1158 lines
35 KiB
C
1158 lines
35 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]/Cd(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)
|
|
*/
|
|
|
|
|
|
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
|
|
/* Subroutine */ int zlaqp3rk_(integer *m, integer *n, integer *nrhs, integer
|
|
*ioffset, integer *nb, doublereal *abstol, doublereal *reltol,
|
|
integer *kp1, doublereal *maxc2nrm, doublecomplex *a, integer *lda,
|
|
logical *done, integer *kb, doublereal *maxc2nrmk, doublereal *
|
|
relmaxc2nrmk, integer *jpiv, doublecomplex *tau, doublereal *vn1,
|
|
doublereal *vn2, doublecomplex *auxv, doublecomplex *f, integer *ldf,
|
|
integer *iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, f_dim1, f_offset, i__1, i__2, i__3;
|
|
doublereal d__1, d__2;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
doublereal temp, temp2;
|
|
integer i__, j, k;
|
|
doublereal tol3z;
|
|
integer itemp;
|
|
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *), zgemv_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *);
|
|
integer minmnfact;
|
|
extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *);
|
|
doublereal myhugeval;
|
|
integer minmnupdt;
|
|
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
|
|
integer if__;
|
|
extern doublereal dlamch_(char *);
|
|
integer kp;
|
|
extern integer idamax_(integer *, doublereal *, integer *);
|
|
extern logical disnan_(doublereal *);
|
|
integer lsticc;
|
|
extern /* Subroutine */ int zlarfg_(integer *, doublecomplex *,
|
|
doublecomplex *, integer *, doublecomplex *);
|
|
doublereal taunan;
|
|
doublecomplex aik;
|
|
|
|
|
|
/* -- LAPACK auxiliary routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Initialize INFO */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--jpiv;
|
|
--tau;
|
|
--vn1;
|
|
--vn2;
|
|
--auxv;
|
|
f_dim1 = *ldf;
|
|
f_offset = 1 + f_dim1 * 1;
|
|
f -= f_offset;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
/* MINMNFACT in the smallest dimension of the submatrix */
|
|
/* A(IOFFSET+1:M,1:N) to be factorized. */
|
|
|
|
/* Computing MIN */
|
|
i__1 = *m - *ioffset;
|
|
minmnfact = f2cmin(i__1,*n);
|
|
/* Computing MIN */
|
|
i__1 = *m - *ioffset, i__2 = *n + *nrhs;
|
|
minmnupdt = f2cmin(i__1,i__2);
|
|
*nb = f2cmin(*nb,minmnfact);
|
|
tol3z = sqrt(dlamch_("Epsilon"));
|
|
myhugeval = dlamch_("Overflow");
|
|
|
|
/* Compute factorization in a while loop over NB columns, */
|
|
/* K is the column index in the block A(1:M,1:N). */
|
|
|
|
k = 0;
|
|
lsticc = 0;
|
|
*done = FALSE_;
|
|
|
|
while(k < *nb && lsticc == 0) {
|
|
++k;
|
|
i__ = *ioffset + k;
|
|
|
|
if (i__ == 1) {
|
|
|
|
/* We are at the first column of the original whole matrix A_orig, */
|
|
/* therefore we use the computed KP1 and MAXC2NRM from the */
|
|
/* main routine. */
|
|
|
|
kp = *kp1;
|
|
|
|
} else {
|
|
|
|
/* Determine the pivot column in K-th step, i.e. the index */
|
|
/* of the column with the maximum 2-norm in the */
