1421 lines
38 KiB
C
1421 lines
38 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static real c_b36 = .5f;
|
|
|
|
/* > \brief \b SLATBS solves a triangular banded system of equations. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SLATBS + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slatbs.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slatbs.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slatbs.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SLATBS( UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, */
|
|
/* SCALE, CNORM, INFO ) */
|
|
|
|
/* CHARACTER DIAG, NORMIN, TRANS, UPLO */
|
|
/* INTEGER INFO, KD, LDAB, N */
|
|
/* REAL SCALE */
|
|
/* REAL AB( LDAB, * ), CNORM( * ), X( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SLATBS solves one of the triangular systems */
|
|
/* > */
|
|
/* > A *x = s*b or A**T*x = s*b */
|
|
/* > */
|
|
/* > with scaling to prevent overflow, where A is an upper or lower */
|
|
/* > triangular band matrix. Here A**T denotes the transpose of A, x and b */
|
|
/* > are n-element vectors, and s is a scaling factor, usually less than */
|
|
/* > or equal to 1, chosen so that the components of x will be less than */
|
|
/* > the overflow threshold. If the unscaled problem will not cause */
|
|
/* > overflow, the Level 2 BLAS routine STBSV is called. If the matrix A */
|
|
/* > is singular (A(j,j) = 0 for some j), then s is set to 0 and a */
|
|
/* > non-trivial solution to A*x = 0 is returned. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > Specifies whether the matrix A is upper or lower triangular. */
|
|
/* > = 'U': Upper triangular */
|
|
/* > = 'L': Lower triangular */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TRANS */
|
|
/* > \verbatim */
|
|
/* > TRANS is CHARACTER*1 */
|
|
/* > Specifies the operation applied to A. */
|
|
/* > = 'N': Solve A * x = s*b (No transpose) */
|
|
/* > = 'T': Solve A**T* x = s*b (Transpose) */
|
|
/* > = 'C': Solve A**T* x = s*b (Conjugate transpose = Transpose) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] DIAG */
|
|
/* > \verbatim */
|
|
/* > DIAG is CHARACTER*1 */
|
|
/* > Specifies whether or not the matrix A is unit triangular. */
|
|
/* > = 'N': Non-unit triangular */
|
|
/* > = 'U': Unit triangular */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NORMIN */
|
|
/* > \verbatim */
|
|
/* > NORMIN is CHARACTER*1 */
|
|
/* > Specifies whether CNORM has been set or not. */
|
|
/* > = 'Y': CNORM contains the column norms on entry */
|
|
/* > = 'N': CNORM is not set on entry. On exit, the norms will */
|
|
/* > be computed and stored in CNORM. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The order of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KD */
|
|
/* > \verbatim */
|
|
/* > KD is INTEGER */
|
|
/* > The number of subdiagonals or superdiagonals in the */
|
|
/* > triangular matrix A. KD >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] AB */
|
|
/* > \verbatim */
|
|
/* > AB is REAL array, dimension (LDAB,N) */
|
|
/* > The upper or lower triangular band matrix A, stored in the */
|
|
/* > first KD+1 rows of the array. The j-th column of A is stored */
|
|
/* > in the j-th column of the array AB as follows: */
|
|
/* > if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for f2cmax(1,j-kd)<=i<=j; */
|
|
/* > if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=f2cmin(n,j+kd). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array AB. LDAB >= KD+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] X */
|
|
/* > \verbatim */
|
|
/* > X is REAL array, dimension (N) */
|
|
/* > On entry, the right hand side b of the triangular system. */
|
|
/* > On exit, X is overwritten by the solution vector x. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SCALE */
|
|
/* > \verbatim */
|
|
/* > SCALE is REAL */
|
|
/* > The scaling factor s for the triangular system */
|
|
/* > A * x = s*b or A**T* x = s*b. */
|
|
/* > If SCALE = 0, the matrix A is singular or badly scaled, and */
|
|
/* > the vector x is an exact or approximate solution to A*x = 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] CNORM */
|
|
/* > \verbatim */
|
|
/* > CNORM is REAL array, dimension (N) */
|
|
/* > */
|
|
/* > If NORMIN = 'Y', CNORM is an input argument and CNORM(j) */
|
|
/* > contains the norm of the off-diagonal part of the j-th column */
|
|
/* > of A. If TRANS = 'N', CNORM(j) must be greater than or equal */
|
|
/* > to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) */
|
|
/* > must be greater than or equal to the 1-norm. */
|
|
/* > */
|
|
/* > If NORMIN = 'N', CNORM is an output argument and CNORM(j) */
|
|
/* > returns the 1-norm of the offdiagonal part of the j-th column */
