1337 lines
46 KiB
C
1337 lines
46 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 {
|
|
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)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* > \brief <b> CGESVXX computes the solution to system of linear equations A * X = B for GE matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CGESVXX + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesvxx
|
|
.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesvxx
|
|
.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesvxx
|
|
.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CGESVXX( FACT, TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, */
|
|
/* EQUED, R, C, B, LDB, X, LDX, RCOND, RPVGRW, */
|
|
/* BERR, N_ERR_BNDS, ERR_BNDS_NORM, */
|
|
/* ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK, */
|
|
/* INFO ) */
|
|
|
|
/* CHARACTER EQUED, FACT, TRANS */
|
|
/* INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS, */
|
|
/* $ N_ERR_BNDS */
|
|
/* REAL RCOND, RPVGRW */
|
|
/* INTEGER IPIV( * ) */
|
|
/* COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ), */
|
|
/* $ X( LDX , * ),WORK( * ) */
|
|
/* REAL R( * ), C( * ), PARAMS( * ), BERR( * ), */
|
|
/* $ ERR_BNDS_NORM( NRHS, * ), */
|
|
/* $ ERR_BNDS_COMP( NRHS, * ), RWORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CGESVXX uses the LU factorization to compute the solution to a */
|
|
/* > complex system of linear equations A * X = B, where A is an */
|
|
/* > N-by-N matrix and X and B are N-by-NRHS matrices. */
|
|
/* > */
|
|
/* > If requested, both normwise and maximum componentwise error bounds */
|
|
/* > are returned. CGESVXX will return a solution with a tiny */
|
|
/* > guaranteed error (O(eps) where eps is the working machine */
|
|
/* > precision) unless the matrix is very ill-conditioned, in which */
|
|
/* > case a warning is returned. Relevant condition numbers also are */
|
|
/* > calculated and returned. */
|
|
/* > */
|
|
/* > CGESVXX accepts user-provided factorizations and equilibration */
|
|
/* > factors; see the definitions of the FACT and EQUED options. */
|
|
/* > Solving with refinement and using a factorization from a previous */
|
|
/* > CGESVXX call will also produce a solution with either O(eps) */
|
|
/* > errors or warnings, but we cannot make that claim for general */
|
|
/* > user-provided factorizations and equilibration factors if they */
|
|
/* > differ from what CGESVXX would itself produce. */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Description: */
|
|
/* ================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The following steps are performed: */
|
|
/* > */
|
|
/* > 1. If FACT = 'E', real scaling factors are computed to equilibrate */
|
|
/* > the system: */
|
|
/* > */
|
|
/* > TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */
|
|
/* > TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */
|
|
/* > TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */
|
|
/* > */
|
|
/* > Whether or not the system will be equilibrated depends on the */
|
|
/* > scaling of the matrix A, but if equilibration is used, A is */
|
|
/* > overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */
|
|
/* > or diag(C)*B (if TRANS = 'T' or 'C'). */
|
|
/* > */
|
|
/* > 2. If FACT = 'N' or 'E', the LU decomposition is used to factor */
|
|
/* > the matrix A (after equilibration if FACT = 'E') as */
|
|
/* > */
|
|
/* > A = P * L * U, */
|
|
/* > */
|
|
/* > where P is a permutation matrix, L is a unit lower triangular */
|
|
/* > matrix, and U is upper triangular. */
|
|
/* > */
|
|
/* > 3. 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 (see */
|
|
/* > argument RCOND). If the reciprocal of the condition number is less */
|
|
/* > than machine precision, the routine still goes on to solve for X */
|
|
/* > and compute error bounds as described below. */
|
|
/* > */
|
|
/* > 4. The system of equations is solved for X using the factored form */
|
|
/* > of A. */
|
|
/* > */
|
|
/* > 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */
|
|
/* > the routine will use iterative refinement to try to get a small */
|
|