|
|
/* submatrix A(I:M,K:N). */
|
|
|
|
i__1 = *n - k + 1;
|
|
kp = k - 1 + idamax_(&i__1, &vn1[k], &c__1);
|
|
|
|
/* Determine the maximum column 2-norm and the relative maximum */
|
|
/* column 2-norm of the submatrix A(I:M,K:N) in step K. */
|
|
|
|
*maxc2nrmk = vn1[kp];
|
|
|
|
/* ============================================================ */
|
|
|
|
/* Check if the submatrix A(I:M,K:N) contains NaN, set */
|
|
/* INFO parameter to the column number, where the first NaN */
|
|
/* is found and return from the routine. */
|
|
/* We need to check the condition only if the */
|
|
/* column index (same as row index) of the original whole */
|
|
/* matrix is larger than 1, since the condition for whole */
|
|
/* original matrix is checked in the main routine. */
|
|
|
|
if (disnan_(maxc2nrmk)) {
|
|
|
|
*done = TRUE_;
|
|
|
|
/* Set KB, the number of factorized partial columns */
|
|
/* that are non-zero in each step in the block, */
|
|
/* i.e. the rank of the factor R. */
|
|
/* Set IF, the number of processed rows in the block, which */
|
|
/* is the same as the number of processed rows in */
|
|
/* the original whole matrix A_orig. */
|
|
|
|
*kb = k - 1;
|
|
if__ = i__ - 1;
|
|
*info = *kb + kp;
|
|
|
|
/* Set RELMAXC2NRMK to NaN. */
|
|
|
|
*relmaxc2nrmk = *maxc2nrmk;
|
|
|
|
/* There is no need to apply the block reflector to the */
|
|
/* residual of the matrix A stored in A(KB+1:M,KB+1:N), */
|
|
/* since the submatrix contains NaN and we stop */
|
|
/* the computation. */
|
|
/* But, we need to apply the block reflector to the residual */
|
|
/* right hand sides stored in A(KB+1:M,N+1:N+NRHS), if the */
|
|
/* residual right hand sides exist. This occurs */
|
|
/* when ( NRHS != 0 AND KB <= (M-IOFFSET) ): */
|
|
|
|
/* A(I+1:M,N+1:N+NRHS) := A(I+1:M,N+1:N+NRHS) - */
|
|
/* A(I+1:M,1:KB) * F(N+1:N+NRHS,1:KB)**H. */
|
|
if (*nrhs > 0 && *kb < *m - *ioffset) {
|
|
i__1 = *m - if__;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &i__1, nrhs,
|
|
kb, &z__1, &a[if__ + 1 + a_dim1], lda, &f[*n + 1
|
|
+ f_dim1], ldf, &c_b2, &a[if__ + 1 + (*n + 1) *
|
|
a_dim1], lda);
|
|
}
|
|
|
|
/* There is no need to recompute the 2-norm of the */
|
|
/* difficult columns, since we stop the factorization. */
|
|
|
|
/* Array TAU(KF+1:MINMNFACT) is not set and contains */
|
|
/* undefined elements. */
|
|
|
|
/* Return from the routine. */
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return, if the submatrix A(I:M,K:N) is */
|
|
/* a zero matrix. We need to check it only if the column index */
|
|
/* (same as row index) is larger than 1, since the condition */
|
|
/* for the whole original matrix A_orig is checked in the main */
|
|
/* routine. */
|
|
|
|
if (*maxc2nrmk == 0.) {
|
|
|
|
*done = TRUE_;
|
|
|
|
/* Set KB, the number of factorized partial columns */
|
|
/* that are non-zero in each step in the block, */
|
|
/* i.e. the rank of the factor R. */
|
|
