1203 lines
40 KiB
C
1203 lines
40 KiB
C
/* f2c.h -- Standard Fortran to C header file */
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/** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
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- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
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#ifndef F2C_INCLUDE
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#define F2C_INCLUDE
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#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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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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#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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#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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#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) = conj(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) (cimag(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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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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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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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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_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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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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_Complex double 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 += conj(Cd(&x[i])) * Cd(&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 += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
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}
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}
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pCd(z) = zdotc;
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}
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static inline void cdotu_(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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_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 += 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 += 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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static inline void zdotu_(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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_Complex double 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 += Cd(&x[i]) * Cd(&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 += Cd(&x[i*incx]) * Cd(&y[i*incy]);
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}
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}
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pCd(z) = zdotc;
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}
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#endif
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/* -- translated by f2c (version 20000121).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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/* Table of constant values */
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static integer c_n1 = -1;
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static integer c__0 = 0;
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static integer c__1 = 1;
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/* > \brief \b DGBRFSX */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DGBRFSX + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbrfsx
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.f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgbrfsx
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.f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgbrfsx
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.f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DGBRFSX( TRANS, EQUED, N, KL, KU, NRHS, AB, LDAB, AFB, */
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/* LDAFB, IPIV, R, C, B, LDB, X, LDX, RCOND, */
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/* BERR, N_ERR_BNDS, ERR_BNDS_NORM, */
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/* ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, IWORK, */
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/* INFO ) */
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/* CHARACTER TRANS, EQUED */
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/* INTEGER INFO, LDAB, LDAFB, LDB, LDX, N, KL, KU, NRHS, */
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/* $ NPARAMS, N_ERR_BNDS */
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/* DOUBLE PRECISION RCOND */
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/* INTEGER IPIV( * ), IWORK( * ) */
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/* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */
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/* $ X( LDX , * ),WORK( * ) */
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/* DOUBLE PRECISION R( * ), C( * ), PARAMS( * ), BERR( * ), */
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/* $ ERR_BNDS_NORM( NRHS, * ), */
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/* $ ERR_BNDS_COMP( NRHS, * ) */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DGBRFSX improves the computed solution to a system of linear */
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/* > equations and provides error bounds and backward error estimates */
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/* > for the solution. In addition to normwise error bound, the code */
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/* > provides maximum componentwise error bound if possible. See */
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/* > comments for ERR_BNDS_NORM and ERR_BNDS_COMP for details of the */
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/* > error bounds. */
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/* > */
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/* > The original system of linear equations may have been equilibrated */
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/* > before calling this routine, as described by arguments EQUED, R */
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/* > and C below. In this case, the solution and error bounds returned */
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/* > are for the original unequilibrated system. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \verbatim */
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/* > Some optional parameters are bundled in the PARAMS array. These */
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/* > settings determine how refinement is performed, but often the */
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/* > defaults are acceptable. If the defaults are acceptable, users */
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/* > can pass NPARAMS = 0 which prevents the source code from accessing */
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/* > the PARAMS argument. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TRANS */
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/* > \verbatim */
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/* > TRANS is CHARACTER*1 */
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/* > Specifies the form of the system of equations: */
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/* > = 'N': A * X = B (No transpose) */
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/* > = 'T': A**T * X = B (Transpose) */
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/* > = 'C': A**H * X = B (Conjugate transpose = Transpose) */
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/* > \endverbatim */
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/* > */
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/* > \param[in] EQUED */
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/* > \verbatim */
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/* > EQUED is CHARACTER*1 */
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/* > Specifies the form of equilibration that was done to A */
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/* > before calling this routine. This is needed to compute */
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/* > the solution and error bounds correctly. */
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/* > = 'N': No equilibration */