/* > error and error bounds. Refinement calculates the residual to at */
|
|
/* > least twice the working precision. */
|
|
/* > */
|
|
/* > 6. If equilibration was used, the matrix X is premultiplied by */
|
|
/* > diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */
|
|
/* > that it solves the original system before equilibration. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \verbatim */
|
|
/* > Some optional parameters are bundled in the PARAMS array. These */
|
|
/* > settings determine how refinement is performed, but often the */
|
|
/* > defaults are acceptable. If the defaults are acceptable, users */
|
|
/* > can pass NPARAMS = 0 which prevents the source code from accessing */
|
|
/* > the PARAMS argument. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] FACT */
|
|
/* > \verbatim */
|
|
/* > FACT is CHARACTER*1 */
|
|
/* > Specifies whether or not the factored form of the matrix A is */
|
|
/* > supplied on entry, and if not, whether the matrix A should be */
|
|
/* > equilibrated before it is factored. */
|
|
/* > = 'F': On entry, AF and IPIV contain the factored form of A. */
|
|
/* > If EQUED is not 'N', the matrix A has been */
|
|
/* > equilibrated with scaling factors given by R and C. */
|
|
/* > A, AF, and IPIV are not modified. */
|
|
/* > = 'N': The matrix A will be copied to AF and factored. */
|
|
/* > = 'E': The matrix A will be equilibrated if necessary, then */
|
|
/* > copied to AF 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 number of linear equations, i.e., 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 matrices B and X. NRHS >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX array, dimension (LDA,N) */
|
|
/* > On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */
|
|
/* > not 'N', then A must have been equilibrated by the scaling */
|
|
/* > factors in R and/or C. A is not modified if FACT = 'F' or */
|
|
/* > 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
|
|
/* > */
|
|
/* > On exit, if EQUED .ne. 'N', A is scaled as follows: */
|
|
/* > EQUED = 'R': A := diag(R) * A */
|
|
/* > EQUED = 'C': A := A * diag(C) */
|
|
/* > EQUED = 'B': A := diag(R) * A * diag(C). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AF */
|
|
/* > \verbatim */
|
|
/* > AF is COMPLEX array, dimension (LDAF,N) */
|
|
/* > If FACT = 'F', then AF is an input argument and on entry */
|
|
/* > contains the factors L and U from the factorization */
|
|
/* > A = P*L*U as computed by CGETRF. If EQUED .ne. 'N', then */
|
|
/* > AF is the factored form of the equilibrated matrix A. */
|
|
/* > */
|
|
/* > If FACT = 'N', then AF is an output argument and on exit */
|
|
/* > returns the factors L and U from the factorization A = P*L*U */
|
|
/* > of the original matrix A. */
|
|
/* > */
|
|
/* > If FACT = 'E', then AF is an output argument and on exit */
|
|
/* > returns the factors L and U from the factorization A = P*L*U */
|
|
/* > of the equilibrated matrix A (see the description of A for */
|
|
/* > the form of the equilibrated matrix). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAF */
|
|
/* > \verbatim */
|
|
/* > LDAF is INTEGER */
|
|
/* > The leading dimension of the array AF. LDAF >= f2cmax(1,N). */
|
|
/* > \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 factorization A = P*L*U */
|
|
/* > as computed by CGETRF; row i of the matrix was interchanged */
|
|
/* > with row IPIV(i). */
|
|
/* > */
|
|
/* > If FACT = 'N', then IPIV is an output argument and on exit */
|
|
/* > contains the pivot indices from the factorization A = P*L*U */
|
|
/* > of the original matrix A. */
|
|
/* > */
|
|
/* > If FACT = 'E', then IPIV is an output argument and on exit */
|
|
/* > contains the pivot indices from the factorization A = P*L*U */
|
|
/* > of the equilibrated matrix A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] EQUED */
|
|
/* > \verbatim */
|
|
/* > EQUED is CHARACTER*1 */
|
|
/* > Specifies the form of equilibration that was done. */
|
|
/* > = 'N': No equilibration (always true if FACT = 'N'). */
|
|
/* > = 'R': Row equilibration, i.e., A has been premultiplied by */
|
|
/* > diag(R). */
|
|
/* > = 'C': Column equilibration, i.e., A has been postmultiplied */
|