|
|
/* > of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -k, the k-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup realOTHERauxiliary */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > A rough bound on x is computed; if that is less than overflow, STBSV */
|
|
/* > is called, otherwise, specific code is used which checks for possible */
|
|
/* > overflow or divide-by-zero at every operation. */
|
|
/* > */
|
|
/* > A columnwise scheme is used for solving A*x = b. The basic algorithm */
|
|
/* > if A is lower triangular is */
|
|
/* > */
|
|
/* > x[1:n] := b[1:n] */
|
|
/* > for j = 1, ..., n */
|
|
/* > x(j) := x(j) / A(j,j) */
|
|
/* > x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] */
|
|
/* > end */
|
|
/* > */
|
|
/* > Define bounds on the components of x after j iterations of the loop: */
|
|
/* > M(j) = bound on x[1:j] */
|
|
/* > G(j) = bound on x[j+1:n] */
|
|
/* > Initially, let M(0) = 0 and G(0) = f2cmax{x(i), i=1,...,n}. */
|
|
/* > */
|
|
/* > Then for iteration j+1 we have */
|
|
/* > M(j+1) <= G(j) / | A(j+1,j+1) | */
|
|
/* > G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | */
|
|
/* > <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) */
|
|
/* > */
|
|
/* > where CNORM(j+1) is greater than or equal to the infinity-norm of */
|
|
/* > column j+1 of A, not counting the diagonal. Hence */
|
|
/* > */
|
|
/* > G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) */
|
|
/* > 1<=i<=j */
|
|
/* > and */
|
|
/* > */
|
|
/* > |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) */
|
|
/* > 1<=i< j */
|
|
/* > */
|
|
/* > Since |x(j)| <= M(j), we use the Level 2 BLAS routine STBSV if the */
|
|
/* > reciprocal of the largest M(j), j=1,..,n, is larger than */
|
|
/* > f2cmax(underflow, 1/overflow). */
|
|
/* > */
|
|
/* > The bound on x(j) is also used to determine when a step in the */
|
|
/* > columnwise method can be performed without fear of overflow. If */
|
|
/* > the computed bound is greater than a large constant, x is scaled to */
|
|
/* > prevent overflow, but if the bound overflows, x is set to 0, x(j) to */
|
|
/* > 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. */
|
|
/* > */
|
|
/* > Similarly, a row-wise scheme is used to solve A**T*x = b. The basic */
|
|
/* > algorithm for A upper triangular is */
|
|
/* > */
|
|
/* > for j = 1, ..., n */
|
|
/* > x(j) := ( b(j) - A[1:j-1,j]**T * x[1:j-1] ) / A(j,j) */
|
|
/* > end */
|
|
/* > */
|
|
/* > We simultaneously compute two bounds */
|
|
/* > G(j) = bound on ( b(i) - A[1:i-1,i]**T * x[1:i-1] ), 1<=i<=j */
|
|
/* > M(j) = bound on x(i), 1<=i<=j */
|
|
/* > */
|
|
/* > The initial values are G(0) = 0, M(0) = f2cmax{b(i), i=1,..,n}, and we */
|
|
/* > add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. */
|
|
/* > Then the bound on x(j) is */
|
|
/* > */
|
|
/* > M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | */
|
|
/* > */
|
|
/* > <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) */
|
|
/* > 1<=i<=j */
|
|
/* > */
|
|
/* > and we can safely call STBSV if 1/M(n) and 1/G(n) are both greater */
|
|
/* > than f2cmax(underflow, 1/overflow). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void slatbs_(char *uplo, char *trans, char *diag, char *
|
|
normin, integer *n, integer *kd, real *ab, integer *ldab, real *x,
|
|
real *scale, real *cnorm, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
|
|
real r__1, r__2, r__3;
|
|
|
|
/* Local variables */
|
|
integer jinc, jlen;
|
|
real xbnd;
|
|
integer imax;
|
|
real tmax, tjjs;
|
|
extern real sdot_(integer *, real *, integer *, real *, integer *);
|
|
real xmax, grow, sumj;
|
|
integer i__, j, maind;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
|
|
real tscal, uscal;
|
|
integer jlast;
|
|
extern real sasum_(integer *, real *, integer *);
|
|
logical upper;
|
|
extern /* Subroutine */ void stbsv_(char *, char *, char *, integer *,
|
|
integer *, real *, integer *, real *, integer *), saxpy_(integer *, real *, real *, integer *, real *,
|
|
integer *);
|
|
real xj;
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
real bignum;
|
|
extern integer isamax_(integer *, real *, integer *);
|
|
logical notran;
|
|
integer jfirst;
|
|
real smlnum;
|
|
logical nounit;
|
|
real rec, tjj;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
ab_dim1 = *ldab;
|
|
ab_offset = 1 + ab_dim1 * 1;
|
|
ab -= ab_offset;
|
|
--x;
|
|
--cnorm;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
upper = lsame_(uplo, "U");
|
|
notran = lsame_(trans, "N");
|
|
nounit = lsame_(diag, "N");
|
|
|
|
/* Test the input parameters. */
|
|
|
|
if (! upper && ! lsame_(uplo, "L")) {
|
|
*info = -1;
|
|
} else if (! notran && ! lsame_(trans, "T") && !
