1268 lines
40 KiB
C
1268 lines
40 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define 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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#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;
|
|
static doublereal c_b6 = -1.;
|
|
static doublereal c_b8 = 1.;
|
|
|
|
/* > \brief \b DLA_GBRFSX_EXTENDED improves the computed solution to a system of linear equations for general
|
|
banded matrices by performing extra-precise iterative refinement and provides error bounds and backwar
|
|
d error estimates for the solution. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLA_GBRFSX_EXTENDED + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbr
|
|
fsx_extended.f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbr
|
|
fsx_extended.f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbr
|
|
fsx_extended.f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU, */
|
|
/* NRHS, AB, LDAB, AFB, LDAFB, IPIV, */
|
|
/* COLEQU, C, B, LDB, Y, LDY, */
|
|
/* BERR_OUT, N_NORMS, ERR_BNDS_NORM, */
|
|
/* ERR_BNDS_COMP, RES, AYB, DY, */
|
|
/* Y_TAIL, RCOND, ITHRESH, RTHRESH, */
|
|
/* DZ_UB, IGNORE_CWISE, INFO ) */
|
|
|
|
/* INTEGER INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS, */
|
|
/* $ PREC_TYPE, TRANS_TYPE, N_NORMS, ITHRESH */
|
|
/* LOGICAL COLEQU, IGNORE_CWISE */
|
|
/* DOUBLE PRECISION RTHRESH, DZ_UB */
|
|
/* INTEGER IPIV( * ) */
|
|
/* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */
|
|
/* $ Y( LDY, * ), RES(*), DY(*), Y_TAIL(*) */
|
|
/* DOUBLE PRECISION C( * ), AYB(*), RCOND, BERR_OUT(*), */
|
|
/* $ ERR_BNDS_NORM( NRHS, * ), */
|
|
/* $ ERR_BNDS_COMP( NRHS, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > */
|
|
/* > DLA_GBRFSX_EXTENDED improves the computed solution to a system of */
|
|
/* > linear equations by performing extra-precise iterative refinement */
|
|
/* > and provides error bounds and backward error estimates for the solution. */
|
|
/* > This subroutine is called by DGBRFSX to perform iterative refinement. */
|
|
/* > In addition to normwise error bound, the code provides maximum */
|
|
/* > componentwise error bound if possible. See comments for ERR_BNDS_NORM */
|
|
/* > and ERR_BNDS_COMP for details of the error bounds. Note that this */
|
|
/* > subroutine is only resonsible for setting the second fields of */
|
|
/* > ERR_BNDS_NORM and ERR_BNDS_COMP. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] PREC_TYPE */
|
|
/* > \verbatim */
|
|
/* > PREC_TYPE is INTEGER */
|
|
/* > Specifies the intermediate precision to be used in refinement. */
|
|
/* > The value is defined by ILAPREC(P) where P is a CHARACTER and P */
|
|
/* > = 'S': Single */
|
|
/* > = 'D': Double */
|
|
/* > = 'I': Indigenous */
|
|
/* > = 'X' or 'E': Extra */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TRANS_TYPE */
|
|
/* > \verbatim */
|
|
/* > TRANS_TYPE is INTEGER */
|
|
/* > Specifies the transposition operation on A. */
|
|
/* > The value is defined by ILATRANS(T) where T is a CHARACTER and T */
|
|
/* > = 'N': No transpose */
|
|
/* > = 'T': Transpose */
|
|
/* > = 'C': 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] KL */
|
|
/* > \verbatim */
|
|
/* > KL is INTEGER */
|
|