|
/* > by diag(C). */
|
|
/* > = 'B': Both row and column equilibration, i.e., A has been */
|
|
/* > replaced by diag(R) * A * diag(C). */
|
|
/* > EQUED is an input argument if FACT = 'F'; otherwise, it is an */
|
|
/* > output argument. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] R */
|
|
/* > \verbatim */
|
|
/* > R is REAL array, dimension (N) */
|
|
/* > The row scale factors for A. If EQUED = 'R' or 'B', A is */
|
|
/* > multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
|
|
/* > is not accessed. R is an input argument if FACT = 'F'; */
|
|
/* > otherwise, R is an output argument. If FACT = 'F' and */
|
|
/* > EQUED = 'R' or 'B', each element of R must be positive. */
|
|
/* > If R is output, each element of R is a power of the radix. */
|
|
/* > If R is input, each element of R should be a power of the radix */
|
|
/* > to ensure a reliable solution and error estimates. Scaling by */
|
|
/* > powers of the radix does not cause rounding errors unless the */
|
|
/* > result underflows or overflows. Rounding errors during scaling */
|
|
/* > lead to refining with a matrix that is not equivalent to the */
|
|
/* > input matrix, producing error estimates that may not be */
|
|
/* > reliable. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] C */
|
|
/* > \verbatim */
|
|
/* > C is REAL array, dimension (N) */
|
|
/* > The column scale factors for A. If EQUED = 'C' or 'B', A is */
|
|
/* > multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
|
|
/* > is not accessed. C is an input argument if FACT = 'F'; */
|
|
/* > otherwise, C is an output argument. If FACT = 'F' and */
|
|
/* > EQUED = 'C' or 'B', each element of C must be positive. */
|
|
/* > If C is output, each element of C is a power of the radix. */
|
|
/* > If C is input, each element of C should be a power of the radix */
|
|
/* > to ensure a reliable solution and error estimates. Scaling by */
|
|
/* > powers of the radix does not cause rounding errors unless the */
|
|
/* > result underflows or overflows. Rounding errors during scaling */
|
|
/* > lead to refining with a matrix that is not equivalent to the */
|
|
/* > input matrix, producing error estimates that may not be */
|
|
/* > reliable. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX array, dimension (LDB,NRHS) */
|
|
/* > On entry, the N-by-NRHS right hand side matrix B. */
|
|
/* > On exit, */
|
|
/* > if EQUED = 'N', B is not modified; */
|
|
/* > if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
|
|
/* > diag(R)*B; */
|
|
/* > if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
|
|
/* > overwritten by diag(C)*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, the N-by-NRHS solution matrix X to the original */
|
|
/* > system of equations. Note that A and B are modified on exit */
|
|
/* > if EQUED .ne. 'N', and the solution to the equilibrated system is */
|
|
/* > inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */
|
|
/* > inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */
|
|
/* > \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 */
|
|
/* > Reciprocal scaled condition number. This is an estimate of the */
|
|
/* > reciprocal Skeel condition number of the matrix A after */
|
|
/* > equilibration (if done). If this is less than the machine */
|
|
/* > precision (in particular, if it is zero), the matrix is singular */
|
|
/* > to working precision. Note that the error may still be small even */
|
|
/* > if this number is very small and the matrix appears ill- */
|
|
/* > conditioned. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RPVGRW */
|
|
/* > \verbatim */
|
|
/* > RPVGRW is REAL */
|
|
/* > Reciprocal pivot growth. On exit, this contains the reciprocal */
|
|
/* > pivot growth factor norm(A)/norm(U). The "f2cmax absolute element" */
|
|
/* > norm is used. If this is much less than 1, then the stability of */
|
|
/* > the LU factorization of the (equilibrated) matrix A could be poor. */
|
|
/* > This also means that the solution X, estimated condition numbers, */
|
|
/* > and error bounds could be unreliable. If factorization fails with */
|
|
/* > 0<INFO<=N, then this contains the reciprocal pivot growth factor */