|
|
lsame_(trans, "C")) {
|
|
*info = -2;
|
|
} else if (! nounit && ! lsame_(diag, "U")) {
|
|
*info = -3;
|
|
} else if (! lsame_(normin, "Y") && ! lsame_(normin,
|
|
"N")) {
|
|
*info = -4;
|
|
} else if (*n < 0) {
|
|
*info = -5;
|
|
} else if (*kd < 0) {
|
|
*info = -6;
|
|
} else if (*ldab < *kd + 1) {
|
|
*info = -8;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SLATBS", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Determine machine dependent parameters to control overflow. */
|
|
|
|
smlnum = slamch_("Safe minimum") / slamch_("Precision");
|
|
bignum = 1.f / smlnum;
|
|
*scale = 1.f;
|
|
|
|
if (lsame_(normin, "N")) {
|
|
|
|
/* Compute the 1-norm of each column, not including the diagonal. */
|
|
|
|
if (upper) {
|
|
|
|
/* A is upper triangular. */
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
/* Computing MIN */
|
|
i__2 = *kd, i__3 = j - 1;
|
|
jlen = f2cmin(i__2,i__3);
|
|
cnorm[j] = sasum_(&jlen, &ab[*kd + 1 - jlen + j * ab_dim1], &
|
|
c__1);
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
|
|
/* A is lower triangular. */
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
/* Computing MIN */
|
|
i__2 = *kd, i__3 = *n - j;
|
|
jlen = f2cmin(i__2,i__3);
|
|
if (jlen > 0) {
|
|
cnorm[j] = sasum_(&jlen, &ab[j * ab_dim1 + 2], &c__1);
|
|
} else {
|
|
cnorm[j] = 0.f;
|
|
}
|
|
/* L20: */
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Scale the column norms by TSCAL if the maximum element in CNORM is */
|
|
/* greater than BIGNUM. */
|
|
|
|
imax = isamax_(n, &cnorm[1], &c__1);
|
|
tmax = cnorm[imax];
|
|
if (tmax <= bignum) {
|
|
tscal = 1.f;
|
|
} else {
|
|
tscal = 1.f / (smlnum * tmax);
|
|
sscal_(n, &tscal, &cnorm[1], &c__1);
|
|
}
|
|
|
|
/* Compute a bound on the computed solution vector to see if the */
|
|
/* Level 2 BLAS routine STBSV can be used. */
|
|
|
|
j = isamax_(n, &x[1], &c__1);
|
|
xmax = (r__1 = x[j], abs(r__1));
|
|
xbnd = xmax;
|
|
if (notran) {
|
|
|
|
/* Compute the growth in A * x = b. */
|
|
|
|
if (upper) {
|
|
jfirst = *n;
|
|
jlast = 1;
|
|
jinc = -1;
|
|
maind = *kd + 1;
|
|
} else {
|
|
jfirst = 1;
|
|
jlast = *n;
|
|
jinc = 1;
|
|
maind = 1;
|
|
}
|
|
|
|
if (tscal != 1.f) {
|
|
grow = 0.f;
|
|
goto L50;
|
|
}
|
|
|
|
if (nounit) {
|
|
|
|
/* A is non-unit triangular. */
|
|
|
|
/* Compute GROW = 1/G(j) and XBND = 1/M(j). */
|
|
/* Initially, G(0) = f2cmax{x(i), i=1,...,n}. */
|
|
|
|
grow = 1.f / f2cmax(xbnd,smlnum);
|
|
xbnd = grow;
|
|
i__1 = jlast;
|
|
i__2 = jinc;
|
|
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
|
|
|
|
/* Exit the loop if the growth factor is too small. */
|
