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#include "rb_lapack.h"
extern VOID zgerfsx_(char* trans, char* equed, integer* n, integer* nrhs, doublecomplex* a, integer* lda, doublecomplex* af, integer* ldaf, integer* ipiv, doublereal* r, doublereal* c, doublecomplex* b, integer* ldb, doublecomplex* x, integer* ldx, doublereal* rcond, doublereal* berr, integer* n_err_bnds, doublereal* err_bnds_norm, doublereal* err_bnds_comp, integer* nparams, doublereal* params, doublecomplex* work, doublereal* rwork, integer* info);
static VALUE
rblapack_zgerfsx(int argc, VALUE *argv, VALUE self){
#ifdef USEXBLAS
VALUE rblapack_trans;
char trans;
VALUE rblapack_equed;
char equed;
VALUE rblapack_a;
doublecomplex *a;
VALUE rblapack_af;
doublecomplex *af;
VALUE rblapack_ipiv;
integer *ipiv;
VALUE rblapack_r;
doublereal *r;
VALUE rblapack_c;
doublereal *c;
VALUE rblapack_b;
doublecomplex *b;
VALUE rblapack_x;
doublecomplex *x;
VALUE rblapack_params;
doublereal *params;
VALUE rblapack_rcond;
doublereal rcond;
VALUE rblapack_berr;
doublereal *berr;
VALUE rblapack_err_bnds_norm;
doublereal *err_bnds_norm;
VALUE rblapack_err_bnds_comp;
doublereal *err_bnds_comp;
VALUE rblapack_info;
integer info;
VALUE rblapack_x_out__;
doublecomplex *x_out__;
VALUE rblapack_params_out__;
doublereal *params_out__;
doublecomplex *work;
doublereal *rwork;
integer lda;
integer n;
integer ldaf;
integer ldb;
integer nrhs;
integer ldx;
integer nparams;
integer n_err_bnds;
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 rcond, berr, err_bnds_norm, err_bnds_comp, info, x, params = NumRu::Lapack.zgerfsx( trans, equed, a, af, ipiv, r, c, b, x, params, [:usage => usage, :help => help])\n\n\nFORTRAN MANUAL\n SUBROUTINE ZGERFSX( TRANS, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV, R, C, B, LDB, X, LDX, RCOND, BERR, N_ERR_BNDS, ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK, INFO )\n\n* Purpose\n* =======\n*\n* ZGERFSX improves the computed solution to a system of linear\n* equations and provides error bounds and backward error estimates\n* for the solution. In addition to normwise error bound, the code\n* provides maximum componentwise error bound if possible. See\n* comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the\n* error bounds.\n*\n* The original system of linear equations may have been equilibrated\n* before calling this routine, as described by arguments EQUED, R\n* and C below. In this case, the solution and error bounds returned\n* are for the original unequilibrated system.\n*\n\n* Arguments\n* =========\n*\n* Some optional parameters are bundled in the PARAMS array. These\n* settings determine how refinement is performed, but often the\n* defaults are acceptable. If the defaults are acceptable, users\n* can pass NPARAMS = 0 which prevents the source code from accessing\n* the PARAMS argument.\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 = Transpose)\n*\n* EQUED (input) CHARACTER*1\n* Specifies the form of equilibration that was done to A\n* before calling this routine. This is needed to compute\n* the solution and error bounds correctly.\n* = 'N': No equilibration\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* The right hand side B has been changed accordingly.\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 matrices B and X. NRHS >= 0.\n*\n* A (input) COMPLEX*16 array, dimension (LDA,N)\n* The original N-by-N matrix A.\n*\n* LDA (input) INTEGER\n* The leading dimension of the array A. LDA >= max(1,N).\n*\n* AF (input) COMPLEX*16 array, dimension (LDAF,N)\n* The factors L and U from the factorization A = P*L*U\n* as computed by ZGETRF.