|
|
/* > for the leading INFO columns of A. In CGESVX, this quantity is */
|
|
/* > returned in WORK(1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BERR */
|
|
/* > \verbatim */
|
|
/* > BERR is REAL array, dimension (NRHS) */
|
|
/* > Componentwise relative backward error. This is the */
|
|
/* > componentwise relative backward error of each solution vector X(j) */
|
|
/* > (i.e., the smallest relative change in any element of A or B that */
|
|
/* > makes X(j) an exact solution). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N_ERR_BNDS */
|
|
/* > \verbatim */
|
|
/* > N_ERR_BNDS is INTEGER */
|
|
/* > Number of error bounds to return for each right hand side */
|
|
/* > and each type (normwise or componentwise). See ERR_BNDS_NORM and */
|
|
/* > ERR_BNDS_COMP below. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ERR_BNDS_NORM */
|
|
/* > \verbatim */
|
|
/* > ERR_BNDS_NORM is REAL array, dimension (NRHS, N_ERR_BNDS) */
|
|
/* > For each right-hand side, this array contains information about */
|
|
/* > various error bounds and condition numbers corresponding to the */
|
|
/* > normwise relative error, which is defined as follows: */
|
|
/* > */
|
|
/* > Normwise relative error in the ith solution vector: */
|
|
/* > max_j (abs(XTRUE(j,i) - X(j,i))) */
|
|
/* > ------------------------------ */
|
|
/* > max_j abs(X(j,i)) */
|
|
/* > */
|
|
/* > The array is indexed by the type of error information as described */
|
|
/* > below. There currently are up to three pieces of information */
|
|
/* > returned. */
|
|
/* > */
|
|
/* > The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
|
|
/* > right-hand side. */
|
|
/* > */
|
|
/* > The second index in ERR_BNDS_NORM(:,err) contains the following */
|
|
/* > three fields: */
|
|
/* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */
|
|
/* > reciprocal condition number is less than the threshold */
|
|
/* > sqrt(n) * slamch('Epsilon'). */
|
|
/* > */
|
|
/* > err = 2 "Guaranteed" error bound: The estimated forward error, */
|
|
/* > almost certainly within a factor of 10 of the true error */
|
|
/* > so long as the next entry is greater than the threshold */
|
|
/* > sqrt(n) * slamch('Epsilon'). This error bound should only */
|
|
/* > be trusted if the previous boolean is true. */
|
|
/* > */
|
|
/* > err = 3 Reciprocal condition number: Estimated normwise */
|
|
/* > reciprocal condition number. Compared with the threshold */
|
|
/* > sqrt(n) * slamch('Epsilon') to determine if the error */
|
|
/* > estimate is "guaranteed". These reciprocal condition */
|
|
/* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
|
|
/* > appropriately scaled matrix Z. */
|
|
/* > Let Z = S*A, where S scales each row by a power of the */
|
|
/* > radix so all absolute row sums of Z are approximately 1. */
|
|
/* > */
|
|
/* > See Lapack Working Note 165 for further details and extra */
|
|
/* > cautions. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] ERR_BNDS_COMP */
|
|
/* > \verbatim */
|
|
/* > ERR_BNDS_COMP is REAL array, dimension (NRHS, N_ERR_BNDS) */
|
|
/* > For each right-hand side, this array contains information about */
|
|
/* > various error bounds and condition numbers corresponding to the */
|
|
/* > componentwise relative error, which is defined as follows: */
|
|
/* > */
|
|
/* > Componentwise relative error in the ith solution vector: */
|
|
/* > abs(XTRUE(j,i) - X(j,i)) */
|
|
/* > max_j ---------------------- */
|
|
/* > abs(X(j,i)) */
|
|
/* > */
|
|
/* > The array is indexed by the right-hand side i (on which the */
|
|
/* > componentwise relative error depends), and the type of error */
|
|
/* > information as described below. There currently are up to three */
|
|
/* > pieces of information returned for each right-hand side. If */
|
|
/* > componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
|
|
/* > ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most */
|
|
/* > the first (:,N_ERR_BNDS) entries are returned. */
|
|
/* > */
|
|
/* > The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
|
|
/* > right-hand side. */
|
|
/* > */
|
|
/* > The second index in ERR_BNDS_COMP(:,err) contains the following */
