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#include "rb_lapack.h"
extern VOID sbdsqr_(char* uplo, integer* n, integer* ncvt, integer* nru, integer* ncc, real* d, real* e, real* vt, integer* ldvt, real* u, integer* ldu, real* c, integer* ldc, real* work, integer* info);
static VALUE
rblapack_sbdsqr(int argc, VALUE *argv, VALUE self){
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_nru;
integer nru;
VALUE rblapack_d;
real *d;
VALUE rblapack_e;
real *e;
VALUE rblapack_vt;
real *vt;
VALUE rblapack_u;
real *u;
VALUE rblapack_c;
real *c;
VALUE rblapack_info;
integer info;
VALUE rblapack_d_out__;
real *d_out__;
VALUE rblapack_e_out__;
real *e_out__;
VALUE rblapack_vt_out__;
real *vt_out__;
VALUE rblapack_u_out__;
real *u_out__;
VALUE rblapack_c_out__;
real *c_out__;
real *work;
integer n;
integer ldvt;
integer ncvt;
integer ldu;
integer ldc;
integer ncc;
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 info, d, e, vt, u, c = NumRu::Lapack.sbdsqr( uplo, nru, d, e, vt, u, c, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO )\n\n* Purpose\n* =======\n*\n* SBDSQR computes the singular values and, optionally, the right and/or\n* left singular vectors from the singular value decomposition (SVD) of\n* a real N-by-N (upper or lower) bidiagonal matrix B using the implicit\n* zero-shift QR algorithm. The SVD of B has the form\n* \n* B = Q * S * P**T\n* \n* where S is the diagonal matrix of singular values, Q is an orthogonal\n* matrix of left singular vectors, and P is an orthogonal matrix of\n* right singular vectors. If left singular vectors are requested, this\n* subroutine actually returns U*Q instead of Q, and, if right singular\n* vectors are requested, this subroutine returns P**T*VT instead of\n* P**T, for given real input matrices U and VT. When U and VT are the\n* orthogonal matrices that reduce a general matrix A to bidiagonal\n* form: A = U*B*VT, as computed by SGEBRD, then\n* \n* A = (U*Q) * S * (P**T*VT)\n* \n* is the SVD of A. Optionally, the subroutine may also compute Q**T*C\n* for a given real input matrix C.\n*\n* See \"Computing Small Singular Values of Bidiagonal Matrices With\n* Guaranteed High Relative Accuracy,\" by J. Demmel and W. Kahan,\n* LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11,\n* no. 5, pp. 873-912, Sept 1990) and\n* \"Accurate singular values and differential qd algorithms,\" by\n* B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics\n* Department, University of California at Berkeley, July 1992\n* for a detailed description of the algorithm.\n*\n\n* Arguments\n* =========\n*\n* UPLO (input) CHARACTER*1\n* = 'U': B is upper bidiagonal;\n* = 'L': B is lower bidiagonal.\n*\n* N (input) INTEGER\n* The order of the matrix B. N >= 0.\n*\n* NCVT (input) INTEGER\n* The number of columns of the matrix VT. NCVT >= 0.\n*\n* NRU (input) INTEGER\n* The number of rows of the matrix U. NRU >= 0.\n*\n* NCC (input) INTEGER\n* The number of columns of the matrix C. NCC >= 0.\n*\n* D (input/output) REAL array, dimension (N)\n* On entry, the n diagonal elements of the bidiagonal matrix B.\n* On exit, if INFO=0, the singular values of B in decreasing\n* order.\n*\n* E (input/output) REAL array, dimension (N-1)\n* On entry, the N-1 offdiagonal elements of the bidiagonal\n* matrix B.