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#include "rb_lapack.h"
extern VOID zgelsd_(integer* m, integer* n, integer* nrhs, doublecomplex* a, integer* lda, doublecomplex* b, integer* ldb, doublereal* s, doublereal* rcond, integer* rank, doublecomplex* work, integer* lwork, doublereal* rwork, integer* iwork, integer* info);
static VALUE
rblapack_zgelsd(int argc, VALUE *argv, VALUE self){
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_rcond;
doublereal rcond;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_s;
doublereal *s;
VALUE rblapack_rank;
integer rank;
VALUE rblapack_work;
doublecomplex *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_b_out__;
doublecomplex *b_out__;
doublereal *rwork;
integer *iwork;
integer lda;
integer n;
integer m;
integer nrhs;
integer ldb;
integer c__9;
integer c__0;
integer liwork;
integer lrwork;
integer nlvl;
integer smlsiz;
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 s, rank, work, info, b = NumRu::Lapack.zgelsd( a, b, rcond, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZGELSD( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, RWORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZGELSD computes the minimum-norm solution to a real linear least\n* squares problem:\n* minimize 2-norm(| b - A*x |)\n* using the singular value decomposition (SVD) of A. A is an M-by-N\n* matrix which may be rank-deficient.\n*\n* Several right hand side vectors b and solution vectors x can be\n* handled in a single call; they are stored as the columns of the\n* M-by-NRHS right hand side matrix B and the N-by-NRHS solution\n* matrix X.\n*\n* The problem is solved in three steps:\n* (1) Reduce the coefficient matrix A to bidiagonal form with\n* Householder transformations, reducing the original problem\n* into a \"bidiagonal least squares problem\" (BLS)\n* (2) Solve the BLS using a divide and conquer approach.\n* (3) Apply back all the Householder transformations to solve\n* the original least squares problem.\n*\n* The effective rank of A is determined by treating as zero those\n* singular values which are less than RCOND times the largest singular\n* value.\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* M (input) INTEGER\n* The number of rows of the matrix A. M >= 0.\n*\n* N (input) INTEGER\n* The number of columns 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 matrices B and X. NRHS >= 0.\n*\n* A (input) COMPLEX*16 array, dimension (LDA,N)\n* On entry, the M-by-N matrix A.\n* On exit, A has been destroyed.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,M).\n*\n* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)\n* On entry, the M-by-NRHS right hand side matrix B.\n* On exit, B is overwritten by the N-by-NRHS solution matrix X.\n* If m >= n and RANK = n, the residual sum-of-squares for\n* the solution in the i-th column is given by the sum of\n* squares of the modulus of elements n+1:m in that column.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,M,N).\n*\n* S (output) DOUBLE PRECISION array, dimension (min(M,N))\n* The singular values of A in decreasing order.\n* The condition number of A in the 2-norm = S(1)/S(min(m,n)).\n*\n* RCOND (input) DOUBLE PRECISION\n* RCOND is used to determine the effective rank of A.\n* Singular values S(i) <= RCOND*S(1) are treated as zero.\n* If RCOND < 0, machine precision is used instead.\n*\n* RANK (output) INTEGER\n* The effective rank of A, i.e., the number of singular values\n* which are greater than RCOND*S(1).\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 dimension of the array WORK. LWORK must be at least 1.\n* The exact minimum amount of workspace needed depends on M,\n* N and NRHS. As long as LWORK is at least\n* 2*N + N*NRHS\n* if M is greater than or equal to N or\n* 2*M + M*NRHS\n* if M is less than N, the code will execute correctly.\n* For good performance, LWORK should generally be larger.\n*\n* If LWORK = -1, then a workspace query is assumed; the routine\n* only calculates the optimal size of the array WORK and the\n* minimum sizes of the arrays RWORK and IWORK, and returns\n* these values as the first entries of the WORK, RWORK and\n* IWORK arrays, and no error message related to LWORK is issued\n* by XERBLA.