618 lines
16 KiB
C
618 lines
16 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#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]);}
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#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]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#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++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#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]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* -- translated by f2c (version 20000121).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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/* > \brief <b> SGTSV computes the solution to system of linear equations A * X = B for GT matrices </b> */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download SGTSV + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgtsv.f
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"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgtsv.f
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"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgtsv.f
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"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO ) */
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/* INTEGER INFO, LDB, N, NRHS */
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/* REAL B( LDB, * ), D( * ), DL( * ), DU( * ) */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > SGTSV solves the equation */
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/* > */
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/* > A*X = B, */
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/* > */
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/* > where A is an n by n tridiagonal matrix, by Gaussian elimination with */
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/* > partial pivoting. */
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/* > */
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/* > Note that the equation A**T*X = B may be solved by interchanging the */
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/* > order of the arguments DU and DL. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The order of the matrix A. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] NRHS */
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/* > \verbatim */
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/* > NRHS is INTEGER */
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/* > The number of right hand sides, i.e., the number of columns */
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/* > of the matrix B. NRHS >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] DL */
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/* > \verbatim */
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/* > DL is REAL array, dimension (N-1) */
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/* > On entry, DL must contain the (n-1) sub-diagonal elements of */
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/* > A. */
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/* > */
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/* > On exit, DL is overwritten by the (n-2) elements of the */
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/* > second super-diagonal of the upper triangular matrix U from */
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/* > the LU factorization of A, in DL(1), ..., DL(n-2). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] D */
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/* > \verbatim */
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/* > D is REAL array, dimension (N) */
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/* > On entry, D must contain the diagonal elements of A. */
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/* > */
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/* > On exit, D is overwritten by the n diagonal elements of U. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] DU */
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/* > \verbatim */
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/* > DU is REAL array, dimension (N-1) */
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/* > On entry, DU must contain the (n-1) super-diagonal elements */
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/* > of A. */
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/* > */
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/* > On exit, DU is overwritten by the (n-1) elements of the first */
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/* > super-diagonal of U. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] B */
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/* > \verbatim */
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/* > B is REAL array, dimension (LDB,NRHS) */
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/* > On entry, the N by NRHS matrix of right hand side matrix B. */
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/* > On exit, if INFO = 0, the N by NRHS solution matrix X. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDB */
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/* > \verbatim */
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/* > LDB is INTEGER */
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/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value */
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/* > > 0: if INFO = i, U(i,i) is exactly zero, and the solution */
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/* > has not been computed. The factorization has not been */
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/* > completed unless i = N. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date December 2016 */
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/* > \ingroup realGTsolve */
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/* ===================================================================== */
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/* Subroutine */ void sgtsv_(integer *n, integer *nrhs, real *dl, real *d__,
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real *du, real *b, integer *ldb, integer *info)
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{
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/* System generated locals */
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integer b_dim1, b_offset, i__1, i__2;
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real r__1, r__2;
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/* Local variables */
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real fact, temp;
