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#include "rb_lapack.h"
extern VOID dposvx_(char* fact, char* uplo, integer* n, integer* nrhs, doublereal* a, integer* lda, doublereal* af, integer* ldaf, char* equed, doublereal* s, doublereal* b, integer* ldb, doublereal* x, integer* ldx, doublereal* rcond, doublereal* ferr, doublereal* berr, doublereal* work, integer* iwork, integer* info);
static VALUE
rblapack_dposvx(int argc, VALUE *argv, VALUE self){
VALUE rblapack_fact;
char fact;
VALUE rblapack_uplo;
char uplo;
VALUE rblapack_a;
doublereal *a;
VALUE rblapack_af;
doublereal *af;
VALUE rblapack_equed;
char equed;
VALUE rblapack_s;
doublereal *s;
VALUE rblapack_b;
doublereal *b;
VALUE rblapack_x;
doublereal *x;
VALUE rblapack_rcond;
doublereal rcond;
VALUE rblapack_ferr;
doublereal *ferr;
VALUE rblapack_berr;
doublereal *berr;
VALUE rblapack_info;
integer info;
VALUE rblapack_a_out__;
doublereal *a_out__;
VALUE rblapack_af_out__;
doublereal *af_out__;
VALUE rblapack_s_out__;
doublereal *s_out__;
VALUE rblapack_b_out__;
doublereal *b_out__;
doublereal *work;
integer *iwork;
integer lda;
integer n;
integer ldaf;
integer ldb;
integer nrhs;
integer ldx;
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 x, rcond, ferr, berr, info, a, af, equed, s, b = NumRu::Lapack.dposvx( fact, uplo, a, af, equed, s, b, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE DPOSVX( FACT, UPLO, N, NRHS, A, LDA, AF, LDAF, EQUED, S, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* DPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to\n* compute the solution to a real system of linear equations\n* A * X = B,\n* where A is an N-by-N symmetric positive definite matrix and X and B\n* are N-by-NRHS matrices.\n*\n* Error bounds on the solution and a condition estimate are also\n* provided.\n*\n* Description\n* ===========\n*\n* The following steps are performed:\n*\n* 1. If FACT = 'E', real scaling factors are computed to equilibrate\n* the system:\n* diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B\n* Whether or not the system will be equilibrated depends on the\n* scaling of the matrix A, but if equilibration is used, A is\n* overwritten by diag(S)*A*diag(S) and B by diag(S)*B.\n*\n* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to\n* factor the matrix A (after equilibration if FACT = 'E') as\n* A = U**T* U, if UPLO = 'U', or\n* A = L * L**T, if UPLO = 'L',\n* where U is an upper triangular matrix and L is a lower triangular\n* matrix.\n*\n* 3. If the leading i-by-i principal minor is not positive definite,\n* then the routine returns with INFO = i. Otherwise, the factored\n* form of A is used to estimate the condition number of the matrix\n* A. If the reciprocal of the condition number is less than machine\n* precision, INFO = N+1 is returned as a warning, but the routine\n* still goes on to solve for X and compute error bounds as\n* described below.\n*\n* 4. The system of equations is solved for X using the factored form\n* of A.\n*\n* 5. Iterative refinement is applied to improve the computed solution\n* matrix and calculate error bounds and backward error estimates\n* for it.\n*\n* 6. If equilibration was used, the matrix X is premultiplied by\n* diag(S) so that it solves the original system before\n* equilibration.\n*\n\n* Arguments\n* =========\n*\n* FACT (input) CHARACTER*1\n* Specifies whether or not the factored form of the matrix A is\n* supplied on entry, and if not, whether the matrix A should be\n* equilibrated before it is factored.\n* = 'F': On entry, AF contains the factored form of A.\n* If EQUED = 'Y', the matrix A has been equilibrated\n* with scaling factors given by S. A and AF will not\n* be modified.\n* = 'N': The matrix A will be copied to AF and factored.\n* = 'E': The matrix A will be equilibrated if necessary, then\n* copied to AF and factored.\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 matrices B and X. NRHS >= 0.\n*\n* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n* On entry, the symmetric matrix A, except if FACT = 'F' and\n* EQUED = 'Y', then A must contain the equilibrated matrix\n* diag(S)*A*diag(S). 