/* Set IF, the number of processed rows in the block, which */
|
|
/* is the same as the number of processed rows in */
|
|
/* the original whole matrix A_orig. */
|
|
|
|
*kb = k - 1;
|
|
if__ = i__ - 1;
|
|
*relmaxc2nrmk = 0.;
|
|
|
|
/* There is no need to apply the block reflector to the */
|
|
/* residual of the matrix A stored in A(KB+1:M,KB+1:N), */
|
|
/* since the submatrix is zero and we stop the computation. */
|
|
/* But, we need to apply the block reflector to the residual */
|
|
/* right hand sides stored in A(KB+1:M,N+1:N+NRHS), if the */
|
|
/* residual right hand sides exist. This occurs */
|
|
/* when ( NRHS != 0 AND KB <= (M-IOFFSET) ): */
|
|
|
|
/* A(I+1:M,N+1:N+NRHS) := A(I+1:M,N+1:N+NRHS) - */
|
|
/* A(I+1:M,1:KB) * F(N+1:N+NRHS,1:KB)**H. */
|
|
|
|
if (*nrhs > 0 && *kb < *m - *ioffset) {
|
|
i__1 = *m - if__;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &i__1, nrhs,
|
|
kb, &z__1, &a[if__ + 1 + a_dim1], lda, &f[*n + 1
|
|
+ f_dim1], ldf, &c_b2, &a[if__ + 1 + (*n + 1) *
|
|
a_dim1], lda);
|
|
}
|
|
|
|
/* There is no need to recompute the 2-norm of the */
|
|
/* difficult columns, since we stop the factorization. */
|
|
|
|
/* Set TAUs corresponding to the columns that were not */
|
|
/* factorized to ZERO, i.e. set TAU(KB+1:MINMNFACT) = CZERO, */
|
|
/* which is equivalent to seting TAU(K:MINMNFACT) = CZERO. */
|
|
|
|
i__1 = minmnfact;
|
|
for (j = k; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
tau[i__2].r = 0., tau[i__2].i = 0.;
|
|
}
|
|
|
|
/* Return from the routine. */
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
/* ============================================================ */
|
|
|
|
/* Check if the submatrix A(I:M,K:N) contains Inf, */
|
|
/* set INFO parameter to the column number, where */
|
|
/* the first Inf is found plus N, and continue */
|
|
/* the computation. */
|
|
/* We need to check the condition only if the */
|
|
/* column index (same as row index) of the original whole */
|
|
/* matrix is larger than 1, since the condition for whole */
|
|
/* original matrix is checked in the main routine. */
|
|
|
|
if (*info == 0 && *maxc2nrmk > myhugeval) {
|
|
*info = *n + k - 1 + kp;
|
|
}
|
|
|
|
/* ============================================================ */
|
|
|
|
/* Test for the second and third tolerance stopping criteria. */
|
|
/* NOTE: There is no need to test for ABSTOL.GE.ZERO, since */
|
|
/* MAXC2NRMK is non-negative. Similarly, there is no need */
|
|
/* to test for RELTOL.GE.ZERO, since RELMAXC2NRMK is */
|
|
/* non-negative. */
|
|
/* We need to check the condition only if the */
|
|
/* column index (same as row index) of the original whole */
|
|
/* matrix is larger than 1, since the condition for whole */
|
|
/* original matrix is checked in the main routine. */
|
|
|
|
*relmaxc2nrmk = *maxc2nrmk / *maxc2nrm;
|
|
|
|
if (*maxc2nrmk <= *abstol || *relmaxc2nrmk <= *reltol) {
|
|
|
|
*done = TRUE_;
|
|
|
|
