1078 lines
30 KiB
C
1078 lines
30 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 doublecomplex c_b1 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* > \brief \b ZGBRFS */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZGBRFS + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbrfs.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbrfs.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbrfs.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, */
|
|
/* IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, */
|
|
/* INFO ) */
|
|
|
|
/* CHARACTER TRANS */
|
|
/* INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS */
|
|
/* INTEGER IPIV( * ) */
|
|
/* DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) */
|
|
/* COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */
|
|
/* $ WORK( * ), X( LDX, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZGBRFS improves the computed solution to a system of linear */
|
|
/* > equations when the coefficient matrix is banded, and provides */
|
|
/* > error bounds and backward error estimates for the solution. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] TRANS */
|
|
/* > \verbatim */
|
|
/* > TRANS is CHARACTER*1 */
|
|
/* > Specifies the form of the system of equations: */
|
|
/* > = 'N': A * X = B (No transpose) */
|
|
/* > = 'T': A**T * X = B (Transpose) */
|
|
/* > = 'C': A**H * X = B (Conjugate transpose) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] 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 matrices B and X. NRHS >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] AB */
|
|
/* > \verbatim */
|
|
/* > AB is COMPLEX*16 array, dimension (LDAB,N) */
|
|
/* > The original band matrix A, stored in rows 1 to KL+KU+1. */
|
|
/* > The j-th column of A is stored in the j-th column of the */
|
|
/* > array AB as follows: */
|
|
/* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(n,j+kl). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array AB. LDAB >= KL+KU+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] AFB */
|
|
/* > \verbatim */
|
|
/* > AFB is COMPLEX*16 array, dimension (LDAFB,N) */
|
|
/* > Details of the LU factorization of the band matrix A, as */
|
|
/* > computed by ZGBTRF. U is stored as an upper triangular band */
|
|
/* > matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
|
|
/* > the multipliers used during the factorization are stored in */
|
|
/* > rows KL+KU+2 to 2*KL+KU+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAFB */
|
|
/* > \verbatim */
|
|
/* > LDAFB is INTEGER */
|
|
/* > The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (N) */
|
|
/* > The pivot indices from ZGBTRF; for 1<=i<=N, row i of the */
|
|
/* > matrix was interchanged with row IPIV(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX*16 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] X */
|
|
/* > \verbatim */
|
|
/* > X is COMPLEX*16 array, dimension (LDX,NRHS) */
|
|
/* > On entry, the solution matrix X, as computed by ZGBTRS. */
|
|
/* > On exit, the improved solution matrix X. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX */
|
|
/* > \verbatim */
|
|
/* > LDX is INTEGER */
|
|
/* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] FERR */
|
|
/* > \verbatim */
|
|
/* > FERR is DOUBLE PRECISION array, dimension (NRHS) */
|
|
/* > The estimated forward error bound for each solution vector */
|
|
/* > X(j) (the j-th column of the solution matrix X). */
|
|
