955 lines
29 KiB
C
955 lines
29 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 int logical;
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typedef short int shortlogical;
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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 pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(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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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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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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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(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<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief <b> CGTSVX computes the solution to system of linear equations A * X = B for GT matrices </b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CGTSVX + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgtsvx.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgtsvx.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgtsvx.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, */
|
|
/* DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, */
|
|
/* WORK, RWORK, INFO ) */
|
|
|
|
/* CHARACTER FACT, TRANS */
|
|
/* INTEGER INFO, LDB, LDX, N, NRHS */
|
|
/* REAL RCOND */
|
|
/* INTEGER IPIV( * ) */
|
|
/* REAL BERR( * ), FERR( * ), RWORK( * ) */
|
|
/* COMPLEX B( LDB, * ), D( * ), DF( * ), DL( * ), */
|
|
/* $ DLF( * ), DU( * ), DU2( * ), DUF( * ), */
|
|
/* $ WORK( * ), X( LDX, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CGTSVX uses the LU factorization to compute the solution to a complex */
|
|
/* > system of linear equations A * X = B, A**T * X = B, or A**H * 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) */
|
|
/* > \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 COMPLEX array, dimension (N-1) */
|
|
/* > The (n-1) subdiagonal elements of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D */
|
|
/* > \verbatim */
|
|
/* > D is COMPLEX array, dimension (N) */
|
|
/* > The n diagonal elements of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] DU */
|
|
/* > \verbatim */
|
|
/* > DU is COMPLEX array, dimension (N-1) */
|
|
/* > The (n-1) superdiagonal elements of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] DLF */
|
|
/* > \verbatim */
|
|
/* > DLF is COMPLEX 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 CGTTRF. */
|
|
/* > */
|
|
/* > 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 CGTTRF. */
|
|
/* > */
|
|
/* > 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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is REAL 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 complexGTsolve */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cgtsvx_(char *fact, char *trans, integer *n, integer *
|
|
nrhs, complex *dl, complex *d__, complex *du, complex *dlf, complex *
|
|
df, complex *duf, complex *du2, integer *ipiv, complex *b, integer *
|
|
ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr,
|
|
complex *work, real *rwork, 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 */ void ccopy_(integer *, complex *, integer *,
|
|
complex *, integer *);
|
|
extern real slamch_(char *), clangt_(char *, integer *, complex *,
|
|
complex *, complex *);
|
|
logical nofact;
|
|
extern /* Subroutine */ void clacpy_(char *, integer *, integer *, complex
|
|
*, integer *, complex *, integer *), cgtcon_(char *,
|
|
integer *, complex *, complex *, complex *, complex *, integer *,
|
|
real *, real *, complex *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
extern void cgtrfs_(char *, integer *, integer *, complex
|
|
*, complex *, complex *, complex *, complex *, complex *, complex
|
|
*, integer *, complex *, integer *, complex *, integer *, real *,
|
|
real *, complex *, real *, integer *), cgttrf_(integer *,
|
|
complex *, complex *, complex *, complex *, integer *, integer *);
|
|
logical notran;
|
|
extern /* Subroutine */ void cgttrs_(char *, integer *, integer *, complex
|
|
*, complex *, complex *, complex *, integer *, complex *, 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;
|
|
--rwork;
|
|
|
|
/* 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_("CGTSVX", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
if (nofact) {
|
|
|
|
/* Compute the LU factorization of A. */
|
|
|
|
ccopy_(n, &d__[1], &c__1, &df[1], &c__1);
|
|
if (*n > 1) {
|
|
i__1 = *n - 1;
|
|
ccopy_(&i__1, &dl[1], &c__1, &dlf[1], &c__1);
|
|
i__1 = *n - 1;
|
|
ccopy_(&i__1, &du[1], &c__1, &duf[1], &c__1);
|
|
}
|
|
cgttrf_(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;
|
|
}
|
|
}
|
|
|
|
/* Compute the norm of the matrix A. */
|
|
|
|
if (notran) {
|
|
*(unsigned char *)norm = '1';
|
|
} else {
|
|
*(unsigned char *)norm = 'I';
|
|
}
|
|
anorm = clangt_(norm, n, &dl[1], &d__[1], &du[1]);
|
|
|
|
/* Compute the reciprocal of the condition number of A. */
|
|
|
|
cgtcon_(norm, n, &dlf[1], &df[1], &duf[1], &du2[1], &ipiv[1], &anorm,
|
|
rcond, &work[1], info);
|
|
|
|
/* Compute the solution vectors X. */
|
|
|
|
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
|
|
cgttrs_(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. */
|
|
|
|
cgtrfs_(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], &rwork[1], info);
|
|
|
|
/* Set INFO = N+1 if the matrix is singular to working precision. */
|
|
|
|
if (*rcond < slamch_("Epsilon")) {
|
|
*info = *n + 1;
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of CGTSVX */
|
|
|
|
} /* cgtsvx_ */
|
|
|