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#include "rb_lapack.h"
extern VOID sgbsvx_(char* fact, char* trans, integer* n, integer* kl, integer* ku, integer* nrhs, real* ab, integer* ldab, real* afb, integer* ldafb, integer* ipiv, char* equed, real* r, real* c, real* b, integer* ldb, real* x, integer* ldx, real* rcond, real* ferr, real* berr, real* work, integer* iwork, integer* info);
static VALUE
rblapack_sgbsvx(int argc, VALUE *argv, VALUE self){
VALUE rblapack_fact;
char fact;
VALUE rblapack_trans;
char trans;
VALUE rblapack_kl;
integer kl;
VALUE rblapack_ku;
integer ku;
VALUE rblapack_ab;
real *ab;
VALUE rblapack_b;
real *b;
VALUE rblapack_afb;
real *afb;
VALUE rblapack_ipiv;
integer *ipiv;
VALUE rblapack_equed;
char equed;
VALUE rblapack_r;
real *r;
VALUE rblapack_c;
real *c;
VALUE rblapack_x;
real *x;
VALUE rblapack_rcond;
real rcond;
VALUE rblapack_ferr;
real *ferr;
VALUE rblapack_berr;
real *berr;
VALUE rblapack_work;
real *work;
VALUE rblapack_info;
integer info;
VALUE rblapack_ab_out__;
real *ab_out__;
VALUE rblapack_afb_out__;
real *afb_out__;
VALUE rblapack_ipiv_out__;
integer *ipiv_out__;
VALUE rblapack_r_out__;
real *r_out__;
VALUE rblapack_c_out__;
real *c_out__;
VALUE rblapack_b_out__;
real *b_out__;
integer *iwork;
integer ldab;
integer n;
integer ldb;
integer nrhs;
integer ldafb;
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, work, info, ab, afb, ipiv, equed, r, c, b = NumRu::Lapack.sgbsvx( fact, trans, kl, ku, ab, b, [:afb => afb, :ipiv => ipiv, :equed => equed, :r => r, :c => c, :usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE SGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO )\n\n* Purpose\n* =======\n*\n* SGBSVX uses the LU factorization to compute the solution to a real\n* system of linear equations A * X = B, A**T * X = B, or A**H * X = B,\n* where A is a band matrix of order N with KL subdiagonals and KU\n* superdiagonals, and X and B 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 by this subroutine:\n*\n* 1. If FACT = 'E', real scaling factors are computed to equilibrate\n* the system:\n* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B\n* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B\n* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*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(R)*A*diag(C) and B by diag(R)*B (if TRANS='N')\n* or diag(C)*B (if TRANS = 'T' or 'C').\n*\n* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the\n* matrix A (after equilibration if FACT = 'E') as\n* A = L * U,\n* where L is a product of permutation and unit lower triangular\n* matrices with KL subdiagonals, and U is upper triangular with\n* KL+KU superdiagonals.\n*\n* 3. If some U(i,i)=0, so that U is exactly singular, then the routine\n* returns with INFO = i. Otherwise, the factored form of A is used\n* to estimate the condition number of the matrix A. If the\n* reciprocal of the condition number is less than machine precision,\n* INFO = N+1 is returned as a warning, but the routine still goes on\n* to solve for X and compute error bounds as 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(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so\n* that it solves the original system before 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, AFB and IPIV contain the factored form of\n* A. If EQUED is not 'N', the matrix A has been\n* equilibrated with scaling factors given by R and C.\n* AB, AFB, and IPIV are not modified.\n* = 'N': The matrix A will be copied to AFB and factored.\n* = 'E': The matrix A will be equilibrated if necessary, then\n* copied to AFB and factored.\n*\n* TRANS (input) CHARACTER*1\n* Specifies the form of the system of equations.\n* = 'N': A * X = B (No transpose)\n* = 'T': A**T * X = B (Transpose)\n* = 'C': A**H * X = B (Transpose)\n*\n* N (input) INTEGER\n* The number of linear equations, i.e., the order of the\n* matrix A. N >= 0.\n*\n* KL (input) INTEGER\n* The number of subdiagonals within the band of A. KL >= 0.\n*\n* KU (input) INTEGER\n* The number of superdiagonals within the band of A. KU >= 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* AB (input/output) REAL array, dimension (LDAB,N)\n* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.