1157 lines
32 KiB
C
1157 lines
32 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* > \brief \b DLALN2 solves a 1-by-1 or 2-by-2 linear system of equations of the specified form. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download DLALN2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaln2.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaln2.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaln2.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DLALN2( LTRANS, NA, NW, SMIN, CA, A, LDA, D1, D2, B, */
|
|
/* LDB, WR, WI, X, LDX, SCALE, XNORM, INFO ) */
|
|
|
|
/* LOGICAL LTRANS */
|
|
/* INTEGER INFO, LDA, LDB, LDX, NA, NW */
|
|
/* DOUBLE PRECISION CA, D1, D2, SCALE, SMIN, WI, WR, XNORM */
|
|
/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DLALN2 solves a system of the form (ca A - w D ) X = s B */
|
|
/* > or (ca A**T - w D) X = s B with possible scaling ("s") and */
|
|
/* > perturbation of A. (A**T means A-transpose.) */
|
|
/* > */
|
|
/* > A is an NA x NA real matrix, ca is a real scalar, D is an NA x NA */
|
|
/* > real diagonal matrix, w is a real or complex value, and X and B are */
|
|
/* > NA x 1 matrices -- real if w is real, complex if w is complex. NA */
|
|
/* > may be 1 or 2. */
|
|
/* > */
|
|
/* > If w is complex, X and B are represented as NA x 2 matrices, */
|
|
/* > the first column of each being the real part and the second */
|
|
/* > being the imaginary part. */
|
|
/* > */
|
|
/* > "s" is a scaling factor (<= 1), computed by DLALN2, which is */
|
|
/* > so chosen that X can be computed without overflow. X is further */
|
|
/* > scaled if necessary to assure that norm(ca A - w D)*norm(X) is less */
|
|
/* > than overflow. */
|
|
/* > */
|
|
/* > If both singular values of (ca A - w D) are less than SMIN, */
|
|
/* > SMIN*identity will be used instead of (ca A - w D). If only one */
|
|
/* > singular value is less than SMIN, one element of (ca A - w D) will be */
|
|
/* > perturbed enough to make the smallest singular value roughly SMIN. */
|
|
/* > If both singular values are at least SMIN, (ca A - w D) will not be */
|
|
/* > perturbed. In any case, the perturbation will be at most some small */
|
|
/* > multiple of f2cmax( SMIN, ulp*norm(ca A - w D) ). The singular values */
|
|
/* > are computed by infinity-norm approximations, and thus will only be */
|
|
/* > correct to a factor of 2 or so. */
|
|
/* > */
|
|
/* > Note: all input quantities are assumed to be smaller than overflow */
|
|
/* > by a reasonable factor. (See BIGNUM.) */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] LTRANS */
|
|
/* > \verbatim */
|
|
/* > LTRANS is LOGICAL */
|
|
/* > =.TRUE.: A-transpose will be used. */
|
|
/* > =.FALSE.: A will be used (not transposed.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NA */
|
|
/* > \verbatim */
|
|
/* > NA is INTEGER */
|
|