\n*\n* LDAF (input) INTEGER\n* The leading dimension of the array AF. LDAF >= max(1,N).\n*\n* IPIV (input) INTEGER array, dimension (N)\n* The pivot indices from ZGETRF; for 1<=i<=N, row i of the\n* matrix was interchanged with row IPIV(i).\n*\n* R (input) DOUBLE PRECISION 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. \n* If R is accessed, each element of R should be a power of the radix\n* to ensure a reliable solution and error estimates. Scaling by\n* powers of the radix does not cause rounding errors unless the\n* result underflows or overflows. Rounding errors during scaling\n* lead to refining with a matrix that is not equivalent to the\n* input matrix, producing error estimates that may not be\n* reliable.\n*\n* C (input) DOUBLE PRECISION 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.\n* If C is accessed, each element of C should be a power of the radix\n* to ensure a reliable solution and error estimates. Scaling by\n* powers of the radix does not cause rounding errors unless the\n* result underflows or overflows. Rounding errors during scaling\n* lead to refining with a matrix that is not equivalent to the\n* input matrix, producing error estimates that may not be\n* reliable.\n*\n* B (input) COMPLEX*16 array, dimension (LDB,NRHS)\n* The 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 (input/output) COMPLEX*16 array, dimension (LDX,NRHS)\n* On entry, the solution matrix X, as computed by ZGETRS.\n* On exit, the improved solution matrix 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* Reciprocal scaled condition number. This is an estimate of the\n* reciprocal Skeel condition number of the matrix A after\n* equilibration (if done). If this is less than the machine\n* precision (in particular, if it is zero), the matrix is singular\n* to working precision. Note that the error may still be small even\n* if this number is very small and the matrix appears ill-\n* conditioned.\n*\n* BERR (output) DOUBLE PRECISION array, dimension (NRHS)\n* Componentwise relative backward error. This is the\n* componentwise relative backward error of each solution vector X(j)\n* (i.e., the smallest relative change in any element of A or B that\n* makes X(j) an exact solution).\n*\n* N_ERR_BNDS (input) INTEGER\n* Number of error bounds to return for each right hand side\n* and each type (normwise or componentwise). See ERR_BNDS_NORM and\n* ERR_BNDS_COMP below.\n*\n* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)\n* For each right-hand side, this array contains information about\n* various error bounds and condition numbers corresponding to the\n* normwise relative error, which is defined as follows:\n*\n* Normwise relative error in the ith solution vector:\n* max_j (abs(XTRUE(j,i) - X(j,i)))\n* ------------------------------\n* max_j abs(X(j,i))\n*\n* The array is indexed by the type of error information as described\n* below. There currently are up to three pieces of information\n* returned.\n*\n* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith\n* right-hand side.\n*\n* The second index in ERR_BNDS_NORM(:,err) contains the following\n* three fields:\n* err = 1 \"Trust/don't trust\" boolean. Trust the answer if the\n* reciprocal condition number is less than the threshold\n* sqrt(n) * dlamch('Epsilon').\n*\n* err = 2 \"Guaranteed\" error bound: The estimated forward error,\n* almost certainly within a factor of 10 of the true error\n* so long as the next entry is greater than the threshold\n* sqrt(n) * dlamch('Epsilon'). This error bound should only\n* be trusted if the previous boolean is true.