968 lines
27 KiB
C
968 lines
27 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 integer c__0 = 0;
|
|
|
|
/* > \brief \b SLAMTSQR */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, */
|
|
/* $ LDT, C, LDC, WORK, LWORK, INFO ) */
|
|
|
|
|
|
/* CHARACTER SIDE, TRANS */
|
|
/* INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC */
|
|
/* DOUBLE A( LDA, * ), WORK( * ), C(LDC, * ), */
|
|
/* $ T( LDT, * ) */
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SLAMTSQR overwrites the general real M-by-N matrix C with */
|
|
/* > */
|
|
/* > */
|
|
/* > SIDE = 'L' SIDE = 'R' */
|
|
/* > TRANS = 'N': Q * C C * Q */
|
|
/* > TRANS = 'T': Q**T * C C * Q**T */
|
|
/* > where Q is a real orthogonal matrix defined as the product */
|
|
/* > of blocked elementary reflectors computed by tall skinny */
|
|
/* > QR factorization (DLATSQR) */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] SIDE */
|
|
/* > \verbatim */
|
|
/* > SIDE is CHARACTER*1 */
|
|
/* > = 'L': apply Q or Q**T from the Left; */
|
|
/* > = 'R': apply Q or Q**T from the Right. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TRANS */
|
|
/* > \verbatim */
|
|
/* > TRANS is CHARACTER*1 */
|
|
/* > = 'N': No transpose, apply Q; */
|
|
/* > = 'T': Transpose, apply Q**T. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \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 C. M >= N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] K */
|
|
/* > \verbatim */
|
|
/* > K is INTEGER */
|
|
/* > The number of elementary reflectors whose product defines */
|
|
/* > the matrix Q. */
|
|
/* > N >= K >= 0; */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] MB */
|
|
/* > \verbatim */
|
|
/* > MB is INTEGER */
|
|
/* > The block size to be used in the blocked QR. */
|
|
/* > MB > N. (must be the same as DLATSQR) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NB */
|
|
/* > \verbatim */
|
|
/* > NB is INTEGER */
|
|
/* > The column block size to be used in the blocked QR. */
|
|
/* > N >= NB >= 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is REAL array, dimension (LDA,K) */
|
|
/* > The i-th column must contain the vector which defines the */
|
|
/* > blockedelementary reflector H(i), for i = 1,2,...,k, as */
|
|
/* > returned by DLATSQR in the first k columns of */
|
|
/* > its array argument A. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > The leading dimension of the array A. */
|
|
/* > If SIDE = 'L', LDA >= f2cmax(1,M); */
|
|
/* > if SIDE = 'R', LDA >= f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] T */
|
|
/* > \verbatim */
|
|
/* > T is REAL array, dimension */
|
|
/* > ( N * Number of blocks(CEIL(M-K/MB-K)), */
|
|
/* > The blocked upper triangular block reflectors stored in compact form */
|
|
/* > as a sequence of upper triangular blocks. See below */
|
|
/* > for further details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDT */
|
|
/* > \verbatim */
|
|
/* > LDT is INTEGER */
|
|
/* > The leading dimension of the array T. LDT >= NB. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] C */
