1094 lines
31 KiB
C
1094 lines
31 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__1 = 1;
|
|
static real c_b6 = 0.f;
|
|
static integer c__0 = 0;
|
|
static real c_b11 = 1.f;
|
|
|
|
/* > \brief \b SLALSD uses the singular value decomposition of A to solve the least squares problem. */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download SLALSD + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slalsd.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slalsd.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slalsd.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE SLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, */
|
|
/* RANK, WORK, IWORK, INFO ) */
|
|
|
|
/* CHARACTER UPLO */
|
|
/* INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ */
|
|
/* REAL RCOND */
|
|
/* INTEGER IWORK( * ) */
|
|
/* REAL B( LDB, * ), D( * ), E( * ), WORK( * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > SLALSD uses the singular value decomposition of A to solve the least */
|
|
/* > squares problem of finding X to minimize the Euclidean norm of each */
|
|
/* > column of A*X-B, where A is N-by-N upper bidiagonal, and X and B */
|
|
/* > are N-by-NRHS. The solution X overwrites B. */
|
|
/* > */
|
|
/* > The singular values of A smaller than RCOND times the largest */
|
|
/* > singular value are treated as zero in solving the least squares */
|
|
/* > problem; in this case a minimum norm solution is returned. */
|
|
/* > The actual singular values are returned in D in ascending order. */
|
|
/* > */
|
|
/* > This code makes very mild assumptions about floating point */
|
|
/* > arithmetic. It will work on machines with a guard digit in */
|
|
/* > add/subtract, or on those binary machines without guard digits */
|
|
/* > which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. */
|
|
/* > It could conceivably fail on hexadecimal or decimal machines */
|
|
/* > without guard digits, but we know of none. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > = 'U': D and E define an upper bidiagonal matrix. */
|
|
/* > = 'L': D and E define a lower bidiagonal matrix. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SMLSIZ */
|
|
/* > \verbatim */
|
|
/* > SMLSIZ is INTEGER */
|
|
/* > The maximum size of the subproblems at the bottom of the */
|
|
/* > computation tree. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The dimension of the bidiagonal matrix. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] NRHS */
|
|
/* > \verbatim */
|
|
/* > NRHS is INTEGER */
|
|
/* > The number of columns of B. NRHS must be at least 1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] D */
|
|
/* > \verbatim */
|
|
/* > D is REAL array, dimension (N) */
|
|
/* > On entry D contains the main diagonal of the bidiagonal */
|
|
/* > matrix. On exit, if INFO = 0, D contains its singular values. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] E */
|
|
/* > \verbatim */
|
|
/* > E is REAL array, dimension (N-1) */
|
|
/* > Contains the super-diagonal entries of the bidiagonal matrix. */
|
|
/* > On exit, E has been destroyed. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is REAL array, dimension (LDB,NRHS) */
|
|
/* > On input, B contains the right hand sides of the least */
|
|
/* > squares problem. On output, B contains the solution X. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > The leading dimension of B in the calling subprogram. */
|
|
/* > LDB must be at least f2cmax(1,N). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] RCOND */
|
|
/* > \verbatim */
|
|
/* > RCOND is REAL */
|
|
/* > The singular values of A less than or equal to RCOND times */
|
|
/* > the largest singular value are treated as zero in solving */
|
|
/* > the least squares problem. If RCOND is negative, */
|
|
/* > machine precision is used instead. */
|
|
/* > For example, if diag(S)*X=B were the least squares problem, */
|
|
/* > where diag(S) is a diagonal matrix of singular values, the */
|
|
/* > solution would be X(i) = B(i) / S(i) if S(i) is greater than */
|
|
/* > RCOND*f2cmax(S), and X(i) = 0 if S(i) is less than or equal to */
|
|
/* > RCOND*f2cmax(S). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] RANK */
|
|