/* > The size of the matrix A. It may (only) be 1 or 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NW */
|
|
/* > \verbatim */
|
|
/* > NW is INTEGER */
|
|
/* > 1 if "w" is real, 2 if "w" is complex. It may only be 1 */
|
|
/* > or 2. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SMIN */
|
|
/* > \verbatim */
|
|
/* > SMIN is DOUBLE PRECISION */
|
|
/* > The desired lower bound on the singular values of A. This */
|
|
/* > should be a safe distance away from underflow or overflow, */
|
|
/* > say, between (underflow/machine precision) and (machine */
|
|
/* > precision * overflow ). (See BIGNUM and ULP.) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] CA */
|
|
/* > \verbatim */
|
|
/* > CA is DOUBLE PRECISION */
|
|
/* > The coefficient c, which A is multiplied by. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is DOUBLE PRECISION array, dimension (LDA,NA) */
|
|
/* > The NA x NA matrix A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of A. It must be at least NA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D1 */
|
|
/* > \verbatim */
|
|
/* > D1 is DOUBLE PRECISION */
|
|
/* > The 1,1 element in the diagonal matrix D. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] D2 */
|
|
/* > \verbatim */
|
|
/* > D2 is DOUBLE PRECISION */
|
|
/* > The 2,2 element in the diagonal matrix D. Not used if NA=1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] B */
|
|
/* > \verbatim */
|
|
/* > B is DOUBLE PRECISION array, dimension (LDB,NW) */
|
|
/* > The NA x NW matrix B (right-hand side). If NW=2 ("w" is */
|
|
/* > complex), column 1 contains the real part of B and column 2 */
|
|
/* > contains the imaginary part. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of B. It must be at least NA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WR */
|
|
/* > \verbatim */
|
|
/* > WR is DOUBLE PRECISION */
|
|
/* > The real part of the scalar "w". */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] WI */
|
|
/* > \verbatim */
|
|
/* > WI is DOUBLE PRECISION */
|
|
/* > The imaginary part of the scalar "w". Not used if NW=1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] X */
|
|
/* > \verbatim */
|
|
/* > X is DOUBLE PRECISION array, dimension (LDX,NW) */
|
|
/* > The NA x NW matrix X (unknowns), as computed by DLALN2. */
|
|
/* > If NW=2 ("w" is complex), on exit, column 1 will contain */
|
|
/* > the real part of X and column 2 will contain the imaginary */
|
|
/* > part. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDX */
|
|
/* > \verbatim */
|
|
/* > LDX is INTEGER */
|
|
/* > The leading dimension of X. It must be at least NA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] SCALE */
|
|
/* > \verbatim */
|
|
/* > SCALE is DOUBLE PRECISION */
|
|
/* > The scale factor that B must be multiplied by to insure */
|
|
/* > that overflow does not occur when computing X. Thus, */
|
|
/* > (ca A - w D) X will be SCALE*B, not B (ignoring */
|
|