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. A is not modified if\n* FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit.\n*\n* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by\n* diag(S)*A*diag(S).\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,N).\n*\n* AF (input or output) DOUBLE PRECISION array, dimension (LDAF,N)\n* If FACT = 'F', then AF is an input argument and on entry\n* contains the triangular factor U or L from the Cholesky\n* factorization A = U**T*U or A = L*L**T, in the same storage\n* format as A. If EQUED .ne. 'N', then AF is the factored form\n* of the equilibrated matrix diag(S)*A*diag(S).\n*\n* If FACT = 'N', then AF is an output argument and on exit\n* returns the triangular factor U or L from the Cholesky\n* factorization A = U**T*U or A = L*L**T of the original\n* matrix A.\n*\n* If FACT = 'E', then AF is an output argument and on exit\n* returns the triangular factor U or L from the Cholesky\n* factorization A = U**T*U or A = L*L**T of the equilibrated\n* matrix A (see the description of A for the form of the\n* equilibrated matrix).\n*\n* LDAF (input) INTEGER\n* The leading dimension of the array AF. LDAF >= max(1,N).\n*\n* EQUED (input or output) CHARACTER*1\n* Specifies the form of equilibration that was done.\n* = 'N': No equilibration (always true if FACT = 'N').\n* = 'Y': Equilibration was done, i.e., A has been replaced by\n* diag(S) * A * diag(S).\n* EQUED is an input argument if FACT = 'F'; otherwise, it is an\n* output argument.\n*\n* S (input or output) DOUBLE PRECISION array, dimension (N)\n* The scale factors for A; not accessed if EQUED = 'N'. S is\n* an input argument if FACT = 'F'; otherwise, S is an output\n* argument. If FACT = 'F' and EQUED = 'Y', each element of S\n* must be positive.\n*\n* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)\n* On entry, the N-by-NRHS right hand side matrix B.\n* On exit, if EQUED = 'N', B is not modified; if EQUED = 'Y',\n* B is overwritten by diag(S) * B.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,N).\n*\n* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)\n* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X to\n* the original system of equations. Note that if EQUED = 'Y',\n* A and B are modified on exit, and the solution to the\n* equilibrated system is inv(diag(S))*X.\n*\n* LDX (input) INTEGER\n* The leading dimension of the array X. LDX >= max(1,N).\n*\n* RCOND (output) DOUBLE PRECISION\n* The estimate of the reciprocal condition number of the matrix\n* A after equilibration (if done). If RCOND is less than the\n* machine precision (in particular, if RCOND = 0), the matrix\n* is singular to working precision. This condition is\n* indicated by a return code of INFO > 0.\n*\n* FERR (output) DOUBLE PRECISION array, dimension (NRHS)\n* The estimated forward error bound for each solution vector\n* X(j) (the j-th column of the solution matrix X).\n* If XTRUE is the true solution corresponding to X(j), FERR(j)\n* is an estimated upper bound for the magnitude of the largest\n* element in (X(j) - XTRUE) divided by the magnitude of the\n* largest element in X(j). The estimate is as reliable as\n* the estimate for RCOND, and is almost always a slight\n* overestimate of the true error.\n*\n* BERR (output) DOUBLE PRECISION array, dimension (NRHS)\n* The componentwise relative backward error of each solution\n* vector X(j) (i.e., the smallest relative change in\n* any element of A or B that makes X(j) an exact solution).\n*\n* WORK (workspace) DOUBLE PRECISION array, dimension (3*N)\n*\n* IWORK (workspace) INTEGER array, dimension (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: if INFO = i, and i is\n* <= N: the leading minor of order i of A is\n* not positive definite, so the factorization\n* could not be completed, and the solution has not\n* been computed. RCOND = 0 is returned.\n* = N+1: U is nonsingular, but RCOND is less than machine\n* precision, meaning that the matrix is singular\n* to working precision. Nevertheless, the\n* solution and error bounds are computed because\n* there are a number of situations where the\n* computed solution can be more accurate than the\n* value of RCOND would suggest.\n*\n\n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n x, rcond, ferr, berr, info, a, af, equed, s, b = NumRu::Lapack.dposvx( fact, uplo, a, af, equed, s, b, [: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_fact = argv[0];