\n* On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E\n* will contain the diagonal and superdiagonal elements of a\n* bidiagonal matrix orthogonally equivalent to the one given\n* as input.\n*\n* VT (input/output) REAL array, dimension (LDVT, NCVT)\n* On entry, an N-by-NCVT matrix VT.\n* On exit, VT is overwritten by P**T * VT.\n* Not referenced if NCVT = 0.\n*\n* LDVT (input) INTEGER\n* The leading dimension of the array VT.\n* LDVT >= max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0.\n*\n* U (input/output) REAL array, dimension (LDU, N)\n* On entry, an NRU-by-N matrix U.\n* On exit, U is overwritten by U * Q.\n* Not referenced if NRU = 0.\n*\n* LDU (input) INTEGER\n* The leading dimension of the array U. LDU >= max(1,NRU).\n*\n* C (input/output) REAL array, dimension (LDC, NCC)\n* On entry, an N-by-NCC matrix C.\n* On exit, C is overwritten by Q**T * C.\n* Not referenced if NCC = 0.\n*\n* LDC (input) INTEGER\n* The leading dimension of the array C.\n* LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0.\n*\n* WORK (workspace) REAL array, dimension (4*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:\n* if NCVT = NRU = NCC = 0,\n* = 1, a split was marked by a positive value in E\n* = 2, current block of Z not diagonalized after 30*N\n* iterations (in inner while loop)\n* = 3, termination criterion of outer while loop not met \n* (program created more than N unreduced blocks)\n* else NCVT = NRU = NCC = 0,\n* the algorithm did not converge; D and E contain the\n* elements of a bidiagonal matrix which is orthogonally\n* similar to the input matrix B; if INFO = i, i\n* elements of E have not converged to zero.\n*\n* Internal Parameters\n* ===================\n*\n* TOLMUL REAL, default = max(10,min(100,EPS**(-1/8)))\n* TOLMUL controls the convergence criterion of the QR loop.\n* If it is positive, TOLMUL*EPS is the desired relative\n* precision in the computed singular values.\n* If it is negative, abs(TOLMUL*EPS*sigma_max) is the\n* desired absolute accuracy in the computed singular\n* values (corresponds to relative accuracy\n* abs(TOLMUL*EPS) in the largest singular value.\n* abs(TOLMUL) should be between 1 and 1/EPS, and preferably\n* between 10 (for fast convergence) and .1/EPS\n* (for there to be some accuracy in the results).\n* Default is to lose at either one eighth or 2 of the\n* available decimal digits in each computed singular value\n* (whichever is smaller).\n*\n* MAXITR INTEGER, default = 6\n* MAXITR controls the maximum number of passes of the\n* algorithm through its inner loop. The algorithms stops\n* (and so fails to converge) if the number of passes\n* through the inner loop exceeds MAXITR*N**2.\n*\n\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n info, d, e, vt, u, c = NumRu::Lapack.sbdsqr( uplo, nru, d, e, vt, u, c, [: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_nru = argv[1];
rblapack_d = argv[2];
rblapack_e = argv[3];
rblapack_vt = argv[4];
rblapack_u = argv[5];
rblapack_c = argv[6];
if (argc == 7) {
} else if (rblapack_options != Qnil) {
} else {
}
uplo = StringValueCStr(rblapack_uplo)[0];
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (3th argument) must be NArray");
if (NA_RANK(rblapack_d) != 1)
rb_raise(rb_eArgError, "rank of d (3th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_d);
if (NA_TYPE(rblapack_d) != NA_SFLOAT)
