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#include "rb_lapack.h"
extern VOID dgesvj_(char* joba, char* jobu, char* jobv, integer* m, integer* n, doublereal* a, integer* lda, doublereal* sva, integer* mv, doublereal* v, integer* ldv, doublereal* work, integer* lwork, integer* info);
static VALUE
rblapack_dgesvj(int argc, VALUE *argv, VALUE self){
VALUE rblapack_joba;
char joba;
VALUE rblapack_jobu;
char jobu;
VALUE rblapack_jobv;
char jobv;
VALUE rblapack_m;
integer m;
VALUE rblapack_a;
doublereal *a;
VALUE rblapack_mv;
integer mv;
VALUE rblapack_v;
doublereal *v;
VALUE rblapack_work;
doublereal *work;
VALUE rblapack_lwork;
integer lwork;
VALUE rblapack_sva;
doublereal *sva;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublereal *a_out__;
VALUE rblapack_v_out__;
doublereal *v_out__;
VALUE rblapack_work_out__;
doublereal *work_out__;
integer lda;
integer n;
integer ldv;
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 sva, info, a, v, work = NumRu::Lapack.dgesvj( joba, jobu, jobv, m, a, mv, v, work, [:lwork => lwork, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, LDV, WORK, LWORK, INFO )\n\n* Purpose\n* =======\n*\n* DGESVJ computes the singular value decomposition (SVD) of a real\n* M-by-N matrix A, where M >= N. The SVD of A is written as\n* [++] [xx] [x0] [xx]\n* A = U * SIGMA * V^t, [++] = [xx] * [ox] * [xx]\n* [++] [xx]\n* where SIGMA is an N-by-N diagonal matrix, U is an M-by-N orthonormal\n* matrix, and V is an N-by-N orthogonal matrix. The diagonal elements\n* of SIGMA are the singular values of A. The columns of U and V are the\n* left and the right singular vectors of A, respectively.\n*\n* Further Details\n* ~~~~~~~~~~~~~~~\n* The orthogonal N-by-N matrix V is obtained as a product of Jacobi plane\n* rotations. The rotations are implemented as fast scaled rotations of\n* Anda and Park [1]. In the case of underflow of the Jacobi angle, a\n* modified Jacobi transformation of Drmac [4] is used. Pivot strategy uses\n* column interchanges of de Rijk [2]. The relative accuracy of the computed\n* singular values and the accuracy of the computed singular vectors (in\n* angle metric) is as guaranteed by the theory of Demmel and Veselic [3].\n* The condition number that determines the accuracy in the full rank case\n* is essentially min_{D=diag} kappa(A*D), where kappa(.) is the\n* spectral condition number. The best performance of this Jacobi SVD\n* procedure is achieved if used in an accelerated version of Drmac and\n* Veselic [5,6], and it is the kernel routine in the SIGMA library [7].\n* Some tunning parameters (marked with [TP]) are available for the\n* implementer.\n* The computational range for the nonzero singular values is the machine\n* number interval ( UNDERFLOW , OVERFLOW ). In extreme cases, even\n* denormalized singular values can be computed with the corresponding\n* gradual loss of accurate digits.\n*\n* Contributors\n* ~~~~~~~~~~~~\n* Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)\n*\n* References\n* ~~~~~~~~~~\n* [1] A. A. Anda and H. Park: Fast plane rotations with dynamic scaling.\n* SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174.\n* [2] P. P. M. De Rijk: A one-sided Jacobi algorithm for computing the\n* singular value decomposition on a vector computer.\n* SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371.\n* [3] J. Demmel and K. Veselic: Jacobi method is more accurate than QR.\n* [4] Z. Drmac: Implementation of Jacobi rotations for accurate singular\n* value computation in floating point arithmetic.\n* SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222.\n* [5] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm I.\n* SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342.\n* LAPACK Working note 169.\n* [6] Z. Drmac and K. Veselic: New fast and accurate Jacobi SVD algorithm II.\n* SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362.\n* LAPACK Working note 170.