/* Set KB, the number of factorized partial columns */
|
|
/* that are non-zero in each step in the block, */
|
|
/* i.e. the rank of the factor R. */
|
|
/* Set IF, the number of processed rows in the block, which */
|
|
/* is the same as the number of processed rows in */
|
|
/* the original whole matrix A_orig; */
|
|
|
|
*kb = k - 1;
|
|
if__ = i__ - 1;
|
|
|
|
/* Apply the block reflector to the residual of the */
|
|
/* matrix A and the residual of the right hand sides B, if */
|
|
/* the residual matrix and and/or the residual of the right */
|
|
/* hand sides exist, i.e. if the submatrix */
|
|
/* A(I+1:M,KB+1:N+NRHS) exists. This occurs when */
|
|
/* KB < MINMNUPDT = f2cmin( M-IOFFSET, N+NRHS ): */
|
|
|
|
/* A(IF+1:M,K+1:N+NRHS) := A(IF+1:M,KB+1:N+NRHS) - */
|
|
/* A(IF+1:M,1:KB) * F(KB+1:N+NRHS,1:KB)**H. */
|
|
|
|
if (*kb < minmnupdt) {
|
|
i__1 = *m - if__;
|
|
i__2 = *n + *nrhs - *kb;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &i__1, &
|
|
i__2, kb, &z__1, &a[if__ + 1 + a_dim1], lda, &f[*
|
|
kb + 1 + f_dim1], ldf, &c_b2, &a[if__ + 1 + (*kb
|
|
+ 1) * a_dim1], lda);
|
|
}
|
|
|
|
/* There is no need to recompute the 2-norm of the */
|
|
/* difficult columns, since we stop the factorization. */
|
|
|
|
/* Set TAUs corresponding to the columns that were not */
|
|
/* factorized to ZERO, i.e. set TAU(KB+1:MINMNFACT) = CZERO, */
|
|
/* which is equivalent to seting TAU(K:MINMNFACT) = CZERO. */
|
|
|
|
i__1 = minmnfact;
|
|
for (j = k; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
tau[i__2].r = 0., tau[i__2].i = 0.;
|
|
}
|
|
|
|
/* Return from the routine. */
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
/* ============================================================ */
|
|
|
|
/* End ELSE of IF(I.EQ.1) */
|
|
|
|
}
|
|
|
|
/* =============================================================== */
|
|
|
|
/* If the pivot column is not the first column of the */
|
|
/* subblock A(1:M,K:N): */
|
|
/* 1) swap the K-th column and the KP-th pivot column */
|
|
/* in A(1:M,1:N); */
|
|
/* 2) swap the K-th row and the KP-th row in F(1:N,1:K-1) */
|
|
/* 3) copy the K-th element into the KP-th element of the partial */
|
|
/* and exact 2-norm vectors VN1 and VN2. (Swap is not needed */
|
|
/* for VN1 and VN2 since we use the element with the index */
|
|
/* larger than K in the next loop step.) */
|
|
/* 4) Save the pivot interchange with the indices relative to the */
|
|
/* the original matrix A_orig, not the block A(1:M,1:N). */
|
|
|
|
if (kp != k) {
|
|
zswap_(m, &a[kp * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
|
|
i__1 = k - 1;
|
|
zswap_(&i__1, &f[kp + f_dim1], ldf, &f[k + f_dim1], ldf);
|
|
vn1[kp] = vn1[k];
|
|
vn2[kp] = vn2[k];
|
|
itemp = jpiv[kp];
|
|
jpiv[kp] = jpiv[k];
|
|
jpiv[k] = itemp;
|
|
}
|
|
|
|
/* Apply previous Householder reflectors to column K: */
|
|
/* A(I:M,K) := A(I:M,K) - A(I:M,1:K-1)*F(K,1:K-1)**H. */
|
|