/* > The number of subdiagonals within the band of A. KL >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KU */
|
|
/* > \verbatim */
|
|
/* > KU is INTEGER */
|
|
/* > The number of superdiagonals within the band of A. KU >= 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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] AB */
|
|
/* > \verbatim */
|
|
/* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */
|
|
/* > On entry, the N-by-N matrix AB. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array AB. LDBA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] AFB */
|
|
/* > \verbatim */
|
|
/* > AFB is DOUBLE PRECISION array, dimension (LDAFB,N) */
|
|
/* > The factors L and U from the factorization */
|
|
/* > A = P*L*U as computed by DGBTRF. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAFB */
|
|
/* > \verbatim */
|
|
/* > LDAFB is INTEGER */
|
|
/* > The leading dimension of the array AF. LDAFB >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (N) */
|
|
/* > The pivot indices from the factorization A = P*L*U */
|
|
/* > as computed by DGBTRF; row i of the matrix was interchanged */
|
|
/* > with row IPIV(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] COLEQU */
|
|
/* > \verbatim */
|
|
/* > COLEQU is LOGICAL */
|
|
/* > If .TRUE. then column equilibration was done to A before calling */
|
|
/* > this routine. This is needed to compute the solution and error */
|
|
/* > bounds correctly. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] C */
|
|
/* > \verbatim */
|
|
/* > C is DOUBLE PRECISION array, dimension (N) */
|
|
/* > The column scale factors for A. If COLEQU = .FALSE., C */
|
|
/* > is not accessed. 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] B */
|
|
/* > \verbatim */
|
|
/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
|
|
/* > The 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[in,out] Y */
|
|
/* > \verbatim */
|
|
/* > Y is DOUBLE PRECISION array, dimension (LDY,NRHS) */
|
|
/* > On entry, the solution matrix X, as computed by DGBTRS. */
|
|
/* > On exit, the improved solution matrix Y. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDY */
|
|
/* > \verbatim */
|
|
/* > LDY is INTEGER */
|
|
/* > The leading dimension of the array Y. LDY >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BERR_OUT */
|
|
/* > \verbatim */
|
|
/* > BERR_OUT is DOUBLE PRECISION array, dimension (NRHS) */
|
|
/* > On exit, BERR_OUT(j) contains the componentwise relative backward */
|
|
/* > error for right-hand-side j from the formula */
|
|
/* > f2cmax(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
|
|
/* > where abs(Z) is the componentwise absolute value of the matrix */
|
|
/* > or vector Z. This is computed by DLA_LIN_BERR. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N_NORMS */
|
|
/* > \verbatim */
|
|
/* > N_NORMS is INTEGER */
|
|
/* > Determines which error bounds to return (see ERR_BNDS_NORM */
|
|
/* > and ERR_BNDS_COMP). */
|
|
/* > If N_NORMS >= 1 return normwise error bounds. */
|
|
/* > If N_NORMS >= 2 return componentwise error bounds. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] ERR_BNDS_NORM */
|
|
/* > \verbatim */
|
|
/* > ERR_BNDS_NORM is DOUBLE PRECISION 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. */
|
|
/* > */
|
|