/* > \verbatim */
|
|
/* > RANK is INTEGER */
|
|
/* > The number of singular values of A greater than RCOND times */
|
|
/* > the largest singular value. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] WORK */
|
|
/* > \verbatim */
|
|
/* > WORK is REAL array, dimension at least */
|
|
/* > (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2), */
|
|
/* > where NLVL = f2cmax(0, INT(log_2 (N/(SMLSIZ+1))) + 1). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IWORK */
|
|
/* > \verbatim */
|
|
/* > IWORK is INTEGER array, dimension at least */
|
|
/* > (3*N*NLVL + 11*N) */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit. */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
|
/* > > 0: The algorithm failed to compute a singular value while */
|
|
/* > working on the submatrix lying in rows and columns */
|
|
/* > INFO/(N+1) through MOD(INFO,N+1). */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup realOTHERcomputational */
|
|
|
|
/* > \par Contributors: */
|
|
/* ================== */
|
|
/* > */
|
|
/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */
|
|
/* > California at Berkeley, USA \n */
|
|
/* > Osni Marques, LBNL/NERSC, USA \n */
|
|
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int slalsd_(char *uplo, integer *smlsiz, integer *n, integer
|
|
*nrhs, real *d__, real *e, real *b, integer *ldb, real *rcond,
|
|
integer *rank, real *work, integer *iwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer b_dim1, b_offset, i__1, i__2;
|
|
real r__1;
|
|
|
|
/* Local variables */
|
|
integer difl, difr;
|
|
real rcnd;
|
|
integer perm, nsub, nlvl, sqre, bxst;
|
|
extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
|
|
integer *, real *, real *);
|
|
integer c__, i__, j, k;
|
|
real r__;
|
|
integer s, u, z__;
|
|
extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
|
|
integer *, real *, real *, integer *, real *, integer *, real *,
|
|
real *, integer *);
|
|
integer poles, sizei, nsize;
|
|
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
|
|
integer *);
|
|
integer nwork, icmpq1, icmpq2;
|
|
real cs;
|
|
integer bx;
|
|
real sn;
|
|
integer st;
|
|
extern real slamch_(char *);
|
|
extern /* Subroutine */ int slasda_(integer *, integer *, integer *,
|
|
integer *, real *, real *, real *, integer *, real *, integer *,
|
|
real *, real *, real *, real *, integer *, integer *, integer *,
|
|
integer *, real *, real *, real *, real *, integer *, integer *);
|
|
integer vt;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slalsa_(
|
|
integer *, integer *, integer *, integer *, real *, integer *,
|
|
real *, integer *, real *, integer *, real *, integer *, real *,
|
|
real *, real *, real *, integer *, integer *, integer *, integer *
|
|
, real *, real *, real *, real *, integer *, integer *), slascl_(
|
|
char *, integer *, integer *, real *, real *, integer *, integer *
|
|
, real *, integer *, integer *);
|
|
integer givcol;
|
|
extern integer isamax_(integer *, real *, integer *);
|
|
extern /* Subroutine */ int slasdq_(char *, integer *, integer *, integer
|
|
*, integer *, integer *, real *, real *, real *, integer *, real *
|
|
, integer *, real *, integer *, real *, integer *),
|
|
slacpy_(char *, integer *, integer *, real *, integer *, real *,
|
|
integer *), slartg_(real *, real *, real *, real *, real *
|
|
), slaset_(char *, integer *, integer *, real *, real *, real *,
|
|
integer *);
|
|
real orgnrm;
|
|
integer givnum;
|
|
extern real slanst_(char *, integer *, real *, real *);
|
|
extern /* Subroutine */ int slasrt_(char *, integer *, real *, integer *);
|
|
integer givptr, nm1, smlszp, st1;
|
|
real eps;
|
|
integer iwk;
|
|
real tol;
|
|
|
|
|
|
/* -- LAPACK computational routine (version 3.7.0) -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
/* December 2016 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
--d__;
|
|
--e;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
b -= b_offset;
|
|
--work;
|
|
--iwork;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
|
|
if (*n < 0) {
|
|
*info = -3;
|
|
} else if (*nrhs < 1) {
|
|
*info = -4;
|
|
} else if (*ldb < 1 || *ldb < *n) {
|
|
*info = -8;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("SLALSD", &i__1, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