\n* [7] Z. Drmac: SIGMA - mathematical software library for accurate SVD, PSV,\n* QSVD, (H,K)-SVD computations.\n* Department of Mathematics, University of Zagreb, 2008.\n*\n* Bugs, Examples and Comments\n* ~~~~~~~~~~~~~~~~~~~~~~~~~~~\n* Please report all bugs and send interesting test examples and comments to\n* drmac@math.hr. Thank you.\n*\n\n* Arguments\n* =========\n*\n* JOBA (input) CHARACTER* 1\n* Specifies the structure of A.\n* = 'L': The input matrix A is lower triangular;\n* = 'U': The input matrix A is upper triangular;\n* = 'G': The input matrix A is general M-by-N matrix, M >= N.\n*\n* JOBU (input) CHARACTER*1\n* Specifies whether to compute the left singular vectors\n* (columns of U):\n* = 'U': The left singular vectors corresponding to the nonzero\n* singular values are computed and returned in the leading\n* columns of A. See more details in the description of A.\n* The default numerical orthogonality threshold is set to\n* approximately TOL=CTOL*EPS, CTOL=DSQRT(M), EPS=DLAMCH('E').\n* = 'C': Analogous to JOBU='U', except that user can control the\n* level of numerical orthogonality of the computed left\n* singular vectors. TOL can be set to TOL = CTOL*EPS, where\n* CTOL is given on input in the array WORK.\n* No CTOL smaller than ONE is allowed. CTOL greater\n* than 1 / EPS is meaningless. The option 'C'\n* can be used if M*EPS is satisfactory orthogonality\n* of the computed left singular vectors, so CTOL=M could\n* save few sweeps of Jacobi rotations.\n* See the descriptions of A and WORK(1).\n* = 'N': The matrix U is not computed. However, see the\n* description of A.\n*\n* JOBV (input) CHARACTER*1\n* Specifies whether to compute the right singular vectors, that\n* is, the matrix V:\n* = 'V' : the matrix V is computed and returned in the array V\n* = 'A' : the Jacobi rotations are applied to the MV-by-N\n* array V. In other words, the right singular vector\n* matrix V is not computed explicitly, instead it is\n* applied to an MV-by-N matrix initially stored in the\n* first MV rows of V.\n* = 'N' : the matrix V is not computed and the array V is not\n* referenced\n*\n* M (input) INTEGER\n* The number of rows of the input matrix A. M >= 0.\n*\n* N (input) INTEGER\n* The number of columns of the input matrix A.\n* M >= N >= 0.\n*\n* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n* On entry, the M-by-N matrix A.\n* On exit :\n* If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C' :\n* If INFO .EQ. 0 :\n* RANKA orthonormal columns of U are returned in the\n* leading RANKA columns of the array A. Here RANKA <= N\n* is the number of computed singular values of A that are\n* above the underflow threshold DLAMCH('S'). The singular\n* vectors corresponding to underflowed or zero singular\n* values are not computed. The value of RANKA is returned\n* in the array WORK as RANKA=NINT(WORK(2)). Also see the\n* descriptions of SVA and WORK. The computed columns of U\n* are mutually numerically orthogonal up to approximately\n* TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'),\n* see the description of JOBU.\n* If INFO .GT. 0 :\n* the procedure DGESVJ did not converge in the given number\n* of iterations (sweeps). In that case, the computed\n* columns of U may not be orthogonal up to TOL. The output\n* U (stored in A), SIGMA (given by the computed singular\n* values in SVA(1:N)) and V is still a decomposition of the\n* input matrix A in the sense that the residual\n* ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small.\n*\n* If JOBU .EQ. 'N' :\n* If INFO .EQ. 0 :\n* Note that the left singular vectors are 'for free' in the\n* one-sided Jacobi SVD algorithm. However, if only the\n* singular values are needed, the level of numerical\n* orthogonality of U is not an issue and iterations are\n* stopped when the columns of the iterated matrix are\n* numerically orthogonal up to approximately M*EPS. Thus,\n* on exit, A contains the columns of U scaled with the\n* corresponding singular values.