|
|
|
if (grow <= smlnum) {
|
|
goto L50;
|
|
}
|
|
|
|
/* M(j) = G(j-1) / abs(A(j,j)) */
|
|
|
|
tjj = (r__1 = ab[maind + j * ab_dim1], abs(r__1));
|
|
/* Computing MIN */
|
|
r__1 = xbnd, r__2 = f2cmin(1.f,tjj) * grow;
|
|
xbnd = f2cmin(r__1,r__2);
|
|
if (tjj + cnorm[j] >= smlnum) {
|
|
|
|
/* G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) */
|
|
|
|
grow *= tjj / (tjj + cnorm[j]);
|
|
} else {
|
|
|
|
/* G(j) could overflow, set GROW to 0. */
|
|
|
|
grow = 0.f;
|
|
}
|
|
/* L30: */
|
|
}
|
|
grow = xbnd;
|
|
} else {
|
|
|
|
/* A is unit triangular. */
|
|
|
|
/* Compute GROW = 1/G(j), where G(0) = f2cmax{x(i), i=1,...,n}. */
|
|
|
|
/* Computing MIN */
|
|
r__1 = 1.f, r__2 = 1.f / f2cmax(xbnd,smlnum);
|
|
grow = f2cmin(r__1,r__2);
|
|
i__2 = jlast;
|
|
i__1 = jinc;
|
|
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
|
|
|
|
/* Exit the loop if the growth factor is too small. */
|
|
|
|
if (grow <= smlnum) {
|
|
goto L50;
|
|
}
|
|
|
|
/* G(j) = G(j-1)*( 1 + CNORM(j) ) */
|
|
|
|
grow *= 1.f / (cnorm[j] + 1.f);
|
|
/* L40: */
|
|
}
|
|
}
|
|
L50:
|
|
|
|
;
|
|
} else {
|
|
|
|
/* Compute the growth in A**T * x = b. */
|
|
|
|
if (upper) {
|
|
jfirst = 1;
|
|
jlast = *n;
|
|
jinc = 1;
|
|
maind = *kd + 1;
|
|
} else {
|
|
jfirst = *n;
|
|
jlast = 1;
|
|
jinc = -1;
|
|
maind = 1;
|
|
}
|
|
|
|
if (tscal != 1.f) {
|
|
grow = 0.f;
|
|
goto L80;
|
|
}
|
|
|
|
if (nounit) {
|
|
|
|
/* A is non-unit triangular. */
|
|
|
|
/* Compute GROW = 1/G(j) and XBND = 1/M(j). */
|
|
/* Initially, M(0) = f2cmax{x(i), i=1,...,n}. */
|
|
|
|
grow = 1.f / f2cmax(xbnd,smlnum);
|
|
xbnd = grow;
|
|
i__1 = jlast;
|
|
i__2 = jinc;
|
|
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
|
|
|
|
/* Exit the loop if the growth factor is too small. */
|
|
|
|
if (grow <= smlnum) {
|
|
goto L80;
|
|
}
|
|
|
|
/* G(j) = f2cmax( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) */
|
|
|
|
xj = cnorm[j] + 1.f;
|
|
/* Computing MIN */
|
|
r__1 = grow, r__2 = xbnd / xj;
|
|
grow = f2cmin(r__1,r__2);
|
|
|
|
/* M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) */
|
|
|
|
tjj = (r__1 = ab[maind + j * ab_dim1], abs(r__1));
|
|
if (xj > tjj) {
|
|
xbnd *= tjj / xj;
|
|
}
|
|
/* L60: */
|
|
}
|
|
grow = f2cmin(grow,xbnd);
|
|
} else {
|
|
|
|
/* A is unit triangular. */
|
|
|
|
/* Compute GROW = 1/G(j), where G(0) = f2cmax{x(i), i=1,...,n}. */
|
|
|
|
/* Computing MIN */
|
|
r__1 = 1.f, r__2 = 1.f / f2cmax(xbnd,smlnum);
|
|
grow = f2cmin(r__1,r__2);
|
|
i__2 = jlast;
|
|
i__1 = jinc;
|
|
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
|
|
|
|
