591 lines
18 KiB
C
591 lines
18 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]/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 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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#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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/* -- translated by f2c (version 20000121).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c_n1 = -1;
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/* > \brief \b SGGQRF */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download SGGQRF + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggqrf.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggqrf.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggqrf.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE SGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK, */
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/* LWORK, INFO ) */
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/* INTEGER INFO, LDA, LDB, LWORK, M, N, P */
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/* REAL A( LDA, * ), B( LDB, * ), TAUA( * ), TAUB( * ), */
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/* $ WORK( * ) */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > SGGQRF computes a generalized QR factorization of an N-by-M matrix A */
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/* > and an N-by-P matrix B: */
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/* > */
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/* > A = Q*R, B = Q*T*Z, */
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/* > */
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/* > where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal */
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/* > matrix, and R and T assume one of the forms: */
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/* > */
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/* > if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N, */
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/* > ( 0 ) N-M N M-N */
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/* > M */
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/* > */
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/* > where R11 is upper triangular, and */
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/* > */
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/* > if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P, */
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/* > P-N N ( T21 ) P */
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/* > P */
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/* > */
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/* > where T12 or T21 is upper triangular. */
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/* > */
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/* > In particular, if B is square and nonsingular, the GQR factorization */
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/* > of A and B implicitly gives the QR factorization of inv(B)*A: */
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/* > */
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/* > inv(B)*A = Z**T*(inv(T)*R) */
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/* > */
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/* > where inv(B) denotes the inverse of the matrix B, and Z**T denotes the */
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/* > transpose of the matrix Z. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The number of rows of the matrices A and B. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] M */
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/* > \verbatim */
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/* > M is INTEGER */
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/* > The number of columns of the matrix A. M >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] P */
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/* > \verbatim */
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/* > P is INTEGER */
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/* > The number of columns of the matrix B. P >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is REAL array, dimension (LDA,M) */
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/* > On entry, the N-by-M matrix A. */
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/* > On exit, the elements on and above the diagonal of the array */
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/* > contain the f2cmin(N,M)-by-M upper trapezoidal matrix R (R is */
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/* > upper triangular if N >= M); the elements below the diagonal, */
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/* > with the array TAUA, represent the orthogonal matrix Q as a */
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/* > product of f2cmin(N,M) elementary reflectors (see Further */
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/* > Details). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= f2cmax(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] TAUA */
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/* > \verbatim */
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/* > TAUA is REAL array, dimension (f2cmin(N,M)) */
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/* > The scalar factors of the elementary reflectors which */
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/* > represent the orthogonal matrix Q (see Further Details). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] B */
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/* > \verbatim */
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/* > B is REAL array, dimension (LDB,P) */
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/* > On entry, the N-by-P matrix B. */
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/* > On exit, if N <= P, the upper triangle of the subarray */
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/* > B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; */
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/* > if N > P, the elements on and above the (N-P)-th subdiagonal */
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/* > contain the N-by-P upper trapezoidal matrix T; the remaining */
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/* > elements, with the array TAUB, represent the orthogonal */
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/* > matrix Z as a product of elementary reflectors (see Further */
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/* > Details). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDB */
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/* > \verbatim */
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/* > LDB is INTEGER */
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/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] TAUB */
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/* > \verbatim */
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/* > TAUB is REAL array, dimension (f2cmin(N,P)) */
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/* > The scalar factors of the elementary reflectors which */
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/* > represent the orthogonal matrix Z (see Further Details). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] WORK */
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/* > \verbatim */
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/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
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/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LWORK */
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/* > \verbatim */
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/* > LWORK is INTEGER */
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/* > The dimension of the array WORK. LWORK >= f2cmax(1,N,M,P). */
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/* > For optimum performance LWORK >= f2cmax(N,M,P)*f2cmax(NB1,NB2,NB3), */
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/* > where NB1 is the optimal blocksize for the QR factorization */
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/* > of an N-by-M matrix, NB2 is the optimal blocksize for the */
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/* > RQ factorization of an N-by-P matrix, and NB3 is the optimal */
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/* > blocksize for a call of SORMQR. */
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/* > */
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/* > If LWORK = -1, then a workspace query is assumed; the routine */
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/* > only calculates the optimal size of the WORK array, returns */
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/* > this value as the first entry of the WORK array, and no error */
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/* > message related to LWORK is issued by XERBLA. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \date December 2016 */