/* > If XTRUE is the true solution corresponding to X(j), FERR(j) */
|
|
/* > is an estimated upper bound for the magnitude of the largest */
|
|
/* > element in (X(j) - XTRUE) divided by the magnitude of the */
|
|
/* > largest element in X(j). The estimate is as reliable as */
|
|
/* > the estimate for RCOND, and is almost always a slight */
|
|
/* > overestimate of the true error. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] BERR */
|
|
/* > \verbatim */
|
|
/* > BERR is DOUBLE PRECISION array, dimension (NRHS) */
|
|
/* > The componentwise relative backward error of each solution */
|
|
/* > vector X(j) (i.e., the smallest relative change in */
|
|
/* > any element of A or B that makes X(j) an exact solution). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* > \par Internal Parameters: */
|
|
/* ========================= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > ITMAX is the maximum number of steps of iterative refinement. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16GBcomputational */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zgbrfs_(char *trans, integer *n, integer *kl, integer *
|
|
ku, integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex *
|
|
afb, integer *ldafb, integer *ipiv, doublecomplex *b, integer *ldb,
|
|
doublecomplex *x, integer *ldx, doublereal *ferr, doublereal *berr,
|
|
doublecomplex *work, doublereal *rwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
|
|
x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
|
|
doublereal d__1, d__2, d__3, d__4;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
integer kase;
|
|
doublereal safe1, safe2;
|
|
integer i__, j, k;
|
|
doublereal s;
|
|
extern logical lsame_(char *, char *);
|
|
integer isave[3];
|
|
extern /* Subroutine */ void zgbmv_(char *, integer *, integer *, integer *
|
|
, integer *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *);
|
|
integer count;
|
|
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *), zlacn2_(
|
|
integer *, doublecomplex *, doublecomplex *, doublereal *,
|
|
integer *, integer *);
|
|
integer kk;
|
|
extern doublereal dlamch_(char *);
|
|
doublereal xk;
|
|
integer nz;
|
|
doublereal safmin;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
logical notran;
|
|
char transn[1], transt[1];
|
|
doublereal lstres;
|
|
extern /* Subroutine */ void zgbtrs_(char *, integer *, integer *, integer
|
|
*, integer *, doublecomplex *, integer *, integer *,
|
|
doublecomplex *, integer *, integer *);
|
|
doublereal eps;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
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;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
x_dim1 = *ldx;
|
|
x_offset = 1 + x_dim1 * 1;
|
|
x -= x_offset;
|
|
--ferr;
|
|
--berr;
|
|
--work;
|
|
--rwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
notran = lsame_(trans, "N");
|
|
if (! notran && ! lsame_(trans, "T") && ! lsame_(
|
|
trans, "C")) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*kl < 0) {
|
|
*info = -3;
|
|
} else if (*ku < 0) {
|
|
*info = -4;
|
|
} else if (*nrhs < 0) {
|
|
*info = -5;
|
|
} else if (*ldab < *kl + *ku + 1) {
|
|
*info = -7;
|
|
} else if (*ldafb < (*kl << 1) + *ku + 1) {
|
|
*info = -9;
|
|
} else if (*ldb < f2cmax(1,*n)) {
|
|
*info = -12;
|
|
} else if (*ldx < f2cmax(1,*n)) {
|
|
*info = -14;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZGBRFS", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0 || *nrhs == 0) {
|
|