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/* > = 'R': Row equilibration, i.e., A has been premultiplied by */
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/* > diag(R). */
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/* > = 'C': Column equilibration, i.e., A has been postmultiplied */
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/* > by diag(C). */
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/* > = 'B': Both row and column equilibration, i.e., A has been */
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/* > replaced by diag(R) * A * diag(C). */
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/* > The right hand side B has been changed accordingly. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The order of the matrix A. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] KL */
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/* > \verbatim */
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/* > KL is INTEGER */
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/* > The number of subdiagonals within the band of A. KL >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] KU */
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/* > \verbatim */
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/* > KU is INTEGER */
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/* > The number of superdiagonals within the band of A. KU >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] NRHS */
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/* > \verbatim */
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/* > NRHS is INTEGER */
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/* > The number of right hand sides, i.e., the number of columns */
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/* > of the matrices B and X. NRHS >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] AB */
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/* > \verbatim */
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/* > AB is DOUBLE PRECISION array, dimension (LDAB,N) */
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/* > The original band matrix A, stored in rows 1 to KL+KU+1. */
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/* > The j-th column of A is stored in the j-th column of the */
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/* > array AB as follows: */
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/* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(n,j+kl). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDAB */
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/* > \verbatim */
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/* > LDAB is INTEGER */
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/* > The leading dimension of the array AB. LDAB >= KL+KU+1. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] AFB */
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/* > \verbatim */
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/* > AFB is DOUBLE PRECISION array, dimension (LDAFB,N) */
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/* > Details of the LU factorization of the band matrix A, as */
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/* > computed by DGBTRF. U is stored as an upper triangular band */
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/* > matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
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/* > the multipliers used during the factorization are stored in */
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/* > rows KL+KU+2 to 2*KL+KU+1. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDAFB */
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/* > \verbatim */
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/* > LDAFB is INTEGER */
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/* > The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] IPIV */
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/* > \verbatim */
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/* > IPIV is INTEGER array, dimension (N) */
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/* > The pivot indices from DGETRF; for 1<=i<=N, row i of the */
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/* > matrix was interchanged with row IPIV(i). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] R */
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/* > \verbatim */
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/* > R is DOUBLE PRECISION array, dimension (N) */
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/* > The row scale factors for A. If EQUED = 'R' or 'B', A is */
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/* > multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
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/* > is not accessed. R is an input argument if FACT = 'F'; */
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/* > otherwise, R is an output argument. If FACT = 'F' and */
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/* > EQUED = 'R' or 'B', each element of R must be positive. */
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/* > If R is output, each element of R is a power of the radix. */
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/* > If R is input, each element of R should be a power of the radix */
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/* > to ensure a reliable solution and error estimates. Scaling by */
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/* > powers of the radix does not cause rounding errors unless the */
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/* > result underflows or overflows. Rounding errors during scaling */
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/* > lead to refining with a matrix that is not equivalent to the */
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/* > input matrix, producing error estimates that may not be */
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/* > reliable. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] C */
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/* > \verbatim */
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/* > C is DOUBLE PRECISION array, dimension (N) */
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/* > The column scale factors for A. If EQUED = 'C' or 'B', A is */
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/* > multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
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/* > is not accessed. C is an input argument if FACT = 'F'; */
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/* > otherwise, C is an output argument. If FACT = 'F' and */
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/* > EQUED = 'C' or 'B', each element of C must be positive. */
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/* > If C is output, each element of C is a power of the radix. */
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/* > If C is input, each element of C should be a power of the radix */
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/* > to ensure a reliable solution and error estimates. Scaling by */
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/* > powers of the radix does not cause rounding errors unless the */
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/* > result underflows or overflows. Rounding errors during scaling */
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/* > lead to refining with a matrix that is not equivalent to the */
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/* > input matrix, producing error estimates that may not be */
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/* > reliable. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] B */
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/* > \verbatim */
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/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
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/* > The right hand side matrix B. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDB */
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/* > \verbatim */
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/* > LDB is INTEGER */
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/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] X */
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/* > \verbatim */
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/* > X is DOUBLE PRECISION array, dimension (LDX,NRHS) */
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/* > On entry, the solution matrix X, as computed by DGETRS. */