\n*\n* err = 3 Reciprocal condition number: Estimated normwise\n* reciprocal condition number. Compared with the threshold\n* sqrt(n) * dlamch('Epsilon') to determine if the error\n* estimate is \"guaranteed\". These reciprocal condition\n* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some\n* appropriately scaled matrix Z.\n* Let Z = S*A, where S scales each row by a power of the\n* radix so all absolute row sums of Z are approximately 1.\n*\n* See Lapack Working Note 165 for further details and extra\n* cautions.\n*\n* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)\n* For each right-hand side, this array contains information about\n* various error bounds and condition numbers corresponding to the\n* componentwise relative error, which is defined as follows:\n*\n* Componentwise relative error in the ith solution vector:\n* abs(XTRUE(j,i) - X(j,i))\n* max_j ----------------------\n* abs(X(j,i))\n*\n* The array is indexed by the right-hand side i (on which the\n* componentwise relative error depends), and the type of error\n* information as described below. There currently are up to three\n* pieces of information returned for each right-hand side. If\n* componentwise accuracy is not requested (PARAMS(3) = 0.0), then\n* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most\n* the first (:,N_ERR_BNDS) entries are returned.\n*\n* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith\n* right-hand side.\n*\n* The second index in ERR_BNDS_COMP(:,err) contains the following\n* three fields:\n* err = 1 \"Trust/don't trust\" boolean. Trust the answer if the\n* reciprocal condition number is less than the threshold\n* sqrt(n) * dlamch('Epsilon').\n*\n* err = 2 \"Guaranteed\" error bound: The estimated forward error,\n* almost certainly within a factor of 10 of the true error\n* so long as the next entry is greater than the threshold\n* sqrt(n) * dlamch('Epsilon'). This error bound should only\n* be trusted if the previous boolean is true.\n*\n* err = 3 Reciprocal condition number: Estimated componentwise\n* reciprocal condition number. Compared with the threshold\n* sqrt(n) * dlamch('Epsilon') to determine if the error\n* estimate is \"guaranteed\". These reciprocal condition\n* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some\n* appropriately scaled matrix Z.\n* Let Z = S*(A*diag(x)), where x is the solution for the\n* current right-hand side and S scales each row of\n* A*diag(x) by a power of the radix so all absolute row\n* sums of Z are approximately 1.\n*\n* See Lapack Working Note 165 for further details and extra\n* cautions.\n*\n* NPARAMS (input) INTEGER\n* Specifies the number of parameters set in PARAMS. If .LE. 0, the\n* PARAMS array is never referenced and default values are used.\n*\n* PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS\n* Specifies algorithm parameters. If an entry is .LT. 0.0, then\n* that entry will be filled with default value used for that\n* parameter. Only positions up to NPARAMS are accessed; defaults\n* are used for higher-numbered parameters.\n*\n* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative\n* refinement or not.\n* Default: 1.0D+0\n* = 0.0 : No refinement is performed, and no error bounds are\n* computed.\n* = 1.0 : Use the double-precision refinement algorithm,\n* possibly with doubled-single computations if the\n* compilation environment does not support DOUBLE\n* PRECISION.\n* (other values are reserved for future use)\n*\n* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual\n* computations allowed for refinement.