1075 lines
30 KiB
C
1075 lines
30 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef blasint logical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/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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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static integer c__3 = 3;
|
|
static integer c__2 = 2;
|
|
|
|
/* Subroutine */ int zgeqp3rk_(integer *m, integer *n, integer *nrhs, integer
|
|
*kmax, doublereal *abstol, doublereal *reltol, doublecomplex *a,
|
|
integer *lda, integer *k, doublereal *maxc2nrmk, doublereal *
|
|
relmaxc2nrmk, integer *jpiv, doublecomplex *tau, doublecomplex *work,
|
|
integer *lwork, doublereal *rwork, integer *iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2;
|
|
doublereal d__1, d__2;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
doublereal maxc2nrm;
|
|
logical done;
|
|
extern /* Subroutine */ int zlaqp2rk_(integer *, integer *, integer *,
|
|
integer *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, doublecomplex *, integer *, integer *, doublereal *,
|
|
doublereal *, integer *, doublecomplex *, doublereal *,
|
|
doublereal *, doublecomplex *, integer *), zlaqp3rk_(integer *,
|
|
integer *, integer *, integer *, integer *, doublereal *,
|
|
doublereal *, integer *, doublereal *, doublecomplex *, integer *,
|
|
logical *, integer *, doublereal *, doublereal *, integer *,
|
|
doublecomplex *, doublereal *, doublereal *, doublecomplex *,
|
|
doublecomplex *, integer *, integer *, integer *);
|
|
integer jmax, j, jmaxc2nrm, jmaxb, nbmin, iinfo, n_sub__, minmn;
|
|
doublereal myhugeval;
|
|
integer jb;
|
|
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
|
|
integer nb, kf;
|
|
extern doublereal dlamch_(char *);
|
|
extern integer idamax_(integer *, doublereal *, integer *);
|
|
integer nx;
|
|
doublereal safmin;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *);
|
|
extern logical disnan_(doublereal *);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
integer kp1, lwkopt;
|
|
logical lquery;
|
|
integer jbf;
|
|
doublereal eps;
|
|
integer iws, ioffset;
|
|
|
|
|
|
/* -- LAPACK computational routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test input arguments */
|
|
/* ==================== */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--jpiv;
|
|
--tau;
|
|
--work;
|
|
--rwork;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
lquery = *lwork == -1;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*nrhs < 0) {
|
|
*info = -3;
|
|
} else if (*kmax < 0) {
|
|
*info = -4;
|
|
} else if (disnan_(abstol)) {
|
|
*info = -5;
|
|
} else if (disnan_(reltol)) {
|
|
*info = -6;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -8;
|
|
}
|
|
|
|
/* If the input parameters M, N, NRHS, KMAX, LDA are valid: */
|
|
/* a) Test the input workspace size LWORK for the minimum */
|
|
/* size requirement IWS. */
|
|
/* b) Determine the optimal block size NB and optimal */
|
|
/* workspace size LWKOPT to be returned in WORK(1) */
|
|
/* in case of (1) LWORK < IWS, (2) LQUERY = .TRUE., */
|
|
/* (3) when routine exits. */
|
|
/* Here, IWS is the miminum workspace required for unblocked */
|
|
/* code. */
|
|
|
|
if (*info == 0) {
|
|
minmn = f2cmin(*m,*n);