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/* > On exit, the improved solution matrix X. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDX */
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/* > \verbatim */
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/* > LDX is INTEGER */
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/* > The leading dimension of the array X. LDX >= f2cmax(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] RCOND */
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/* > \verbatim */
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/* > RCOND is DOUBLE PRECISION */
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/* > Reciprocal scaled condition number. This is an estimate of the */
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/* > reciprocal Skeel condition number of the matrix A after */
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/* > equilibration (if done). If this is less than the machine */
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/* > precision (in particular, if it is zero), the matrix is singular */
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/* > to working precision. Note that the error may still be small even */
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/* > if this number is very small and the matrix appears ill- */
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/* > conditioned. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] BERR */
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/* > \verbatim */
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/* > BERR is DOUBLE PRECISION array, dimension (NRHS) */
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/* > Componentwise relative backward error. This is the */
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/* > componentwise relative backward error of each solution vector X(j) */
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/* > (i.e., the smallest relative change in any element of A or B that */
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/* > makes X(j) an exact solution). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N_ERR_BNDS */
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/* > \verbatim */
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/* > N_ERR_BNDS is INTEGER */
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/* > Number of error bounds to return for each right hand side */
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/* > and each type (normwise or componentwise). See ERR_BNDS_NORM and */
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/* > ERR_BNDS_COMP below. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] ERR_BNDS_NORM */
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/* > \verbatim */
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/* > ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
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/* > For each right-hand side, this array contains information about */
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/* > various error bounds and condition numbers corresponding to the */
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/* > normwise relative error, which is defined as follows: */
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/* > */
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/* > Normwise relative error in the ith solution vector: */
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/* > max_j (abs(XTRUE(j,i) - X(j,i))) */
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/* > ------------------------------ */
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/* > max_j abs(X(j,i)) */
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/* > */
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/* > The array is indexed by the type of error information as described */
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/* > below. There currently are up to three pieces of information */
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/* > returned. */
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/* > */
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/* > The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
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/* > right-hand side. */
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/* > */
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/* > The second index in ERR_BNDS_NORM(:,err) contains the following */
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/* > three fields: */
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/* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */
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/* > reciprocal condition number is less than the threshold */
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/* > sqrt(n) * dlamch('Epsilon'). */
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/* > */
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/* > err = 2 "Guaranteed" error bound: The estimated forward error, */
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/* > almost certainly within a factor of 10 of the true error */
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/* > so long as the next entry is greater than the threshold */
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/* > sqrt(n) * dlamch('Epsilon'). This error bound should only */
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/* > be trusted if the previous boolean is true. */
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/* > */
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/* > err = 3 Reciprocal condition number: Estimated normwise */
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/* > reciprocal condition number. Compared with the threshold */
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/* > sqrt(n) * dlamch('Epsilon') to determine if the error */
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/* > estimate is "guaranteed". These reciprocal condition */
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/* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
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/* > appropriately scaled matrix Z. */
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/* > Let Z = S*A, where S scales each row by a power of the */
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/* > radix so all absolute row sums of Z are approximately 1. */
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/* > */
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/* > See Lapack Working Note 165 for further details and extra */
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/* > cautions. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] ERR_BNDS_COMP */
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/* > \verbatim */
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/* > ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
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/* > For each right-hand side, this array contains information about */
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/* > various error bounds and condition numbers corresponding to the */
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/* > componentwise relative error, which is defined as follows: */
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/* > */
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/* > Componentwise relative error in the ith solution vector: */
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/* > abs(XTRUE(j,i) - X(j,i)) */
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/* > max_j ---------------------- */
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/* > abs(X(j,i)) */
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/* > */
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/* > The array is indexed by the right-hand side i (on which the */
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/* > componentwise relative error depends), and the type of error */
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/* > information as described below. There currently are up to three */
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/* > pieces of information returned for each right-hand side. If */
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/* > componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
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/* > ERR_BNDS_COMP is not accessed. If N_ERR_BNDS < 3, then at most */
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/* > the first (:,N_ERR_BNDS) entries are returned. */
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/* > */