\n* Default: 10\n* Aggressive: Set to 100 to permit convergence using approximate\n* factorizations or factorizations other than LU. If\n* the factorization uses a technique other than\n* Gaussian elimination, the guarantees in\n* err_bnds_norm and err_bnds_comp may no longer be\n* trustworthy.\n*\n* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code\n* will attempt to find a solution with small componentwise\n* relative error in the double-precision algorithm. Positive\n* is true, 0.0 is false.\n* Default: 1.0 (attempt componentwise convergence)\n*\n* WORK (workspace) COMPLEX*16 array, dimension (2*N)\n*\n* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)\n*\n* INFO (output) INTEGER\n* = 0: Successful exit. The solution to every right-hand side is\n* guaranteed.\n* < 0: If INFO = -i, the i-th argument had an illegal value\n* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization\n* has been completed, but the factor U is exactly singular, so\n* the solution and error bounds could not be computed. RCOND = 0\n* is returned.\n* = N+J: The solution corresponding to the Jth right-hand side is\n* not guaranteed. The solutions corresponding to other right-\n* hand sides K with K > J may not be guaranteed as well, but\n* only the first such right-hand side is reported. If a small\n* componentwise error is not requested (PARAMS(3) = 0.0) then\n* the Jth right-hand side is the first with a normwise error\n* bound that is not guaranteed (the smallest J such\n* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)\n* the Jth right-hand side is the first with either a normwise or\n* componentwise error bound that is not guaranteed (the smallest\n* J such that either ERR_BNDS_NORM(J,1) = 0.0 or\n* ERR_BNDS_COMP(J,1) = 0.0). See the definition of\n* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information\n* about all of the right-hand sides check ERR_BNDS_NORM or\n* ERR_BNDS_COMP.\n*\n\n* ==================================================================\n*\n\n");
return Qnil;
}
if (rb_hash_aref(rblapack_options, sUsage) == Qtrue) {
printf("%s\n", "USAGE:\n rcond, berr, err_bnds_norm, err_bnds_comp, info, x, params = NumRu::Lapack.zgerfsx( trans, equed, a, af, ipiv, r, c, b, x, params, [:usage => usage, :help => help])\n");
return Qnil;
}
} else
rblapack_options = Qnil;
if (argc != 10 && argc != 10)
rb_raise(rb_eArgError,"wrong number of arguments (%d for 10)", argc);
rblapack_trans = argv[0];
rblapack_equed = argv[1];
rblapack_a = argv[2];
rblapack_af = argv[3];
rblapack_ipiv = argv[4];
rblapack_r = argv[5];
rblapack_c = argv[6];
rblapack_b = argv[7];
rblapack_x = argv[8];
rblapack_params = argv[9];
if (argc == 10) {
} else if (rblapack_options != Qnil) {
} else {
}
trans = StringValueCStr(rblapack_trans)[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_DCOMPLEX)
rblapack_a = na_change_type(rblapack_a, NA_DCOMPLEX);
a = NA_PTR_TYPE(rblapack_a, doublecomplex*);
if (!NA_IsNArray(rblapack_ipiv))
rb_raise(rb_eArgError, "ipiv (5th argument) must be NArray");
if (NA_RANK(rblapack_ipiv) != 1)
rb_raise(rb_eArgError, "rank of ipiv (5th 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 1 of a");
if (NA_TYPE(rblapack_ipiv) != NA_LINT)
rblapack_ipiv = na_change_type(rblapack_ipiv, NA_LINT);
ipiv = NA_PTR_TYPE(rblapack_ipiv, integer*);
if (!NA_IsNArray(rblapack_c))
rb_raise(rb_eArgError, "c (7th argument) must be NArray");
if (NA_RANK(rblapack_c) != 1)
rb_raise(rb_eArgError, "rank of c (7th argument) 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 a");
if (NA_TYPE(rblapack_c) != NA_DFLOAT)
rblapack_c = na_change_type(rblapack_c, NA_DFLOAT);
c = NA_PTR_TYPE(rblapack_c, doublereal*);