/* > perturbations of A.) It will be at most 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] XNORM */
|
|
/* > \verbatim */
|
|
/* > XNORM is DOUBLE PRECISION */
|
|
/* > The infinity-norm of X, when X is regarded as an NA x NW */
|
|
/* > real matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > An error flag. It will be set to zero if no error occurs, */
|
|
/* > a negative number if an argument is in error, or a positive */
|
|
/* > number if ca A - w D had to be perturbed. */
|
|
/* > The possible values are: */
|
|
/* > = 0: No error occurred, and (ca A - w D) did not have to be */
|
|
/* > perturbed. */
|
|
/* > = 1: (ca A - w D) had to be perturbed to make its smallest */
|
|
/* > (or only) singular value greater than SMIN. */
|
|
/* > NOTE: In the interests of speed, this routine does not */
|
|
/* > check the inputs for errors. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup doubleOTHERauxiliary */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void dlaln2_(logical *ltrans, integer *na, integer *nw,
|
|
doublereal *smin, doublereal *ca, doublereal *a, integer *lda,
|
|
doublereal *d1, doublereal *d2, doublereal *b, integer *ldb,
|
|
doublereal *wr, doublereal *wi, doublereal *x, integer *ldx,
|
|
doublereal *scale, doublereal *xnorm, integer *info)
|
|
{
|
|
/* Initialized data */
|
|
|
|
static logical zswap[4] = { FALSE_,FALSE_,TRUE_,TRUE_ };
|
|
static logical rswap[4] = { FALSE_,TRUE_,FALSE_,TRUE_ };
|
|
static integer ipivot[16] /* was [4][4] */ = { 1,2,3,4,2,1,4,3,3,4,1,2,
|
|
4,3,2,1 };
|
|
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset;
|
|
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
|
|
static doublereal equiv_0[4], equiv_1[4];
|
|
|
|
/* Local variables */
|
|
doublereal bbnd, cmax, ui11r, ui12s, temp, ur11r, ur12s;
|
|
integer j;
|
|
doublereal u22abs;
|
|
integer icmax;
|
|
doublereal bnorm, cnorm, smini;
|
|
#define ci (equiv_0)
|
|
#define cr (equiv_1)
|
|
extern doublereal dlamch_(char *);
|
|
extern /* Subroutine */ void dladiv_(doublereal *, doublereal *,
|
|
doublereal *, doublereal *, doublereal *, doublereal *);
|
|
doublereal bignum, bi1, bi2, br1, br2, smlnum, xi1, xi2, xr1, xr2, ci21,
|
|
ci22, cr21, cr22, li21, csi, ui11, lr21, ui12, ui22;
|
|
#define civ (equiv_0)
|
|
doublereal csr, ur11, ur12, ur22;
|
|
#define crv (equiv_1)
|
|
|
|
|
|
/* -- 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 */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
x_dim1 = *ldx;
|
|
x_offset = 1 + x_dim1 * 1;
|
|
x -= x_offset;
|
|
|
|
/* Function Body */
|
|
|
|
/* Compute BIGNUM */
|
|
|
|
smlnum = 2. * dlamch_("Safe minimum");
|
|
bignum = 1. / smlnum;
|
|
smini = f2cmax(*smin,smlnum);
|
|
|
|
/* Don't check for input errors */
|
|
|
|
*info = 0;
|
|
|
|
/* Standard Initializations */
|
|
|
|
*scale = 1.;
|
|
|
|
if (*na == 1) {
|
|
|
|
/* 1 x 1 (i.e., scalar) system C X = B */
|
|
|
|
if (*nw == 1) {
