1090 lines
32 KiB
C
1090 lines
32 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {0.,0.};
|
|
static doublecomplex c_b2 = {1.,0.};
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
static integer c__0 = 0;
|
|
static integer c__2 = 2;
|
|
|
|
/* > \brief <b> ZGELSY solves overdetermined or underdetermined systems for GE matrices</b> */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZGELSY + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgelsy.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgelsy.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgelsy.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, */
|
|
/* WORK, LWORK, RWORK, INFO ) */
|
|
|
|
/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */
|
|
/* DOUBLE PRECISION RCOND */
|
|
/* INTEGER JPVT( * ) */
|
|
/* DOUBLE PRECISION RWORK( * ) */
|
|
/* COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZGELSY computes the minimum-norm solution to a complex linear least */
|
|
/* > squares problem: */
|
|
/* > minimize || A * X - B || */
|
|
/* > using a complete orthogonal factorization of A. A is an M-by-N */
|
|
/* > matrix which may be rank-deficient. */
|
|
/* > */
|
|
/* > Several right hand side vectors b and solution vectors x can be */
|
|
/* > handled in a single call; they are stored as the columns of the */
|
|
/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
|
|
/* > matrix X. */
|
|
/* > */
|
|
/* > The routine first computes a QR factorization with column pivoting: */
|
|
/* > A * P = Q * [ R11 R12 ] */
|
|
/* > [ 0 R22 ] */
|
|
/* > with R11 defined as the largest leading submatrix whose estimated */
|
|
/* > condition number is less than 1/RCOND. The order of R11, RANK, */
|
|
/* > is the effective rank of A. */
|
|
/* > */
|
|
/* > Then, R22 is considered to be negligible, and R12 is annihilated */
|
|
/* > by unitary transformations from the right, arriving at the */
|
|
/* > complete orthogonal factorization: */
|
|
/* > A * P = Q * [ T11 0 ] * Z */
|
|
/* > [ 0 0 ] */
|
|
/* > The minimum-norm solution is then */
|
|
/* > X = P * Z**H [ inv(T11)*Q1**H*B ] */
|
|
/* > [ 0 ] */
|
|
/* > where Q1 consists of the first RANK columns of Q. */
|
|
/* > */
|
|
/* > This routine is basically identical to the original xGELSX except */
|
|
/* > three differences: */
|
|
/* > o The permutation of matrix B (the right hand side) is faster and */
|
|
/* > more simple. */
|
|
/* > o The call to the subroutine xGEQPF has been substituted by the */
|
|
/* > the call to the subroutine xGEQP3. This subroutine is a Blas-3 */
|
|
/* > version of the QR factorization with column pivoting. */
|
|
/* > o Matrix B (the right hand side) is updated with Blas-3. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NRHS */
|
|
/* > \verbatim */
|
|
/* > NRHS is INTEGER */
|
|
/* > The number of right hand sides, i.e., the number of */
|
|
/* > columns of matrices B and X. NRHS >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension (LDA,N) */
|
|
/* > On entry, the M-by-N matrix A. */
|
|
/* > On exit, A has been overwritten by details of its */
|
|
/* > complete orthogonal factorization. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. LDA >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX*16 array, dimension (LDB,NRHS) */
|
|
/* > On entry, the M-by-NRHS right hand side matrix B. */
|
|
/* > On exit, the N-by-NRHS solution matrix X. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of the array B. LDB >= f2cmax(1,M,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] JPVT */
|
|
/* > \verbatim */
|
|
/* > JPVT is INTEGER array, dimension (N) */
|
|
/* > On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted */
|
|
/* > to the front of AP, otherwise column i is a free column. */
|
|
/* > On exit, if JPVT(i) = k, then the i-th column of A*P */
|
|
/* > was the k-th column of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RCOND */