|
|
if (minmn == 0) {
|
|
iws = 1;
|
|
lwkopt = 1;
|
|
} else {
|
|
|
|
/* Minimal workspace size in case of using only unblocked */
|
|
/* BLAS 2 code in ZLAQP2RK. */
|
|
/* 1) ZLAQP2RK: N+NRHS-1 to use in WORK array that is used */
|
|
/* in ZLARF subroutine inside ZLAQP2RK to apply an */
|
|
/* elementary reflector from the left. */
|
|
/* TOTAL_WORK_SIZE = 3*N + NRHS - 1 */
|
|
|
|
iws = *n + *nrhs - 1;
|
|
|
|
/* Assign to NB optimal block size. */
|
|
|
|
nb = ilaenv_(&c__1, "ZGEQP3RK", " ", m, n, &c_n1, &c_n1, (ftnlen)
|
|
8, (ftnlen)1);
|
|
|
|
/* A formula for the optimal workspace size in case of using */
|
|
/* both unblocked BLAS 2 in ZLAQP2RK and blocked BLAS 3 code */
|
|
/* in ZLAQP3RK. */
|
|
/* 1) ZGEQP3RK, ZLAQP2RK, ZLAQP3RK: 2*N to store full and */
|
|
/* partial column 2-norms. */
|
|
/* 2) ZLAQP2RK: N+NRHS-1 to use in WORK array that is used */
|
|
/* in ZLARF subroutine to apply an elementary reflector */
|
|
/* from the left. */
|
|
/* 3) ZLAQP3RK: NB*(N+NRHS) to use in the work array F that */
|
|
/* is used to apply a block reflector from */
|
|
/* the left. */
|
|
/* 4) ZLAQP3RK: NB to use in the auxilixary array AUX. */
|
|
/* Sizes (2) and ((3) + (4)) should intersect, therefore */
|
|
/* TOTAL_WORK_SIZE = 2*N + NB*( N+NRHS+1 ), given NBMIN=2. */
|
|
|
|
lwkopt = (*n << 1) + nb * (*n + *nrhs + 1);
|
|
}
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
|
|
if (*lwork < iws && ! lquery) {
|
|
*info = -15;
|
|
}
|
|
}
|
|
|
|
/* NOTE: The optimal workspace size is returned in WORK(1), if */
|
|
/* the input parameters M, N, NRHS, KMAX, LDA are valid. */
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZGEQP3RK", &i__1);
|
|
return 0;
|
|
} else if (lquery) {
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible for M=0 or N=0. */
|
|
|
|
if (minmn == 0) {
|
|
*k = 0;
|
|
*maxc2nrmk = 0.;
|
|
*relmaxc2nrmk = 0.;
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return 0;
|
|
}
|
|
|
|
/* ================================================================== */
|
|
|
|
/* Initialize column pivot array JPIV. */
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
jpiv[j] = j;
|
|
}
|
|
|
|
/* ================================================================== */
|
|
|
|
/* Initialize storage for partial and exact column 2-norms. */
|
|
/* a) The elements WORK(1:N) are used to store partial column */
|
|
/* 2-norms of the matrix A, and may decrease in each computation */
|
|
/* step; initialize to the values of complete columns 2-norms. */
|
|
/* b) The elements WORK(N+1:2*N) are used to store complete column */
|
|
/* 2-norms of the matrix A, they are not changed during the */
|
|
/* computation; initialize the values of complete columns 2-norms. */
|
|
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
rwork[j] = dznrm2_(m, &a[j * a_dim1 + 1], &c__1);
|
|
rwork[*n + j] = rwork[j];
|
|
}
|
|
|
|
/* ================================================================== */
|
|
|
|
/* Compute the pivot column index and the maximum column 2-norm */
|
|
/* for the whole original matrix stored in A(1:M,1:N). */
|
|
|
|
kp1 = idamax_(n, &rwork[1], &c__1);
|
|
|
|
/* ==================================================================. */
|
|
|
|
if (disnan_(&maxc2nrm)) {