\n* If INFO .GT. 0 :\n* the procedure DGESVJ did not converge in the given number\n* of iterations (sweeps).\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,M).\n*\n* SVA (workspace/output) DOUBLE PRECISION array, dimension (N)\n* On exit :\n* If INFO .EQ. 0 :\n* depending on the value SCALE = WORK(1), we have:\n* If SCALE .EQ. ONE :\n* SVA(1:N) contains the computed singular values of A.\n* During the computation SVA contains the Euclidean column\n* norms of the iterated matrices in the array A.\n* If SCALE .NE. ONE :\n* The singular values of A are SCALE*SVA(1:N), and this\n* factored representation is due to the fact that some of the\n* singular values of A might underflow or overflow.\n* If INFO .GT. 0 :\n* the procedure DGESVJ did not converge in the given number of\n* iterations (sweeps) and SCALE*SVA(1:N) may not be accurate.\n*\n* MV (input) INTEGER\n* If JOBV .EQ. 'A', then the product of Jacobi rotations in DGESVJ\n* is applied to the first MV rows of V. See the description of JOBV.\n*\n* V (input/output) DOUBLE PRECISION array, dimension (LDV,N)\n* If JOBV = 'V', then V contains on exit the N-by-N matrix of\n* the right singular vectors;\n* If JOBV = 'A', then V contains the product of the computed right\n* singular vector matrix and the initial matrix in\n* the array V.\n* If JOBV = 'N', then V is not referenced.\n*\n* LDV (input) INTEGER\n* The leading dimension of the array V, LDV .GE. 1.\n* If JOBV .EQ. 'V', then LDV .GE. max(1,N).\n* If JOBV .EQ. 'A', then LDV .GE. max(1,MV) .\n*\n* WORK (input/workspace/output) DOUBLE PRECISION array, dimension max(4,M+N).\n* On entry :\n* If JOBU .EQ. 'C' :\n* WORK(1) = CTOL, where CTOL defines the threshold for convergence.\n* The process stops if all columns of A are mutually\n* orthogonal up to CTOL*EPS, EPS=DLAMCH('E').\n* It is required that CTOL >= ONE, i.e. it is not\n* allowed to force the routine to obtain orthogonality\n* below EPS.\n* On exit :\n* WORK(1) = SCALE is the scaling factor such that SCALE*SVA(1:N)\n* are the computed singular values of A.\n* (See description of SVA().)\n* WORK(2) = NINT(WORK(2)) is the number of the computed nonzero\n* singular values.\n* WORK(3) = NINT(WORK(3)) is the number of the computed singular\n* values that are larger than the underflow threshold.\n* WORK(4) = NINT(WORK(4)) is the number of sweeps of Jacobi\n* rotations needed for numerical convergence.\n* WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep.\n* This is useful information in cases when DGESVJ did\n* not converge, as it can be used to estimate whether\n* the output is stil useful and for post festum analysis.\n* WORK(6) = the largest absolute value over all sines of the\n* Jacobi rotation angles in the last sweep. It can be\n* useful for a post festum analysis.\n*\n* LWORK (input) INTEGER\n* length of WORK, WORK >= MAX(6,M+N)\n*\n* INFO (output) INTEGER\n* = 0 : successful exit.\n* < 0 : if INFO = -i, then the i-th argument had an illegal value\n* > 0 : DGESVJ did not converge in the maximal allowed number (30)\n* of sweeps. The output may still be useful. See the\n* description of WORK.\n*\n\n* =====================================================================\n*\n* .. Local Parameters ..\n DOUBLE PRECISION ZERO, HALF, ONE, TWO\n PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0,\n + TWO = 2.0D0 )\n INTEGER NSWEEP\n PARAMETER ( NSWEEP = 30 )\n* ..\n* .. Local Scalars ..\n DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG,\n + BIGTHETA, CS, CTOL, EPSLN, LARGE, MXAAPQ,\n + MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL,\n + SKL, SFMIN, SMALL, SN, T, TEMP1, THETA,\n + THSIGN, TOL\n INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1,\n + ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34,\n + N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP,\n + SWBAND\n LOGICAL APPLV, GOSCALE, LOWER, LSVEC, NOSCALE, ROTOK,\n + RSVEC, UCTOL, UPPER\n* ..\n* .. Local Arrays ..\n DOUBLE PRECISION FASTR( 5 )\n* ..\n* .. Intrinsic Functions ..