\n* The j-th column of A is stored in the j-th column of the\n* array AB as follows:\n* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)\n*\n* If FACT = 'F' and EQUED is not 'N', then A must have been\n* equilibrated by the scaling factors in R and/or C. AB is not\n* modified if FACT = 'F' or 'N', or if FACT = 'E' and\n* EQUED = 'N' on exit.\n*\n* On exit, if EQUED .ne. 'N', A is scaled as follows:\n* EQUED = 'R': A := diag(R) * A\n* EQUED = 'C': A := A * diag(C)\n* EQUED = 'B': A := diag(R) * A * diag(C).\n*\n* LDAB (input) INTEGER\n* The leading dimension of the array AB. LDAB >= KL+KU+1.\n*\n* AFB (input or output) REAL array, dimension (LDAFB,N)\n* If FACT = 'F', then AFB is an input argument and on entry\n* contains details of the LU factorization of the band matrix\n* A, as computed by SGBTRF. U is stored as an upper triangular\n* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,\n* and the multipliers used during the factorization are stored\n* in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is\n* the factored form of the equilibrated matrix A.\n*\n* If FACT = 'N', then AFB is an output argument and on exit\n* returns details of the LU factorization of A.\n*\n* If FACT = 'E', then AFB is an output argument and on exit\n* returns details of the LU factorization of the equilibrated\n* matrix A (see the description of AB for the form of the\n* equilibrated matrix).\n*\n* LDAFB (input) INTEGER\n* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.\n*\n* IPIV (input or output) INTEGER array, dimension (N)\n* If FACT = 'F', then IPIV is an input argument and on entry\n* contains the pivot indices from the factorization A = L*U\n* as computed by SGBTRF; row i of the matrix was interchanged\n* with row IPIV(i).\n*\n* If FACT = 'N', then IPIV is an output argument and on exit\n* contains the pivot indices from the factorization A = L*U\n* of the original matrix A.\n*\n* If FACT = 'E', then IPIV is an output argument and on exit\n* contains the pivot indices from the factorization A = L*U\n* of the equilibrated matrix A.\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* = 'R': Row equilibration, i.e., A has been premultiplied by\n* diag(R).\n* = 'C': Column equilibration, i.e., A has been postmultiplied\n* by diag(C).\n* = 'B': Both row and column equilibration, i.e., A has been\n* replaced by diag(R) * A * diag(C).\n* EQUED is an input argument if FACT = 'F'; otherwise, it is an\n* output argument.\n*\n* R (input or output) REAL array, dimension (N)\n* The row scale factors for A. If EQUED = 'R' or 'B', A is\n* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R\n* is not accessed. R is an input argument if FACT = 'F';\n* otherwise, R is an output argument. If FACT = 'F' and\n* EQUED = 'R' or 'B', each element of R must be positive.\n*\n* C (input or output) REAL array, dimension (N)\n* The column scale factors for A. If EQUED = 'C' or 'B', A is\n* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C\n* is not accessed. C is an input argument if FACT = 'F';\n* otherwise, C is an output argument. If FACT = 'F' and\n* EQUED = 'C' or 'B', each element of C must be positive.\n*\n* B (input/output) REAL array, dimension (LDB,NRHS)\n* On entry, the right hand side matrix B.\n* On exit,\n* if EQUED = 'N', B is not modified;\n* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by\n* diag(R)*B;\n* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is\n* overwritten by diag(C)*B.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,N).\n*\n* X (output) REAL array, dimension (LDX,NRHS)\n* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X\n* to the original system of equations. Note that A and B are\n* modified on exit if EQUED .ne. 'N', and the solution to the\n* equilibrated system is inv(diag(C))*X if TRANS = 'N' and\n* EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C'\n* and EQUED = 'R' or 'B'.\n*\n* LDX (input) INTEGER\n* The leading dimension of the array X. LDX >= max(1,N).