/* f2c.h -- Standard Fortran to C header file */ /** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed." - From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */ #ifndef F2C_INCLUDE #define F2C_INCLUDE #include #include #include #include #include #ifdef complex #undef complex #endif #ifdef I #undef I #endif #if defined(_WIN64) typedef long long BLASLONG; typedef unsigned long long BLASULONG; #else typedef long BLASLONG; typedef unsigned long BLASULONG; #endif #ifdef LAPACK_ILP64 typedef BLASLONG blasint; #if defined(_WIN64) #define blasabs(x) llabs(x) #else #define blasabs(x) labs(x) #endif #else typedef int blasint; #define blasabs(x) abs(x) #endif typedef blasint integer; typedef unsigned int uinteger; typedef char *address; typedef short int shortint; typedef float real; typedef double doublereal; typedef struct { real r, i; } complex; typedef struct { doublereal r, i; } doublecomplex; static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;} static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;} static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;} static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;} #define pCf(z) (*_pCf(z)) #define pCd(z) (*_pCd(z)) typedef int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimag(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; _Complex float zdotc = 0.0; if (incx == 1 && incy == 1) { for (i=0;i \brief \b DGBRFSX */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DGBRFSX + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB, */ /* LDAFB, IPIV, R, C, B, LDB, X, LDX, RCOND, */ /* BERR, N_ERR_BNDS, ERR_BNDS_NORM, */ /* ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, IWORK, */ /* INFO ) */ /* CHARACTER TRANS, EQUED */ /* INTEGER INFO, LDAB, LDAFB, LDB, LDX, N, KL, KU, NRHS, */ /* $ NPARAMS, N_ERR_BNDS */ /* DOUBLE PRECISION RCOND */ /* INTEGER IPIV( * ), IWORK( * ) */ /* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */ /* $ X( LDX , * ),WORK( * ) */ /* DOUBLE PRECISION R( * ), C( * ), PARAMS( * ), BERR( * ), */ /* $ ERR_BNDS_NORM( NRHS, * ), */ /* $ ERR_BNDS_COMP( NRHS, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DGBRFSX improves the computed solution to a system of linear */ /* > equations and provides error bounds and backward error estimates */ /* > for the solution. In addition to normwise error bound, the code */ /* > provides maximum componentwise error bound if possible. See */ /* > comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the */ /* > error bounds. */ /* > */ /* > The original system of linear equations may have been equilibrated */ /* > before calling this routine, as described by arguments EQUED, R */ /* > and C below. In this case, the solution and error bounds returned */ /* > are for the original unequilibrated system. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \verbatim */ /* > Some optional parameters are bundled in the PARAMS array. These */ /* > settings determine how refinement is performed, but often the */ /* > defaults are acceptable. If the defaults are acceptable, users */ /* > can pass NPARAMS = 0 which prevents the source code from accessing */ /* > the PARAMS argument. */ /* > \endverbatim */ /* > */ /* > \param[in] TRANS */ /* > \verbatim */ /* > TRANS is CHARACTER*1 */ /* > Specifies the form of the system of equations: */ /* > = 'N': A * X = B (No transpose) */ /* > = 'T': A**T * X = B (Transpose) */ /* > = 'C': A**H * X = B (Conjugate transpose = Transpose) */ /* > \endverbatim */ /* > */ /* > \param[in] EQUED */ /* > \verbatim */ /* > EQUED is CHARACTER*1 */ /* > Specifies the form of equilibration that was done to A */ /* > before calling this routine. This is needed to compute */ /* > the solution and error bounds correctly. */ /* > = 'N': No equilibration */ /* > = 'R': Row equilibration, i.e., A has been premultiplied by */ /* > diag(R). */ /* > = 'C': Column equilibration, i.e., A has been postmultiplied */ /* > by diag(C). */ /* > = 'B': Both row and column equilibration, i.e., A has been */ /* > replaced by diag(R) * A * diag(C). */ /* > The right hand side B has been changed accordingly. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] KL */ /* > \verbatim */ /* > KL is INTEGER */ /* > The number of subdiagonals within the band of A. KL >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] KU */ /* > \verbatim */ /* > KU is INTEGER */ /* > The number of superdiagonals within the band of A. KU >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] NRHS */ /* > \verbatim */ /* > NRHS is INTEGER */ /* > The number of right hand sides, i.e., the number of columns */ /* > of the matrices B and X. NRHS >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] AB */ /* > \verbatim */ /* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */ /* > The original band matrix A, stored in rows 1 to KL+KU+1. */ /* > The j-th column of A is stored in the j-th column of the */ /* > array AB as follows: */ /* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(n,j+kl). */ /* > \endverbatim */ /* > */ /* > \param[in] LDAB */ /* > \verbatim */ /* > LDAB is INTEGER */ /* > The leading dimension of the array AB. LDAB >= KL+KU+1. */ /* > \endverbatim */ /* > */ /* > \param[in] AFB */ /* > \verbatim */ /* > AFB is DOUBLE PRECISION array, dimension (LDAFB,N) */ /* > Details of the LU factorization of the band matrix A, as */ /* > computed by DGBTRF. U is stored as an upper triangular band */ /* > matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */ /* > the multipliers used during the factorization are stored in */ /* > rows KL+KU+2 to 2*KL+KU+1. */ /* > \endverbatim */ /* > */ /* > \param[in] LDAFB */ /* > \verbatim */ /* > LDAFB is INTEGER */ /* > The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. */ /* > \endverbatim */ /* > */ /* > \param[in] IPIV */ /* > \verbatim */ /* > IPIV is INTEGER array, dimension (N) */ /* > The pivot indices from DGETRF; for 1<=i<=N, row i of the */ /* > matrix was interchanged with row IPIV(i). */ /* > \endverbatim */ /* > */ /* > \param[in,out] R */ /* > \verbatim */ /* > R is DOUBLE PRECISION array, dimension (N) */ /* > The row scale factors for A. If EQUED = 'R' or 'B', A is */ /* > multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ /* > is not accessed. R is an input argument if FACT = 'F'; */ /* > otherwise, R is an output argument. If FACT = 'F' and */ /* > EQUED = 'R' or 'B', each element of R must be positive. */ /* > If R is output, each element of R is a power of the radix. */ /* > If R is input, each element of R should be a power of the radix */ /* > to ensure a reliable solution and error estimates. Scaling by */ /* > powers of the radix does not cause rounding errors unless the */ /* > result underflows or overflows. Rounding errors during scaling */ /* > lead to refining with a matrix that is not equivalent to the */ /* > input matrix, producing error estimates that may not be */ /* > reliable. */ /* > \endverbatim */ /* > */ /* > \param[in,out] C */ /* > \verbatim */ /* > C is DOUBLE PRECISION array, dimension (N) */ /* > The column scale factors for A. If EQUED = 'C' or 'B', A is */ /* > multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ /* > is not accessed. C is an input argument if FACT = 'F'; */ /* > otherwise, C is an output argument. If FACT = 'F' and */ /* > EQUED = 'C' or 'B', each element of C must be positive. */ /* > If C is output, each element of C is a power of the radix. */ /* > If C is input, each element of C should be a power of the radix */ /* > to ensure a reliable solution and error estimates. Scaling by */ /* > powers of the radix does not cause rounding errors unless the */ /* > result underflows or overflows. Rounding errors during scaling */ /* > lead to refining with a matrix that is not equivalent to the */ /* > input matrix, producing error estimates that may not be */ /* > reliable. */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */ /* > The right hand side matrix B. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] X */ /* > \verbatim */ /* > X is DOUBLE PRECISION array, dimension (LDX,NRHS) */ /* > On entry, the solution matrix X, as computed by DGETRS. */ /* > On exit, the improved solution matrix X. */ /* > \endverbatim */ /* > */ /* > \param[in] LDX */ /* > \verbatim */ /* > LDX is INTEGER */ /* > The leading dimension of the array X. LDX >= f2cmax(1,N). */ /* > \endverbatim */ /* > */ /* > \param[out] RCOND */ /* > \verbatim */ /* > RCOND is DOUBLE PRECISION */ /* > Reciprocal scaled condition number. This is an estimate of the */ /* > reciprocal Skeel condition number of the matrix A after */ /* > equilibration (if done). If this is less than