#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 \b SGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download SGTTS2 + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE SGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) */ /* INTEGER ITRANS, LDB, N, NRHS */ /* INTEGER IPIV( * ) */ /* REAL B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > SGTTS2 solves one of the systems of equations */ /* > A*X = B or A**T*X = B, */ /* > with a tridiagonal matrix A using the LU factorization computed */ /* > by SGTTRF. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] ITRANS */ /* > \verbatim */ /* > ITRANS is INTEGER */ /* > Specifies the form of the system of equations. */ /* > = 0: A * X = B (No transpose) */ /* > = 1: A**T* X = B (Transpose) */ /* > = 2: A**T* X = B (Conjugate transpose = Transpose) */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrix A. */ /* > \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) multipliers that define the matrix L from the */ /* > LU factorization of A. */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is REAL array, dimension (N) */ /* > The n diagonal elements of the upper triangular matrix U from */ /* > the LU factorization of A. */ /* > \endverbatim */ /* > */ /* > \param[in] DU */ /* > \verbatim */ /* > DU is REAL array, dimension (N-1) */ /* > The (n-1) elements of the first super-diagonal of U. */ /* > \endverbatim */ /* > */ /* > \param[in] DU2 */ /* > \verbatim */ /* > DU2 is REAL array, dimension (N-2) */ /* > The (n-2) elements of the second super-diagonal of U. */ /* > \endverbatim */ /* > */ /* > \param[in] IPIV */ /* > \verbatim */ /* > IPIV is INTEGER array, dimension (N) */ /* > The pivot indices; for 1 <= i <= n, 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,out] B */ /* > \verbatim */ /* > B is REAL array, dimension (LDB,NRHS) */ /* > On entry, the matrix of right hand side vectors B. */ /* > On exit, B is overwritten by the solution vectors X. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1,N). */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup realGTcomputational */ /* ===================================================================== */ /* Subroutine */ int sgtts2_(integer *itrans, integer *n, integer *nrhs, real *dl, real *d__, real *du, real *du2, integer *ipiv, real *b, integer * ldb) { /* System generated locals */ integer b_dim1, b_offset, i__1, i__2; /* Local variables */ real temp; integer i__, j, ip; /* -- 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..-- */ /* December 2016 */ /* ===================================================================== */ /* Quick return if possible */ /* Parameter adjustments */ --dl; --d__; --du; --du2; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; /* Function Body */ if (*n == 0 || *nrhs == 0) { return 0; } if (*itrans == 0) { /* Solve A*X = B using the LU factorization of A, */ /* overwriting each right hand side vector with its solution. */ if (*nrhs <= 1) { j = 1; L10: /* Solve L*x = b. */ i__1 = *n - 1; for (i__ = 1; i__ <= i__1; ++i__) { ip = ipiv[i__]; temp = b[i__ + 1 - ip + i__ + j * b_dim1] - dl[i__] * b[ip + j * b_dim1]; b[i__ + j * b_dim1] = b[ip + j * b_dim1]; b[i__ + 1 + j * b_dim1] = temp; /* L20: */ } /* Solve U*x = b. */ b[*n + j * b_dim1] /= d__[*n]; if (*n > 1) { b[*n - 1 + j * b_dim1] = (b[*n - 1 + j * b_dim1] - du[*n - 1] * b[*n + j * b_dim1]) / d__[*n - 1]; } for (i__ = *n - 2; i__ >= 1; --i__) { b[i__ + j * b_dim1] = (b[i__ + j * b_dim1] - du[i__] * b[i__ + 1 + j * b_dim1] - du2[i__] * b[i__ + 2 + j * b_dim1] ) / d__[i__]; /* L30: */ } if (j < *nrhs) { ++j; goto L10; } } else { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { /* Solve L*x = b. */ i__2 = *n - 1; for (i__ = 1; i__ <= i__2; ++i__) { if (ipiv[i__] == i__) { b[i__ + 1 + j * b_dim1] -= dl[i__] * b[i__ + j * b_dim1]; } else { temp = b[i__ + j * b_dim1]; b[i__ + j * b_dim1] = b[i__ + 1 + j * b_dim1]; b[i__ + 1 + j * b_dim1] = temp - dl[i__] * b[i__ + j * b_dim1]; } /* L40: */ } /* Solve U*x = b. */ b[*n + j * b_dim1] /= d__[*n]; if (*n > 1) { b[*n - 1 + j * b_dim1] = (b[*n - 1 + j * b_dim1] - du[*n - 1] * b[*n + j * b_dim1]) / d__[*n - 1]; } for (i__ = *n - 2; i__ >= 1; --i__) { b[i__ + j * b_dim1] = (b[i__ + j * b_dim1] - du[i__] * b[ i__ + 1 + j * b_dim1] - du2[i__] * b[i__ + 2 + j * b_dim1]) / d__[i__]; /* L50: */ } /* L60: */ } } } else { /* Solve A**T * X = B. */ if (*nrhs <= 1) { /* Solve U**T*x = b. */ j = 1; L70: b[j * b_dim1 + 1] /= d__[1]; if (*n > 1) { b[j * b_dim1 + 2] = (b[j * b_dim1 + 2] - du[1] * b[j * b_dim1 + 1]) / d__[2]; } i__1 = *n; for (i__ = 3; i__ <= i__1; ++i__) { b[i__ + j * b_dim1] = (b[i__ + j * b_dim1] - du[i__ - 1] * b[ i__ - 1 + j * b_dim1] - du2[i__ - 2] * b[i__ - 2 + j * b_dim1]) / d__[i__]; /* L80: */ } /* Solve L**T*x = b. */ for (i__ = *n - 1; i__ >= 1; --i__) { ip = ipiv[i__]; temp = b[i__ + j * b_dim1] - dl[i__] * b[i__ + 1 + j * b_dim1] ; b[i__ + j * b_dim1] = b[ip + j * b_dim1]; b[ip + j * b_dim1] = temp; /* L90: */ } if (j < *nrhs) { ++j; goto L70; } } else { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { /* Solve U**T*x = b. */ b[j * b_dim1 + 1] /= d__[1]; if (*n > 1) { b[j * b_dim1 + 2] = (b[j * b_dim1 + 2] - du[1] * b[j * b_dim1 + 1]) / d__[2]; } i__2 = *n; for (i__ = 3; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = (b[i__ + j * b_dim1] - du[i__ - 1] * b[i__ - 1 + j * b_dim1] - du2[i__ - 2] * b[i__ - 2 + j * b_dim1]) / d__[i__]; /* L100: */ } for (i__ = *n - 1; i__ >= 1; --i__) { if (ipiv[i__] == i__) { b[i__ + j * b_dim1] -= dl[i__] * b[i__ + 1 + j * b_dim1]; } else { temp = b[i__ + 1 + j * b_dim1]; b[i__ + 1 + j * b_dim1] = b[i__ + j * b_dim1] - dl[ i__] * temp; b[i__ + j * b_dim1] = temp; } /* L110: */ } /* L120: */ } } } /* End of SGTTS2 */ return 0; } /* sgtts2_ */