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = k + j * f_dim1;
|
|
d_cnjg(&z__1, &f[k + j * f_dim1]);
|
|
f[i__2].r = z__1.r, f[i__2].i = z__1.i;
|
|
}
|
|
i__1 = *m - i__ + 1;
|
|
i__2 = k - 1;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemv_("No transpose", &i__1, &i__2, &z__1, &a[i__ + a_dim1], lda,
|
|
&f[k + f_dim1], ldf, &c_b2, &a[i__ + k * a_dim1], &c__1);
|
|
i__1 = k - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = k + j * f_dim1;
|
|
d_cnjg(&z__1, &f[k + j * f_dim1]);
|
|
f[i__2].r = z__1.r, f[i__2].i = z__1.i;
|
|
}
|
|
}
|
|
|
|
/* Generate elementary reflector H(k) using the column A(I:M,K). */
|
|
|
|
if (i__ < *m) {
|
|
i__1 = *m - i__ + 1;
|
|
zlarfg_(&i__1, &a[i__ + k * a_dim1], &a[i__ + 1 + k * a_dim1], &
|
|
c__1, &tau[k]);
|
|
} else {
|
|
i__1 = k;
|
|
tau[i__1].r = 0., tau[i__1].i = 0.;
|
|
}
|
|
|
|
/* Check if TAU(K) contains NaN, set INFO parameter */
|
|
/* to the column number where NaN is found and return from */
|
|
/* the routine. */
|
|
/* NOTE: There is no need to check TAU(K) for Inf, */
|
|
/* since ZLARFG cannot produce TAU(KK) or Householder vector */
|
|
/* below the diagonal containing Inf. Only BETA on the diagonal, */
|
|
/* returned by ZLARFG can contain Inf, which requires */
|
|
/* TAU(K) to contain NaN. Therefore, this case of generating Inf */
|
|
/* by ZLARFG is covered by checking TAU(K) for NaN. */
|
|
|
|
i__1 = k;
|
|
d__1 = tau[i__1].r;
|
|
if (disnan_(&d__1)) {
|
|
i__1 = k;
|
|
taunan = tau[i__1].r;
|
|
} else /* if(complicated condition) */ {
|
|
d__1 = d_imag(&tau[k]);
|
|
if (disnan_(&d__1)) {
|
|
taunan = d_imag(&tau[k]);
|
|
} else {
|
|
taunan = 0.;
|
|
}
|
|
}
|
|
|
|
if (disnan_(&taunan)) {
|
|
|
|
*done = TRUE_;
|
|
|
|
/* Set KB, the number of factorized partial columns */
|
|
/* that are non-zero in each step in the block, */
|
|
/* i.e. the rank of the factor R. */
|
|
/* Set IF, the number of processed rows in the block, which */
|
|
/* is the same as the number of processed rows in */
|
|
/* the original whole matrix A_orig. */
|
|
|
|
*kb = k - 1;
|
|
if__ = i__ - 1;
|
|
*info = k;
|
|
|
|
/* Set MAXC2NRMK and RELMAXC2NRMK to NaN. */
|
|
|
|
*maxc2nrmk = taunan;
|
|
*relmaxc2nrmk = taunan;
|
|
|
|
/* There is no need to apply the block reflector to the */
|
|
/* residual of the matrix A stored in A(KB+1:M,KB+1:N), */
|
|
/* since the submatrix contains NaN and we stop */
|
|
/* the computation. */
|
|
/* But, we need to apply the block reflector to the residual */
|
|
/* right hand sides stored in A(KB+1:M,N+1:N+NRHS), if the */
|
|
/* residual right hand sides exist. This occurs */
|
|
/* when ( NRHS != 0 AND KB <= (M-IOFFSET) ): */
|
|
|
|
/* A(I+1:M,N+1:N+NRHS) := A(I+1:M,N+1:N+NRHS) - */
|
|
/* A(I+1:M,1:KB) * F(N+1:N+NRHS,1:KB)**H. */
|
|
|
|
if (*nrhs > 0 && *kb < *m - *ioffset) {
|
|
i__1 = *m - if__;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &i__1, nrhs, kb,
|
|
&z__1, &a[if__ + 1 + a_dim1], lda, &f[*n + 1 +