\n*\n* RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))\n* LRWORK >=\n* 10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +\n* MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )\n* if M is greater than or equal to N or\n* 10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +\n* MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )\n* if M is less than N, the code will execute correctly.\n* SMLSIZ is returned by ILAENV and is equal to the maximum\n* size of the subproblems at the bottom of the computation\n* tree (usually about 25), and\n* NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )\n* On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK.\n*\n* IWORK (workspace) INTEGER array, dimension (MAX(1,LIWORK))\n* LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN),\n* where MINMN = MIN( M,N ).\n* On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.\n*\n* INFO (output) INTEGER\n* = 0: successful exit\n* < 0: if INFO = -i, the i-th argument had an illegal value.\n* > 0: the algorithm for computing the SVD failed to converge;\n* if INFO = i, i off-diagonal elements of an intermediate\n* bidiagonal form did not converge to zero.\n*\n\n* Further Details\n* ===============\n*\n* Based on contributions by\n* Ming Gu and Ren-Cang Li, Computer Science Division, University of\n* California at Berkeley, USA\n* Osni Marques, LBNL/NERSC, USA\n*\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n s, rank, work, info, b = NumRu::Lapack.zgelsd( a, b, rcond, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 3 && argc != 4)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 3)", argc);
rblapack_a = argv[0];
rblapack_b = argv[1];
rblapack_rcond = argv[2];
if (argc == 4) {
rblapack_lwork = argv[3];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (1th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (1th 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*);
rcond = NUM2DBL(rblapack_rcond);
m = lda;
c__9 = 9;
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (2th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (2th argument) must be %d", 2);
if (NA_SHAPE0(rblapack_b) != m)
rb_raise(rb_eRuntimeError, "shape 0 of b must be lda");
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*);
ldb = MAX(m,n);
if (rblapack_lwork == Qnil)
lwork = m>=n ? 2*n+n*nrhs : 2*m+m*nrhs;
else {
lwork = NUM2INT(rblapack_lwork);
}
c__0 = 0;
smlsiz = ilaenv_(&c__9,"ZGELSD"," ",&c__0,&c__0,&c__0,&c__0);
nlvl = MAX(0,(int)(log(1.0*MIN(m,n)/(smlsiz+1))/log(2.0)));
liwork = MAX(1,3*(MIN(m,n))*nlvl+11*(MIN(m,n)));
lrwork = m>=n ? 10*n+2*n*smlsiz+8*n*nlvl+3*smlsiz*nrhs+(smlsiz+1)*(smlsiz+1) : 10*m+2*m*smlsiz+8*m*nlvl+2*smlsiz*nrhs+(smlsiz+1)*(smlsiz+1);
{
na_shape_t shape[1];
shape[0] = MIN(m,n);
rblapack_s = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
s = NA_PTR_TYPE(rblapack_s, doublereal*);
{
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] = MAX(m, n);
shape[1] = nrhs;
rblapack_b_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, doublecomplex*);
{
VALUE __shape__[3];
__shape__[0] = m < n ? rb_range_new(rblapack_ZERO, INT2NUM(m), Qtrue) : Qtrue;
__shape__[1] = Qtrue;
__shape__[2] = rblapack_b;
na_aset(3, __shape__, rblapack_b_out__);
}
rblapack_b = rblapack_b_out__;
b = b_out__;
rwork = ALLOC_N(doublereal, (MAX(1,lrwork)));
iwork = ALLOC_N(integer, (MAX(1,liwork)));
zgelsd_(&m, &n, &nrhs, a, &lda, b, &ldb, s, &rcond, &rank, work, &lwork, rwork, iwork, &info);
free(rwork);
free(iwork);
rblapack_rank = INT2NUM(rank);
rblapack_info = INT2NUM(info);
{
VALUE __shape__[2];
__shape__[0] = m < n ? Qtrue : rb_range_new(rblapack_ZERO, INT2NUM(n), Qtrue);
__shape__[1] = Qtrue;
rblapack_b = na_aref(2, __shape__, rblapack_b);
}
return rb_ary_new3(5, rblapack_s, rblapack_rank, rblapack_work, rblapack_info, rblapack_b);
}
void
init_lapack_zgelsd(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zgelsd", rblapack_zgelsd, -1);
}
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