|
|
/* > \verbatim */
|
|
/* > RCOND is DOUBLE PRECISION */
|
|
/* > RCOND is used to determine the effective rank of A, which */
|
|
/* > is defined as the order of the largest leading triangular */
|
|
/* > submatrix R11 in the QR factorization with pivoting of A, */
|
|
/* > whose estimated condition number < 1/RCOND. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RANK */
|
|
/* > \verbatim */
|
|
/* > RANK is INTEGER */
|
|
/* > The effective rank of A, i.e., the order of the submatrix */
|
|
/* > R11. This is the same as the order of the submatrix T11 */
|
|
/* > in the complete orthogonal factorization of A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
|
|
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. */
|
|
/* > The unblocked strategy requires that: */
|
|
/* > LWORK >= MN + MAX( 2*MN, N+1, MN+NRHS ) */
|
|
/* > where MN = f2cmin(M,N). */
|
|
/* > The block algorithm requires that: */
|
|
/* > LWORK >= MN + MAX( 2*MN, NB*(N+1), MN+MN*NB, MN+NB*NRHS ) */
|
|
/* > where NB is an upper bound on the blocksize returned */
|
|
/* > by ILAENV for the routines ZGEQP3, ZTZRZF, CTZRQF, ZUNMQR, */
|
|
/* > and ZUNMRZ. */
|
|
/* > */
|
|
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
|
/* > only calculates the optimal size of the WORK array, returns */
|
|
/* > this value as the first entry of the WORK array, and no error */
|
|
/* > message related to LWORK is issued by XERBLA. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RWORK */
|
|
/* > \verbatim */
|
|
/* > RWORK is DOUBLE PRECISION array, dimension (2*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16GEsolve */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA \n */
|
|
/* > E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n */
|
|
/* > G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain \n */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void zgelsy_(integer *m, integer *n, integer *nrhs,
|
|
doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
|
|
integer *jpvt, doublereal *rcond, integer *rank, doublecomplex *work,
|
|
integer *lwork, doublereal *rwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
|
|
doublereal d__1, d__2;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
doublereal anrm, bnrm, smin, smax;
|
|
integer i__, j, iascl, ibscl, ismin, ismax;
|
|
doublecomplex c1, c2;
|
|
doublereal wsize;
|
|
doublecomplex s1, s2;
|
|
extern /* Subroutine */ void zcopy_(integer *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *), ztrsm_(char *, char *, char *, char *
|
|
, integer *, integer *, doublecomplex *, doublecomplex *, integer
|
|
*, doublecomplex *, integer *),
|
|
zlaic1_(integer *, integer *, doublecomplex *, doublereal *,
|
|
doublecomplex *, doublecomplex *, doublereal *, doublecomplex *,
|
|
doublecomplex *), dlabad_(doublereal *, doublereal *), zgeqp3_(
|
|
integer *, integer *, doublecomplex *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, integer *, doublereal *,
|
|
integer *);
|
|
integer nb;
|
|
extern doublereal dlamch_(char *);
|
|
integer mn;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
|
|
integer *, doublereal *);
|
|
doublereal bignum;
|
|
extern /* Subroutine */ void zlascl_(char *, integer *, integer *,
|
|
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
|
|
integer *, integer *);
|
|
integer nb1, nb2, nb3, nb4;
|
|
extern /* Subroutine */ void zlaset_(char *, integer *, integer *,
|
|
doublecomplex *, doublecomplex *, doublecomplex *, integer *);
|
|
doublereal sminpr, smaxpr, smlnum;
|
|
integer lwkopt;
|
|
logical lquery;
|
|
extern /* Subroutine */ void zunmqr_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, integer *, doublecomplex *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *, integer *), zunmrz_(char *, char *, integer *, integer *,
|
|
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
|
|