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/* > The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
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/* > right-hand side. */
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/* > */
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/* > The second index in ERR_BNDS_COMP(:,err) contains the following */
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/* > three fields: */
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/* > err = 1 "Trust/don't trust" boolean. Trust the answer if the */
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/* > reciprocal condition number is less than the threshold */
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/* > sqrt(n) * dlamch('Epsilon'). */
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/* > */
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/* > err = 2 "Guaranteed" error bound: The estimated forward error, */
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/* > almost certainly within a factor of 10 of the true error */
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/* > so long as the next entry is greater than the threshold */
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/* > sqrt(n) * dlamch('Epsilon'). This error bound should only */
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/* > be trusted if the previous boolean is true. */
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/* > */
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/* > err = 3 Reciprocal condition number: Estimated componentwise */
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/* > reciprocal condition number. Compared with the threshold */
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/* > sqrt(n) * dlamch('Epsilon') to determine if the error */
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/* > estimate is "guaranteed". These reciprocal condition */
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/* > numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
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/* > appropriately scaled matrix Z. */
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/* > Let Z = S*(A*diag(x)), where x is the solution for the */
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/* > current right-hand side and S scales each row of */
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/* > A*diag(x) by a power of the radix so all absolute row */
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/* > sums of Z are approximately 1. */
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/* > */
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/* > See Lapack Working Note 165 for further details and extra */
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/* > cautions. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] NPARAMS */
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/* > \verbatim */
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/* > NPARAMS is INTEGER */
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/* > Specifies the number of parameters set in PARAMS. If <= 0, the */
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/* > PARAMS array is never referenced and default values are used. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] PARAMS */
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/* > \verbatim */
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/* > PARAMS is DOUBLE PRECISION array, dimension (NPARAMS) */
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/* > Specifies algorithm parameters. If an entry is < 0.0, then */
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/* > that entry will be filled with default value used for that */
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/* > parameter. Only positions up to NPARAMS are accessed; defaults */
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/* > are used for higher-numbered parameters. */
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/* > */
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/* > PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
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/* > refinement or not. */
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/* > Default: 1.0D+0 */
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/* > = 0.0: No refinement is performed, and no error bounds are */
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/* > computed. */
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/* > = 1.0: Use the double-precision refinement algorithm, */
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/* > possibly with doubled-single computations if the */
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/* > compilation environment does not support DOUBLE */
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/* > PRECISION. */
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/* > (other values are reserved for future use) */
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/* > */
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/* > PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
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/* > computations allowed for refinement. */
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/* > Default: 10 */
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/* > Aggressive: Set to 100 to permit convergence using approximate */
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/* > factorizations or factorizations other than LU. If */
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/* > the factorization uses a technique other than */
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/* > Gaussian elimination, the guarantees in */
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/* > err_bnds_norm and err_bnds_comp may no longer be */
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/* > trustworthy. */
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/* > */
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/* > PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
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/* > will attempt to find a solution with small componentwise */
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/* > relative error in the double-precision algorithm. Positive */
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/* > is true, 0.0 is false. */
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/* > Default: 1.0 (attempt componentwise convergence) */
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/* > \endverbatim */
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/* > */
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/* > \param[out] WORK */
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/* > \verbatim */
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/* > WORK is DOUBLE PRECISION array, dimension (4*N) */
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/* > \endverbatim */
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/* > */
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/* > \param[out] IWORK */
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/* > \verbatim */
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/* > IWORK is INTEGER array, dimension (N) */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: Successful exit. The solution to every right-hand side is */
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/* > guaranteed. */
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/* > < 0: If INFO = -i, the i-th argument had an illegal value */
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/* > > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
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/* > has been completed, but the factor U is exactly singular, so */
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/* > the solution and error bounds could not be computed. RCOND = 0 */
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/* > is returned. */
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/* > = N+J: The solution corresponding to the Jth right-hand side is */
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/* > not guaranteed. The solutions corresponding to other right- */
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/* > hand sides K with K > J may not be guaranteed as well, but */
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/* > only the first such right-hand side is reported. If a small */
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/* > componentwise error is not requested (PARAMS(3) = 0.0) then */