|
|
/* > \verbatim */
|
|
/* > C is REAL array, dimension (LDC,N) */
|
|
/* > On entry, the M-by-N matrix C. */
|
|
/* > On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDC */
|
|
/* > \verbatim */
|
|
/* > LDC is INTEGER */
|
|
/* > The leading dimension of the array C. LDC >= f2cmax(1,M). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > (workspace) REAL array, dimension (MAX(1,LWORK)) */
|
|
/* > */
|
|
/* > \endverbatim */
|
|
/* > \param[in] LWORK */
|
|
/* > \verbatim */
|
|
/* > LWORK is INTEGER */
|
|
/* > The dimension of the array WORK. */
|
|
/* > */
|
|
/* > If SIDE = 'L', LWORK >= f2cmax(1,N)*NB; */
|
|
/* > if SIDE = 'R', LWORK >= f2cmax(1,MB)*NB. */
|
|
/* > 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] 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. */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations, */
|
|
/* > representing Q as a product of other orthogonal matrices */
|
|
/* > Q = Q(1) * Q(2) * . . . * Q(k) */
|
|
/* > where each Q(i) zeros out subdiagonal entries of a block of MB rows of A: */
|
|
/* > Q(1) zeros out the subdiagonal entries of rows 1:MB of A */
|
|
/* > Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A */
|
|
/* > Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A */
|
|
/* > . . . */
|
|
/* > */
|
|
/* > Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors */
|
|
/* > stored under the diagonal of rows 1:MB of A, and by upper triangular */
|
|
/* > block reflectors, stored in array T(1:LDT,1:N). */
|
|
/* > For more information see Further Details in GEQRT. */
|
|
/* > */
|
|
/* > Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors */
|
|
/* > stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular */
|
|
/* > block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N). */
|
|
/* > The last Q(k) may use fewer rows. */
|
|
/* > For more information see Further Details in TPQRT. */
|
|
/* > */
|
|
/* > For more details of the overall algorithm, see the description of */
|
|
/* > Sequential TSQR in Section 2.2 of [1]. */
|
|
/* > */
|
|
/* > [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations, */
|
|
/* > J. Demmel, L. Grigori, M. Hoemmen, J. Langou, */
|
|
/* > SIAM J. Sci. Comput, vol. 34, no. 1, 2012 */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void slamtsqr_(char *side, char *trans, integer *m, integer *
|
|
n, integer *k, integer *mb, integer *nb, real *a, integer *lda, real *
|
|
t, integer *ldt, real *c__, integer *ldc, real *work, integer *lwork,
|
|
integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, c_dim1, c_offset, t_dim1, t_offset, i__1, i__2,
|
|
i__3;
|
|
|
|
/* Local variables */
|
|
logical left, tran;
|
|
integer i__;
|
|
extern logical lsame_(char *, char *);
|
|
logical right;
|
|
integer ii, kk, lw;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
logical notran, lquery;
|
|
integer ctr;
|
|
extern /* Subroutine */ void sgemqrt_(char *, char *, integer *, integer *,
|
|
integer *, integer *, real *, integer *, real *, integer *, real
|
|