\n*\n* RCOND (output) REAL\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) REAL 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) REAL 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/output) REAL array, dimension (3*N)\n* On exit, WORK(1) contains the reciprocal pivot growth\n* factor norm(A)/norm(U). The \"max absolute element\" norm is\n* used. If WORK(1) is much less than 1, then the stability\n* of the LU factorization of the (equilibrated) matrix A\n* could be poor. This also means that the solution X, condition\n* estimator RCOND, and forward error bound FERR could be\n* unreliable. If factorization fails with 0<INFO<=N, then\n* WORK(1) contains the reciprocal pivot growth factor for the\n* leading INFO columns of A.\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: U(i,i) is exactly zero. The factorization\n* has been completed, but the factor U is exactly\n* singular, so the solution and error bounds\n* could not be 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*\n* value of RCOND would suggest.\n\n* =====================================================================\n* Moved setting of INFO = N+1 so INFO does not subsequently get\n* overwritten. Sven, 17 Mar 05. \n* =====================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n x, rcond, ferr, berr, work, info, ab, afb, ipiv, equed, r, c, b = NumRu::Lapack.sgbsvx( fact, trans, kl, ku, ab, b, [:afb => afb, :ipiv => ipiv, :equed => equed, :r => r, :c => c, :usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 6 && argc != 11)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 6)", argc);
rblapack_fact = argv[0];
rblapack_trans = argv[1];
rblapack_kl = argv[2];
rblapack_ku = argv[3];
rblapack_ab = argv[4];
rblapack_b = argv[5];
if (argc == 11) {
rblapack_afb = argv[6];
rblapack_ipiv = argv[7];
rblapack_equed = argv[8];
rblapack_r = argv[9];
rblapack_c = argv[10];
} else if (rblapack_options != Qnil) {
rblapack_afb = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("afb")));
rblapack_ipiv = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("ipiv")));
rblapack_equed = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("equed")));
rblapack_r = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("r")));
rblapack_c = rb_hash_aref(rblapack_options, ID2SYM(rb_intern("c")));
} else {
rblapack_afb = Qnil;
rblapack_ipiv = Qnil;
rblapack_equed = Qnil;
rblapack_r = Qnil;
rblapack_c = Qnil;
}
fact = StringValueCStr(rblapack_fact)[0];
kl = NUM2INT(rblapack_kl);
if (!NA_IsNArray(rblapack_ab))
rb_raise(rb_eArgError, "ab (5th argument) must be NArray");
if (NA_RANK(rblapack_ab) != 2)
rb_raise(rb_eArgError, "rank of ab (5th argument) must be %d", 2);
ldab = NA_SHAPE0(rblapack_ab);
n = NA_SHAPE1(rblapack_ab);
if (NA_TYPE(rblapack_ab) != NA_SFLOAT)
rblapack_ab = na_change_type(rblapack_ab, NA_SFLOAT);
ab = NA_PTR_TYPE(rblapack_ab, real*);
if (rblapack_ipiv != Qnil) {
if (!NA_IsNArray(rblapack_ipiv))
rb_raise(rb_eArgError, "ipiv (option) must be NArray");
if (NA_RANK(rblapack_ipiv) != 1)
rb_raise(rb_eArgError, "rank of ipiv (option) must be %d", 1);
if (NA_SHAPE0(rblapack_ipiv) != n)
rb_raise(rb_eRuntimeError, "shape 0 of ipiv must be the same as shape 1 of ab");
if (NA_TYPE(rblapack_ipiv) != NA_LINT)
rblapack_ipiv = na_change_type(rblapack_ipiv, NA_LINT);
ipiv = NA_PTR_TYPE(rblapack_ipiv, integer*);
}
if (rblapack_r != Qnil) {
if (!NA_IsNArray(rblapack_r))
rb_raise(rb_eArgError, "r (option) must be NArray");
if (NA_RANK(rblapack_r) != 1)
rb_raise(rb_eArgError, "rank of r (option) must be %d", 1);
if (NA_SHAPE0(rblapack_r) != n)
rb_raise(rb_eRuntimeError, "shape 0 of r must be the same as shape 1 of ab");
if (NA_TYPE(rblapack_r) != NA_SFLOAT)
rblapack_r = na_change_type(rblapack_r, NA_SFLOAT);
r = NA_PTR_TYPE(rblapack_r, real*);
}
ldx = n;
trans = StringValueCStr(rblapack_trans)[0];
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (6th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (6th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
nrhs = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_SFLOAT)
rblapack_b = na_change_type(rblapack_b, NA_SFLOAT);
b = NA_PTR_TYPE(rblapack_b, real*);