|
|
|
|
/* Real 1x1 system. */
|
|
|
|
/* C = ca A - w D */
|
|
|
|
csr = *ca * a[a_dim1 + 1] - *wr * *d1;
|
|
cnorm = abs(csr);
|
|
|
|
/* If | C | < SMINI, use C = SMINI */
|
|
|
|
if (cnorm < smini) {
|
|
csr = smini;
|
|
cnorm = smini;
|
|
*info = 1;
|
|
}
|
|
|
|
/* Check scaling for X = B / C */
|
|
|
|
bnorm = (d__1 = b[b_dim1 + 1], abs(d__1));
|
|
if (cnorm < 1. && bnorm > 1.) {
|
|
if (bnorm > bignum * cnorm) {
|
|
*scale = 1. / bnorm;
|
|
}
|
|
}
|
|
|
|
/* Compute X */
|
|
|
|
x[x_dim1 + 1] = b[b_dim1 + 1] * *scale / csr;
|
|
*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1));
|
|
} else {
|
|
|
|
/* Complex 1x1 system (w is complex) */
|
|
|
|
/* C = ca A - w D */
|
|
|
|
csr = *ca * a[a_dim1 + 1] - *wr * *d1;
|
|
csi = -(*wi) * *d1;
|
|
cnorm = abs(csr) + abs(csi);
|
|
|
|
/* If | C | < SMINI, use C = SMINI */
|
|
|
|
if (cnorm < smini) {
|
|
csr = smini;
|
|
csi = 0.;
|
|
cnorm = smini;
|
|
*info = 1;
|
|
}
|
|
|
|
/* Check scaling for X = B / C */
|
|
|
|
bnorm = (d__1 = b[b_dim1 + 1], abs(d__1)) + (d__2 = b[(b_dim1 <<
|
|
1) + 1], abs(d__2));
|
|
if (cnorm < 1. && bnorm > 1.) {
|
|
if (bnorm > bignum * cnorm) {
|
|
*scale = 1. / bnorm;
|
|
}
|
|
}
|
|
|
|
/* Compute X */
|
|
|
|
d__1 = *scale * b[b_dim1 + 1];
|
|
d__2 = *scale * b[(b_dim1 << 1) + 1];
|
|
dladiv_(&d__1, &d__2, &csr, &csi, &x[x_dim1 + 1], &x[(x_dim1 << 1)
|
|
+ 1]);
|
|
*xnorm = (d__1 = x[x_dim1 + 1], abs(d__1)) + (d__2 = x[(x_dim1 <<
|
|
1) + 1], abs(d__2));
|
|
}
|
|
|
|
} else {
|
|
|
|
/* 2x2 System */
|
|
|
|
/* Compute the real part of C = ca A - w D (or ca A**T - w D ) */
|
|
|
|
cr[0] = *ca * a[a_dim1 + 1] - *wr * *d1;
|
|
cr[3] = *ca * a[(a_dim1 << 1) + 2] - *wr * *d2;
|
|
if (*ltrans) {
|
|
cr[2] = *ca * a[a_dim1 + 2];
|
|
cr[1] = *ca * a[(a_dim1 << 1) + 1];
|
|
} else {
|
|
cr[1] = *ca * a[a_dim1 + 2];
|
|
cr[2] = *ca * a[(a_dim1 << 1) + 1];
|
|
}
|
|
|
|
if (*nw == 1) {
|
|
|
|
/* Real 2x2 system (w is real) */
|
|
|
|
/* Find the largest element in C */
|
|
|
|
cmax = 0.;
|
|
icmax = 0;
|
|
|
|
for (j = 1; j <= 4; ++j) {
|
|
if ((d__1 = crv[j - 1], abs(d__1)) > cmax) {
|
|
cmax = (d__1 = crv[j - 1], abs(d__1));
|
|
icmax = j;
|
|
}
|
|
/* L10: */
|
|
}
|
|
|
|
/* If norm(C) < SMINI, use SMINI*identity. */
|
|
|
|
if (cmax < smini) {
|
|
/* Computing MAX */
|
|
d__3 = (d__1 = b[b_dim1 + 1], abs(d__1)), d__4 = (d__2 = b[
|
|
b_dim1 + 2], abs(d__2));
|
|
bnorm = f2cmax(d__3,d__4);
|
|
if (smini < 1. && bnorm > 1.) {
|
|
if (bnorm > bignum * smini) {
|
|
*scale = 1. / bnorm;
|
|
}
|
|
}
|
|
temp = *scale / smini;
|
|
x[x_dim1 + 1] = temp * b[b_dim1 + 1];
|
|
x[x_dim1 + 2] = temp * b[b_dim1 + 2];
|
|
*xnorm = temp * bnorm;
|
|
*info = 1;
|
|
return;
|
|
}
|
|
|
|
/* Gaussian elimination with complete pivoting. */
|
|
|
|
ur11 = crv[icmax - 1];
|
|
cr21 = crv[ipivot[(icmax << 2) - 3] - 1];
|
|
ur12 = crv[ipivot[(icmax << 2) - 2] - 1];
|
|
cr22 = crv[ipivot[(icmax << 2) - 1] - 1];
