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#include "rb_lapack.h"
extern VOID cgtsvx_(char* fact, char* trans, integer* n, integer* nrhs, complex* dl, complex* d, complex* du, complex* dlf, complex* df, complex* duf, complex* du2, integer* ipiv, complex* b, integer* ldb, complex* x, integer* ldx, real* rcond, real* ferr, real* berr, complex* work, real* rwork, integer* info);
static VALUE
rblapack_cgtsvx(int argc, VALUE *argv, VALUE self){
VALUE rblapack_fact;
char fact;
VALUE rblapack_trans;
char trans;
VALUE rblapack_dl;
complex *dl;
VALUE rblapack_d;
complex *d;
VALUE rblapack_du;
complex *du;
VALUE rblapack_dlf;
complex *dlf;
VALUE rblapack_df;
complex *df;
VALUE rblapack_duf;
complex *duf;
VALUE rblapack_du2;
complex *du2;
VALUE rblapack_ipiv;
integer *ipiv;
VALUE rblapack_b;
complex *b;
VALUE rblapack_x;
complex *x;
VALUE rblapack_rcond;
real rcond;
VALUE rblapack_ferr;
real *ferr;
VALUE rblapack_berr;
real *berr;
VALUE rblapack_info;
integer info;
VALUE rblapack_dlf_out__;
complex *dlf_out__;
VALUE rblapack_df_out__;
complex *df_out__;
VALUE rblapack_duf_out__;
complex *duf_out__;
VALUE rblapack_du2_out__;
complex *du2_out__;
VALUE rblapack_ipiv_out__;
integer *ipiv_out__;
complex *work;
real *rwork;
integer n;
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, dlf, df, duf, du2, ipiv = NumRu::Lapack.cgtsvx( fact, trans, dl, d, du, dlf, df, duf, du2, ipiv, b, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE CGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO )\n\n* Purpose\n* =======\n*\n* CGTSVX uses the LU factorization to compute the solution to a complex\n* system of linear equations A * X = B, A**T * X = B, or A**H * X = B,\n* where A is a tridiagonal matrix of order N and X and B are N-by-NRHS\n* 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 = 'N', the LU decomposition is used to factor the matrix A\n* as A = L * U, where L is a product of permutation and unit lower\n* bidiagonal matrices and U is upper triangular with nonzeros in\n* only the main diagonal and first two superdiagonals.\n*\n* 2. 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* 3. The system of equations is solved for X using the factored form\n* of A.\n*\n* 4. Iterative refinement is applied to improve the computed solution\n* matrix and calculate error bounds and backward error estimates\n* for it.\n*\n\n* Arguments\n* =========\n*\n* FACT (input) CHARACTER*1\n* Specifies whether or not the factored form of A has been\n* supplied on entry.\n* = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored form\n* of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not\n* be modified.\n* = 'N': The matrix will be copied to DLF, DF, and DUF\n* 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 (Conjugate transpose)\n*\n* N (input) INTEGER\n* The order 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 matrix B. NRHS >= 0.\n*\n* DL (input) COMPLEX array, dimension (N-1)\n* The (n-1) subdiagonal elements of A.\n*\n* D (input) COMPLEX array, dimension (N)\n* The n diagonal elements of A.\n*\n* DU (input) COMPLEX array, dimension (N-1)\n* The (n-1) superdiagonal elements of A.\n*\n* DLF (input or output) COMPLEX array, dimension (N-1)\n* If FACT = 'F', then DLF is an input argument and on entry\n* contains the (n-1) multipliers that define the matrix L from\n* the LU factorization of A as computed by CGTTRF.\n*\n* If FACT = 'N', then DLF is an output argument and on exit\n* contains the (n-1) multipliers that define the matrix L from\n* the LU factorization of A.\n*\n* DF (input or output) COMPLEX array, dimension (N)\n* If FACT = 'F', then DF is an input argument and on entry\n* contains the n diagonal elements of the upper triangular\n* matrix U from the LU factorization of A.\n*\n* If FACT = 'N', then DF is an output argument and on exit\n* contains the n diagonal elements of the upper triangular\n* matrix U from the LU factorization of A.\n*\n* DUF (input or output) COMPLEX array, dimension (N-1)\n* If FACT = 'F', then DUF is an input argument and on entry\n* contains the (n-1) elements of the first superdiagonal of U.