|
|
/* > three fields: */
|
|
/* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */
|
|
/* > reciprocal condition number is less than the threshold */
|
|
/* > sqrt(n) * slamch('Epsilon'). */
|
|
/* > */
|
|
/* > err = 2 "Guaranteed" error bound: The estimated forward error, */
|
|
/* > almost certainly within a factor of 10 of the true error */
|
|
/* > so long as the next entry is greater than the threshold */
|
|
/* > sqrt(n) * slamch('Epsilon'). This error bound should only */
|
|
/* > be trusted if the previous boolean is true. */
|
|
/* > */
|
|
/* > err = 3 Reciprocal condition number: Estimated componentwise */
|
|
/* > reciprocal condition number. Compared with the threshold */
|
|
/* > sqrt(n) * slamch('Epsilon') to determine if the error */
|
|
/* > estimate is "guaranteed". These reciprocal condition */
|
|
/* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
|
|
/* > appropriately scaled matrix Z. */
|
|
/* > Let Z = S*(A*diag(x)), where x is the solution for the */
|
|
/* > current right-hand side and S scales each row of */
|
|
/* > A*diag(x) by a power of the radix so all absolute row */
|
|
/* > sums of Z are approximately 1. */
|
|
/* > */
|
|
/* > See Lapack Working Note 165 for further details and extra */
|
|
/* > cautions. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NPARAMS */
|
|
/* > \verbatim */
|
|
/* > NPARAMS is INTEGER */
|
|
/* > Specifies the number of parameters set in PARAMS. If <= 0, the */
|
|
/* > PARAMS array is never referenced and default values are used. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] PARAMS */
|
|
/* > \verbatim */
|
|
/* > PARAMS is REAL array, dimension NPARAMS */
|
|
/* > Specifies algorithm parameters. If an entry is < 0.0, then */
|
|
/* > that entry will be filled with default value used for that */
|
|
/* > parameter. Only positions up to NPARAMS are accessed; defaults */
|
|
/* > are used for higher-numbered parameters. */
|
|
/* > */
|
|
/* > PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
|
|
/* > refinement or not. */
|
|
/* > Default: 1.0 */
|
|
/* > = 0.0: No refinement is performed, and no error bounds are */
|
|
/* > computed. */
|
|
/* > = 1.0: Use the double-precision refinement algorithm, */
|
|
/* > possibly with doubled-single computations if the */
|
|
/* > compilation environment does not support DOUBLE */
|
|
/* > PRECISION. */
|
|
/* > (other values are reserved for future use) */
|
|
/* > */
|
|
/* > PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
|
|
/* > computations allowed for refinement. */
|
|
/* > Default: 10 */
|
|
/* > Aggressive: Set to 100 to permit convergence using approximate */
|
|
/* > factorizations or factorizations other than LU. If */
|
|
/* > the factorization uses a technique other than */
|
|
/* > Gaussian elimination, the guarantees in */
|
|
/* > err_bnds_norm and err_bnds_comp may no longer be */
|
|
/* > trustworthy. */
|
|
/* > */
|
|
/* > PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
|
|
/* > will attempt to find a solution with small componentwise */
|
|
/* > relative error in the double-precision algorithm. Positive */
|
|
/* > is true, 0.0 is false. */
|
|
/* > Default: 1.0 (attempt componentwise convergence) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is REAL array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: Successful exit. The solution to every right-hand side is */
|
|
/* > guaranteed. */
|
|
/* > < 0: If INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
|
|
/* > has been completed, but the factor U is exactly singular, so */
|
|
/* > the solution and error bounds could not be computed. RCOND = 0 */
|
|
/* > is returned. */
|
|
/* > = N+J: The solution corresponding to the Jth right-hand side is */
|
|
/* > not guaranteed. The solutions corresponding to other right- */
|
|
/* > hand sides K with K > J may not be guaranteed as well, but */
|
|
/* > only the first such right-hand side is reported. If a small */
|
|
/* > componentwise error is not requested (PARAMS(3) = 0.0) then */
|
|
/* > the Jth right-hand side is the first with a normwise error */
|
|
/* > bound that is not guaranteed (the smallest J such */