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/* > \ingroup realOTHERcomputational */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > The matrix Q is represented as a product of elementary reflectors */
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/* > */
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/* > Q = H(1) H(2) . . . H(k), where k = f2cmin(n,m). */
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/* > */
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/* > Each H(i) has the form */
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/* > */
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/* > H(i) = I - taua * v * v**T */
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/* > */
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/* > where taua is a real scalar, and v is a real vector with */
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/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
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/* > and taua in TAUA(i). */
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/* > To form Q explicitly, use LAPACK subroutine SORGQR. */
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/* > To use Q to update another matrix, use LAPACK subroutine SORMQR. */
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/* > */
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/* > The matrix Z is represented as a product of elementary reflectors */
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/* > */
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/* > Z = H(1) H(2) . . . H(k), where k = f2cmin(n,p). */
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/* > */
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/* > Each H(i) has the form */
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/* > */
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/* > H(i) = I - taub * v * v**T */
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/* > */
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/* > where taub is a real scalar, and v is a real vector with */
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/* > v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in */
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/* > B(n-k+i,1:p-k+i-1), and taub in TAUB(i). */
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/* > To form Z explicitly, use LAPACK subroutine SORGRQ. */
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/* > To use Z to update another matrix, use LAPACK subroutine SORMRQ. */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ void sggqrf_(integer *n, integer *m, integer *p, real *a,
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integer *lda, real *taua, real *b, integer *ldb, real *taub, real *
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work, integer *lwork, integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
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/* Local variables */
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integer lopt, nb;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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extern /* Subroutine */ void sgeqrf_(integer *, integer *, real *, integer
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*, real *, real *, integer *, integer *), sgerqf_(integer *,
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integer *, real *, integer *, real *, real *, integer *, integer *
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);
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integer nb1, nb2, nb3, lwkopt;
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logical lquery;
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extern /* Subroutine */ void sormqr_(char *, char *, integer *, integer *,
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integer *, real *, integer *, real *, real *, integer *, real *,
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integer *, integer *);
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/* -- LAPACK computational routine (version 3.7.0) -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* December 2016 */
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/* ===================================================================== */
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/* Test the input parameters */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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--taua;
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1 * 1;
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b -= b_offset;
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--taub;
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--work;
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/* Function Body */
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*info = 0;
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nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, m, &c_n1, &c_n1, (ftnlen)6, (
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ftnlen)1);
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nb2 = ilaenv_(&c__1, "SGERQF", " ", n, p, &c_n1, &c_n1, (ftnlen)6, (
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ftnlen)1);
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nb3 = ilaenv_(&c__1, "SORMQR", " ", n, m, p, &c_n1, (ftnlen)6, (ftnlen)1);
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/* Computing MAX */
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i__1 = f2cmax(nb1,nb2);
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nb = f2cmax(i__1,nb3);
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/* Computing MAX */
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i__1 = f2cmax(*n,*m);
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lwkopt = f2cmax(i__1,*p) * nb;
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work[1] = (real) lwkopt;
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lquery = *lwork == -1;
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if (*n < 0) {
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*info = -1;
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} else if (*m < 0) {
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*info = -2;
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} else if (*p < 0) {
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*info = -3;
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} else if (*lda < f2cmax(1,*n)) {
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*info = -5;
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} else if (*ldb < f2cmax(1,*n)) {
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*info = -8;
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} else /* if(complicated condition) */ {
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/* Computing MAX */
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i__1 = f2cmax(1,*n), i__1 = f2cmax(i__1,*m);
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if (*lwork < f2cmax(i__1,*p) && ! lquery) {
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*info = -11;
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}
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SGGQRF", &i__1, (ftnlen)6);
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return;
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} else if (lquery) {
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return;
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}
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/* QR factorization of N-by-M matrix A: A = Q*R */
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sgeqrf_(n, m, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
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lopt = work[1];
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/* Update B := Q**T*B. */
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i__1 = f2cmin(*n,*m);
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sormqr_("Left", "Transpose", n, p, &i__1, &a[a_offset], lda, &taua[1], &b[
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b_offset], ldb, &work[1], lwork, info);
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/* Computing MAX */
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i__1 = lopt, i__2 = (integer) work[1];
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lopt = f2cmax(i__1,i__2);
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/* RQ factorization of N-by-P matrix B: B = T*Z. */
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sgerqf_(n, p, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
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/* Computing MAX */
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i__1 = lopt, i__2 = (integer) work[1];
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work[1] = (real) f2cmax(i__1,i__2);
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return;
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/* End of SGGQRF */
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} /* sggqrf_ */
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