\n*\n* If FACT = 'N', then DUF is an output argument and on exit\n* contains the (n-1) elements of the first superdiagonal of U.\n*\n* DU2 (input or output) COMPLEX array, dimension (N-2)\n* If FACT = 'F', then DU2 is an input argument and on entry\n* contains the (n-2) elements of the second superdiagonal of\n* U.\n*\n* If FACT = 'N', then DU2 is an output argument and on exit\n* contains the (n-2) elements of the second superdiagonal of\n* U.\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 LU factorization of A as\n* computed by CGTTRF.\n*\n* If FACT = 'N', then IPIV is an output argument and on exit\n* contains the pivot indices from the LU factorization of A;\n* row i of the matrix was interchanged with row IPIV(i).\n* IPIV(i) will always be either i or i+1; IPIV(i) = i indicates\n* a row interchange was not required.\n*\n* B (input) COMPLEX array, dimension (LDB,NRHS)\n* The N-by-NRHS right hand side matrix B.\n*\n* LDB (input) INTEGER\n* The leading dimension of the array B. LDB >= max(1,N).\n*\n* X (output) COMPLEX array, dimension (LDX,NRHS)\n* If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.\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. If RCOND is less than the machine precision (in\n* particular, if RCOND = 0), the matrix is singular to working\n* precision. This condition is indicated by a return code of\n* 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) COMPLEX array, dimension (2*N)\n*\n* RWORK (workspace) REAL 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 not been completed unless i = N, but the\n* factor U is exactly singular, so the solution\n* and error bounds could not be computed.\n* 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, dlf, df, duf, du2, ipiv = NumRu::Lapack.cgtsvx( fact, trans, dl, d, du, dlf, df, duf, du2, ipiv, b, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 11 && argc != 11)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 11)", argc);
rblapack_fact = argv[0];
rblapack_trans = argv[1];
rblapack_dl = argv[2];
rblapack_d = argv[3];
rblapack_du = argv[4];
rblapack_dlf = argv[5];
rblapack_df = argv[6];
rblapack_duf = argv[7];
rblapack_du2 = argv[8];
rblapack_ipiv = argv[9];
rblapack_b = argv[10];
if (argc == 11) {
} else if (rblapack_options != Qnil) {
} else {
}
fact = StringValueCStr(rblapack_fact)[0];
if (!NA_IsNArray(rblapack_d))
rb_raise(rb_eArgError, "d (4th argument) must be NArray");
if (NA_RANK(rblapack_d) != 1)
rb_raise(rb_eArgError, "rank of d (4th argument) must be %d", 1);
n = NA_SHAPE0(rblapack_d);
if (NA_TYPE(rblapack_d) != NA_SCOMPLEX)
rblapack_d = na_change_type(rblapack_d, NA_SCOMPLEX);
d = NA_PTR_TYPE(rblapack_d, complex*);
if (!NA_IsNArray(rblapack_df))
rb_raise(rb_eArgError, "df (7th argument) must be NArray");
if (NA_RANK(rblapack_df) != 1)
rb_raise(rb_eArgError, "rank of df (7th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_df) != n)
rb_raise(rb_eRuntimeError, "shape 0 of df must be the same as shape 0 of d");
if (NA_TYPE(rblapack_df) != NA_SCOMPLEX)
rblapack_df = na_change_type(rblapack_df, NA_SCOMPLEX);
df = NA_PTR_TYPE(rblapack_df, complex*);
if (!NA_IsNArray(rblapack_ipiv))
rb_raise(rb_eArgError, "ipiv (10th argument) must be NArray");
if (NA_RANK(rblapack_ipiv) != 1)
rb_raise(rb_eArgError, "rank of ipiv (10th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_ipiv) != n)
rb_raise(rb_eRuntimeError, "shape 0 of ipiv must be the same as shape 0 of d");
if (NA_TYPE(rblapack_ipiv) != NA_LINT)
rblapack_ipiv = na_change_type(rblapack_ipiv, NA_LINT);
ipiv = NA_PTR_TYPE(rblapack_ipiv, integer*);
ldx = MAX(1,n);
trans = StringValueCStr(rblapack_trans)[0];
if (!NA_IsNArray(rblapack_du))
rb_raise(rb_eArgError, "du (5th argument) must be NArray");
if (NA_RANK(rblapack_du) != 1)
rb_raise(rb_eArgError, "rank of du (5th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_du) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of du must be %d", n-1);
if (NA_TYPE(rblapack_du) != NA_SCOMPLEX)
rblapack_du = na_change_type(rblapack_du, NA_SCOMPLEX);
du = NA_PTR_TYPE(rblapack_du, complex*);
if (!NA_IsNArray(rblapack_duf))