*, integer *, real *, integer *), stpmqrt_(char *,
|
|
char *, integer *, integer *, integer *, integer *, integer *,
|
|
real *, integer *, real *, integer *, real *, integer *, real *,
|
|
integer *, real *, integer *);
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.1) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* June 2017 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input arguments */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
t_dim1 = *ldt;
|
|
t_offset = 1 + t_dim1 * 1;
|
|
t -= t_offset;
|
|
c_dim1 = *ldc;
|
|
c_offset = 1 + c_dim1 * 1;
|
|
c__ -= c_offset;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
lquery = *lwork < 0;
|
|
notran = lsame_(trans, "N");
|
|
tran = lsame_(trans, "T");
|
|
left = lsame_(side, "L");
|
|
right = lsame_(side, "R");
|
|
if (left) {
|
|
lw = *n * *nb;
|
|
} else {
|
|
lw = *mb * *nb;
|
|
}
|
|
|
|
*info = 0;
|
|
if (! left && ! right) {
|
|
*info = -1;
|
|
} else if (! tran && ! notran) {
|
|
*info = -2;
|
|
} else if (*m < 0) {
|
|
*info = -3;
|
|
} else if (*n < 0) {
|
|
*info = -4;
|
|
} else if (*k < 0) {
|
|
*info = -5;
|
|
} else if (*lda < f2cmax(1,*k)) {
|
|
*info = -9;
|
|
} else if (*ldt < f2cmax(1,*nb)) {
|
|
*info = -11;
|
|
} else if (*ldc < f2cmax(1,*m)) {
|
|
*info = -13;
|
|
} else if (*lwork < f2cmax(1,lw) && ! lquery) {
|
|
*info = -15;
|
|
}
|
|
|
|
/* Determine the block size if it is tall skinny or short and wide */
|
|
|
|
if (*info == 0) {
|
|
work[1] = (real) lw;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SLAMTSQR", &i__1, (ftnlen)8);
|
|
return;
|
|
} else if (lquery) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
/* Computing MIN */
|
|
i__1 = f2cmin(*m,*n);
|
|
if (f2cmin(i__1,*k) == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Computing MAX */
|
|
i__1 = f2cmax(*m,*n);
|
|
if (*mb <= *k || *mb >= f2cmax(i__1,*k)) {
|
|
sgemqrt_(side, trans, m, n, k, nb, &a[a_offset], lda, &t[t_offset],
|
|
ldt, &c__[c_offset], ldc, &work[1], info);
|
|
return;
|
|
}
|
|
|
|
if (left && notran) {
|
|
|
|
/* Multiply Q to the last block of C */
|
|
|
|
kk = (*m - *k) % (*mb - *k);
|
|
ctr = (*m - *k) / (*mb - *k);
|
|
if (kk > 0) {
|
|
ii = *m - kk + 1;
|
|
stpmqrt_("L", "N", &kk, n, k, &c__0, nb, &a[ii + a_dim1], lda, &t[
|
|
(ctr * *k + 1) * t_dim1 + 1], ldt, &c__[c_dim1 + 1], ldc,
|
|
&c__[ii + c_dim1], ldc, &work[1], info);
|
|
} else {
|
|
ii = *m + 1;
|
|
}
|
|
|
|
i__1 = *mb + 1;
|
|
i__2 = -(*mb - *k);
|
|
for (i__ = ii - (*mb - *k); i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__
|
|
+= i__2) {
|
|
|
|
/* Multiply Q to the current block of C (I:I+MB,1:N) */
|
|
|
|
--ctr;
|
|
i__3 = *mb - *k;
|
|
stpmqrt_("L", "N", &i__3, n, k, &c__0, nb, &a[i__ + a_dim1], lda,
|
|
&t[(ctr * *k + 1) * t_dim1 + 1], ldt, &c__[c_dim1 + 1],
|
|
ldc, &c__[i__ + c_dim1], ldc, &work[1], info);
|
|
|
|
}
|
|
|
|
/* Multiply Q to the first block of C (1:MB,1:N) */
|
|
|
|
sgemqrt_("L", "N", mb, n, k, nb, &a[a_dim1 + 1], lda, &t[t_offset],
|
|
ldt, &c__[c_dim1 + 1], ldc, &work[1], info);
|
|
|
|
} else if (left && tran) {
|
|
|
|