/* Exit the loop if the growth factor is too small. */
|
|
|
|
if (grow <= smlnum) {
|
|
goto L80;
|
|
}
|
|
|
|
/* G(j) = ( 1 + CNORM(j) )*G(j-1) */
|
|
|
|
xj = cnorm[j] + 1.f;
|
|
grow /= xj;
|
|
/* L70: */
|
|
}
|
|
}
|
|
L80:
|
|
;
|
|
}
|
|
|
|
if (grow * tscal > smlnum) {
|
|
|
|
/* Use the Level 2 BLAS solve if the reciprocal of the bound on */
|
|
/* elements of X is not too small. */
|
|
|
|
stbsv_(uplo, trans, diag, n, kd, &ab[ab_offset], ldab, &x[1], &c__1);
|
|
} else {
|
|
|
|
/* Use a Level 1 BLAS solve, scaling intermediate results. */
|
|
|
|
if (xmax > bignum) {
|
|
|
|
/* Scale X so that its components are less than or equal to */
|
|
/* BIGNUM in absolute value. */
|
|
|
|
*scale = bignum / xmax;
|
|
sscal_(n, scale, &x[1], &c__1);
|
|
xmax = bignum;
|
|
}
|
|
|
|
if (notran) {
|
|
|
|
/* Solve A * x = b */
|
|
|
|
i__1 = jlast;
|
|
i__2 = jinc;
|
|
for (j = jfirst; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
|
|
|
|
/* Compute x(j) = b(j) / A(j,j), scaling x if necessary. */
|
|
|
|
xj = (r__1 = x[j], abs(r__1));
|
|
if (nounit) {
|
|
tjjs = ab[maind + j * ab_dim1] * tscal;
|
|
} else {
|
|
tjjs = tscal;
|
|
if (tscal == 1.f) {
|
|
goto L95;
|
|
}
|
|
}
|
|
tjj = abs(tjjs);
|
|
if (tjj > smlnum) {
|
|
|
|
/* abs(A(j,j)) > SMLNUM: */
|
|
|
|
if (tjj < 1.f) {
|
|
if (xj > tjj * bignum) {
|
|
|
|
/* Scale x by 1/b(j). */
|
|
|
|
rec = 1.f / xj;
|
|
sscal_(n, &rec, &x[1], &c__1);
|
|
*scale *= rec;
|
|
xmax *= rec;
|
|
}
|
|
}
|
|
x[j] /= tjjs;
|
|
xj = (r__1 = x[j], abs(r__1));
|
|
} else if (tjj > 0.f) {
|
|
|
|
/* 0 < abs(A(j,j)) <= SMLNUM: */
|
|
|
|
if (xj > tjj * bignum) {
|
|
|
|
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM */
|
|
/* to avoid overflow when dividing by A(j,j). */
|
|
|
|
rec = tjj * bignum / xj;
|
|
if (cnorm[j] > 1.f) {
|
|
|
|
/* Scale by 1/CNORM(j) to avoid overflow when */
|
|
/* multiplying x(j) times column j. */
|
|
|
|
rec /= cnorm[j];
|
|
}
|
|
sscal_(n, &rec, &x[1], &c__1);
|
|
*scale *= rec;
|
|
xmax *= rec;
|
|
}
|
|
x[j] /= tjjs;
|
|
xj = (r__1 = x[j], abs(r__1));
|
|
} else {
|
|
|
|
/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */
|
|
/* scale = 0, and compute a solution to A*x = 0. */
|
|
|
|
i__3 = *n;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
x[i__] = 0.f;
|
|
/* L90: */
|
|
}
|
|
x[j] = 1.f;
|
|
xj = 1.f;
|
|
*scale = 0.f;
|
|
xmax = 0.f;
|
|
}
|
|
L95:
|
|
|
|
/* Scale x if necessary to avoid overflow when adding a */
|
|
/* multiple of column j of A. */
|
|
|
|
if (xj > 1.f) {
|
|
rec = 1.f / xj;
|
|
if (cnorm[j] > (bignum - xmax) * rec) {
|
|
|
|
/* Scale x by 1/(2*abs(x(j))). */
|
|
|
|