|
|
|
|
/* Check if the matrix A contains NaN, set INFO parameter */
|
|
/* to the column number where the first NaN is found and return */
|
|
/* from the routine. */
|
|
|
|
*k = 0;
|
|
*info = kp1;
|
|
|
|
/* Set MAXC2NRMK and RELMAXC2NRMK to NaN. */
|
|
|
|
*maxc2nrmk = maxc2nrm;
|
|
*relmaxc2nrmk = maxc2nrm;
|
|
|
|
/* Array TAU is not set and contains undefined elements. */
|
|
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return 0;
|
|
}
|
|
|
|
/* =================================================================== */
|
|
|
|
if (maxc2nrm == 0.) {
|
|
|
|
/* Check is the matrix A is a zero matrix, set array TAU and */
|
|
/* return from the routine. */
|
|
|
|
*k = 0;
|
|
*maxc2nrmk = 0.;
|
|
*relmaxc2nrmk = 0.;
|
|
|
|
i__1 = minmn;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
tau[i__2].r = 0., tau[i__2].i = 0.;
|
|
}
|
|
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return 0;
|
|
|
|
}
|
|
|
|
/* =================================================================== */
|
|
|
|
myhugeval = dlamch_("Overflow");
|
|
|
|
if (maxc2nrm > myhugeval) {
|
|
|
|
/* Check if the matrix A contains +Inf or -Inf, set INFO parameter */
|
|
/* to the column number, where the first +/-Inf is found plus N, */
|
|
/* and continue the computation. */
|
|
|
|
*info = *n + kp1;
|
|
|
|
}
|
|
|
|
/* ================================================================== */
|
|
|
|
/* Quick return if possible for the case when the first */
|
|
/* stopping criterion is satisfied, i.e. KMAX = 0. */
|
|
|
|
if (*kmax == 0) {
|
|
*k = 0;
|
|
*maxc2nrmk = maxc2nrm;
|
|
*relmaxc2nrmk = 1.;
|
|
i__1 = minmn;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
tau[i__2].r = 0., tau[i__2].i = 0.;
|
|
}
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return 0;
|
|
}
|
|
|
|
/* ================================================================== */
|
|
|
|
eps = dlamch_("Epsilon");
|
|
|
|
/* Adjust ABSTOL */
|
|
|
|
if (*abstol >= 0.) {
|
|
safmin = dlamch_("Safe minimum");
|
|
/* Computing MAX */
|
|
d__1 = *abstol, d__2 = safmin * 2.;
|
|
*abstol = f2cmax(d__1,d__2);
|
|
}
|
|
|
|
/* Adjust RELTOL */
|
|
|
|
if (*reltol >= 0.) {
|
|
*reltol = f2cmax(*reltol,eps);
|
|
}
|
|
|
|
/* =================================================================== */
|
|
|
|
/* JMAX is the maximum index of the column to be factorized, */
|
|
/* which is also limited by the first stopping criterion KMAX. */
|
|
|
|
jmax = f2cmin(*kmax,minmn);
|
|
|
|
/* =================================================================== */
|
|
|
|
/* Quick return if possible for the case when the second or third */
|
|
/* stopping criterion for the whole original matrix is satified, */
|
|
/* i.e. MAXC2NRM <= ABSTOL or RELMAXC2NRM <= RELTOL */
|
|
/* (which is ONE <= RELTOL). */
|
|
|
|
if (maxc2nrm <= *abstol || 1. <= *reltol) {
|
|
|
|
*k = 0;
|
|
*maxc2nrmk = maxc2nrm;
|
|
*relmaxc2nrmk = 1.;
|
|
|
|
i__1 = minmn;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
tau[i__2].r = 0., tau[i__2].i = 0.;
|
|
}
|
|
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
return 0;
|
|
}
|
|
|
|
/* ================================================================== */
|
|
/* Factorize columns */
|
|