/* Multiply Q to the first block of C */
|
|
|
|
kk = (*m - *k) % (*mb - *k);
|
|
ii = *m - kk + 1;
|
|
ctr = 1;
|
|
sgemqrt_("L", "T", mb, n, k, nb, &a[a_dim1 + 1], lda, &t[t_offset],
|
|
ldt, &c__[c_dim1 + 1], ldc, &work[1], info);
|
|
|
|
i__2 = ii - *mb + *k;
|
|
i__1 = *mb - *k;
|
|
for (i__ = *mb + 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1)
|
|
{
|
|
|
|
/* Multiply Q to the current block of C (I:I+MB,1:N) */
|
|
|
|
i__3 = *mb - *k;
|
|
stpmqrt_("L", "T", &i__3, n, k, &c__0, nb, &a[i__ + a_dim1], lda,
|
|
&t[(ctr * *k + 1) * t_dim1 + 1], ldt, &c__[c_dim1 + 1],
|
|
ldc, &c__[i__ + c_dim1], ldc, &work[1], info);
|
|
++ctr;
|
|
|
|
}
|
|
if (ii <= *m) {
|
|
|
|
/* Multiply Q to the last block of C */
|
|
|
|
stpmqrt_("L", "T", &kk, n, k, &c__0, nb, &a[ii + a_dim1], lda, &t[
|
|
(ctr * *k + 1) * t_dim1 + 1], ldt, &c__[c_dim1 + 1], ldc,
|
|
&c__[ii + c_dim1], ldc, &work[1], info);
|
|
|
|
}
|
|
|
|
} else if (right && tran) {
|
|
|
|
/* Multiply Q to the last block of C */
|
|
|
|
kk = (*n - *k) % (*mb - *k);
|
|
ctr = (*n - *k) / (*mb - *k);
|
|
if (kk > 0) {
|
|
ii = *n - kk + 1;
|
|
stpmqrt_("R", "T", m, &kk, k, &c__0, nb, &a[ii + a_dim1], lda, &t[
|
|
(ctr * *k + 1) * t_dim1 + 1], ldt, &c__[c_dim1 + 1], ldc,
|
|
&c__[ii * c_dim1 + 1], ldc, &work[1], info);
|
|
} else {
|
|
ii = *n + 1;
|
|
}
|
|
|
|
i__1 = *mb + 1;
|
|
i__2 = -(*mb - *k);
|
|
for (i__ = ii - (*mb - *k); i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__
|
|
+= i__2) {
|
|
|
|
/* Multiply Q to the current block of C (1:M,I:I+MB) */
|
|
|
|
--ctr;
|
|
i__3 = *mb - *k;
|
|
stpmqrt_("R", "T", m, &i__3, k, &c__0, nb, &a[i__ + a_dim1], lda,
|
|
&t[(ctr * *k + 1) * t_dim1 + 1], ldt, &c__[c_dim1 + 1],
|
|
ldc, &c__[i__ * c_dim1 + 1], ldc, &work[1], info);
|
|
|
|
}
|
|
|
|
/* Multiply Q to the first block of C (1:M,1:MB) */
|
|
|
|
sgemqrt_("R", "T", m, mb, k, nb, &a[a_dim1 + 1], lda, &t[t_offset],
|
|
ldt, &c__[c_dim1 + 1], ldc, &work[1], info);
|
|
|
|
} else if (right && notran) {
|
|
|
|
/* Multiply Q to the first block of C */
|
|
|
|
kk = (*n - *k) % (*mb - *k);
|
|
ii = *n - kk + 1;
|
|
ctr = 1;
|
|
sgemqrt_("R", "N", m, mb, k, nb, &a[a_dim1 + 1], lda, &t[t_offset],
|
|
ldt, &c__[c_dim1 + 1], ldc, &work[1], info);
|
|
|
|
i__2 = ii - *mb + *k;
|
|
i__1 = *mb - *k;
|
|
for (i__ = *mb + 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1)
|
|
{
|
|
|
|
/* Multiply Q to the current block of C (1:M,I:I+MB) */
|
|
|
|
i__3 = *mb - *k;
|
|
stpmqrt_("R", "N", m, &i__3, k, &c__0, nb, &a[i__ + a_dim1], lda,
|
|
&t[(ctr * *k + 1) * t_dim1 + 1], ldt, &c__[c_dim1 + 1],
|
|
ldc, &c__[i__ * c_dim1 + 1], ldc, &work[1], info);
|
|
++ctr;
|
|
|
|
}
|
|
if (ii <= *n) {
|
|
|
|
/* Multiply Q to the last block of C */
|
|
|
|
stpmqrt_("R", "N", m, &kk, k, &c__0, nb, &a[ii + a_dim1], lda, &t[
|
|
(ctr * *k + 1) * t_dim1 + 1], ldt, &c__[c_dim1 + 1], ldc,
|
|
&c__[ii * c_dim1 + 1], ldc, &work[1], info);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
work[1] = (real) lw;
|
|
return;
|
|
|
|
/* End of SLAMTSQR */
|
|
|
|
} /* slamtsqr_ */
|
|
|