argv[6];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
rblapack_liwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("liwork")));
} else {
rblapack_lwork = Qnil;
rblapack_liwork = Qnil;
}
itype = NUM2INT(rblapack_itype);
uplo = StringValueCStr(rblapack_uplo)[0];
jobz = StringValueCStr(rblapack_jobz)[0];
if (!NA_IsNArray(rblapack_ap))
rb_raise(rb_eArgError, "ap (4th argument) must be NArray");
if (NA_RANK(rblapack_ap) != 1)
rb_raise(rb_eArgError, "rank of ap (4th argument) must be %d", 1);
ldap = NA_SHAPE0(rblapack_ap);
if (NA_TYPE(rblapack_ap) != NA_SFLOAT)
rblapack_ap = na_change_type(rblapack_ap, NA_SFLOAT);
ap = NA_PTR_TYPE(rblapack_ap, real*);
n = ((int)sqrtf(ldap*8+1.0f)-1)/2;
if (!NA_IsNArray(rblapack_bp))
rb_raise(rb_eArgError, "bp (5th argument) must be NArray");
if (NA_RANK(rblapack_bp) != 1)
rb_raise(rb_eArgError, "rank of bp (5th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_bp) != (n*(n+1)/2))
rb_raise(rb_eRuntimeError, "shape 0 of bp must be %d", n*(n+1)/2);
if (NA_TYPE(rblapack_bp) != NA_SFLOAT)
rblapack_bp = na_change_type(rblapack_bp, NA_SFLOAT);
bp = NA_PTR_TYPE(rblapack_bp, real*);
if (rblapack_liwork == Qnil)
liwork = (lsame_(&jobz,"N")||n<=1) ? 1 : lsame_(&jobz,"V") ? 3+5*n : 0;
else {
liwork = NUM2INT(rblapack_liwork);
}
if (rblapack_lwork == Qnil)
lwork = n<=1 ? 1 : lsame_(&jobz,"N") ? 2*n : lsame_(&jobz,"V") ? 1+6*n+2*n*n : 0;
else {
lwork = NUM2INT(rblapack_lwork);
}
ldz = lsame_(&jobz,"V") ? MAX(1,n) : 1;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_w = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
w = NA_PTR_TYPE(rblapack_w, real*);
{
na_shape_t shape[2];
shape[0] = ldz;
shape[1] = n;
rblapack_z = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
z = NA_PTR_TYPE(rblapack_z, real*);
{
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[1];
shape[0] = MAX(1,liwork);
rblapack_iwork = na_make_object(NA_LINT, 1, shape, cNArray);
}
iwork = NA_PTR_TYPE(rblapack_iwork, integer*);
{
na_shape_t shape[1];
shape[0] = ldap;
rblapack_ap_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
ap_out__ = NA_PTR_TYPE(rblapack_ap_out__, real*);
MEMCPY(ap_out__, ap, real, NA_TOTAL(rblapack_ap));
rblapack_ap = rblapack_ap_out__;
ap = ap_out__;
{
na_shape_t shape[1];
shape[0] = n*(n+1)/2;
rblapack_bp_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
bp_out__ = NA_PTR_TYPE(rblapack_bp_out__, real*);
MEMCPY(bp_out__, bp, real, NA_TOTAL(rblapack_bp));
rblapack_bp = rblapack_bp_out__;
bp = bp_out__;
sspgvd_(&itype, &jobz, &uplo, &n, ap, bp, w, z, &ldz, work, &lwork, iwork, &liwork, &info);
rblapack_info = INT2NUM(info);
return rb_ary_new3(7, rblapack_w, rblapack_z, rblapack_work, rblapack_iwork, rblapack_info, rblapack_ap, rblapack_bp);
}
void
init_lapack_sspgvd(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sspgvd", rblapack_sspgvd, -1);
}
|