rec *= .5f;
|
|
sscal_(n, &rec, &x[1], &c__1);
|
|
*scale *= rec;
|
|
}
|
|
} else if (xj * cnorm[j] > bignum - xmax) {
|
|
|
|
/* Scale x by 1/2. */
|
|
|
|
sscal_(n, &c_b36, &x[1], &c__1);
|
|
*scale *= .5f;
|
|
}
|
|
|
|
if (upper) {
|
|
if (j > 1) {
|
|
|
|
/* Compute the update */
|
|
/* x(f2cmax(1,j-kd):j-1) := x(f2cmax(1,j-kd):j-1) - */
|
|
/* x(j)* A(f2cmax(1,j-kd):j-1,j) */
|
|
|
|
/* Computing MIN */
|
|
i__3 = *kd, i__4 = j - 1;
|
|
jlen = f2cmin(i__3,i__4);
|
|
r__1 = -x[j] * tscal;
|
|
saxpy_(&jlen, &r__1, &ab[*kd + 1 - jlen + j * ab_dim1]
|
|
, &c__1, &x[j - jlen], &c__1);
|
|
i__3 = j - 1;
|
|
i__ = isamax_(&i__3, &x[1], &c__1);
|
|
xmax = (r__1 = x[i__], abs(r__1));
|
|
}
|
|
} else if (j < *n) {
|
|
|
|
/* Compute the update */
|
|
/* x(j+1:f2cmin(j+kd,n)) := x(j+1:f2cmin(j+kd,n)) - */
|
|
/* x(j) * A(j+1:f2cmin(j+kd,n),j) */
|
|
|
|
/* Computing MIN */
|
|
i__3 = *kd, i__4 = *n - j;
|
|
jlen = f2cmin(i__3,i__4);
|
|
if (jlen > 0) {
|
|
r__1 = -x[j] * tscal;
|
|
saxpy_(&jlen, &r__1, &ab[j * ab_dim1 + 2], &c__1, &x[
|
|
j + 1], &c__1);
|
|
}
|
|
i__3 = *n - j;
|
|
i__ = j + isamax_(&i__3, &x[j + 1], &c__1);
|
|
xmax = (r__1 = x[i__], abs(r__1));
|
|
}
|
|
/* L100: */
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Solve A**T * x = b */
|
|
|
|
i__2 = jlast;
|
|
i__1 = jinc;
|
|
for (j = jfirst; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
|
|
|
|
/* Compute x(j) = b(j) - sum A(k,j)*x(k). */
|
|
/* k<>j */
|
|
|
|
xj = (r__1 = x[j], abs(r__1));
|
|
uscal = tscal;
|
|
rec = 1.f / f2cmax(xmax,1.f);
|
|
if (cnorm[j] > (bignum - xj) * rec) {
|
|
|
|
/* If x(j) could overflow, scale x by 1/(2*XMAX). */
|
|
|
|
rec *= .5f;
|
|
if (nounit) {
|
|
tjjs = ab[maind + j * ab_dim1] * tscal;
|
|
} else {
|
|
tjjs = tscal;
|
|
}
|
|
tjj = abs(tjjs);
|
|
if (tjj > 1.f) {
|
|
|
|
/* Divide by A(j,j) when scaling x if A(j,j) > 1. */
|
|
|
|
/* Computing MIN */
|
|
r__1 = 1.f, r__2 = rec * tjj;
|
|
rec = f2cmin(r__1,r__2);
|
|
uscal /= tjjs;
|
|
}
|
|
if (rec < 1.f) {
|
|
sscal_(n, &rec, &x[1], &c__1);
|
|
*scale *= rec;
|
|
xmax *= rec;
|
|
}
|
|
}
|
|
|
|
sumj = 0.f;
|
|
if (uscal == 1.f) {
|
|
|
|
/* If the scaling needed for A in the dot product is 1, */
|
|
/* call SDOT to perform the dot product. */
|
|
|
|
if (upper) {
|
|
/* Computing MIN */
|
|
i__3 = *kd, i__4 = j - 1;
|
|
jlen = f2cmin(i__3,i__4);
|
|
sumj = sdot_(&jlen, &ab[*kd + 1 - jlen + j * ab_dim1],
|
|
&c__1, &x[j - jlen], &c__1);
|
|
} else {
|
|
/* Computing MIN */
|
|
i__3 = *kd, i__4 = *n - j;
|
|
jlen = f2cmin(i__3,i__4);
|
|
if (jlen > 0) {
|
|
sumj = sdot_(&jlen, &ab[j * ab_dim1 + 2], &c__1, &