|
|
eps = slamch_("Epsilon");
|
|
|
|
/* Set up the tolerance. */
|
|
|
|
if (*rcond <= 0.f || *rcond >= 1.f) {
|
|
rcnd = eps;
|
|
} else {
|
|
rcnd = *rcond;
|
|
}
|
|
|
|
*rank = 0;
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*n == 0) {
|
|
return 0;
|
|
} else if (*n == 1) {
|
|
if (d__[1] == 0.f) {
|
|
slaset_("A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb);
|
|
} else {
|
|
*rank = 1;
|
|
slascl_("G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[
|
|
b_offset], ldb, info);
|
|
d__[1] = abs(d__[1]);
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/* Rotate the matrix if it is lower bidiagonal. */
|
|
|
|
if (*(unsigned char *)uplo == 'L') {
|
|
i__1 = *n - 1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
slartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
|
|
d__[i__] = r__;
|
|
e[i__] = sn * d__[i__ + 1];
|
|
d__[i__ + 1] = cs * d__[i__ + 1];
|
|
if (*nrhs == 1) {
|
|
srot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], &
|
|
c__1, &cs, &sn);
|
|
} else {
|
|
work[(i__ << 1) - 1] = cs;
|
|
work[i__ * 2] = sn;
|
|
}
|
|
/* L10: */
|
|
}
|
|
if (*nrhs > 1) {
|
|
i__1 = *nrhs;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = *n - 1;
|
|
for (j = 1; j <= i__2; ++j) {
|
|
cs = work[(j << 1) - 1];
|
|
sn = work[j * 2];
|
|
srot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ *
|
|
b_dim1], &c__1, &cs, &sn);
|
|
/* L20: */
|
|
}
|
|
/* L30: */
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Scale. */
|
|
|
|
nm1 = *n - 1;
|
|
orgnrm = slanst_("M", n, &d__[1], &e[1]);
|
|
if (orgnrm == 0.f) {
|
|
slaset_("A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb);
|
|
return 0;
|
|
}
|
|
|
|
slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info);
|
|
slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1,
|
|
info);
|
|
|
|
/* If N is smaller than the minimum divide size SMLSIZ, then solve */
|
|
/* the problem with another solver. */
|
|
|
|
if (*n <= *smlsiz) {
|
|
nwork = *n * *n + 1;
|
|
slaset_("A", n, n, &c_b6, &c_b11, &work[1], n);
|
|
slasdq_("U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, &
|
|
work[1], n, &b[b_offset], ldb, &work[nwork], info);
|
|
if (*info != 0) {
|
|
return 0;
|
|
}
|
|
tol = rcnd * (r__1 = d__[isamax_(n, &d__[1], &c__1)], abs(r__1));
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (d__[i__] <= tol) {
|
|
slaset_("A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb);
|
|
} else {
|
|
slascl_("G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[
|
|
i__ + b_dim1], ldb, info);
|
|
++(*rank);
|
|
}
|
|
/* L40: */
|
|
}
|
|
sgemm_("T", "N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, &
|
|
c_b6, &work[nwork], n);
|
|
slacpy_("A", n, nrhs, &work[nwork], n, &b[b_offset], ldb);
|
|
|
|
/* Unscale. */
|
|
|
|
slascl_("G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n,
|
|
info);
|
|
slasrt_("D", n, &d__[1], info);
|
|
slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset],
|
|
ldb, info);
|
|
|
|
return 0;
|
|
}
|
|
|
|
/* Book-keeping and setting up some constants. */
|
|
|
|
nlvl = (integer) (log((real) (*n) / (real) (*smlsiz + 1)) / log(2.f)) + 1;
|
|
|
|
smlszp = *smlsiz + 1;
|
|
|
|
u = 1;
|
|
vt = *smlsiz * *n + 1;
|
|
difl = vt + smlszp * *n;
|
|
difr = difl + nlvl * *n;
|
|
z__ = difr + (nlvl * *n << 1);
|
|
c__ = z__ + nlvl * *n;
|
|
s = c__ + *n;
|
|
poles = s + *n;
|
|
givnum = poles + (nlvl << 1) * *n;
|
|
bx = givnum + (nlvl << 1) * *n;
|
|
nwork = bx + *n * *nrhs;
|
|
|
|
sizei = *n + 1;
|
|
k = sizei + *n;
|
|
givptr = k + *n;
|
|
perm = givptr + *n;
|
|
givcol = perm + nlvl * *n;
|
|
iwk = givcol + (nlvl * *n << 1);
|
|
|
|
st = 1;
|
|
sqre = 0;
|
|
icmpq1 = 1;
|
|
icmpq2 = 0;
|
|
nsub = 0;
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if ((r__1 = d__[i__], abs(r__1)) < eps) {
|
|
d__[i__] = r_sign(&eps, &d__[i__]);
|
|
}
|
|
/* L50: */
|
|
}
|
|
|
|
i__1 = nm1;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if ((r__1 = e[i__], abs(r__1)) < eps || i__ == nm1) {
|
|
++nsub;
|
|
iwork[nsub] = st;
|
|
|
|
/* Subproblem found. First determine its size and then */
|
|
/* apply divide and conquer on it. */
|
|
|
|
if (i__ < nm1) {
|
|
|
|