|
|
f_dim1], ldf, &c_b2, &a[if__ + 1 + (*n + 1) * a_dim1],
|
|
lda);
|
|
}
|
|
|
|
/* There is no need to recompute the 2-norm of the */
|
|
/* difficult columns, since we stop the factorization. */
|
|
|
|
/* Array TAU(KF+1:MINMNFACT) is not set and contains */
|
|
/* undefined elements. */
|
|
|
|
/* Return from the routine. */
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* =============================================================== */
|
|
|
|
i__1 = i__ + k * a_dim1;
|
|
aik.r = a[i__1].r, aik.i = a[i__1].i;
|
|
i__1 = i__ + k * a_dim1;
|
|
a[i__1].r = 1., a[i__1].i = 0.;
|
|
|
|
/* =============================================================== */
|
|
|
|
/* Compute the current K-th column of F: */
|
|
/* 1) F(K+1:N,K) := tau(K) * A(I:M,K+1:N)**H * A(I:M,K). */
|
|
|
|
if (k < *n + *nrhs) {
|
|
i__1 = *m - i__ + 1;
|
|
i__2 = *n + *nrhs - k;
|
|
zgemv_("Conjugate transpose", &i__1, &i__2, &tau[k], &a[i__ + (k
|
|
+ 1) * a_dim1], lda, &a[i__ + k * a_dim1], &c__1, &c_b1, &
|
|
f[k + 1 + k * f_dim1], &c__1);
|
|
}
|
|
|
|
/* 2) Zero out elements above and on the diagonal of the */
|
|
/* column K in matrix F, i.e elements F(1:K,K). */
|
|
|
|
i__1 = k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j + k * f_dim1;
|
|
f[i__2].r = 0., f[i__2].i = 0.;
|
|
}
|
|
|
|
/* 3) Incremental updating of the K-th column of F: */
|
|
/* F(1:N,K) := F(1:N,K) - tau(K) * F(1:N,1:K-1) * A(I:M,1:K-1)**H */
|
|
/* * A(I:M,K). */
|
|
|
|
if (k > 1) {
|
|
i__1 = *m - i__ + 1;
|
|
i__2 = k - 1;
|
|
i__3 = k;
|
|
z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
|
|
zgemv_("Conjugate Transpose", &i__1, &i__2, &z__1, &a[i__ +
|
|
a_dim1], lda, &a[i__ + k * a_dim1], &c__1, &c_b1, &auxv[1]
|
|
, &c__1);
|
|
|
|
i__1 = *n + *nrhs;
|
|
i__2 = k - 1;
|
|
zgemv_("No transpose", &i__1, &i__2, &c_b2, &f[f_dim1 + 1], ldf, &
|
|
auxv[1], &c__1, &c_b2, &f[k * f_dim1 + 1], &c__1);
|
|
}
|
|
|
|
/* =============================================================== */
|
|
|
|
/* Update the current I-th row of A: */
|
|
/* A(I,K+1:N+NRHS) := A(I,K+1:N+NRHS) */
|
|
/* - A(I,1:K)*F(K+1:N+NRHS,1:K)**H. */
|
|
|
|
if (k < *n + *nrhs) {
|
|
i__1 = *n + *nrhs - k;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &c__1, &i__1, &k, &
|
|
z__1, &a[i__ + a_dim1], lda, &f[k + 1 + f_dim1], ldf, &
|
|
c_b2, &a[i__ + (k + 1) * a_dim1], lda);
|
|
}
|
|
|
|
i__1 = i__ + k * a_dim1;
|
|
a[i__1].r = aik.r, a[i__1].i = aik.i;
|
|
|
|
/* Update the partial column 2-norms for the residual matrix, */
|
|
/* only if the residual matrix A(I+1:M,K+1:N) exists, i.e. */
|
|
/* when K < MINMNFACT = f2cmin( M-IOFFSET, N ). */
|
|
|
|
if (k < minmnfact) {
|
|
|
|
i__1 = *n;
|
|
for (j = k + 1; j <= i__1; ++j) {
|
|
if (vn1[j] != 0.) {
|
|
|
|
/* NOTE: The following lines follow from the analysis in */
|
|
/* Lapack Working Note 176. */
|
|
|
|
temp = z_abs(&a[i__ + j * a_dim1]) / vn1[j];
|
|
/* Computing MAX */
|
|