/* > This subroutine is only responsible for setting the second field */
|
|
/* > above. */
|
|
/* > See Lapack Working Note 165 for further details and extra */
|
|
/* > cautions. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] ERR_BNDS_COMP */
|
|
/* > \verbatim */
|
|
/* > ERR_BNDS_COMP is DOUBLE PRECISION 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. */
|
|
/* > */
|
|
/* > This subroutine is only responsible for setting the second field */
|
|
/* > above. */
|
|
/* > See Lapack Working Note 165 for further details and extra */
|
|
/* > cautions. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RES */
|
|
/* > \verbatim */
|
|
/* > RES is DOUBLE PRECISION array, dimension (N) */
|
|
/* > Workspace to hold the intermediate residual. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] AYB */
|
|
/* > \verbatim */
|
|
/* > AYB is DOUBLE PRECISION array, dimension (N) */
|
|
/* > Workspace. This can be the same workspace passed for Y_TAIL. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] DY */
|
|
/* > \verbatim */
|
|
/* > DY is DOUBLE PRECISION array, dimension (N) */
|
|
/* > Workspace to hold the intermediate solution. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] Y_TAIL */
|
|
/* > \verbatim */
|
|
/* > Y_TAIL is DOUBLE PRECISION array, dimension (N) */
|
|
/* > Workspace to hold the trailing bits of the intermediate solution. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RCOND */
|
|
/* > \verbatim */
|
|
/* > RCOND is DOUBLE PRECISION */
|
|
/* > 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[in] ITHRESH */
|
|
/* > \verbatim */
|
|
/* > ITHRESH is INTEGER */
|
|
/* > The maximum number of residual computations allowed for */
|
|
/* > refinement. The default is 10. For '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. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RTHRESH */
|
|
/* > \verbatim */
|
|
/* > RTHRESH is DOUBLE PRECISION */
|
|
/* > Determines when to stop refinement if the error estimate stops */
|
|
/* > decreasing. Refinement will stop when the next solution no longer */
|
|
/* > satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is */
|
|
/* > the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The */
|
|
/* > default value is 0.5. For 'aggressive' set to 0.9 to permit */
|
|
/* > convergence on extremely ill-conditioned matrices. See LAWN 165 */
|
|
/* > for more details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] DZ_UB */
|
|
/* > \verbatim */
|
|
/* > DZ_UB is DOUBLE PRECISION */
|
|
/* > Determines when to start considering componentwise convergence. */
|
|
/* > Componentwise convergence is only considered after each component */
|
|
/* > of the solution Y is stable, which we definte as the relative */
|
|
/* > change in each component being less than DZ_UB. The default value */
|
|
/* > is 0.25, requiring the first bit to be stable. See LAWN 165 for */
|
|
/* > more details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IGNORE_CWISE */
|
|
/* > \verbatim */
|
|
/* > IGNORE_CWISE is LOGICAL */
|
|
/* > If .TRUE. then ignore componentwise convergence. Default value */
|
|
/* > is .FALSE.. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: Successful exit. */
|
|
/* > < 0: if INFO = -i, the ith argument to DGBTRS had an illegal */