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/* > the Jth right-hand side is the first with a normwise error */
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/* > bound that is not guaranteed (the smallest J such */
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/* > that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
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/* > the Jth right-hand side is the first with either a normwise or */
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/* > componentwise error bound that is not guaranteed (the smallest */
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/* > J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
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/* > ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
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/* > ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
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/* > about all of the right-hand sides check ERR_BNDS_NORM or */
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/* > ERR_BNDS_COMP. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date April 2012 */
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/* > \ingroup doubleGBcomputational */
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/* ===================================================================== */
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/* Subroutine */ void dgbrfsx_(char *trans, char *equed, integer *n, integer *
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kl, integer *ku, integer *nrhs, doublereal *ab, integer *ldab,
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doublereal *afb, integer *ldafb, integer *ipiv, doublereal *r__,
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doublereal *c__, doublereal *b, integer *ldb, doublereal *x, integer *
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ldx, doublereal *rcond, doublereal *berr, integer *n_err_bnds__,
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doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer *
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nparams, doublereal *params, doublereal *work, integer *iwork,
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integer *info)
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{
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/* System generated locals */
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integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,
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x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
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err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
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doublereal d__1, d__2;
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/* Local variables */
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doublereal illrcond_thresh__, unstable_thresh__, err_lbnd__;
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char norm[1];
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integer ref_type__;
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extern integer ilatrans_(char *);
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logical ignore_cwise__;
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integer j;
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extern logical lsame_(char *, char *);
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doublereal anorm, rcond_tmp__;
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integer prec_type__;
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extern doublereal dlamch_(char *), dlangb_(char *, integer *,
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integer *, integer *, doublereal *, integer *, doublereal *);
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extern /* Subroutine */ void dgbcon_(char *, integer *, integer *, integer
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*, doublereal *, integer *, integer *, doublereal *, doublereal *,
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doublereal *, integer *, integer *);
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extern int xerbla_(char *, integer *, ftnlen);
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logical colequ, notran, rowequ;
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integer trans_type__;
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extern doublereal dla_gbrcond_(char *, integer *, integer *, integer *,
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doublereal *, integer *, doublereal *, integer *, integer *,
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integer *, doublereal *, integer *, doublereal *, integer *);
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extern integer ilaprec_(char *);
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integer ithresh, n_norms__;
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doublereal rthresh, cwise_wrong__;
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extern /* Subroutine */ void dla_gbrfsx_extended_(integer *, integer *,
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integer *, integer *, integer *, integer *, doublereal *, integer
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*, doublereal *, integer *, integer *, logical *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, integer *, doublereal *
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, doublereal *, logical *, integer *);
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/* -- LAPACK computational routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* April 2012 */
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/* ================================================================== */
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/* Check the input parameters. */
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/* Parameter adjustments */
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err_bnds_comp_dim1 = *nrhs;
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err_bnds_comp_offset = 1 + err_bnds_comp_dim1 * 1;
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err_bnds_comp__ -= err_bnds_comp_offset;
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err_bnds_norm_dim1 = *nrhs;
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err_bnds_norm_offset = 1 + err_bnds_norm_dim1 * 1;
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err_bnds_norm__ -= err_bnds_norm_offset;
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ab_dim1 = *ldab;
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ab_offset = 1 + ab_dim1 * 1;
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ab -= ab_offset;
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afb_dim1 = *ldafb;
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afb_offset = 1 + afb_dim1 * 1;
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afb -= afb_offset;
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--ipiv;
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--r__;
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--c__;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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b -= b_offset;
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x_dim1 = *ldx;
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x_offset = 1 + x_dim1 * 1;
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x -= x_offset;
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--berr;
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--params;
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--work;
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--iwork;
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/* Function Body */
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*info = 0;
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trans_type__ = ilatrans_(trans);
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ref_type__ = 1;
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if (*nparams >= 1) {
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if (params[1] < 0.) {
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params[1] = 1.;
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} else {
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ref_type__ = (integer) params[1];
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}
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}
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/* Set default parameters. */
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illrcond_thresh__ = (doublereal) (*n) * dlamch_("Epsilon");
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ithresh = 10;