doublecomplex *, integer *, doublecomplex *, integer *, integer *
|
|
), ztzrzf_(integer *, integer *, doublecomplex *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *, integer *)
|
|
;
|
|
|
|
|
|
/* -- LAPACK driver routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
--jpvt;
|
|
--work;
|
|
--rwork;
|
|
|
|
/* Function Body */
|
|
mn = f2cmin(*m,*n);
|
|
ismin = mn + 1;
|
|
ismax = (mn << 1) + 1;
|
|
|
|
/* Test the input arguments. */
|
|
|
|
*info = 0;
|
|
nb1 = ilaenv_(&c__1, "ZGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
nb2 = ilaenv_(&c__1, "ZGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
|
|
ftnlen)1);
|
|
nb3 = ilaenv_(&c__1, "ZUNMQR", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)
|
|
1);
|
|
nb4 = ilaenv_(&c__1, "ZUNMRQ", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)
|
|
1);
|
|
/* Computing MAX */
|
|
i__1 = f2cmax(nb1,nb2), i__1 = f2cmax(i__1,nb3);
|
|
nb = f2cmax(i__1,nb4);
|
|
/* Computing MAX */
|
|
i__1 = 1, i__2 = mn + (*n << 1) + nb * (*n + 1), i__1 = f2cmax(i__1,i__2),
|
|
i__2 = (mn << 1) + nb * *nrhs;
|
|
lwkopt = f2cmax(i__1,i__2);
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
lquery = *lwork == -1;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*nrhs < 0) {
|
|
*info = -3;
|
|
} else if (*lda < f2cmax(1,*m)) {
|
|
*info = -5;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = f2cmax(1,*m);
|
|
if (*ldb < f2cmax(i__1,*n)) {
|
|
*info = -7;
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__1 = mn << 1, i__2 = *n + 1, i__1 = f2cmax(i__1,i__2), i__2 = mn +
|
|
*nrhs;
|
|
if (*lwork < mn + f2cmax(i__1,i__2) && ! lquery) {
|
|
*info = -12;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("ZGELSY", &i__1, (ftnlen)6);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
/* Computing MIN */
|
|
i__1 = f2cmin(*m,*n);
|
|
if (f2cmin(i__1,*nrhs) == 0) {
|
|
*rank = 0;
|
|
return;
|
|
}
|
|
|
|
/* Get machine parameters */
|
|
|
|
smlnum = dlamch_("S") / dlamch_("P");
|
|
bignum = 1. / smlnum;
|
|
dlabad_(&smlnum, &bignum);
|
|
|
|
/* Scale A, B if f2cmax entries outside range [SMLNUM,BIGNUM] */
|
|
|
|
anrm = zlange_("M", m, n, &a[a_offset], lda, &rwork[1]);
|
|
iascl = 0;
|
|
if (anrm > 0. && anrm < smlnum) {
|
|
|
|
/* Scale matrix norm up to SMLNUM */
|
|
|
|
zlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
|
|
info);
|
|
iascl = 1;
|
|
} else if (anrm > bignum) {
|
|
|
|
/* Scale matrix norm down to BIGNUM */
|
|
|
|
zlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
|
|
info);
|
|
iascl = 2;
|
|
} else if (anrm == 0.) {
|
|
|
|
/* Matrix all zero. Return zero solution. */
|
|
|
|
i__1 = f2cmax(*m,*n);
|
|
zlaset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
|
|
*rank = 0;
|
|
goto L70;
|
|
}
|
|
|
|
bnrm = zlange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1]);
|
|
ibscl = 0;
|
|
if (bnrm > 0. && bnrm < smlnum) {
|
|
|
|
/* Scale matrix norm up to SMLNUM */
|
|
|
|
zlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
ibscl = 1;
|
|
} else if (bnrm > bignum) {
|
|
|
|
/* Scale matrix norm down to BIGNUM */
|
|
|
|
zlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
ibscl = 2;
|
|
}
|
|
|
|
/* Compute QR factorization with column pivoting of A: */
|
|
/* A * P = Q * R */
|
|
|
|
i__1 = *lwork - mn;
|
|
zgeqp3_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &i__1,
|
|
&rwork[1], info);
|
|
i__1 = mn + 1;
|
|
wsize = mn + work[i__1].r;
|
|
|
|
/* complex workspace: MN+NB*(N+1). real workspace 2*N. */
|
|
/* Details of Householder rotations stored in WORK(1:MN). */
|
|
|
|
/* Determine RANK using incremental condition estimation */
|
|
|
|
i__1 = ismin;
|
|
work[i__1].r = 1., work[i__1].i = 0.;
|
|
i__1 = ismax;
|
|
work[i__1].r = 1., work[i__1].i = 0.;
|
|
smax = z_abs(&a[a_dim1 + 1]);
|
|
smin = smax;
|
|
if (z_abs(&a[a_dim1 + 1]) == 0.) {
|
|
*rank = 0;
|
|
i__1 = f2cmax(*m,*n);
|
|