|
|
ur11r = 1. / ur11;
|
|
lr21 = ur11r * cr21;
|
|
ur22 = cr22 - ur12 * lr21;
|
|
|
|
/* If smaller pivot < SMINI, use SMINI */
|
|
|
|
if (abs(ur22) < smini) {
|
|
ur22 = smini;
|
|
*info = 1;
|
|
}
|
|
if (rswap[icmax - 1]) {
|
|
br1 = b[b_dim1 + 2];
|
|
br2 = b[b_dim1 + 1];
|
|
} else {
|
|
br1 = b[b_dim1 + 1];
|
|
br2 = b[b_dim1 + 2];
|
|
}
|
|
br2 -= lr21 * br1;
|
|
/* Computing MAX */
|
|
d__2 = (d__1 = br1 * (ur22 * ur11r), abs(d__1)), d__3 = abs(br2);
|
|
bbnd = f2cmax(d__2,d__3);
|
|
if (bbnd > 1. && abs(ur22) < 1.) {
|
|
if (bbnd >= bignum * abs(ur22)) {
|
|
*scale = 1. / bbnd;
|
|
}
|
|
}
|
|
|
|
xr2 = br2 * *scale / ur22;
|
|
xr1 = *scale * br1 * ur11r - xr2 * (ur11r * ur12);
|
|
if (zswap[icmax - 1]) {
|
|
x[x_dim1 + 1] = xr2;
|
|
x[x_dim1 + 2] = xr1;
|
|
} else {
|
|
x[x_dim1 + 1] = xr1;
|
|
x[x_dim1 + 2] = xr2;
|
|
}
|
|
/* Computing MAX */
|
|
d__1 = abs(xr1), d__2 = abs(xr2);
|
|
*xnorm = f2cmax(d__1,d__2);
|
|
|
|
/* Further scaling if norm(A) norm(X) > overflow */
|
|
|
|
if (*xnorm > 1. && cmax > 1.) {
|
|
if (*xnorm > bignum / cmax) {
|
|
temp = cmax / bignum;
|
|
x[x_dim1 + 1] = temp * x[x_dim1 + 1];
|
|
x[x_dim1 + 2] = temp * x[x_dim1 + 2];
|
|
*xnorm = temp * *xnorm;
|
|
*scale = temp * *scale;
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* Complex 2x2 system (w is complex) */
|
|
|
|
/* Find the largest element in C */
|
|
|
|
ci[0] = -(*wi) * *d1;
|
|
ci[1] = 0.;
|
|
ci[2] = 0.;
|
|
ci[3] = -(*wi) * *d2;
|
|
cmax = 0.;
|
|
icmax = 0;
|
|
|
|
for (j = 1; j <= 4; ++j) {
|
|
if ((d__1 = crv[j - 1], abs(d__1)) + (d__2 = civ[j - 1], abs(
|
|
d__2)) > cmax) {
|
|
cmax = (d__1 = crv[j - 1], abs(d__1)) + (d__2 = civ[j - 1]
|
|
, abs(d__2));
|
|
icmax = j;
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
/* If norm(C) < SMINI, use SMINI*identity. */
|
|
|
|
if (cmax < smini) {
|
|
/* Computing MAX */
|
|
d__5 = (d__1 = b[b_dim1 + 1], abs(d__1)) + (d__2 = b[(b_dim1
|
|
<< 1) + 1], abs(d__2)), d__6 = (d__3 = b[b_dim1 + 2],
|
|
abs(d__3)) + (d__4 = b[(b_dim1 << 1) + 2], abs(d__4));
|
|
bnorm = f2cmax(d__5,d__6);
|
|
if (smini < 1. && bnorm > 1.) {
|
|
if (bnorm > bignum * smini) {
|
|
*scale = 1. / bnorm;
|
|
}
|
|
}
|
|
temp = *scale / smini;
|
|
x[x_dim1 + 1] = temp * b[b_dim1 + 1];
|
|
x[x_dim1 + 2] = temp * b[b_dim1 + 2];
|
|
x[(x_dim1 << 1) + 1] = temp * b[(b_dim1 << 1) + 1];
|
|
x[(x_dim1 << 1) + 2] = temp * b[(b_dim1 << 1) + 2];
|
|
*xnorm = temp * bnorm;
|
|
*info = 1;
|
|
return;
|
|
}
|
|
|
|
/* Gaussian elimination with complete pivoting. */
|
|
|
|
ur11 = crv[icmax - 1];
|
|
ui11 = civ[icmax - 1];
|
|
cr21 = crv[ipivot[(icmax << 2) - 3] - 1];
|
|
ci21 = civ[ipivot[(icmax << 2) - 3] - 1];
|
|
ur12 = crv[ipivot[(icmax << 2) - 2] - 1];
|
|
ui12 = civ[ipivot[(icmax << 2) - 2] - 1];
|
|
cr22 = crv[ipivot[(icmax << 2) - 1] - 1];
|
|
ci22 = civ[ipivot[(icmax << 2) - 1] - 1];
|
|
if (icmax == 1 || icmax == 4) {