/* A subproblem with E(I) small for I < NM1. */
|
|
|
|
nsize = i__ - st + 1;
|
|
iwork[sizei + nsub - 1] = nsize;
|
|
} else if ((r__1 = e[i__], abs(r__1)) >= eps) {
|
|
|
|
/* A subproblem with E(NM1) not too small but I = NM1. */
|
|
|
|
nsize = *n - st + 1;
|
|
iwork[sizei + nsub - 1] = nsize;
|
|
} else {
|
|
|
|
/* A subproblem with E(NM1) small. This implies an */
|
|
/* 1-by-1 subproblem at D(N), which is not solved */
|
|
/* explicitly. */
|
|
|
|
nsize = i__ - st + 1;
|
|
iwork[sizei + nsub - 1] = nsize;
|
|
++nsub;
|
|
iwork[nsub] = *n;
|
|
iwork[sizei + nsub - 1] = 1;
|
|
scopy_(nrhs, &b[*n + b_dim1], ldb, &work[bx + nm1], n);
|
|
}
|
|
st1 = st - 1;
|
|
if (nsize == 1) {
|
|
|
|
/* This is a 1-by-1 subproblem and is not solved */
|
|
/* explicitly. */
|
|
|
|
scopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n);
|
|
} else if (nsize <= *smlsiz) {
|
|
|
|
/* This is a small subproblem and is solved by SLASDQ. */
|
|
|
|
slaset_("A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1],
|
|
n);
|
|
slasdq_("U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[
|
|
st], &work[vt + st1], n, &work[nwork], n, &b[st +
|
|
b_dim1], ldb, &work[nwork], info);
|
|
if (*info != 0) {
|
|
return 0;
|
|
}
|
|
slacpy_("A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx +
|
|
st1], n);
|
|
} else {
|
|
|
|
/* A large problem. Solve it using divide and conquer. */
|
|
|
|
slasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], &
|
|
work[u + st1], n, &work[vt + st1], &iwork[k + st1], &
|
|
work[difl + st1], &work[difr + st1], &work[z__ + st1],
|
|
&work[poles + st1], &iwork[givptr + st1], &iwork[
|
|
givcol + st1], n, &iwork[perm + st1], &work[givnum +
|
|
st1], &work[c__ + st1], &work[s + st1], &work[nwork],
|
|
&iwork[iwk], info);
|
|
if (*info != 0) {
|
|
return 0;
|
|
}
|
|
bxst = bx + st1;
|
|
slalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, &
|
|
work[bxst], n, &work[u + st1], n, &work[vt + st1], &
|
|
iwork[k + st1], &work[difl + st1], &work[difr + st1],
|
|
&work[z__ + st1], &work[poles + st1], &iwork[givptr +
|
|
st1], &iwork[givcol + st1], n, &iwork[perm + st1], &
|
|
work[givnum + st1], &work[c__ + st1], &work[s + st1],
|
|
&work[nwork], &iwork[iwk], info);
|
|
if (*info != 0) {
|
|
return 0;
|
|
}
|
|
}
|
|
st = i__ + 1;
|
|
}
|
|
/* L60: */
|
|
}
|
|
|
|
/* Apply the singular values and treat the tiny ones as zero. */
|
|
|
|
tol = rcnd * (r__1 = d__[isamax_(n, &d__[1], &c__1)], abs(r__1));
|
|
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
|
|
/* Some of the elements in D can be negative because 1-by-1 */
|
|
/* subproblems were not solved explicitly. */
|
|
|
|
if ((r__1 = d__[i__], abs(r__1)) <= tol) {
|
|
slaset_("A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n);
|
|
} else {
|
|
++(*rank);
|
|
slascl_("G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[
|
|
bx + i__ - 1], n, info);
|
|
}
|
|
d__[i__] = (r__1 = d__[i__], abs(r__1));
|
|
/* L70: */
|
|
}
|
|
|
|
/* Now apply back the right singular vectors. */
|
|
|
|
icmpq2 = 1;
|
|
i__1 = nsub;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
st = iwork[i__];
|
|
st1 = st - 1;
|
|
nsize = iwork[sizei + i__ - 1];
|
|
bxst = bx + st1;
|
|
if (nsize == 1) {
|
|
scopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb);
|
|
} else if (nsize <= *smlsiz) {
|
|
sgemm_("T", "N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n,
|
|
&work[bxst], n, &c_b6, &b[st + b_dim1], ldb);
|
|
} else {
|
|
slalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st +
|
|
b_dim1], ldb, &work[u + st1], n, &work[vt + st1], &iwork[
|
|
k + st1], &work[difl + st1], &work[difr + st1], &work[z__
|
|
+ st1], &work[poles + st1], &iwork[givptr + st1], &iwork[
|
|
givcol + st1], n, &iwork[perm + st1], &work[givnum + st1],
|
|
&work[c__ + st1], &work[s + st1], &work[nwork], &iwork[
|
|
iwk], info);
|
|
if (*info != 0) {
|
|
return 0;
|
|
}
|
|
}
|
|
/* L80: */
|
|
}
|
|
|
|
/* Unscale and sort the singular values. */
|
|
|
|
slascl_("G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info);
|
|
slasrt_("D", n, &d__[1], info);
|
|
slascl_("G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb,
|
|
info);
|
|
|
|
return 0;
|
|
|
|
/* End of SLALSD */
|
|
|
|
} /* slalsd_ */
|
|
|