|
|
/* > that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
|
|
/* > the Jth right-hand side is the first with either a normwise or */
|
|
/* > componentwise error bound that is not guaranteed (the smallest */
|
|
/* > J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
|
|
/* > ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
|
|
/* > ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
|
|
/* > about all of the right-hand sides check ERR_BNDS_NORM or */
|
|
/* > ERR_BNDS_COMP. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date April 2012 */
|
|
|
|
/* > \ingroup complexGEsolve */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cgesvxx_(char *fact, char *trans, integer *n, integer *
|
|
nrhs, complex *a, integer *lda, complex *af, integer *ldaf, integer *
|
|
ipiv, char *equed, real *r__, real *c__, complex *b, integer *ldb,
|
|
complex *x, integer *ldx, real *rcond, real *rpvgrw, real *berr,
|
|
integer *n_err_bnds__, real *err_bnds_norm__, real *err_bnds_comp__,
|
|
integer *nparams, real *params, complex *work, real *rwork, integer *
|
|
info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
|
|
x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
|
|
err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
|
|
real r__1, r__2;
|
|
|
|
/* Local variables */
|
|
real amax;
|
|
extern real cla_gerpvgrw_(integer *, integer *, complex *, integer *,
|
|
complex *, integer *);
|
|
integer j;
|
|
extern logical lsame_(char *, char *);
|
|
real rcmin, rcmax;
|
|
logical equil;
|
|
extern /* Subroutine */ void claqge_(integer *, integer *, complex *,
|
|
integer *, real *, real *, real *, real *, real *, char *)
|
|
;
|
|
real colcnd;
|
|
extern real slamch_(char *);
|
|
logical nofact;
|
|
extern /* Subroutine */ void cgetrf_(integer *, integer *, complex *,
|
|
integer *, integer *, integer *), clacpy_(char *, integer *,
|
|
integer *, complex *, integer *, complex *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
real bignum;
|
|
integer infequ;
|
|
logical colequ;
|
|
extern /* Subroutine */ void cgetrs_(char *, integer *, integer *, complex
|
|
*, integer *, integer *, complex *, integer *, integer *);
|
|
real rowcnd;
|
|
logical notran;
|
|
real smlnum;
|
|
logical rowequ;
|
|
extern /* Subroutine */ void clascl2_(integer *, integer *, real *,
|
|
complex *, integer *), cgeequb_(integer *, integer *, complex *,
|
|
integer *, real *, real *, real *, real *, real *, integer *),
|
|
cgerfsx_(char *, char *, integer *, integer *, complex *, integer
|
|
*, complex *, integer *, integer *, real *, real *, complex *,
|
|
integer *, complex *, integer *, real *, real *, integer *, real *
|
|
, real *, integer *, real *, complex *, real *, 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..-- */
|
|
/* April 2012 */
|
|
|
|
|
|
/* ================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
err_bnds_comp_dim1 = *nrhs;
|
|
err_bnds_comp_offset = 1 + err_bnds_comp_dim1 * 1;
|
|
err_bnds_comp__ -= err_bnds_comp_offset;
|
|
err_bnds_norm_dim1 = *nrhs;
|
|
err_bnds_norm_offset = 1 + err_bnds_norm_dim1 * 1;
|
|
err_bnds_norm__ -= err_bnds_norm_offset;
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
af_dim1 = *ldaf;
|
|
af_offset = 1 + af_dim1 * 1;
|
|
af -= af_offset;
|
|
--ipiv;
|
|
--r__;
|
|
--c__;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
x_dim1 = *ldx;
|
|
x_offset = 1 + x_dim1 * 1;
|
|
x -= x_offset;
|
|
--berr;
|
|
--params;
|
|
--work;
|
|
--rwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
nofact = lsame_(fact, "N");
|
|
equil = lsame_(fact, "E");
|
|
notran = lsame_(trans, "N");
|
|
smlnum = slamch_("Safe minimum");
|
|
bignum = 1.f / smlnum;
|
|
if (nofact || equil) {
|
|
*(unsigned char *)equed = 'N';
|
|
rowequ = FALSE_;
|
|
colequ = FALSE_;
|
|
} else {
|
|
rowequ = lsame_(equed, "R") || lsame_(equed,
|
|
"B");
|
|
colequ = lsame_(equed, "C") || lsame_(equed,
|
|
"B");
|
|
}
|
|
|
|
/* Default is failure. If an input parameter is wrong or */
|
|
/* factorization fails, make everything look horrible. Only the */
|
|
/* pivot growth is set here, the rest is initialized in CGERFSX. */
|
|
|
|
*rpvgrw = 0.f;
|
|
|
|