if (rblapack_equed != Qnil) {
equed = StringValueCStr(rblapack_equed)[0];
}
ku = NUM2INT(rblapack_ku);
if (rblapack_c != Qnil) {
if (!NA_IsNArray(rblapack_c))
rb_raise(rb_eArgError, "c (option) must be NArray");
if (NA_RANK(rblapack_c) != 1)
rb_raise(rb_eArgError, "rank of c (option) must be %d", 1);
if (NA_SHAPE0(rblapack_c) != n)
rb_raise(rb_eRuntimeError, "shape 0 of c must be the same as shape 1 of ab");
if (NA_TYPE(rblapack_c) != NA_SFLOAT)
rblapack_c = na_change_type(rblapack_c, NA_SFLOAT);
c = NA_PTR_TYPE(rblapack_c, real*);
}
ldafb = 2*kl+ku+1;
if (rblapack_afb != Qnil) {
if (!NA_IsNArray(rblapack_afb))
rb_raise(rb_eArgError, "afb (option) must be NArray");
if (NA_RANK(rblapack_afb) != 2)
rb_raise(rb_eArgError, "rank of afb (option) must be %d", 2);
if (NA_SHAPE0(rblapack_afb) != ldafb)
rb_raise(rb_eRuntimeError, "shape 0 of afb must be 2*kl+ku+1");
if (NA_SHAPE1(rblapack_afb) != n)
rb_raise(rb_eRuntimeError, "shape 1 of afb must be the same as shape 1 of ab");
if (NA_TYPE(rblapack_afb) != NA_SFLOAT)
rblapack_afb = na_change_type(rblapack_afb, NA_SFLOAT);
afb = NA_PTR_TYPE(rblapack_afb, real*);
}
{
na_shape_t shape[2];
shape[0] = ldx;
shape[1] = nrhs;
rblapack_x = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
x = NA_PTR_TYPE(rblapack_x, real*);
{
na_shape_t shape[1];
shape[0] = nrhs;
rblapack_ferr = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
ferr = NA_PTR_TYPE(rblapack_ferr, real*);
{
na_shape_t shape[1];
shape[0] = nrhs;
rblapack_berr = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
berr = NA_PTR_TYPE(rblapack_berr, real*);
{
na_shape_t shape[1];
shape[0] = 3*n;
rblapack_work = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
work = NA_PTR_TYPE(rblapack_work, real*);
{
na_shape_t shape[2];
shape[0] = ldab;
shape[1] = n;
rblapack_ab_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
ab_out__ = NA_PTR_TYPE(rblapack_ab_out__, real*);
MEMCPY(ab_out__, ab, real, NA_TOTAL(rblapack_ab));
rblapack_ab = rblapack_ab_out__;
ab = ab_out__;
{
na_shape_t shape[2];
shape[0] = ldafb;
shape[1] = n;
rblapack_afb_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
afb_out__ = NA_PTR_TYPE(rblapack_afb_out__, real*);
if (rblapack_afb != Qnil) {
MEMCPY(afb_out__, afb, real, NA_TOTAL(rblapack_afb));
}
rblapack_afb = rblapack_afb_out__;
afb = afb_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_ipiv_out__ = na_make_object(NA_LINT, 1, shape, cNArray);
}
ipiv_out__ = NA_PTR_TYPE(rblapack_ipiv_out__, integer*);
if (rblapack_ipiv != Qnil) {
MEMCPY(ipiv_out__, ipiv, integer, NA_TOTAL(rblapack_ipiv));
}
rblapack_ipiv = rblapack_ipiv_out__;
ipiv = ipiv_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_r_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
r_out__ = NA_PTR_TYPE(rblapack_r_out__, real*);
if (rblapack_r != Qnil) {
MEMCPY(r_out__, r, real, NA_TOTAL(rblapack_r));
}
rblapack_r = rblapack_r_out__;
r = r_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_c_out__ = na_make_object(NA_SFLOAT, 1, shape, cNArray);
}
c_out__ = NA_PTR_TYPE(rblapack_c_out__, real*);
if (rblapack_c != Qnil) {
MEMCPY(c_out__, c, real, NA_TOTAL(rblapack_c));
}
rblapack_c = rblapack_c_out__;
c = c_out__;
{
na_shape_t shape[2];
shape[0] = ldb;
shape[1] = nrhs;
rblapack_b_out__ = na_make_object(NA_SFLOAT, 2, shape, cNArray);
}
b_out__ = NA_PTR_TYPE(rblapack_b_out__, real*);
MEMCPY(b_out__, b, real, NA_TOTAL(rblapack_b));
rblapack_b = rblapack_b_out__;
b = b_out__;
iwork = ALLOC_N(integer, (n));
sgbsvx_(&fact, &trans, &n, &kl, &ku, &nrhs, ab, &ldab, afb, &ldafb, ipiv, &equed, r, c, b, &ldb, x, &ldx, &rcond, ferr, berr, work, iwork, &info);
free(iwork);
rblapack_rcond = rb_float_new((double)rcond);
rblapack_info = INT2NUM(info);
rblapack_equed = rb_str_new(&equed,1);
return rb_ary_new3(13, rblapack_x, rblapack_rcond, rblapack_ferr, rblapack_berr, rblapack_work, rblapack_info, rblapack_ab, rblapack_afb, rblapack_ipiv, rblapack_equed, rblapack_r, rblapack_c, rblapack_b);
}
void
init_lapack_sgbsvx(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "sgbsvx", rblapack_sgbsvx, -1);
}
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