|
|
|
|
/* Code when off-diagonals of pivoted C are real */
|
|
|
|
if (abs(ur11) > abs(ui11)) {
|
|
temp = ui11 / ur11;
|
|
/* Computing 2nd power */
|
|
d__1 = temp;
|
|
ur11r = 1. / (ur11 * (d__1 * d__1 + 1.));
|
|
ui11r = -temp * ur11r;
|
|
} else {
|
|
temp = ur11 / ui11;
|
|
/* Computing 2nd power */
|
|
d__1 = temp;
|
|
ui11r = -1. / (ui11 * (d__1 * d__1 + 1.));
|
|
ur11r = -temp * ui11r;
|
|
}
|
|
lr21 = cr21 * ur11r;
|
|
li21 = cr21 * ui11r;
|
|
ur12s = ur12 * ur11r;
|
|
ui12s = ur12 * ui11r;
|
|
ur22 = cr22 - ur12 * lr21;
|
|
ui22 = ci22 - ur12 * li21;
|
|
} else {
|
|
|
|
/* Code when diagonals of pivoted C are real */
|
|
|
|
ur11r = 1. / ur11;
|
|
ui11r = 0.;
|
|
lr21 = cr21 * ur11r;
|
|
li21 = ci21 * ur11r;
|
|
ur12s = ur12 * ur11r;
|
|
ui12s = ui12 * ur11r;
|
|
ur22 = cr22 - ur12 * lr21 + ui12 * li21;
|
|
ui22 = -ur12 * li21 - ui12 * lr21;
|
|
}
|
|
u22abs = abs(ur22) + abs(ui22);
|
|
|
|
/* If smaller pivot < SMINI, use SMINI */
|
|
|
|
if (u22abs < smini) {
|
|
ur22 = smini;
|
|
ui22 = 0.;
|
|
*info = 1;
|
|
}
|
|
if (rswap[icmax - 1]) {
|
|
br2 = b[b_dim1 + 1];
|
|
br1 = b[b_dim1 + 2];
|
|
bi2 = b[(b_dim1 << 1) + 1];
|
|
bi1 = b[(b_dim1 << 1) + 2];
|
|
} else {
|
|
br1 = b[b_dim1 + 1];
|
|
br2 = b[b_dim1 + 2];
|
|
bi1 = b[(b_dim1 << 1) + 1];
|
|
bi2 = b[(b_dim1 << 1) + 2];
|
|
}
|
|
br2 = br2 - lr21 * br1 + li21 * bi1;
|
|
bi2 = bi2 - li21 * br1 - lr21 * bi1;
|
|
/* Computing MAX */
|
|
d__1 = (abs(br1) + abs(bi1)) * (u22abs * (abs(ur11r) + abs(ui11r))
|
|
), d__2 = abs(br2) + abs(bi2);
|
|
bbnd = f2cmax(d__1,d__2);
|
|
if (bbnd > 1. && u22abs < 1.) {
|
|
if (bbnd >= bignum * u22abs) {
|
|
*scale = 1. / bbnd;
|
|
br1 = *scale * br1;
|
|
bi1 = *scale * bi1;
|
|
br2 = *scale * br2;
|
|
bi2 = *scale * bi2;
|
|
}
|
|
}
|
|
|
|
dladiv_(&br2, &bi2, &ur22, &ui22, &xr2, &xi2);
|
|
xr1 = ur11r * br1 - ui11r * bi1 - ur12s * xr2 + ui12s * xi2;
|
|
xi1 = ui11r * br1 + ur11r * bi1 - ui12s * xr2 - ur12s * xi2;
|
|
if (zswap[icmax - 1]) {
|
|
x[x_dim1 + 1] = xr2;
|
|
x[x_dim1 + 2] = xr1;
|
|
x[(x_dim1 << 1) + 1] = xi2;
|
|
x[(x_dim1 << 1) + 2] = xi1;
|
|
} else {
|
|
x[x_dim1 + 1] = xr1;
|
|
x[x_dim1 + 2] = xr2;
|
|
x[(x_dim1 << 1) + 1] = xi1;
|
|
x[(x_dim1 << 1) + 2] = xi2;
|
|
}
|
|
/* Computing MAX */
|
|
d__1 = abs(xr1) + abs(xi1), d__2 = abs(xr2) + abs(xi2);
|
|
*xnorm = f2cmax(d__1,d__2);
|
|
|
|
/* Further scaling if norm(A) norm(X) > overflow */
|
|
|
|
if (*xnorm > 1. && cmax > 1.) {
|
|
if (*xnorm > bignum / cmax) {
|
|
temp = cmax / bignum;
|
|
x[x_dim1 + 1] = temp * x[x_dim1 + 1];
|
|
x[x_dim1 + 2] = temp * x[x_dim1 + 2];
|
|
x[(x_dim1 << 1) + 1] = temp * x[(x_dim1 << 1) + 1];
|
|
x[(x_dim1 << 1) + 2] = temp * x[(x_dim1 << 1) + 2];
|
|
*xnorm = temp * *xnorm;
|
|
*scale = temp * *scale;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of DLALN2 */
|
|
|
|
} /* dlaln2_ */
|
|
|
|
#undef crv
|
|
#undef civ
|
|
#undef cr
|
|
#undef ci
|
|
|
|
|