/* Test the input parameters. PARAMS is not tested until CGERFSX. */
|
|
|
|
if (! nofact && ! equil && ! 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 (*lda < f2cmax(1,*n)) {
|
|
*info = -6;
|
|
} else if (*ldaf < f2cmax(1,*n)) {
|
|
*info = -8;
|
|
} else if (lsame_(fact, "F") && ! (rowequ || colequ
|
|
|| lsame_(equed, "N"))) {
|
|
*info = -10;
|
|
} else {
|
|
if (rowequ) {
|
|
rcmin = bignum;
|
|
rcmax = 0.f;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
/* Computing MIN */
|
|
r__1 = rcmin, r__2 = r__[j];
|
|
rcmin = f2cmin(r__1,r__2);
|
|
/* Computing MAX */
|
|
r__1 = rcmax, r__2 = r__[j];
|
|
rcmax = f2cmax(r__1,r__2);
|
|
/* L10: */
|
|
}
|
|
if (rcmin <= 0.f) {
|
|
*info = -11;
|
|
} else if (*n > 0) {
|
|
rowcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
|
|
} else {
|
|
rowcnd = 1.f;
|
|
}
|
|
}
|
|
if (colequ && *info == 0) {
|
|
rcmin = bignum;
|
|
rcmax = 0.f;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
/* Computing MIN */
|
|
r__1 = rcmin, r__2 = c__[j];
|
|
rcmin = f2cmin(r__1,r__2);
|
|
/* Computing MAX */
|
|
r__1 = rcmax, r__2 = c__[j];
|
|
rcmax = f2cmax(r__1,r__2);
|
|
/* L20: */
|
|
}
|
|
if (rcmin <= 0.f) {
|
|
*info = -12;
|
|
} else if (*n > 0) {
|
|
colcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
|
|
} else {
|
|
colcnd = 1.f;
|
|
}
|
|
}
|
|
if (*info == 0) {
|
|
if (*ldb < f2cmax(1,*n)) {
|
|
*info = -14;
|
|
} else if (*ldx < f2cmax(1,*n)) {
|
|
*info = -16;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CGESVXX", &i__1, (ftnlen)7);
|
|
return;
|
|
}
|
|
|
|
if (equil) {
|
|
|
|
/* Compute row and column scalings to equilibrate the matrix A. */
|
|
|
|
cgeequb_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd,
|
|
&amax, &infequ);
|
|
if (infequ == 0) {
|
|
|
|
/* Equilibrate the matrix. */
|
|
|
|
claqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &
|
|
colcnd, &amax, equed);
|
|
rowequ = lsame_(equed, "R") || lsame_(equed,
|
|
"B");
|
|
colequ = lsame_(equed, "C") || lsame_(equed,
|
|
"B");
|
|
}
|
|
|
|
/* If the scaling factors are not applied, set them to 1.0. */
|
|
|
|
if (! rowequ) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
r__[j] = 1.f;
|
|
}
|
|
}
|
|
if (! colequ) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
c__[j] = 1.f;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Scale the right-hand side. */
|
|
|
|
if (notran) {
|
|
if (rowequ) {
|
|
clascl2_(n, nrhs, &r__[1], &b[b_offset], ldb);
|
|
}
|
|
} else {
|
|
if (colequ) {
|
|
clascl2_(n, nrhs, &c__[1], &b[b_offset], ldb);
|
|
}
|
|
}
|
|
|
|
if (nofact || equil) {
|
|
|
|
/* Compute the LU factorization of A. */
|
|
|
|
clacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
|
|
cgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
|
|
|
|
/* Return if INFO is non-zero. */
|
|
|
|
if (*info > 0) {
|
|
|
|
/* Pivot in column INFO is exactly 0 */
|
|
/* Compute the reciprocal pivot growth factor of the */
|
|
/* leading rank-deficient INFO columns of A. */
|
|
|
|
*rpvgrw = cla_gerpvgrw_(n, info, &a[a_offset], lda, &af[
|
|
af_offset], ldaf);
|
|
return;
|
|
}
|
|
}
|
|
|
|
/* Compute the reciprocal pivot growth factor RPVGRW. */
|
|
|
|
*rpvgrw = cla_gerpvgrw_(n, n, &a[a_offset], lda, &af[af_offset], ldaf);
|
|
|
|
/* Compute the solution matrix X. */
|
|
|
|
clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
|
|
cgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx,
|
|
info);
|
|
|
|
/* Use iterative refinement to improve the computed solution and */
|
|
/* compute error bounds and backward error estimates for it. */
|
|
|
|
cgerfsx_(trans, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &
|
|
ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb, &x[x_offset], ldx,
|
|
rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[
|
|
err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset],
|
|
nparams, ¶ms[1], &work[1], &rwork[1], info);
|
|
|
|
/* Scale solutions. */
|
|
|
|
if (colequ && notran) {
|
|
clascl2_(n, nrhs, &c__[1], &x[x_offset], ldx);
|
|
} else if (rowequ && ! notran) {
|
|
clascl2_(n, nrhs, &r__[1], &x[x_offset], ldx);
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of CGESVXX */
|
|
|
|
} /* cgesvxx_ */
|
|
|