/* ================================================================== */
|
|
|
|
/* Determine the block size. */
|
|
|
|
nbmin = 2;
|
|
nx = 0;
|
|
|
|
if (nb > 1 && nb < minmn) {
|
|
|
|
/* Determine when to cross over from blocked to unblocked code. */
|
|
/* (for N less than NX, unblocked code should be used). */
|
|
|
|
/* Computing MAX */
|
|
i__1 = 0, i__2 = ilaenv_(&c__3, "ZGEQP3RK", " ", m, n, &c_n1, &c_n1, (
|
|
ftnlen)8, (ftnlen)1);
|
|
nx = f2cmax(i__1,i__2);
|
|
|
|
if (nx < minmn) {
|
|
|
|
/* Determine if workspace is large enough for blocked code. */
|
|
|
|
if (*lwork < lwkopt) {
|
|
|
|
/* Not enough workspace to use optimal block size that */
|
|
/* is currently stored in NB. */
|
|
/* Reduce NB and determine the minimum value of NB. */
|
|
|
|
nb = (*lwork - (*n << 1)) / (*n + 1);
|
|
/* Computing MAX */
|
|
i__1 = 2, i__2 = ilaenv_(&c__2, "ZGEQP3RK", " ", m, n, &c_n1,
|
|
&c_n1, (ftnlen)8, (ftnlen)1);
|
|
nbmin = f2cmax(i__1,i__2);
|
|
|
|
}
|
|
}
|
|
}
|
|
|
|
/* ================================================================== */
|
|
|
|
/* DONE is the boolean flag to rerpresent the case when the */
|
|
/* factorization completed in the block factorization routine, */
|
|
/* before the end of the block. */
|
|
|
|
done = FALSE_;
|
|
|
|
/* J is the column index. */
|
|
|
|
j = 1;
|
|
|
|
/* (1) Use blocked code initially. */
|
|
|
|
/* JMAXB is the maximum column index of the block, when the */
|
|
/* blocked code is used, is also limited by the first stopping */
|
|
/* criterion KMAX. */
|
|
|
|
/* Computing MIN */
|
|
i__1 = *kmax, i__2 = minmn - nx;
|
|
jmaxb = f2cmin(i__1,i__2);
|
|
|
|
if (nb >= nbmin && nb < jmax && jmaxb > 0) {
|
|
|
|
/* Loop over the column blocks of the matrix A(1:M,1:JMAXB). Here: */
|
|
/* J is the column index of a column block; */
|
|
/* JB is the column block size to pass to block factorization */
|
|
/* routine in a loop step; */
|
|
/* JBF is the number of columns that were actually factorized */
|
|
/* that was returned by the block factorization routine */
|
|
/* in a loop step, JBF <= JB; */
|
|
/* N_SUB is the number of columns in the submatrix; */
|
|
/* IOFFSET is the number of rows that should not be factorized. */
|
|
|
|
while(j <= jmaxb) {
|
|
|
|
/* Computing MIN */
|
|
i__1 = nb, i__2 = jmaxb - j + 1;
|
|
jb = f2cmin(i__1,i__2);
|
|
n_sub__ = *n - j + 1;
|
|
ioffset = j - 1;
|
|
|
|
/* Factorize JB columns among the columns A(J:N). */
|
|
|
|
i__1 = *n + *nrhs - j + 1;
|
|
zlaqp3rk_(m, &n_sub__, nrhs, &ioffset, &jb, abstol, reltol, &kp1,
|
|
&maxc2nrm, &a[j * a_dim1 + 1], lda, &done, &jbf,
|
|
maxc2nrmk, relmaxc2nrmk, &jpiv[j], &tau[j], &rwork[j], &
|
|
rwork[*n + j], &work[1], &work[jb + 1], &i__1, &iwork[1],
|
|
&iinfo);
|
|
|
|
/* Set INFO on the first occurence of Inf. */
|
|
|
|
if (iinfo > n_sub__ && *info == 0) {
|
|
*info = (ioffset << 1) + iinfo;
|
|
}
|
|
|
|
if (done) {
|
|
|
|
/* Either the submatrix is zero before the end of the */
|
|
/* column block, or ABSTOL or RELTOL criterion is */
|
|
/* satisfied before the end of the column block, we can */
|
|
/* return from the routine. Perform the following before */
|
|
/* returning: */
|
|
/* a) Set the number of factorized columns K, */
|
|
/* K = IOFFSET + JBF from the last call of blocked */