|
|
/* > value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date June 2017 */
|
|
|
|
/* > \ingroup doubleGBcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dla_gbrfsx_extended_(integer *prec_type__, integer *
|
|
trans_type__, integer *n, integer *kl, integer *ku, integer *nrhs,
|
|
doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb,
|
|
integer *ipiv, logical *colequ, doublereal *c__, doublereal *b,
|
|
integer *ldb, doublereal *y, integer *ldy, doublereal *berr_out__,
|
|
integer *n_norms__, doublereal *err_bnds_norm__, doublereal *
|
|
err_bnds_comp__, doublereal *res, doublereal *ayb, doublereal *dy,
|
|
doublereal *y_tail__, doublereal *rcond, integer *ithresh, doublereal
|
|
*rthresh, doublereal *dz_ub__, logical *ignore_cwise__, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
|
|
y_dim1, y_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
|
|
err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3;
|
|
doublereal d__1, d__2;
|
|
char ch__1[1];
|
|
|
|
/* Local variables */
|
|
doublereal dx_x__, dz_z__;
|
|
extern /* Subroutine */ void dla_lin_berr_(integer *, integer *, integer *
|
|
, doublereal *, doublereal *, doublereal *);
|
|
doublereal ymin;
|
|
extern /* Subroutine */ void blas_dgbmv_x_(integer *, integer *, integer *
|
|
, integer *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
integer *);
|
|
doublereal dxratmax, dzratmax;
|
|
integer y_prec_state__;
|
|
extern /* Subroutine */ void blas_dgbmv2_x_(integer *, integer *, integer
|
|
*, integer *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
|
|
integer *, integer *);
|
|
integer i__, j, m;
|
|
extern /* Subroutine */ void dla_gbamv_(integer *, integer *, integer *,
|
|
integer *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *),
|
|
dgbmv_(char *, integer *, integer *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, doublereal *, integer *,
|
|
doublereal *, doublereal *, integer *), dcopy_(integer *,
|
|
doublereal *, integer *, doublereal *, integer *);
|
|
doublereal dxrat;
|
|
logical incr_prec__;
|
|
doublereal dzrat;
|
|
extern /* Subroutine */ void daxpy_(integer *, doublereal *, doublereal *,
|
|
integer *, doublereal *, integer *);
|
|
char trans[1];
|
|
doublereal normx, normy, myhugeval, prev_dz_z__;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal yk;
|
|
extern /* Subroutine */ void dgbtrs_(char *, integer *, integer *, integer
|
|
*, integer *, doublereal *, integer *, integer *, doublereal *,
|
|
integer *, integer *);
|
|
doublereal final_dx_x__;
|
|
extern /* Subroutine */ void dla_wwaddw_(integer *, doublereal *,
|
|
doublereal *, doublereal *);
|
|
doublereal final_dz_z__, normdx;
|
|
extern /* Character */ VOID chla_transtype_(char *, integer *);
|
|
doublereal prevnormdx;
|
|
integer cnt;
|
|
doublereal dyk, eps;
|
|
integer x_state__, z_state__;
|
|
doublereal incr_thresh__;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* 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;
|
|
ab_dim1 = *ldab;
|
|
ab_offset = 1 + ab_dim1 * 1;
|
|
ab -= ab_offset;
|
|
afb_dim1 = *ldafb;
|
|
afb_offset = 1 + afb_dim1 * 1;
|
|
afb -= afb_offset;
|
|
--ipiv;
|
|
--c__;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
y_dim1 = *ldy;
|
|
y_offset = 1 + y_dim1 * 1;
|
|
y -= y_offset;