the machine */ /* > precision (in particular, if it is zero), the matrix is singular */ /* > to working precision. Note that the error may still be small even */ /* > if this number is very small and the matrix appears ill- */ /* > conditioned. */ /* > \endverbatim */ /* > */ /* > \param[out] BERR */ /* > \verbatim */ /* > BERR is DOUBLE PRECISION array, dimension (NRHS) */ /* > Componentwise relative backward error. This is the */ /* > componentwise relative backward error of each solution vector X(j) */ /* > (i.e., the smallest relative change in any element of A or B that */ /* > makes X(j) an exact solution). */ /* > \endverbatim */ /* > */ /* > \param[in] N_ERR_BNDS */ /* > \verbatim */ /* > N_ERR_BNDS is INTEGER */ /* > Number of error bounds to return for each right hand side */ /* > and each type (normwise or componentwise). See ERR_BNDS_NORM and */ /* > ERR_BNDS_COMP below. */ /* > \endverbatim */ /* > */ /* > \param[out] ERR_BNDS_NORM */ /* > \verbatim */ /* > ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ /* > For each right-hand side, this array contains information about */ /* > various error bounds and condition numbers corresponding to the */ /* > normwise relative error, which is defined as follows: */ /* > */ /* > Normwise relative error in the ith solution vector: */ /* > max_j (abs(XTRUE(j,i) - X(j,i))) */ /* > ------------------------------ */ /* > max_j abs(X(j,i)) */ /* > */ /* > The array is indexed by the type of error information as described */ /* > below. There currently are up to three pieces of information */ /* > returned. */ /* > */ /* > The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ /* > right-hand side. */ /* > */ /* > The second index in ERR_BNDS_NORM(:,err) contains the following */ /* > three fields: */ /* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* > reciprocal condition number is less than the threshold */ /* > sqrt(n) * dlamch('Epsilon'). */ /* > */ /* > err = 2 "Guaranteed" error bound: The estimated forward error, */ /* > almost certainly within a factor of 10 of the true error */ /* > so long as the next entry is greater than the threshold */ /* > sqrt(n) * dlamch('Epsilon'). This error bound should only */ /* > be trusted if the previous boolean is true. */ /* > */ /* > err = 3 Reciprocal condition number: Estimated normwise */ /* > reciprocal condition number. Compared with the threshold */ /* > sqrt(n) * dlamch('Epsilon') to determine if the error */ /* > estimate is "guaranteed". These reciprocal condition */ /* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* > appropriately scaled matrix Z. */ /* > Let Z = S*A, where S scales each row by a power of the */ /* > radix so all absolute row sums of Z are approximately 1. */ /* > */ /* > See Lapack Working Note 165 for further details and extra */ /* > cautions. */ /* > \endverbatim */ /* > */ /* > \param[out] ERR_BNDS_COMP */ /* > \verbatim */ /* > ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ /* > For each right-hand side, this array contains information about */ /* > various error bounds and condition numbers corresponding to the */ /* > componentwise relative error, which is defined as follows: */ /* > */ /* > Componentwise relative error in the ith solution vector: */ /* > abs(XTRUE(j,i) - X(j,i)) */ /* > max_j ---------------------- */ /* > abs(X(j,i)) */ /* > */ /* > The array is indexed by the right-hand side i (on which the */ /* > componentwise relative error depends), and the type of error */ /* > information as described below. There currently are up to three */ /* > pieces of information returned for each right-hand side. If */ /* > componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ /* > ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most */ /* > the first (:,N_ERR_BNDS) entries are returned. */ /* > */ /* > The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ /* > right-hand side. */ /* > */ /* > The second index in ERR_BNDS_COMP(:,err) contains the following */ /* > three fields: */ /* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* > reciprocal condition number is less than the threshold */ /* > sqrt(n) * dlamch('Epsilon'). */ /* > */ /* > err = 2 "Guaranteed" error bound: The estimated forward error, */ /* > almost certainly within a factor of 10 of the true error */ /* > so long as the