d__1 = 0., d__2 = (temp + 1.) * (1. - temp);
|
|
temp = f2cmax(d__1,d__2);
|
|
/* Computing 2nd power */
|
|
d__1 = vn1[j] / vn2[j];
|
|
temp2 = temp * (d__1 * d__1);
|
|
if (temp2 <= tol3z) {
|
|
|
|
/* At J-index, we have a difficult column for the */
|
|
/* update of the 2-norm. Save the index of the previous */
|
|
/* difficult column in IWORK(J-1). */
|
|
/* NOTE: ILSTCC > 1, threfore we can use IWORK only */
|
|
/* with N-1 elements, where the elements are */
|
|
/* shifted by 1 to the left. */
|
|
|
|
iwork[j - 1] = lsticc;
|
|
|
|
/* Set the index of the last difficult column LSTICC. */
|
|
|
|
lsticc = j;
|
|
|
|
} else {
|
|
vn1[j] *= sqrt(temp);
|
|
}
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
/* End of while loop. */
|
|
|
|
}
|
|
|
|
/* Now, afler the loop: */
|
|
/* Set KB, the number of factorized columns in the block; */
|
|
/* Set IF, the number of processed rows in the block, which */
|
|
/* is the same as the number of processed rows in */
|
|
/* the original whole matrix A_orig, IF = IOFFSET + KB. */
|
|
|
|
*kb = k;
|
|
if__ = i__;
|
|
|
|
/* Apply the block reflector to the residual of the matrix A */
|
|
/* and the residual of the right hand sides B, if the residual */
|
|
/* matrix and and/or the residual of the right hand sides */
|
|
/* exist, i.e. if the submatrix A(I+1:M,KB+1:N+NRHS) exists. */
|
|
/* This occurs when KB < MINMNUPDT = f2cmin( M-IOFFSET, N+NRHS ): */
|
|
|
|
/* A(IF+1:M,K+1:N+NRHS) := A(IF+1:M,KB+1:N+NRHS) - */
|
|
/* A(IF+1:M,1:KB) * F(KB+1:N+NRHS,1:KB)**H. */
|
|
|
|
if (*kb < minmnupdt) {
|
|
i__1 = *m - if__;
|
|
i__2 = *n + *nrhs - *kb;
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("No transpose", "Conjugate transpose", &i__1, &i__2, kb, &z__1,
|
|
&a[if__ + 1 + a_dim1], lda, &f[*kb + 1 + f_dim1], ldf, &c_b2,
|
|
&a[if__ + 1 + (*kb + 1) * a_dim1], lda);
|
|
}
|
|
|
|
/* Recompute the 2-norm of the difficult columns. */
|
|
/* Loop over the index of the difficult columns from the largest */
|
|
/* to the smallest index. */
|
|
|
|
while(lsticc > 0) {
|
|
|
|
/* LSTICC is the index of the last difficult column is greater */
|
|
/* than 1. */
|
|
/* ITEMP is the index of the previous difficult column. */
|
|
|
|
itemp = iwork[lsticc - 1];
|
|
|
|
/* Compute the 2-norm explicilty for the last difficult column and */
|
|
/* save it in the partial and exact 2-norm vectors VN1 and VN2. */
|
|
|
|
/* NOTE: The computation of VN1( LSTICC ) relies on the fact that */
|
|
/* DZNRM2 does not fail on vectors with norm below the value of */
|
|
/* SQRT(DLAMCH('S')) */
|
|
|
|
i__1 = *m - if__;
|
|
vn1[lsticc] = dznrm2_(&i__1, &a[if__ + 1 + lsticc * a_dim1], &c__1);
|
|
vn2[lsticc] = vn1[lsticc];
|
|
|
|
/* Downdate the index of the last difficult column to */
|
|
/* the index of the previous difficult column. */
|
|
|
|
lsticc = itemp;
|
|
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of ZLAQP3RK */
|
|
|
|
} /* zlaqp3rk_ */
|
|
|