rb_raise(rb_eArgError, "duf (8th argument) must be NArray");
if (NA_RANK(rblapack_duf) != 1)
rb_raise(rb_eArgError, "rank of duf (8th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_duf) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of duf must be %d", n-1);
if (NA_TYPE(rblapack_duf) != NA_SCOMPLEX)
rblapack_duf = na_change_type(rblapack_duf, NA_SCOMPLEX);
duf = NA_PTR_TYPE(rblapack_duf, complex*);
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (11th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (11th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
nrhs = NA_SHAPE1(rblapack_b);
if (NA_TYPE(rblapack_b) != NA_SCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_SCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, complex*);
if (!NA_IsNArray(rblapack_dl))
rb_raise(rb_eArgError, "dl (3th argument) must be NArray");
if (NA_RANK(rblapack_dl) != 1)
rb_raise(rb_eArgError, "rank of dl (3th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_dl) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of dl must be %d", n-1);
if (NA_TYPE(rblapack_dl) != NA_SCOMPLEX)
rblapack_dl = na_change_type(rblapack_dl, NA_SCOMPLEX);
dl = NA_PTR_TYPE(rblapack_dl, complex*);
if (!NA_IsNArray(rblapack_du2))
rb_raise(rb_eArgError, "du2 (9th argument) must be NArray");
if (NA_RANK(rblapack_du2) != 1)
rb_raise(rb_eArgError, "rank of du2 (9th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_du2) != (n-2))
rb_raise(rb_eRuntimeError, "shape 0 of du2 must be %d", n-2);
if (NA_TYPE(rblapack_du2) != NA_SCOMPLEX)
rblapack_du2 = na_change_type(rblapack_du2, NA_SCOMPLEX);
du2 = NA_PTR_TYPE(rblapack_du2, complex*);
if (!NA_IsNArray(rblapack_dlf))
rb_raise(rb_eArgError, "dlf (6th argument) must be NArray");
if (NA_RANK(rblapack_dlf) != 1)
rb_raise(rb_eArgError, "rank of dlf (6th argument) must be %d", 1);
if (NA_SHAPE0(rblapack_dlf) != (n-1))
rb_raise(rb_eRuntimeError, "shape 0 of dlf must be %d", n-1);
if (NA_TYPE(rblapack_dlf) != NA_SCOMPLEX)
rblapack_dlf = na_change_type(rblapack_dlf, NA_SCOMPLEX);
dlf = NA_PTR_TYPE(rblapack_dlf, complex*);
{
na_shape_t shape[2];
shape[0] = ldx;
shape[1] = nrhs;
rblapack_x = na_make_object(NA_SCOMPLEX, 2, shape, cNArray);
}
x = NA_PTR_TYPE(rblapack_x, complex*);
{
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] = n-1;
rblapack_dlf_out__ = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
dlf_out__ = NA_PTR_TYPE(rblapack_dlf_out__, complex*);
MEMCPY(dlf_out__, dlf, complex, NA_TOTAL(rblapack_dlf));
rblapack_dlf = rblapack_dlf_out__;
dlf = dlf_out__;
{
na_shape_t shape[1];
shape[0] = n;
rblapack_df_out__ = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
df_out__ = NA_PTR_TYPE(rblapack_df_out__, complex*);
MEMCPY(df_out__, df, complex, NA_TOTAL(rblapack_df));
rblapack_df = rblapack_df_out__;
df = df_out__;
{
na_shape_t shape[1];
shape[0] = n-1;
rblapack_duf_out__ = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
duf_out__ = NA_PTR_TYPE(rblapack_duf_out__, complex*);
MEMCPY(duf_out__, duf, complex, NA_TOTAL(rblapack_duf));
rblapack_duf = rblapack_duf_out__;
duf = duf_out__;
{
na_shape_t shape[1];
shape[0] = n-2;
rblapack_du2_out__ = na_make_object(NA_SCOMPLEX, 1, shape, cNArray);
}
du2_out__ = NA_PTR_TYPE(rblapack_du2_out__, complex*);
MEMCPY(du2_out__, du2, complex, NA_TOTAL(rblapack_du2));
rblapack_du2 = rblapack_du2_out__;
du2 = du2_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*);
MEMCPY(ipiv_out__, ipiv, integer, NA_TOTAL(rblapack_ipiv));
rblapack_ipiv = rblapack_ipiv_out__;
ipiv = ipiv_out__;
work = ALLOC_N(complex, (2*n));
rwork = ALLOC_N(real, (n));
cgtsvx_(&fact, &trans, &n, &nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, &ldb, x, &ldx, &rcond, ferr, berr, work, rwork, &info);
free(work);
free(rwork);
rblapack_rcond = rb_float_new((double)rcond);
rblapack_info = INT2NUM(info);
return rb_ary_new3(10, rblapack_x, rblapack_rcond, rblapack_ferr, rblapack_berr, rblapack_info, rblapack_dlf, rblapack_df, rblapack_duf, rblapack_du2, rblapack_ipiv);
}
void
init_lapack_cgtsvx(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "cgtsvx", rblapack_cgtsvx, -1);
}
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