\n INTRINSIC DABS, DMAX1, DMIN1, DBLE, MIN0, DSIGN, DSQRT\n* ..\n* .. External Functions ..\n* ..\n* from BLAS\n DOUBLE PRECISION DDOT, DNRM2\n EXTERNAL DDOT, DNRM2\n INTEGER IDAMAX\n EXTERNAL IDAMAX\n* from LAPACK\n DOUBLE PRECISION DLAMCH\n EXTERNAL DLAMCH\n LOGICAL LSAME\n EXTERNAL LSAME\n* ..\n* .. External Subroutines ..\n* ..\n* from BLAS\n EXTERNAL DAXPY, DCOPY, DROTM, DSCAL, DSWAP\n* from LAPACK\n EXTERNAL DLASCL, DLASET, DLASSQ, XERBLA\n*\n EXTERNAL DGSVJ0, DGSVJ1\n* ..\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n sva, info, a, v, work = NumRu::Lapack.dgesvj( joba, jobu, jobv, m, a, mv, v, work, [:lwork => lwork, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 8 && argc != 9)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 8)", argc);
rblapack_joba = argv[0];
rblapack_jobu = argv[1];
rblapack_jobv = argv[2];
rblapack_m = argv[3];
rblapack_a = argv[4];
rblapack_mv = argv[5];
rblapack_v = argv[6];
rblapack_work = argv[7];
if (argc == 9) {
rblapack_lwork = argv[8];
} else if (rblapack_options != Qnil) {
rblapack_lwork = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("lwork")));
} else {
rblapack_lwork = Qnil;
}
joba = StringValueCStr(rblapack_joba)[0];
jobv = StringValueCStr(rblapack_jobv)[0];
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (5th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (5th argument) must be %d", 2);
lda = NA_SHAPE0(rblapack_a);
n = NA_SHAPE1(rblapack_a);
if (NA_TYPE(rblapack_a) != NA_DFLOAT)
rblapack_a = na_change_type(rblapack_a, NA_DFLOAT);
a = NA_PTR_TYPE(rblapack_a, doublereal*);
if (!NA_IsNArray(rblapack_v))
rb_raise(rb_eArgError, "v (7th argument) must be NArray");
if (NA_RANK(rblapack_v) != 2)
rb_raise(rb_eArgError, "rank of v (7th argument) must be %d", 2);
ldv = NA_SHAPE0(rblapack_v);
if (NA_SHAPE1(rblapack_v) != n)
rb_raise(rb_eRuntimeError, "shape 1 of v must be the same as shape 1 of a");
if (NA_TYPE(rblapack_v) != NA_DFLOAT)
rblapack_v = na_change_type(rblapack_v, NA_DFLOAT);
v = NA_PTR_TYPE(rblapack_v, doublereal*);
jobu = StringValueCStr(rblapack_jobu)[0];
mv = NUM2INT(rblapack_mv);
m = NUM2INT(rblapack_m);
lwork = MAX(4,m+n);
if (!NA_IsNArray(rblapack_work))
rb_raise(rb_eArgError, "work (8th argument) must be NArray");
if (NA_RANK(rblapack_work) != 1)
rb_raise(rb_eArgError, "rank of work (8th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_work) != lwork)
rb_raise(rb_eRuntimeError, "shape 0 of work must be MAX(4,m+n)");
if (NA_TYPE(rblapack_work) != NA_DFLOAT)
rblapack_work = na_change_type(rblapack_work, NA_DFLOAT);
work = NA_PTR_TYPE(rblapack_work, doublereal*);
{
na_shape_t shape[1];
shape[0] = n;
rblapack_sva = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
sva = NA_PTR_TYPE(rblapack_sva, doublereal*);
{
na_shape_t shape[2];
shape[0] = lda;
shape[1] = n;
rblapack_a_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
a_out__ = NA_PTR_TYPE(rblapack_a_out__, doublereal*);
MEMCPY(a_out__, a, doublereal, NA_TOTAL(rblapack_a));
rblapack_a = rblapack_a_out__;
a = a_out__;
{
na_shape_t shape[2];
shape[0] = ldv;
shape[1] = n;
rblapack_v_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
v_out__ = NA_PTR_TYPE(rblapack_v_out__, doublereal*);
MEMCPY(v_out__, v, doublereal, NA_TOTAL(rblapack_v));
rblapack_v = rblapack_v_out__;
v = v_out__;
{
na_shape_t shape[1];
shape[0] = lwork;
rblapack_work_out__ = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
work_out__ = NA_PTR_TYPE(rblapack_work_out__, doublereal*);
MEMCPY(work_out__, work, doublereal, NA_TOTAL(rblapack_work));
rblapack_work = rblapack_work_out__;
work = work_out__;
dgesvj_(&joba, &jobu, &jobv, &m, &n, a, &lda, sva, &mv, v, &ldv, work, &lwork, &info);
rblapack_info = INT2NUM(info);
return rb_ary_new3(5, rblapack_sva, rblapack_info, rblapack_a, rblapack_v, rblapack_work);
}
void
init_lapack_dgesvj(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dgesvj", rblapack_dgesvj, -1);
}
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