#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; #ifdef _MSC_VER static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;} static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;} static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;} static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;} #else 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;} #endif #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)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #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) = conjf(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) (cimagf(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; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else 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; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else 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; } #endif 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; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief SGTSVX computes the solution to system of linear equations A * X = B for GT matrices */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGTSVX + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, */ /* DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, */ /* WORK, IWORK, INFO ) */ /* CHARACTER FACT, TRANS */ /* INTEGER INFO, LDB, LDX, N, NRHS */ /* REAL RCOND */ /* INTEGER IPIV( * ), IWORK( * ) */ /* REAL B( LDB, * ), BERR( * ), D( * ), DF( * ), */ /* $ DL( * ), DLF( * ), DU( * ), DU2( * ), DUF( * ), */ /* $ FERR( * ), WORK( * ), X( LDX, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGTSVX uses the LU factorization to compute the solution to a real */ /* > system of linear equations A * X = B or A**T * X = B, */ /* > where A is a tridiagonal matrix of order N and X and B are N-by-NRHS */ /* > matrices. */ /* > */ /* > Error bounds on the solution and a condition estimate are also */ /* > provided. */ /* > \endverbatim */ /* > \par Description: */ /* ================= */ /* > */ /* > \verbatim */ /* > */ /* > The following steps are performed: */ /* > */ /* > 1. If FACT = 'N', the LU decomposition is used to factor the matrix A */ /* > as A = L * U, where L is a product of permutation and unit lower */ /* > bidiagonal matrices and U is upper triangular with nonzeros in */ /* > only the main diagonal and first two superdiagonals. */ /* > */ /* > 2. If some U(i,i)=0, so that U is exactly singular, then the routine */ /* > returns with INFO = i. Otherwise, the factored form of A is used */ /* > to estimate the condition number of the matrix A. If the */ /* > reciprocal of the condition number is less than machine precision, */ /* > INFO = N+1 is returned as a warning, but the routine still goes on */ /* > to solve for X and compute error bounds as described below. */ /* > */ /* > 3. The system of equations is solved for X using the factored form */ /* > of A. */ /* > */ /* > 4. Iterative refinement is applied to improve the computed solution */ /* > matrix and calculate error bounds and backward error estimates */ /* > for it. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] FACT */ /* > \verbatim */ /* > FACT is CHARACTER*1 */ /* > Specifies whether or not the factored form of A has been */ /* > supplied on entry. */ /* > = 'F': DLF, DF, DUF, DU2, and IPIV contain the factored */ /* > form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV */ /* > will not be modified. */ /* > = 'N': The matrix will be copied to DLF, DF, and DUF */ /* > and factored. */ /* > \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] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. N >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] NRHS */ /* > \verbatim */ /* > NRHS is INTEGER */ /* > The number of right hand sides, i.e., the number of columns */ /* > of the matrix B. NRHS >= 0. */ /* > \endverbatim */ /* > */ /* > \param[in] DL */ /* > \verbatim */ /* > DL is REAL array, dimension (N-1) */ /* > The (n-1) subdiagonal elements of A. */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is REAL array, dimension (N) */ /* > The n diagonal elements of A. */ /* > \endverbatim */ /* > */ /* > \param[in] DU */ /* > \verbatim */ /* > DU is REAL array, dimension (N-1) */ /* > The (n-1) superdiagonal elements of A. */ /* > \endverbatim */ /* > */ /* > \param[in,out] DLF */ /* > \verbatim */ /* > DLF is REAL array, dimension (N-1) */ /* > If FACT = 'F', then DLF is an input argument and on entry */ /* > contains the (n-1) multipliers that define the matrix L from */ /* > the LU factorization of A as computed by SGTTRF. */ /* > */ /* > If FACT = 'N', then DLF is an output argument and on exit */ /* > contains the (n-1) multipliers that define the matrix L from */ /* > the LU factorization of A. */ /* > \endverbatim */ /* > */ /* > \param[in,out] DF */ /* > \verbatim */ /* > DF is REAL array, dimension (N) */ /* > If FACT = 'F', then DF is an input argument and on entry */ /* > contains the n diagonal elements of the upper triangular */ /* > matrix U from the LU factorization of A. */ /* > */ /* > If FACT = 'N', then DF is an output argument and on exit */ /* > contains the n diagonal elements of the upper triangular */ /* > matrix U from the LU factorization of A. */ /* > \endverbatim */ /* > */ /* > \param[in,out] DUF */ /* > \verbatim */ /* > DUF is REAL array, dimension (N-1) */ /* > If FACT = 'F', then DUF is an input argument and on entry */ /* > contains the (n-1) elements of the first superdiagonal of U. */ /* > */ /* > If FACT = 'N', then DUF is an output argument and on exit */ /* > contains the (n-1) elements of the first superdiagonal of U. */ /* > \endverbatim */ /* > */ /* > \param[in,out] DU2 */ /* > \verbatim */ /* > DU2 is REAL array, dimension (N-2) */ /* > If FACT = 'F', then DU2 is an input argument and on entry */ /* > contains the (n-2) elements of the second superdiagonal of */ /* > U. */ /* > */ /* > If FACT = 'N', then DU2 is an output argument and on exit */ /* > contains the (n-2) elements of the second superdiagonal of */ /* > U. */ /* > \endverbatim */ /* > */ /* > \param[in,out] IPIV */ /* > \verbatim */ /* > IPIV is INTEGER array, dimension (N) */ /* > If FACT = 'F', then IPIV is an input argument