rblapack_uplo = argv[1];
rblapack_a = argv[2];
rblapack_af = argv[3];
rblapack_equed = argv[4];
rblapack_s = argv[5];
rblapack_b = argv[6];
if (argc == 7) {
} else if (rblapack_options != Qnil) {
} else {
}
fact = StringValueCStr(rblapack_fact)[0];
if (!NA_IsNArray(rblapack_a))
rb_raise(rb_eArgError, "a (3th argument) must be NArray");
if (NA_RANK(rblapack_a) != 2)
rb_raise(rb_eArgError, "rank of a (3th 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*);
equed = StringValueCStr(rblapack_equed)[0];
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (7th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (7th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
nrhs = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_DFLOAT)
rblapack_b = na_change_type(rblapack_b, NA_DFLOAT);
b = NA_PTR_TYPE(rblapack_b, doublereal*);
uplo = StringValueCStr(rblapack_uplo)[0];
if (!NA_IsNArray(rblapack_s))
rb_raise(rb_eArgError, "s (6th argument) must be NArray");
if (NA_RANK(rblapack_s) != 1)
rb_raise(rb_eArgError, "rank of s (6th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_s) != n)
rb_raise(rb_eRuntimeError, "shape 0 of s must be the same as shape 1 of a");
if (NA_TYPE(rblapack_s) != NA_DFLOAT)
rblapack_s = na_change_type(rblapack_s, NA_DFLOAT);
s = NA_PTR_TYPE(rblapack_s, doublereal*);
if (!NA_IsNArray(rblapack_af))
rb_raise(rb_eArgError, "af (4th argument) must be NArray");
if (NA_RANK(rblapack_af) != 2)
rb_raise(rb_eArgError, "rank of af (4th argument) must be %d", 2);
ldaf = NA_SHAPE0(rblapack_af);
if (NA_SHAPE1(rblapack_af) != n)
rb_raise(rb_eRuntimeError, "shape 1 of af must be the same as shape 1 of a");
if (NA_TYPE(rblapack_af) != NA_DFLOAT)
rblapack_af = na_change_type(rblapack_af, NA_DFLOAT);
af = NA_PTR_TYPE(rblapack_af, doublereal*);
ldx = MAX(1,n);
{
na_shape_t shape[2];
shape[0] = ldx;
shape[1] = nrhs;
rblapack_x = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
x = NA_PTR_TYPE(rblapack_x, doublereal*);
{
na_shape_t shape[1];
shape[0] = nrhs;
rblapack_ferr = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
ferr = NA_PTR_TYPE(rblapack_ferr, doublereal*);
{
na_shape_t shape[1];
shape[0] = nrhs;
rblapack_berr = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
berr = NA_PTR_TYPE(rblapack_berr, 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] = ldaf;
shape[1] = n;
rblapack_af_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
af_out__ = NA_PTR_TYPE(rblapack_af_out__, doublereal*);
MEMCPY(af_out__, af, doublereal, NA_TOTAL(rblapack_af));
rblapack_af = rblapack_af_out__;
af = af_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_s_out__ = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
s_out__ = NA_PTR_TYPE(rblapack_s_out__, doublereal*);
MEMCPY(s_out__, s, doublereal, NA_TOTAL(rblapack_s));
rblapack_s = rblapack_s_out__;
s = s_out__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = nrhs;
rblapack_b_out__ = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, doublereal*);
MEMCPY(b_out__, b, doublereal, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
work = ALLOC_N(doublereal, (3*n));
iwork = ALLOC_N(integer, (n));
dposvx_(&fact, &uplo, &n, &nrhs, a, &lda, af, &ldaf, &equed, s, b, &ldb, x, &ldx, &rcond, ferr, berr, work, iwork, &info);
free(work);
free(iwork);
rblapack_rcond = rb_float_new((double)rcond);
rblapack_info = INT2NUM(info);
rblapack_equed = rb_str_new(&equed,1);
return rb_ary_new3(10, rblapack_x, rblapack_rcond, rblapack_ferr, rblapack_berr, rblapack_info, rblapack_a, rblapack_af, rblapack_equed, rblapack_s, rblapack_b);
}
void
init_lapack_dposvx(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "dposvx", rblapack_dposvx, -1);
}
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