if (!NA_IsNArray(rblapack_x))
rb_raise(rb_eArgError, "x (9th argument) must be NArray");
if (NA_RANK(rblapack_x) != 2)
rb_raise(rb_eArgError, "rank of x (9th argument) must be %d", 2);
ldx = NA_SHAPE0(rblapack_x);
nrhs = NA_SHAPE1(rblapack_x);
if (NA_TYPE(rblapack_x) != NA_DCOMPLEX)
rblapack_x = na_change_type(rblapack_x, NA_DCOMPLEX);
x = NA_PTR_TYPE(rblapack_x, doublecomplex*);
n_err_bnds = 3;
equed = StringValueCStr(rblapack_equed)[0];
if (!NA_IsNArray(rblapack_r))
rb_raise(rb_eArgError, "r (6th argument) must be NArray");
if (NA_RANK(rblapack_r) != 1)
rb_raise(rb_eArgError, "rank of r (6th argument) 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 a");
if (NA_TYPE(rblapack_r) != NA_DFLOAT)
rblapack_r = na_change_type(rblapack_r, NA_DFLOAT);
r = NA_PTR_TYPE(rblapack_r, doublereal*);
if (!NA_IsNArray(rblapack_params))
rb_raise(rb_eArgError, "params (10th argument) must be NArray");
if (NA_RANK(rblapack_params) != 1)
rb_raise(rb_eArgError, "rank of params (10th argument) must be %d", 1);
nparams = NA_SHAPE0(rblapack_params);
if (NA_TYPE(rblapack_params) != NA_DFLOAT)
rblapack_params = na_change_type(rblapack_params, NA_DFLOAT);
params = NA_PTR_TYPE(rblapack_params, 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_DCOMPLEX)
rblapack_af = na_change_type(rblapack_af, NA_DCOMPLEX);
af = NA_PTR_TYPE(rblapack_af, doublecomplex*);
if (!NA_IsNArray(rblapack_b))
rb_raise(rb_eArgError, "b (8th argument) must be NArray");
if (NA_RANK(rblapack_b) != 2)
rb_raise(rb_eArgError, "rank of b (8th argument) must be %d", 2);
ldb = NA_SHAPE0(rblapack_b);
if (NA_SHAPE1(rblapack_b) != nrhs)
rb_raise(rb_eRuntimeError, "shape 1 of b must be the same as shape 1 of x");
if (NA_TYPE(rblapack_b) != NA_DCOMPLEX)
rblapack_b = na_change_type(rblapack_b, NA_DCOMPLEX);
b = NA_PTR_TYPE(rblapack_b, doublecomplex*);
{
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] = nrhs;
shape[1] = n_err_bnds;
rblapack_err_bnds_norm = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
err_bnds_norm = NA_PTR_TYPE(rblapack_err_bnds_norm, doublereal*);
{
na_shape_t shape[2];
shape[0] = nrhs;
shape[1] = n_err_bnds;
rblapack_err_bnds_comp = na_make_object(NA_DFLOAT, 2, shape, cNArray);
}
err_bnds_comp = NA_PTR_TYPE(rblapack_err_bnds_comp, doublereal*);
{
na_shape_t shape[2];
shape[0] = ldx;
shape[1] = nrhs;
rblapack_x_out__ = na_make_object(NA_DCOMPLEX, 2, shape, cNArray);
}
x_out__ = NA_PTR_TYPE(rblapack_x_out__, doublecomplex*);
MEMCPY(x_out__, x, doublecomplex, NA_TOTAL(rblapack_x));
rblapack_x = rblapack_x_out__;
x = x_out__;
{
na_shape_t shape[1];
shape[0] = nparams;
rblapack_params_out__ = na_make_object(NA_DFLOAT, 1, shape, cNArray);
}
params_out__ = NA_PTR_TYPE(rblapack_params_out__, doublereal*);
MEMCPY(params_out__, params, doublereal, NA_TOTAL(rblapack_params));
rblapack_params = rblapack_params_out__;
params = params_out__;
work = ALLOC_N(doublecomplex, (2*n));
rwork = ALLOC_N(doublereal, (2*n));
zgerfsx_(&trans, &equed, &n, &nrhs, a, &lda, af, &ldaf, ipiv, r, c, b, &ldb, x, &ldx, &rcond, berr, &n_err_bnds, err_bnds_norm, err_bnds_comp, &nparams, params, work, rwork, &info);
free(work);
free(rwork);
rblapack_rcond = rb_float_new((double)rcond);
rblapack_info = INT2NUM(info);
return rb_ary_new3(7, rblapack_rcond, rblapack_berr, rblapack_err_bnds_norm, rblapack_err_bnds_comp, rblapack_info, rblapack_x, rblapack_params);
#else
return Qnil;
#endif
}
void
init_lapack_zgerfsx(VALUE mLapack, VALUE sH, VALUE sU, VALUE zero){
sHelp = sH;
sUsage = sU;
rblapack_ZERO = zero;
rb_define_module_function(mLapack, "zgerfsx", rblapack_zgerfsx, -1);
}
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