and on entry */ /* > contains the pivot indices from the LU factorization of A as */ /* > computed by SGTTRF. */ /* > */ /* > If FACT = 'N', then IPIV is an output argument and on exit */ /* > contains the pivot indices from the LU factorization of A; */ /* > row i of the matrix was interchanged with row IPIV(i). */ /* > IPIV(i) will always be either i or i+1; IPIV(i) = i indicates */ /* > a row interchange was not required. */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is REAL array, dimension (LDB,NRHS) */ /* > The N-by-NRHS 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[out] X */ /* > \verbatim */ /* > X is REAL array, dimension (LDX,NRHS) */ /* > If INFO = 0 or INFO = N+1, the N-by-NRHS 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 REAL */ /* > The estimate of the reciprocal condition number of the matrix */ /* > A. If RCOND is less than the machine precision (in */ /* > particular, if RCOND = 0), the matrix is singular to working */ /* > precision. This condition is indicated by a return code of */ /* > INFO > 0. */ /* > \endverbatim */ /* > */ /* > \param[out] FERR */ /* > \verbatim */ /* > FERR is REAL array, dimension (NRHS) */ /* > The estimated forward error bound for each solution vector */ /* > X(j) (the j-th column of the solution matrix X). */ /* > If XTRUE is the true solution corresponding to X(j), FERR(j) */ /* > is an estimated upper bound for the magnitude of the largest */ /* > element in (X(j) - XTRUE) divided by the magnitude of the */ /* > largest element in X(j). The estimate is as reliable as */ /* > the estimate for RCOND, and is almost always a slight */ /* > overestimate of the true error. */ /* > \endverbatim */ /* > */ /* > \param[out] BERR */ /* > \verbatim */ /* > BERR is REAL array, dimension (NRHS) */ /* > 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[out] WORK */ /* > \verbatim */ /* > WORK is REAL array, dimension (3*N) */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (N) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > = 0: successful exit */ /* > < 0: if INFO = -i, the i-th argument had an illegal value */ /* > > 0: if INFO = i, and i is */ /* > <= N: U(i,i) is exactly zero. The factorization */ /* > has not been completed unless i = N, but the */ /* > factor U is exactly singular, so the solution */ /* > and error bounds could not be computed. */ /* > RCOND = 0 is returned. */ /* > = N+1: U is nonsingular, but RCOND is less than machine */ /* > precision, meaning that the matrix is singular */ /* > to working precision. Nevertheless, the */ /* > solution and error bounds are computed because */ /* > there are a number of situations where the */ /* > computed solution can be more accurate than the */ /* > value of RCOND would suggest. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup realGTsolve */ /* ===================================================================== */ /* Subroutine */ int sgtsvx_(char *fact, char *trans, integer *n, integer * nrhs, real *dl, real *d__, real *du, real *dlf, real *df, real *duf, real *du2, integer *ipiv, real *b, integer *ldb, real *x, integer * ldx, real *rcond, real *ferr, real *berr, real *work, integer *iwork, integer *info) { /* System generated locals */ integer b_dim1, b_offset, x_dim1, x_offset, i__1; /* Local variables */ char norm[1]; extern logical lsame_(char *, char *); real anorm; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *); extern real slamch_(char *); logical nofact; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); extern real slangt_(char *, integer *, real *, real *, real *); extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), sgtcon_(char *, integer *, real *, real *, real *, real *, integer *, real *, real *, real *, integer *, integer *); logical notran; extern /* Subroutine */ int sgtrfs_(char *, integer *, integer *, real *, real *, real *, real *, real *, real *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *, integer *, integer *), sgttrf_(integer *, real *, real *, real *, real *, integer *, integer *), sgttrs_(char *, integer *, integer *, real *, real *, real *, real *, integer *, real *, integer *, integer *); /* -- LAPACK driver 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..-- */ /* December 2016 */ /* ===================================================================== */ /* Parameter adjustments */ --dl; --d__; --du; --dlf; --df; --duf; --du2; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1 * 1; x -= x_offset; --ferr; --berr; --work; --iwork; /* Function Body */ *info = 0; nofact = lsame_(fact, "N"); notran = lsame_(trans, "N"); if (! nofact && ! lsame_(fact, "F")) { *info = -1; } else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*ldb < f2cmax(1,*n)) { *info = -14; } else if (*ldx < f2cmax(1,*n)) { *info = -16; } if (*info != 0) { i__1 = -(*info); xerbla_("SGTSVX", &i__1, (ftnlen)6); return 0; } if (nofact) { /* Compute the LU factorization of A. */ scopy_(n, &d__[1], &c__1, &df[1], &c__1); if (*n > 1) { i__1 = *n - 1; scopy_(&i__1, &dl[1], &c__1, &dlf[1], &c__1); i__1 = *n - 1; scopy_(&i__1, &du[1], &c__1, &duf[1], &c__1); } sgttrf_(n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], info); /* Return if INFO is non-zero. */ if (*info > 0) { *rcond = 0.f; return 0; } } /* Compute the norm of the matrix A. */ if (notran) { *(unsigned char *)norm = '1'; } else { *(unsigned char *)norm = 'I'; } anorm = slangt_(norm, n, &dl[1], &d__[1], &du[1]); /* Compute the reciprocal of the condition number of A. */ sgtcon_(norm, n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &anorm, rcond, &work[1], &iwork[1], info); /* Compute the solution vectors X. */ slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); sgttrs_(trans, n, nrhs, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &x[ x_offset], ldx, info); /* Use iterative refinement to improve the computed solutions and */ /* compute error bounds and backward error estimates for them. */ sgtrfs_(trans, n, nrhs, &dl[1], &d__[1], &du[1], &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1] , &berr[1], &work[1], &iwork[1], info); /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < slamch_("Epsilon")) { *info = *n + 1; } return 0; /* End of SGTSVX */ } /* sgtsvx_ */