zlaset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb);
|
|
goto L70;
|
|
} else {
|
|
*rank = 1;
|
|
}
|
|
|
|
L10:
|
|
if (*rank < mn) {
|
|
i__ = *rank + 1;
|
|
zlaic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
|
|
i__ + i__ * a_dim1], &sminpr, &s1, &c1);
|
|
zlaic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
|
|
i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
|
|
|
|
if (smaxpr * *rcond <= sminpr) {
|
|
i__1 = *rank;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = ismin + i__ - 1;
|
|
i__3 = ismin + i__ - 1;
|
|
z__1.r = s1.r * work[i__3].r - s1.i * work[i__3].i, z__1.i =
|
|
s1.r * work[i__3].i + s1.i * work[i__3].r;
|
|
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
|
|
i__2 = ismax + i__ - 1;
|
|
i__3 = ismax + i__ - 1;
|
|
z__1.r = s2.r * work[i__3].r - s2.i * work[i__3].i, z__1.i =
|
|
s2.r * work[i__3].i + s2.i * work[i__3].r;
|
|
work[i__2].r = z__1.r, work[i__2].i = z__1.i;
|
|
/* L20: */
|
|
}
|
|
i__1 = ismin + *rank;
|
|
work[i__1].r = c1.r, work[i__1].i = c1.i;
|
|
i__1 = ismax + *rank;
|
|
work[i__1].r = c2.r, work[i__1].i = c2.i;
|
|
smin = sminpr;
|
|
smax = smaxpr;
|
|
++(*rank);
|
|
goto L10;
|
|
}
|
|
}
|
|
|
|
/* complex workspace: 3*MN. */
|
|
|
|
/* Logically partition R = [ R11 R12 ] */
|
|
/* [ 0 R22 ] */
|
|
/* where R11 = R(1:RANK,1:RANK) */
|
|
|
|
/* [R11,R12] = [ T11, 0 ] * Y */
|
|
|
|
if (*rank < *n) {
|
|
i__1 = *lwork - (mn << 1);
|
|
ztzrzf_(rank, n, &a[a_offset], lda, &work[mn + 1], &work[(mn << 1) +
|
|
1], &i__1, info);
|
|
}
|
|
|
|
/* complex workspace: 2*MN. */
|
|
/* Details of Householder rotations stored in WORK(MN+1:2*MN) */
|
|
|
|
/* B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS) */
|
|
|
|
i__1 = *lwork - (mn << 1);
|
|
zunmqr_("Left", "Conjugate transpose", m, nrhs, &mn, &a[a_offset], lda, &
|
|
work[1], &b[b_offset], ldb, &work[(mn << 1) + 1], &i__1, info);
|
|
/* Computing MAX */
|
|
i__1 = (mn << 1) + 1;
|
|
d__1 = wsize, d__2 = (mn << 1) + work[i__1].r;
|
|
wsize = f2cmax(d__1,d__2);
|
|
|
|
/* complex workspace: 2*MN+NB*NRHS. */
|
|
|
|
/* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
|
|
|
|
ztrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b2, &a[
|
|
a_offset], lda, &b[b_offset], ldb);
|
|
|
|
i__1 = *nrhs;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = *rank + 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * b_dim1;
|
|
b[i__3].r = 0., b[i__3].i = 0.;
|
|
/* L30: */
|
|
}
|
|
/* L40: */
|
|
}
|
|
|
|
/* B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS) */
|
|
|
|
if (*rank < *n) {
|
|
i__1 = *n - *rank;
|
|
i__2 = *lwork - (mn << 1);
|
|
zunmrz_("Left", "Conjugate transpose", n, nrhs, rank, &i__1, &a[
|
|
a_offset], lda, &work[mn + 1], &b[b_offset], ldb, &work[(mn <<
|
|
1) + 1], &i__2, info);
|
|
}
|
|
|
|
/* complex workspace: 2*MN+NRHS. */
|
|
|
|
/* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
|
|
|
|
i__1 = *nrhs;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = jpvt[i__];
|
|
i__4 = i__ + j * b_dim1;
|
|
work[i__3].r = b[i__4].r, work[i__3].i = b[i__4].i;
|
|
/* L50: */
|
|
}
|
|
zcopy_(n, &work[1], &c__1, &b[j * b_dim1 + 1], &c__1);
|
|
/* L60: */
|
|
}
|
|
|
|
/* complex workspace: N. */
|
|
|
|
/* Undo scaling */
|
|
|
|
if (iascl == 1) {
|
|
zlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
zlascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset],
|
|
lda, info);
|
|
} else if (iascl == 2) {
|
|
zlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
zlascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset],
|
|
lda, info);
|
|
}
|
|
if (ibscl == 1) {
|
|
zlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
} else if (ibscl == 2) {
|
|
zlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
}
|
|
|
|
L70:
|
|
z__1.r = (doublereal) lwkopt, z__1.i = 0.;
|
|
work[1].r = z__1.r, work[1].i = z__1.i;
|
|
|
|
return;
|
|
|
|
/* End of ZGELSY */
|
|
|
|
} /* zgelsy_ */
|
|
|