|
|
x[j + 1], &c__1);
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* Otherwise, use in-line code for the dot product. */
|
|
|
|
if (upper) {
|
|
/* Computing MIN */
|
|
i__3 = *kd, i__4 = j - 1;
|
|
jlen = f2cmin(i__3,i__4);
|
|
i__3 = jlen;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
sumj += ab[*kd + i__ - jlen + j * ab_dim1] *
|
|
uscal * x[j - jlen - 1 + i__];
|
|
/* L110: */
|
|
}
|
|
} else {
|
|
/* Computing MIN */
|
|
i__3 = *kd, i__4 = *n - j;
|
|
jlen = f2cmin(i__3,i__4);
|
|
i__3 = jlen;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
sumj += ab[i__ + 1 + j * ab_dim1] * uscal * x[j +
|
|
i__];
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
|
|
|
|
if (uscal == tscal) {
|
|
|
|
/* Compute x(j) := ( x(j) - sumj ) / A(j,j) if 1/A(j,j) */
|
|
/* was not used to scale the dotproduct. */
|
|
|
|
x[j] -= sumj;
|
|
xj = (r__1 = x[j], abs(r__1));
|
|
if (nounit) {
|
|
|
|
/* Compute x(j) = x(j) / A(j,j), scaling if necessary. */
|
|
|
|
tjjs = ab[maind + j * ab_dim1] * tscal;
|
|
} else {
|
|
tjjs = tscal;
|
|
if (tscal == 1.f) {
|
|
goto L135;
|
|
}
|
|
}
|
|
tjj = abs(tjjs);
|
|
if (tjj > smlnum) {
|
|
|
|
/* abs(A(j,j)) > SMLNUM: */
|
|
|
|
if (tjj < 1.f) {
|
|
if (xj > tjj * bignum) {
|
|
|
|
/* Scale X by 1/abs(x(j)). */
|
|
|
|
rec = 1.f / xj;
|
|
sscal_(n, &rec, &x[1], &c__1);
|
|
*scale *= rec;
|
|
xmax *= rec;
|
|
}
|
|
}
|
|
x[j] /= tjjs;
|
|
} else if (tjj > 0.f) {
|
|
|
|
/* 0 < abs(A(j,j)) <= SMLNUM: */
|
|
|
|
if (xj > tjj * bignum) {
|
|
|
|
/* Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. */
|
|
|
|
rec = tjj * bignum / xj;
|
|
sscal_(n, &rec, &x[1], &c__1);
|
|
*scale *= rec;
|
|
xmax *= rec;
|
|
}
|
|
x[j] /= tjjs;
|
|
} else {
|
|
|
|
/* A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and */
|
|
/* scale = 0, and compute a solution to A**T*x = 0. */
|
|
|
|
i__3 = *n;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
x[i__] = 0.f;
|
|
/* L130: */
|
|
}
|
|
x[j] = 1.f;
|
|
*scale = 0.f;
|
|
xmax = 0.f;
|
|
}
|
|
L135:
|
|
;
|
|
} else {
|
|
|
|
/* Compute x(j) := x(j) / A(j,j) - sumj if the dot */
|
|
/* product has already been divided by 1/A(j,j). */
|
|
|
|
x[j] = x[j] / tjjs - sumj;
|
|
}
|
|
/* Computing MAX */
|
|
r__2 = xmax, r__3 = (r__1 = x[j], abs(r__1));
|
|
xmax = f2cmax(r__2,r__3);
|
|
/* L140: */
|
|
}
|
|
}
|
|
*scale /= tscal;
|
|
}
|
|
|
|
/* Scale the column norms by 1/TSCAL for return. */
|
|
|
|
if (tscal != 1.f) {
|
|
r__1 = 1.f / tscal;
|
|
sscal_(n, &r__1, &cnorm[1], &c__1);
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of SLATBS */
|
|
|
|
} /* slatbs_ */
|
|
|