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rthresh = .5;
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unstable_thresh__ = .25;
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ignore_cwise__ = FALSE_;
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if (*nparams >= 2) {
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if (params[2] < 0.) {
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params[2] = (doublereal) ithresh;
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} else {
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ithresh = (integer) params[2];
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}
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}
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if (*nparams >= 3) {
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if (params[3] < 0.) {
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if (ignore_cwise__) {
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params[3] = 0.;
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} else {
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params[3] = 1.;
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}
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} else {
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ignore_cwise__ = params[3] == 0.;
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}
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}
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if (ref_type__ == 0 || *n_err_bnds__ == 0) {
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n_norms__ = 0;
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} else if (ignore_cwise__) {
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n_norms__ = 1;
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} else {
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n_norms__ = 2;
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}
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notran = lsame_(trans, "N");
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rowequ = lsame_(equed, "R") || lsame_(equed, "B");
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colequ = lsame_(equed, "C") || lsame_(equed, "B");
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/* Test input parameters. */
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if (trans_type__ == -1) {
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*info = -1;
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} else if (! rowequ && ! colequ && ! lsame_(equed, "N")) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (*kl < 0) {
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*info = -4;
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} else if (*ku < 0) {
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*info = -5;
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} else if (*nrhs < 0) {
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*info = -6;
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} else if (*ldab < *kl + *ku + 1) {
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*info = -8;
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} else if (*ldafb < (*kl << 1) + *ku + 1) {
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*info = -10;
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} else if (*ldb < f2cmax(1,*n)) {
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*info = -13;
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} else if (*ldx < f2cmax(1,*n)) {
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*info = -15;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DGBRFSX", &i__1, (ftnlen)7);
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return;
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}
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/* Quick return if possible. */
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if (*n == 0 || *nrhs == 0) {
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*rcond = 1.;
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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berr[j] = 0.;
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if (*n_err_bnds__ >= 1) {
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err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
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err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
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}
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if (*n_err_bnds__ >= 2) {
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err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 0.;
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err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 0.;
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}
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if (*n_err_bnds__ >= 3) {
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err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 1.;
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err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 1.;
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}
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}
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return;
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}
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/* Default to failure. */
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*rcond = 0.;
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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berr[j] = 1.;
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if (*n_err_bnds__ >= 1) {
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err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
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err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
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}
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if (*n_err_bnds__ >= 2) {
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err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
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err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
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}
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if (*n_err_bnds__ >= 3) {
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err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = 0.;
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err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = 0.;
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}
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}
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/* Compute the norm of A and the reciprocal of the condition */
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/* number of A. */
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if (notran) {
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*(unsigned char *)norm = 'I';
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} else {
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*(unsigned char *)norm = '1';
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}
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anorm = dlangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &work[1]);
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dgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], &anorm, rcond,
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&work[1], &iwork[1], info);
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/* Perform refinement on each right-hand side */
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if (ref_type__ != 0 && *info == 0) {
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prec_type__ = ilaprec_("E");
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if (notran) {
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dla_gbrfsx_extended_(&prec_type__, &trans_type__, n, kl, ku,
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nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &
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ipiv[1], &colequ, &c__[1], &b[b_offset], ldb, &x[x_offset]
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, ldx, &berr[1], &n_norms__, &err_bnds_norm__[
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err_bnds_norm_offset], &err_bnds_comp__[
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err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n
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<< 1) + 1], &work[1], rcond, &ithresh, &rthresh, &