i__1 = *nrhs;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
ferr[j] = 0.;
|
|
berr[j] = 0.;
|
|
/* L10: */
|
|
}
|
|
return;
|
|
}
|
|
|
|
if (notran) {
|
|
*(unsigned char *)transn = 'N';
|
|
*(unsigned char *)transt = 'C';
|
|
} else {
|
|
*(unsigned char *)transn = 'C';
|
|
*(unsigned char *)transt = 'N';
|
|
}
|
|
|
|
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
|
|
|
|
/* Computing MIN */
|
|
i__1 = *kl + *ku + 2, i__2 = *n + 1;
|
|
nz = f2cmin(i__1,i__2);
|
|
eps = dlamch_("Epsilon");
|
|
safmin = dlamch_("Safe minimum");
|
|
safe1 = nz * safmin;
|
|
safe2 = safe1 / eps;
|
|
|
|
/* Do for each right hand side */
|
|
|
|
i__1 = *nrhs;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
|
|
count = 1;
|
|
lstres = 3.;
|
|
L20:
|
|
|
|
/* Loop until stopping criterion is satisfied. */
|
|
|
|
/* Compute residual R = B - op(A) * X, */
|
|
/* where op(A) = A, A**T, or A**H, depending on TRANS. */
|
|
|
|
zcopy_(n, &b[j * b_dim1 + 1], &c__1, &work[1], &c__1);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgbmv_(trans, n, n, kl, ku, &z__1, &ab[ab_offset], ldab, &x[j *
|
|
x_dim1 + 1], &c__1, &c_b1, &work[1], &c__1);
|
|
|
|
/* Compute componentwise relative backward error from formula */
|
|
|
|
/* f2cmax(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) ) */
|
|
|
|
/* where abs(Z) is the componentwise absolute value of the matrix */
|
|
/* or vector Z. If the i-th component of the denominator is less */
|
|
/* than SAFE2, then SAFE1 is added to the i-th components of the */
|
|
/* numerator and denominator before dividing. */
|
|
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * b_dim1;
|
|
rwork[i__] = (d__1 = b[i__3].r, abs(d__1)) + (d__2 = d_imag(&b[
|
|
i__ + j * b_dim1]), abs(d__2));
|
|
/* L30: */
|
|
}
|
|
|
|
/* Compute abs(op(A))*abs(X) + abs(B). */
|
|
|
|
if (notran) {
|
|
i__2 = *n;
|
|
for (k = 1; k <= i__2; ++k) {
|
|
kk = *ku + 1 - k;
|
|
i__3 = k + j * x_dim1;
|
|
xk = (d__1 = x[i__3].r, abs(d__1)) + (d__2 = d_imag(&x[k + j *
|
|
x_dim1]), abs(d__2));
|
|
/* Computing MAX */
|
|
i__3 = 1, i__4 = k - *ku;
|
|
/* Computing MIN */
|
|
i__6 = *n, i__7 = k + *kl;
|
|
i__5 = f2cmin(i__6,i__7);
|
|
for (i__ = f2cmax(i__3,i__4); i__ <= i__5; ++i__) {
|
|
i__3 = kk + i__ + k * ab_dim1;
|
|
rwork[i__] += ((d__1 = ab[i__3].r, abs(d__1)) + (d__2 =
|
|
d_imag(&ab[kk + i__ + k * ab_dim1]), abs(d__2))) *
|
|
xk;
|
|
/* L40: */
|
|
}
|
|
/* L50: */
|
|
}
|
|
} else {
|
|
i__2 = *n;
|
|
for (k = 1; k <= i__2; ++k) {
|
|
s = 0.;
|
|
kk = *ku + 1 - k;
|
|
/* Computing MAX */
|
|
i__5 = 1, i__3 = k - *ku;
|
|
/* Computing MIN */
|
|
i__6 = *n, i__7 = k + *kl;
|
|
i__4 = f2cmin(i__6,i__7);
|
|
for (i__ = f2cmax(i__5,i__3); i__ <= i__4; ++i__) {
|
|
i__5 = kk + i__ + k * ab_dim1;
|
|
i__3 = i__ + j * x_dim1;
|
|
s += ((d__1 = ab[i__5].r, abs(d__1)) + (d__2 = d_imag(&ab[
|
|
kk + i__ + k * ab_dim1]), abs(d__2))) * ((d__3 =
|
|
x[i__3].r, abs(d__3)) + (d__4 = d_imag(&x[i__ + j
|
|
* x_dim1]), abs(d__4)));
|
|
/* L60: */
|
|
}
|
|
rwork[k] += s;
|
|
/* L70: */
|
|
}
|
|
}
|
|
s = 0.;
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
if (rwork[i__] > safe2) {
|
|
/* Computing MAX */
|
|
i__4 = i__;
|
|
d__3 = s, d__4 = ((d__1 = work[i__4].r, abs(d__1)) + (d__2 =
|
|
d_imag(&work[i__]), abs(d__2))) / rwork[i__];
|
|
s = f2cmax(d__3,d__4);
|
|
} else {
|
|
/* Computing MAX */
|
|
i__4 = i__;
|
|
d__3 = s, d__4 = ((d__1 = work[i__4].r, abs(d__1)) + (d__2 =
|
|
d_imag(&work[i__]), abs(d__2)) + safe1) / (rwork[i__]