|
|
--berr_out__;
|
|
--res;
|
|
--ayb;
|
|
--dy;
|
|
--y_tail__;
|
|
|
|
/* Function Body */
|
|
if (*info != 0) {
|
|
return;
|
|
}
|
|
chla_transtype_(ch__1, trans_type__);
|
|
*(unsigned char *)trans = *(unsigned char *)&ch__1[0];
|
|
eps = dlamch_("Epsilon");
|
|
myhugeval = dlamch_("Overflow");
|
|
/* Force MYHUGEVAL to Inf */
|
|
myhugeval *= myhugeval;
|
|
/* Using MYHUGEVAL may lead to spurious underflows. */
|
|
incr_thresh__ = (doublereal) (*n) * eps;
|
|
m = *kl + *ku + 1;
|
|
i__1 = *nrhs;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
y_prec_state__ = 1;
|
|
if (y_prec_state__ == 2) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
y_tail__[i__] = 0.;
|
|
}
|
|
}
|
|
dxrat = 0.;
|
|
dxratmax = 0.;
|
|
dzrat = 0.;
|
|
dzratmax = 0.;
|
|
final_dx_x__ = myhugeval;
|
|
final_dz_z__ = myhugeval;
|
|
prevnormdx = myhugeval;
|
|
prev_dz_z__ = myhugeval;
|
|
dz_z__ = myhugeval;
|
|
dx_x__ = myhugeval;
|
|
x_state__ = 1;
|
|
z_state__ = 0;
|
|
incr_prec__ = FALSE_;
|
|
i__2 = *ithresh;
|
|
for (cnt = 1; cnt <= i__2; ++cnt) {
|
|
|
|
/* Compute residual RES = B_s - op(A_s) * Y, */
|
|
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
|
|
|
|
dcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
|
|
if (y_prec_state__ == 0) {
|
|
dgbmv_(trans, &m, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[
|
|
j * y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1);
|
|
} else if (y_prec_state__ == 1) {
|
|
blas_dgbmv_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[
|
|
ab_offset], ldab, &y[j * y_dim1 + 1], &c__1, &c_b8, &
|
|
res[1], &c__1, prec_type__);
|
|
} else {
|
|
blas_dgbmv2_x__(trans_type__, n, n, kl, ku, &c_b6, &ab[
|
|
ab_offset], ldab, &y[j * y_dim1 + 1], &y_tail__[1], &
|
|
c__1, &c_b8, &res[1], &c__1, prec_type__);
|
|
}
|
|
/* XXX: RES is no longer needed. */
|
|
dcopy_(n, &res[1], &c__1, &dy[1], &c__1);
|
|
dgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1]
|
|
, &dy[1], n, info);
|
|
|
|
/* Calculate relative changes DX_X, DZ_Z and ratios DXRAT, DZRAT. */
|
|
|
|
normx = 0.;
|
|
normy = 0.;
|
|
normdx = 0.;
|
|
dz_z__ = 0.;
|
|
ymin = myhugeval;
|
|
i__3 = *n;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
yk = (d__1 = y[i__ + j * y_dim1], abs(d__1));
|
|
dyk = (d__1 = dy[i__], abs(d__1));
|
|
if (yk != 0.) {
|
|
/* Computing MAX */
|
|
d__1 = dz_z__, d__2 = dyk / yk;
|
|
dz_z__ = f2cmax(d__1,d__2);
|
|
} else if (dyk != 0.) {
|
|
dz_z__ = myhugeval;
|
|
}
|
|
ymin = f2cmin(ymin,yk);
|
|
normy = f2cmax(normy,yk);
|
|
if (*colequ) {
|
|
/* Computing MAX */
|
|
d__1 = normx, d__2 = yk * c__[i__];
|
|
normx = f2cmax(d__1,d__2);
|
|
/* Computing MAX */
|
|
d__1 = normdx, d__2 = dyk * c__[i__];
|
|
normdx = f2cmax(d__1,d__2);
|
|
} else {
|
|
normx = normy;
|
|
normdx = f2cmax(normdx,dyk);
|
|
}
|
|
}
|
|
if (normx != 0.) {
|
|
dx_x__ = normdx / normx;
|
|
} else if (normdx == 0.) {
|
|
dx_x__ = 0.;
|
|
} else {
|
|
dx_x__ = myhugeval;
|
|
}
|
|
dxrat = normdx / prevnormdx;
|
|
dzrat = dz_z__ / prev_dz_z__;
|
|
|
|
/* Check termination criteria. */
|
|
|
|
if (! (*ignore_cwise__) && ymin * *rcond < incr_thresh__ * normy
|
|
&& y_prec_state__ < 2) {
|
|
incr_prec__ = TRUE_;
|
|
}
|
|
if (x_state__ == 3 && dxrat <= *rthresh) {
|
|
x_state__ = 1;
|
|
}
|
|
if (x_state__ == 1) {