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unstable_thresh__, &ignore_cwise__, info);
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} else {
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dla_gbrfsx_extended_(&prec_type__, &trans_type__, n, kl, ku,
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nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &
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ipiv[1], &rowequ, &r__[1], &b[b_offset], ldb, &x[x_offset]
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, ldx, &berr[1], &n_norms__, &err_bnds_norm__[
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err_bnds_norm_offset], &err_bnds_comp__[
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err_bnds_comp_offset], &work[*n + 1], &work[1], &work[(*n
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<< 1) + 1], &work[1], rcond, &ithresh, &rthresh, &
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unstable_thresh__, &ignore_cwise__, info);
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}
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}
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/* Computing MAX */
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d__1 = 10., d__2 = sqrt((doublereal) (*n));
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err_lbnd__ = f2cmax(d__1,d__2) * dlamch_("Epsilon");
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if (*n_err_bnds__ >= 1 && n_norms__ >= 1) {
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/* Compute scaled normwise condition number cond(A*C). */
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if (colequ && notran) {
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rcond_tmp__ = dla_gbrcond_(trans, n, kl, ku, &ab[ab_offset],
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ldab, &afb[afb_offset], ldafb, &ipiv[1], &c_n1, &c__[1],
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info, &work[1], &iwork[1]);
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} else if (rowequ && ! notran) {
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rcond_tmp__ = dla_gbrcond_(trans, n, kl, ku, &ab[ab_offset],
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ldab, &afb[afb_offset], ldafb, &ipiv[1], &c_n1, &r__[1],
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info, &work[1], &iwork[1]);
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} else {
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rcond_tmp__ = dla_gbrcond_(trans, n, kl, ku, &ab[ab_offset],
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ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__0, &r__[1],
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info, &work[1], &iwork[1]);
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}
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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/* Cap the error at 1.0. */
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if (*n_err_bnds__ >= 2 && err_bnds_norm__[j + (err_bnds_norm_dim1
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<< 1)] > 1.) {
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err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
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}
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/* Threshold the error (see LAWN). */
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if (rcond_tmp__ < illrcond_thresh__) {
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err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = 1.;
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err_bnds_norm__[j + err_bnds_norm_dim1] = 0.;
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if (*info <= *n) {
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*info = *n + j;
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}
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} else if (err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] <
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err_lbnd__) {
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err_bnds_norm__[j + (err_bnds_norm_dim1 << 1)] = err_lbnd__;
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err_bnds_norm__[j + err_bnds_norm_dim1] = 1.;
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}
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/* Save the condition number. */
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if (*n_err_bnds__ >= 3) {
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err_bnds_norm__[j + err_bnds_norm_dim1 * 3] = rcond_tmp__;
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}
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}
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}
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if (*n_err_bnds__ >= 1 && n_norms__ >= 2) {
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/* Compute componentwise condition number cond(A*diag(Y(:,J))) for */
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/* each right-hand side using the current solution as an estimate of */
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/* the true solution. If the componentwise error estimate is too */
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/* large, then the solution is a lousy estimate of truth and the */
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/* estimated RCOND may be too optimistic. To avoid misleading users, */
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/* the inverse condition number is set to 0.0 when the estimated */
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/* cwise error is at least CWISE_WRONG. */
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cwise_wrong__ = sqrt(dlamch_("Epsilon"));
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i__1 = *nrhs;
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for (j = 1; j <= i__1; ++j) {
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if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
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cwise_wrong__) {
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rcond_tmp__ = dla_gbrcond_(trans, n, kl, ku, &ab[ab_offset],
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ldab, &afb[afb_offset], ldafb, &ipiv[1], &c__1, &x[j *
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x_dim1 + 1], info, &work[1], &iwork[1]);
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} else {
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rcond_tmp__ = 0.;
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}
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/* Cap the error at 1.0. */
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if (*n_err_bnds__ >= 2 && err_bnds_comp__[j + (err_bnds_comp_dim1
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<< 1)] > 1.) {
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err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
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}
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/* Threshold the error (see LAWN). */
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if (rcond_tmp__ < illrcond_thresh__) {
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err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = 1.;
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err_bnds_comp__[j + err_bnds_comp_dim1] = 0.;
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if (params[3] == 1. && *info < *n + j) {
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*info = *n + j;
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}
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} else if (err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] <
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err_lbnd__) {
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err_bnds_comp__[j + (err_bnds_comp_dim1 << 1)] = err_lbnd__;
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err_bnds_comp__[j + err_bnds_comp_dim1] = 1.;
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}
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/* Save the condition number. */
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if (*n_err_bnds__ >= 3) {
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err_bnds_comp__[j + err_bnds_comp_dim1 * 3] = rcond_tmp__;
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}
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}
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}
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return;
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/* End of DGBRFSX */
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} /* dgbrfsx_ */
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