|
|
/* routine. */
|
|
/* NOTE: 1) MAXC2NRMK and RELMAXC2NRMK are returned */
|
|
/* by the block factorization routine; */
|
|
/* 2) The remaining TAUs are set to ZERO by the */
|
|
/* block factorization routine. */
|
|
|
|
*k = ioffset + jbf;
|
|
|
|
/* Set INFO on the first occurrence of NaN, NaN takes */
|
|
/* prcedence over Inf. */
|
|
|
|
if (iinfo <= n_sub__ && iinfo > 0) {
|
|
*info = ioffset + iinfo;
|
|
}
|
|
|
|
/* Return from the routine. */
|
|
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
j += jbf;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
/* Use unblocked code to factor the last or only block. */
|
|
/* J = JMAX+1 means we factorized the maximum possible number of */
|
|
/* columns, that is in ELSE clause we need to compute */
|
|
/* the MAXC2NORM and RELMAXC2NORM to return after we processed */
|
|
/* the blocks. */
|
|
|
|
if (j <= jmax) {
|
|
|
|
/* N_SUB is the number of columns in the submatrix; */
|
|
/* IOFFSET is the number of rows that should not be factorized. */
|
|
|
|
n_sub__ = *n - j + 1;
|
|
ioffset = j - 1;
|
|
|
|
i__1 = jmax - j + 1;
|
|
zlaqp2rk_(m, &n_sub__, nrhs, &ioffset, &i__1, abstol, reltol, &kp1, &
|
|
maxc2nrm, &a[j * a_dim1 + 1], lda, &kf, maxc2nrmk,
|
|
relmaxc2nrmk, &jpiv[j], &tau[j], &rwork[j], &rwork[*n + j], &
|
|
work[1], &iinfo);
|
|
|
|
/* ABSTOL or RELTOL criterion is satisfied when the number of */
|
|
/* the factorized columns KF is smaller then the number */
|
|
/* of columns JMAX-J+1 supplied to be factorized by the */
|
|
/* unblocked routine, we can return from */
|
|
/* the routine. Perform the following before returning: */
|
|
/* a) Set the number of factorized columns K, */
|
|
/* b) MAXC2NRMK and RELMAXC2NRMK are returned by the */
|
|
/* unblocked factorization routine above. */
|
|
|
|
*k = j - 1 + kf;
|
|
|
|
/* Set INFO on the first exception occurence. */
|
|
|
|
/* Set INFO on the first exception occurence of Inf or NaN, */
|
|
/* (NaN takes precedence over Inf). */
|
|
|
|
if (iinfo > n_sub__ && *info == 0) {
|
|
*info = (ioffset << 1) + iinfo;
|
|
} else if (iinfo <= n_sub__ && iinfo > 0) {
|
|
*info = ioffset + iinfo;
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Compute the return values for blocked code. */
|
|
|
|
/* Set the number of factorized columns if the unblocked routine */
|
|
/* was not called. */
|
|
|
|
*k = jmax;
|
|
|
|
/* If there exits a residual matrix after the blocked code: */
|
|
/* 1) compute the values of MAXC2NRMK, RELMAXC2NRMK of the */
|
|
/* residual matrix, otherwise set them to ZERO; */
|
|
/* 2) Set TAU(K+1:MINMN) to ZERO. */
|
|
|
|
if (*k < minmn) {
|
|
i__1 = *n - *k;
|
|
jmaxc2nrm = *k + idamax_(&i__1, &rwork[*k + 1], &c__1);
|
|
*maxc2nrmk = rwork[jmaxc2nrm];
|
|
if (*k == 0) {
|
|
*relmaxc2nrmk = 1.;
|
|
} else {
|
|
*relmaxc2nrmk = *maxc2nrmk / maxc2nrm;
|
|
}
|
|
|
|
i__1 = minmn;
|
|
for (j = *k + 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
tau[i__2].r = 0., tau[i__2].i = 0.;
|
|
}
|
|
|
|
} else {
|
|
*maxc2nrmk = 0.;
|
|
*relmaxc2nrmk = 0.;
|
|
|
|
}
|
|
|
|
/* END IF( J.LE.JMAX ) THEN */
|
|
|
|
}
|
|
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
|
|
return 0;
|
|
|
|
/* End of ZGEQP3RK */
|
|
|
|
} /* zgeqp3rk_ */
|
|
|