next entry is greater than the threshold */ /* > sqrt(n) * dlamch('Epsilon'). This error bound should only */ /* > be trusted if the previous boolean is true. */ /* > */ /* > err = 3 Reciprocal condition number: Estimated componentwise */ /* > reciprocal condition number. Compared with the threshold */ /* > sqrt(n) * dlamch('Epsilon') to determine if the error */ /* > estimate is "guaranteed". These reciprocal condition */ /* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* > appropriately scaled matrix Z. */ /* > Let Z = S*(A*diag(x)), where x is the solution for the */ /* > current right-hand side and S scales each row of */ /* > A*diag(x) by a power of the radix so all absolute row */ /* > sums of Z are approximately 1. */ /* > */ /* > See Lapack Working Note 165 for further details and extra */ /* > cautions. */ /* > \endverbatim */ /* > */ /* > \param[in] NPARAMS */ /* > \verbatim */ /* > NPARAMS is INTEGER */ /* > Specifies the number of parameters set in PARAMS. If <= 0, the */ /* > PARAMS array is never referenced and default values are used. */ /* > \endverbatim */ /* > */ /* > \param[in,out] PARAMS */ /* > \verbatim */ /* > PARAMS is DOUBLE PRECISION array, dimension (NPARAMS) */ /* > Specifies algorithm parameters. If an entry is < 0.0, then */ /* > that entry will be filled with default value used for that */ /* > parameter. Only positions up to NPARAMS are accessed; defaults */ /* > are used for higher-numbered parameters. */ /* > */ /* > PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ /* > refinement or not. */ /* > Default: 1.0D+0 */ /* > = 0.0: No refinement is performed, and no error bounds are */ /* > computed. */ /* > = 1.0: Use the double-precision refinement algorithm, */ /* > possibly with doubled-single computations if the */ /* > compilation environment does not support DOUBLE */ /* > PRECISION. */ /* > (other values are reserved for future use) */ /* > */ /* > PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ /* > computations allowed for refinement. */ /* > Default: 10 */ /* > Aggressive: Set to 100 to permit convergence using approximate */ /* > factorizations or factorizations other than LU. If */ /* > the factorization uses a technique other than */ /* > Gaussian elimination, the guarantees in */ /* > err_bnds_norm and err_bnds_comp may no longer be */ /* > trustworthy. */ /* > */ /* > PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ /* > will attempt to find a solution with small componentwise */ /* > relative error in the double-precision algorithm. Positive */ /* > is true, 0.0 is false. */ /* > Default: 1.0 (attempt componentwise convergence) */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is DOUBLE PRECISION array, dimension (4*N) */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: Successful exit. The solution to every right-hand side is */ /* > guaranteed. */ /* > < 0: If INFO = -i, the i-th argument had an illegal value */ /* > > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ /* > has been completed, but the factor U is exactly singular, so */ /* > the solution and error bounds could not be computed. RCOND = 0 */ /* > is returned. */ /* > = N+J: The solution corresponding to the Jth right-hand side is */ /* > not guaranteed. The solutions corresponding to other right- */ /* > hand sides K with K > J may not be guaranteed as well, but */ /* > only the first such right-hand side is reported. If a small */ /* > componentwise error is not requested (PARAMS(3) = 0.0) then */ /* > the Jth right-hand side is the first with a normwise error */ /* > bound that is not guaranteed (the smallest J such */ /* > that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ /* > the Jth right-hand side is the first with either a normwise or */ /* > componentwise error bound that is not guaranteed (the smallest */ /* > J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ /* > ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ /* > ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ /* > about all of the right-hand sides check ERR_BNDS_NORM or */ /* > ERR_BNDS_COMP. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date April 2012 */ /* > \ingroup doubleGBcomputational */ /* ===================================================================== */ /* Subroutine */ int dgbrfsx_(char *trans, char *equed, integer *n, integer * kl, integer *ku, integer *nrhs, doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb, integer *ipiv, doublereal *r__, doublereal *c__, doublereal *b, integer *ldb, doublereal *x, integer * ldx, doublereal *rcond, doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer * nparams, doublereal *params, doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1; doublereal d__1, d__2; /* Local variables */ doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__; char norm[1]; integer ref_type__; extern integer ilatrans_(char *); logical ignore_cwise__; integer j; extern logical lsame_(char *, char *); doublereal anorm, rcond_tmp__; integer prec_type__; extern doublereal dlamch_(char *), dlangb_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ int dgbcon_(char *, integer *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), xerbla_(char *, integer *, ftnlen); logical colequ, notran, rowequ; integer trans_type__; extern doublereal dla_gbrcond_(char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *); extern integer ilaprec_(char *); integer ithresh, n_norms__; doublereal rthresh, cwise_wrong__; extern /* Subroutine */ int dla_gbrfsx_extended_(integer *, integer *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, logical *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *, doublereal * , doublereal *, logical *, integer *); /* -- LAPACK computational routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* April 2012 */ /* ================================================================== */ /* Check the input parameters. */ /* Parameter adjustments */ err_bnds_comp_dim1 = *nrhs; err_bnds_comp_offset = 1 + err_bnds_comp_dim1 * 1; err_bnds_comp__ -= err_bnds_comp_offset; err_bnds_norm_dim1 = *nrhs; err_bnds_norm_offset = 1 + err_bnds_norm_dim1 * 1; err_bnds_norm__ -= err_bnds_norm_offset; ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; afb_dim1 = *ldafb; afb_offset = 1 + afb_dim1 * 1; afb -= afb_offset; --ipiv; --r__; --c__; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1 * 1; x -= x_offset; --berr; --params; --work; --iwork; /* Function Body */ *info = 0; trans_type__ = ilatrans_(trans); ref_type__ = 1; if (*nparams >= 1) { if (params[1] < 0.) { params[1] = 1.; } else { ref_type__ = (integer) params[1]; } } /* Set default parameters. */ illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon"); ithresh = 10; rthresh = .5; unstable_thresh__ = .25; ignore_cwise__ = FALSE_; if (*nparams >= 2) { if (params[2] < 0.) { params[2] = (doublereal) ithresh; } else { ithresh = (integer) params[2]; } } if (*nparams >= 3) { if (params[3] < 0.) { if (ignore_cwise__) { params[3] = 0.; } else { params[3] = 1.; } } else { ignore_cwise__ = params[3] == 0.; } } if (ref_type__ == 0 || *n_err_bnds__ == 0) { n_norms__ = 0; } else if (ignore_cwise__) { n_norms__ = 1; } else { n_norms__ = 2; } notran = lsame_(trans, "N"); rowequ = lsame_(equed, "R") || lsame_(equed, "B"); colequ = lsame_(equed, "C") || lsame_(equed, "B"); /* Test input parameters. */ if (trans_type__ == -1) { *info = -1; } else if (! rowequ && ! colequ && ! lsame_(equed, "N")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*kl < 0) { *info = -4; } else if (*ku < 0) { *info = -5; } else if (*nrhs < 0) { *info = -6; } else if (*ldab < *kl + *ku + 1) { *info = -8; } else if (*ldafb < (*kl << 1) + *ku + 1) { *info = -10; } else if (*ldb < f2cmax(1,*n)) { *info = -13; } else if (*ldx < f2cmax(1,*n)) { *info = -15; } if (*info != 0) { i__1 = -(*info); xerbla_("DGBRFSX", &i__1, (ftnlen)7); return 0; } /* Quick return if possible. */ if (*n == 0 || *nrhs == 0) { *rcond = 1.; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { berr[j] = 0.; if (*n_err_bnds__ >= 1) { err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } if (*n_err_bnds__ >= 2) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.; err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.; } if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.; } } return 0; } /* Default to failure. */ *rcond = 0.; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { berr[j] = 1.; if (*n_err_bnds__ >= 1) { err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } if (*n_err_bnds__ >= 2) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; } if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.; err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.; } } /* Compute