|
|
+ safe1);
|
|
s = f2cmax(d__3,d__4);
|
|
}
|
|
/* L80: */
|
|
}
|
|
berr[j] = s;
|
|
|
|
/* Test stopping criterion. Continue iterating if */
|
|
/* 1) The residual BERR(J) is larger than machine epsilon, and */
|
|
/* 2) BERR(J) decreased by at least a factor of 2 during the */
|
|
/* last iteration, and */
|
|
/* 3) At most ITMAX iterations tried. */
|
|
|
|
if (berr[j] > eps && berr[j] * 2. <= lstres && count <= 5) {
|
|
|
|
/* Update solution and try again. */
|
|
|
|
zgbtrs_(trans, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &ipiv[1]
|
|
, &work[1], n, info);
|
|
zaxpy_(n, &c_b1, &work[1], &c__1, &x[j * x_dim1 + 1], &c__1);
|
|
lstres = berr[j];
|
|
++count;
|
|
goto L20;
|
|
}
|
|
|
|
/* Bound error from formula */
|
|
|
|
/* norm(X - XTRUE) / norm(X) .le. FERR = */
|
|
/* norm( abs(inv(op(A)))* */
|
|
/* ( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X) */
|
|
|
|
/* where */
|
|
/* norm(Z) is the magnitude of the largest component of Z */
|
|
/* inv(op(A)) is the inverse of op(A) */
|
|
/* abs(Z) is the componentwise absolute value of the matrix or */
|
|
/* vector Z */
|
|
/* NZ is the maximum number of nonzeros in any row of A, plus 1 */
|
|
/* EPS is machine epsilon */
|
|
|
|
/* The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B)) */
|
|
/* is incremented by SAFE1 if the i-th component of */
|
|
/* abs(op(A))*abs(X) + abs(B) is less than SAFE2. */
|
|
|
|
/* Use ZLACN2 to estimate the infinity-norm of the matrix */
|
|
/* inv(op(A)) * diag(W), */
|
|
/* where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
|
|
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
if (rwork[i__] > safe2) {
|
|
i__4 = i__;
|
|
rwork[i__] = (d__1 = work[i__4].r, abs(d__1)) + (d__2 =
|
|
d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
|
|
;
|
|
} else {
|
|
i__4 = i__;
|
|
rwork[i__] = (d__1 = work[i__4].r, abs(d__1)) + (d__2 =
|
|
d_imag(&work[i__]), abs(d__2)) + nz * eps * rwork[i__]
|
|
+ safe1;
|
|
}
|
|
/* L90: */
|
|
}
|
|
|
|
kase = 0;
|
|
L100:
|
|
zlacn2_(n, &work[*n + 1], &work[1], &ferr[j], &kase, isave);
|
|
if (kase != 0) {
|
|
if (kase == 1) {
|
|
|
|
/* Multiply by diag(W)*inv(op(A)**H). */
|
|
|
|
zgbtrs_(transt, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
|
|
ipiv[1], &work[1], n, info);
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__4 = i__;
|
|
i__5 = i__;
|
|
i__3 = i__;
|
|
z__1.r = rwork[i__5] * work[i__3].r, z__1.i = rwork[i__5]
|
|
* work[i__3].i;
|
|
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
|
|
/* L110: */
|
|
}
|
|
} else {
|
|
|
|
/* Multiply by inv(op(A))*diag(W). */
|
|
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__4 = i__;
|
|
i__5 = i__;
|
|
i__3 = i__;
|
|
z__1.r = rwork[i__5] * work[i__3].r, z__1.i = rwork[i__5]
|
|
* work[i__3].i;
|
|
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
|
|
/* L120: */
|
|
}
|
|
zgbtrs_(transn, n, kl, ku, &c__1, &afb[afb_offset], ldafb, &
|
|
ipiv[1], &work[1], n, info);
|
|
}
|
|
goto L100;
|
|
}
|
|
|
|
/* Normalize error. */
|
|
|
|
lstres = 0.;
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
/* Computing MAX */
|
|
i__4 = i__ + j * x_dim1;
|
|
d__3 = lstres, d__4 = (d__1 = x[i__4].r, abs(d__1)) + (d__2 =
|
|
d_imag(&x[i__ + j * x_dim1]), abs(d__2));
|
|
lstres = f2cmax(d__3,d__4);
|
|
/* L130: */
|
|
}
|
|
if (lstres != 0.) {
|
|
ferr[j] /= lstres;
|
|
}
|
|
|
|
/* L140: */
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZGBRFS */
|
|
|
|
} /* zgbrfs_ */
|
|
|