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integer i__, j;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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/* -- LAPACK driver routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* December 2016 */
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/* ===================================================================== */
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/* Parameter adjustments */
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--dl;
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--d__;
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--du;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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b -= b_offset;
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/* Function Body */
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*info = 0;
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if (*n < 0) {
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*info = -1;
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} else if (*nrhs < 0) {
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*info = -2;
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} else if (*ldb < f2cmax(1,*n)) {
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*info = -7;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SGTSV ", &i__1, (ftnlen)5);
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return;
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}
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if (*n == 0) {
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return;
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}
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if (*nrhs == 1) {
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i__1 = *n - 2;
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for (i__ = 1; i__ <= i__1; ++i__) {
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if ((r__1 = d__[i__], abs(r__1)) >= (r__2 = dl[i__], abs(r__2))) {
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/* No row interchange required */
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if (d__[i__] != 0.f) {
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fact = dl[i__] / d__[i__];
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d__[i__ + 1] -= fact * du[i__];
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b[i__ + 1 + b_dim1] -= fact * b[i__ + b_dim1];
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} else {
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*info = i__;
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return;
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}
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dl[i__] = 0.f;
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} else {
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/* Interchange rows I and I+1 */
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fact = d__[i__] / dl[i__];
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d__[i__] = dl[i__];
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temp = d__[i__ + 1];
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d__[i__ + 1] = du[i__] - fact * temp;
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dl[i__] = du[i__ + 1];
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du[i__ + 1] = -fact * dl[i__];
|
|
du[i__] = temp;
|
|
temp = b[i__ + b_dim1];
|
|
b[i__ + b_dim1] = b[i__ + 1 + b_dim1];
|
|
b[i__ + 1 + b_dim1] = temp - fact * b[i__ + 1 + b_dim1];
|
|
}
|
|
/* L10: */
|
|
}
|
|
if (*n > 1) {
|
|
i__ = *n - 1;
|
|
if ((r__1 = d__[i__], abs(r__1)) >= (r__2 = dl[i__], abs(r__2))) {
|
|
if (d__[i__] != 0.f) {
|
|
fact = dl[i__] / d__[i__];
|
|
d__[i__ + 1] -= fact * du[i__];
|
|
b[i__ + 1 + b_dim1] -= fact * b[i__ + b_dim1];
|
|
} else {
|
|
*info = i__;
|
|
return;
|
|
}
|
|
} else {
|
|
fact = d__[i__] / dl[i__];
|
|
d__[i__] = dl[i__];
|
|
temp = d__[i__ + 1];
|
|
d__[i__ + 1] = du[i__] - fact * temp;
|
|
du[i__] = temp;
|
|
temp = b[i__ + b_dim1];
|
|
b[i__ + b_dim1] = b[i__ + 1 + b_dim1];
|
|
b[i__ + 1 + b_dim1] = temp - fact * b[i__ + 1 + b_dim1];
|
|
}
|
|
}
|
|
if (d__[*n] == 0.f) {
|
|
*info = *n;
|
|
return;
|
|
}
|
|
} else {
|
|
i__1 = *n - 2;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if ((r__1 = d__[i__], abs(r__1)) >= (r__2 = dl[i__], abs(r__2))) {
|
|
|
|
/* No row interchange required */
|
|
|
|
if (d__[i__] != 0.f) {
|
|
fact = dl[i__] / d__[i__];
|
|
d__[i__ + 1] -= fact * du[i__];
|
|
i__2 = *nrhs;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
b[i__ + 1 + j * b_dim1] -= fact * b[i__ + j * b_dim1];
|
|
/* L20: */
|
|
}
|
|
} else {
|
|
*info = i__;
|
|
return;
|
|
}
|
|
dl[i__] = 0.f;
|
|
} else {
|
|
|
|
/* Interchange rows I and I+1 */
|
|
|
|
fact = d__[i__] / dl[i__];
|
|
d__[i__] = dl[i__];
|
|
temp = d__[i__ + 1];
|
|
d__[i__ + 1] = du[i__] - fact * temp;
|
|
dl[i__] = du[i__ + 1];
|
|
du[i__ + 1] = -fact * dl[i__];
|
|
du[i__] = temp;
|
|
i__2 = *nrhs;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
temp = b[i__ + j * b_dim1];
|
|
b[i__ + j * b_dim1] = b[i__ + 1 + j * b_dim1];
|
|
b[i__ + 1 + j * b_dim1] = temp - fact * b[i__ + 1 + j *
|
|
b_dim1];
|
|
/* L30: */
|
|
}
|
|
}
|
|
/* L40: */
|
|
}
|
|
if (*n > 1) {
|
|
i__ = *n - 1;
|
|
if ((r__1 = d__[i__], abs(r__1)) >= (r__2 = dl[i__], abs(r__2))) {
|
|
if (d__[i__] != 0.f) {
|
|
fact = dl[i__] / d__[i__];
|
|
d__[i__ + 1] -= fact * du[i__];
|
|
i__1 = *nrhs;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
b[i__ + 1 + j * b_dim1] -= fact * b[i__ + j * b_dim1];
|
|
/* L50: */
|
|
}
|
|
} else {
|
|
*info = i__;
|
|
return;
|
|
}
|
|
} else {
|
|
fact = d__[i__] / dl[i__];
|
|
d__[i__] = dl[i__];
|
|
temp = d__[i__ + 1];
|
|
d__[i__ + 1] = du[i__] - fact * temp;
|
|
du[i__] = temp;
|
|
i__1 = *nrhs;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = b[i__ + j * b_dim1];
|
|
b[i__ + j * b_dim1] = b[i__ + 1 + j * b_dim1];
|
|
b[i__ + 1 + j * b_dim1] = temp - fact * b[i__ + 1 + j *
|
|
b_dim1];
|
|
/* L60: */
|
|
}
|
|
}
|
|
}
|
|
if (d__[*n] == 0.f) {
|
|
*info = *n;
|
|
return;
|
|
}
|
|
}
|
|
|
|
/* Back solve with the matrix U from the factorization. */
|
|
|
|
if (*nrhs <= 2) {
|
|
j = 1;
|
|
L70:
|
|
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] - dl[i__] * b[i__ + 2 + j * b_dim1]) / d__[
|
|
i__];
|
|
/* L80: */
|
|
}
|
|
if (j < *nrhs) {
|
|
++j;
|
|
goto L70;
|
|
}
|
|
} else {
|
|
i__1 = *nrhs;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
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] - dl[i__] * b[i__ + 2 + j * b_dim1])
|
|
/ d__[i__];
|
|
/* L90: */
|
|
}
|
|
/* L100: */
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of SGTSV */
|
|
|
|
} /* sgtsv_ */
|
|
|