the norm of A and the reciprocal of the condition */ /* number of A. */ if (notran) { *(unsigned char *)norm = 'I'; } else { *(unsigned char *)norm = '1'; } anorm = dlangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &work[1]); dgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], &anorm, rcond, &work[1], &iwork[1], info); /* Perform refinement on each right-hand side */ if (ref_type__ != 0 && *info == 0) { prec_type__ = ilaprec_("E"); if (notran) { dla_gbrfsx_extended_(&prec_type__, &trans_type__, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, & ipiv[1], &colequ, &c__[1], &b[b_offset], ldb, &x[x_offset] , ldx, &berr[1], &n_norms__, &err_bnds_norm__[ err_bnds_norm_offset], &err_bnds_comp__[ err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n << 1) + 1], &work[1], rcond, &ithresh, &rthresh, & unstable_thresh__, &ignore_cwise__, info); } else { dla_gbrfsx_extended_(&prec_type__, &trans_type__, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, & ipiv[1], &rowequ, &r__[1], &b[b_offset], ldb, &x[x_offset] , ldx, &berr[1], &n_norms__, &err_bnds_norm__[ err_bnds_norm_offset], &err_bnds_comp__[ err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n << 1) + 1], &work[1], rcond, &ithresh, &rthresh, & unstable_thresh__, &ignore_cwise__, info); } } /* Computing MAX */ d__1 = 10., d__2 = sqrt((doublereal) (*n)); err_lbnd__ = f2cmax(d__1,d__2) * dlamch_("Epsilon"); if (*n_err_bnds__ >= 1 && n_norms__ >= 1) { /* Compute scaled normwise condition number cond(A*C). */ if (colequ && notran) { rcond_tmp__ = dla_gbrcond_(trans, n, kl, ku, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &ipiv[1], &c_n1, &c__[1], info, &work[1], &iwork[1]); } else if (rowequ && ! notran) { rcond_tmp__ = dla_gbrcond_(trans, n, kl, ku, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &ipiv[1], &c_n1, &r__[1], info, &work[1], &iwork[1]); } else { rcond_tmp__ = dla_gbrcond_(trans, n, kl, ku, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__0, &r__[1], info, &work[1], &iwork[1]); } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { /* Cap the error at 1.0. */ if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] > 1.) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; } /* Threshold the error (see LAWN). */ if (rcond_tmp__ < illrcond_thresh__) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.; err_bnds_norm__[j + err_bnds_norm_dim1] = 0.; if (*info <= *n) { *info = *n + j; } } else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] < err_lbnd__) { err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__; err_bnds_norm__[j + err_bnds_norm_dim1] = 1.; } /* Save the condition number. */ if (*n_err_bnds__ >= 3) { err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__; } } } if (*n_err_bnds__ >= 1 && n_norms__ >= 2) { /* Compute componentwise condition number cond(A*diag(Y(:,J))) for */ /* each right-hand side using the current solution as an estimate of */ /* the true solution. If the componentwise error estimate is too */ /* large, then the solution is a lousy estimate of truth and the */ /* estimated RCOND may be too optimistic. To avoid misleading users, */ /* the inverse condition number is set to 0.0 when the estimated */ /* cwise error is at least CWISE_WRONG. */ cwise_wrong__ = sqrt(dlamch_("Epsilon")); i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < cwise_wrong__) { rcond_tmp__ = dla_gbrcond_(trans, n, kl, ku, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__1, &x[j * x_dim1 + 1], info, &work[1], &iwork[1]); } else { rcond_tmp__ = 0.; } /* Cap the error at 1.0. */ if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] > 1.) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; } /* Threshold the error (see LAWN). */ if (rcond_tmp__ < illrcond_thresh__) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.; err_bnds_comp__[j + err_bnds_comp_dim1] = 0.; if (params[3] == 1. && *info < *n + j) { *info = *n + j; } } else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] < err_lbnd__) { err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__; err_bnds_comp__[j + err_bnds_comp_dim1] = 1.; } /* Save the condition number. */ if (*n_err_bnds__ >= 3) { err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__; } } } return 0; /* End of DGBRFSX */ } /* dgbrfsx_ */