rblapack_d = na_change_type(rblapack_d, NA_SFLOAT);
d = NA_PTR_TYPE(rblapack_d, real*);
if (!NA_IsNArray(rblapack_vt))
rb_raise(rb_eArgError, "vt (5th argument) must be NArray");
if (NA_RANK(rblapack_vt) != 2)
rb_raise(rb_eArgError, "rank of vt (5th argument) must be %d", 2);
ldvt = NA_SHAPE0(rblapack_vt);
ncvt = NA_SHAPE1(rblapack_vt);
if (NA_TYPE(rblapack_vt) != NA_SFLOAT)
rblapack_vt = na_change_type(rblapack_vt, NA_SFLOAT);
vt = NA_PTR_TYPE(rblapack_vt, real*);
if (!NA_IsNArray(rblapack_c))
rb_raise(rb_eArgError, "c (7th argument) must be NArray");
if (NA_RANK(rblapack_c) != 2)
rb_raise(rb_eArgError, "rank of c (7th argument) must be %d", 2);
ldc = NA_SHAPE0(rblapack_c);
ncc = NA_SHAPE1(rblapack_c);
if (NA_TYPE(rblapack_c) != NA_SFLOAT)
rblapack_c = na_change_type(rblapack_c, NA_SFLOAT);
c = NA_PTR_TYPE(rblapack_c, real*);
nru = NUM2INT(rblapack_nru);
if (!NA_IsNArray(rblapack_u))
rb_raise(rb_eArgError, "u (6th argument) must be NArray");
if (NA_RANK(rblapack_u) != 2)
rb_raise(rb_eArgError, "rank of u (6th argument) must be %d", 2);
ldu = NA_SHAPE0(rblapack_u);
if (NA_SHAPE1(rblapack_u) != n)
rb_raise(rb_eRuntimeError, "shape 1 of u must be the same as shape 0 of d");
if (NA_TYPE(rblapack_u) != NA_SFLOAT)
rblapack_u = na_change_type(rblapack_u, NA_SFLOAT);
u = NA_PTR_TYPE(rblapack_u, real*);
if (!NA_IsNArray(rblapack_e))
rb_raise(rb_eArgError, "e (4th argument) must be NArray");
if (NA_RANK(rblapack_e) != 1)
rb_raise(rb_eArgError, "rank of e (4th 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_SFLOAT)
rblapack_e = na_change_type(rblapack_e, NA_SFLOAT);
e = NA_PTR_TYPE(rblapack_e, real*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_d_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
d_out__ = NA_PTR_TYPE(rblapack_d_out__, real*);
MEMCPY(d_out__, d, real, NA_TOTAL(rblapack_d));
rblapack_d = rblapack_d_out__;
d = d_out__;
{
na_shape_t shape[1];
shape[0] = n-1;
rblapack_e_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
e_out__ = NA_PTR_TYPE(rblapack_e_out__, real*);
MEMCPY(e_out__, e, real, NA_TOTAL(rblapack_e));
rblapack_e = rblapack_e_out__;
e = e_out__;
{
na_shape_t shape[2];
shape[0] = ldvt;
shape[1] = ncvt;
rblapack_vt_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
vt_out__ = NA_PTR_TYPE(rblapack_vt_out__, real*);
MEMCPY(vt_out__, vt, real, NA_TOTAL(rblapack_vt));
rblapack_vt = rblapack_vt_out__;
vt = vt_out__;
{
na_shape_t shape[2];
shape[0] = ldu;
shape[1] = n;
rblapack_u_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
u_out__ = NA_PTR_TYPE(rblapack_u_out__, real*);
MEMCPY(u_out__, u, real, NA_TOTAL(rblapack_u));
rblapack_u = rblapack_u_out__;
u = u_out__;
{
na_shape_t shape[2];
shape[0] = ldc;
shape[1] = ncc;
rblapack_c_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
c_out__ = NA_PTR_TYPE(rblapack_c_out__, real*);
MEMCPY(c_out__, c, real, NA_TOTAL(rblapack_c));
rblapack_c = rblapack_c_out__;
c = c_out__;
work = ALLOC_N(real, (4*n));
sbdsqr_(&uplo, &n, &ncvt, &nru, &ncc, d, e, vt, &ldvt, u, &ldu, c, &ldc, work, &info);
free(work);
rblapack_info = INT2NUM(info);
return rb_ary_new3(6, rblapack_info, rblapack_d, rblapack_e, rblapack_vt, rblapack_u, rblapack_c);
}
void
init_lapack_sbdsqr(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sbdsqr", rblapack_sbdsqr, -1);
}
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