|
|
if (dx_x__ <= eps) {
|
|
x_state__ = 2;
|
|
} else if (dxrat > *rthresh) {
|
|
if (y_prec_state__ != 2) {
|
|
incr_prec__ = TRUE_;
|
|
} else {
|
|
x_state__ = 3;
|
|
}
|
|
} else {
|
|
if (dxrat > dxratmax) {
|
|
dxratmax = dxrat;
|
|
}
|
|
}
|
|
if (x_state__ > 1) {
|
|
final_dx_x__ = dx_x__;
|
|
}
|
|
}
|
|
if (z_state__ == 0 && dz_z__ <= *dz_ub__) {
|
|
z_state__ = 1;
|
|
}
|
|
if (z_state__ == 3 && dzrat <= *rthresh) {
|
|
z_state__ = 1;
|
|
}
|
|
if (z_state__ == 1) {
|
|
if (dz_z__ <= eps) {
|
|
z_state__ = 2;
|
|
} else if (dz_z__ > *dz_ub__) {
|
|
z_state__ = 0;
|
|
dzratmax = 0.;
|
|
final_dz_z__ = myhugeval;
|
|
} else if (dzrat > *rthresh) {
|
|
if (y_prec_state__ != 2) {
|
|
incr_prec__ = TRUE_;
|
|
} else {
|
|
z_state__ = 3;
|
|
}
|
|
} else {
|
|
if (dzrat > dzratmax) {
|
|
dzratmax = dzrat;
|
|
}
|
|
}
|
|
if (z_state__ > 1) {
|
|
final_dz_z__ = dz_z__;
|
|
}
|
|
}
|
|
|
|
/* Exit if both normwise and componentwise stopped working, */
|
|
/* but if componentwise is unstable, let it go at least two */
|
|
/* iterations. */
|
|
|
|
if (x_state__ != 1) {
|
|
if (*ignore_cwise__) {
|
|
goto L666;
|
|
}
|
|
if (z_state__ == 3 || z_state__ == 2) {
|
|
goto L666;
|
|
}
|
|
if (z_state__ == 0 && cnt > 1) {
|
|
goto L666;
|
|
}
|
|
}
|
|
if (incr_prec__) {
|
|
incr_prec__ = FALSE_;
|
|
++y_prec_state__;
|
|
i__3 = *n;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
y_tail__[i__] = 0.;
|
|
}
|
|
}
|
|
prevnormdx = normdx;
|
|
prev_dz_z__ = dz_z__;
|
|
|
|
/* Update soluton. */
|
|
|
|
if (y_prec_state__ < 2) {
|
|
daxpy_(n, &c_b8, &dy[1], &c__1, &y[j * y_dim1 + 1], &c__1);
|
|
} else {
|
|
dla_wwaddw_(n, &y[j * y_dim1 + 1], &y_tail__[1], &dy[1]);
|
|
}
|
|
}
|
|
/* Target of "IF (Z_STOP .AND. X_STOP)". Sun's f77 won't CALL MYEXIT. */
|
|
L666:
|
|
|
|
/* Set final_* when cnt hits ithresh. */
|
|
|
|
if (x_state__ == 1) {
|
|
final_dx_x__ = dx_x__;
|
|
}
|
|
if (z_state__ == 1) {
|
|
final_dz_z__ = dz_z__;
|
|
}
|
|
|
|
/* Compute error bounds. */
|
|
|
|
if (*n_norms__ >= 1) {
|
|
err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = final_dx_x__ / (
|
|
1 - dxratmax);
|
|
}
|
|
if (*n_norms__ >= 2) {
|
|
err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = final_dz_z__ / (
|
|
1 - dzratmax);
|
|
}
|
|
|
|
/* Compute componentwise relative backward error from formula */
|
|
/* f2cmax(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) ) */
|
|
/* where abs(Z) is the componentwise absolute value of the matrix */
|
|
/* or vector Z. */
|
|
|
|
/* Compute residual RES = B_s - op(A_s) * Y, */
|
|
/* op(A) = A, A**T, or A**H depending on TRANS (and type). */
|
|
|
|
dcopy_(n, &b[j * b_dim1 + 1], &c__1, &res[1], &c__1);
|
|
dgbmv_(trans, n, n, kl, ku, &c_b6, &ab[ab_offset], ldab, &y[j *
|
|
y_dim1 + 1], &c__1, &c_b8, &res[1], &c__1);
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
ayb[i__] = (d__1 = b[i__ + j * b_dim1], abs(d__1));
|
|
}
|
|
|
|
/* Compute abs(op(A_s))*abs(Y) + abs(B_s). */
|
|
|
|
dla_gbamv_(trans_type__, n, n, kl, ku, &c_b8, &ab[ab_offset], ldab, &
|
|
y[j * y_dim1 + 1], &c__1, &c_b8, &ayb[1], &c__1);
|
|
dla_lin_berr_(n, n, &c__1, &res[1], &ayb[1], &berr_out__[j]);
|
|
|
|
/* End of loop for each RHS */
|
|
|
|
}
|
|
|
|
return;
|
|
} /* dla_gbrfsx_extended__ */
|
|
|