Use f2c translations of LAPACK when no Fortran compiler is available (#3539)
* Add C equivalents of the Fortran routines from Reference-LAPACK as fallbacks, and C_LAPACK variable to trigger their use
This commit is contained in:
Martin Kroeker
GitHub
986
lapack-netlib/SRC/sbdsdc.c
Normal file
986
lapack-netlib/SRC/sbdsdc.c
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@@ -0,0 +1,986 @@
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/* f2c.h -- Standard Fortran to C header file */
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/** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
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- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
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#ifndef F2C_INCLUDE
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#define F2C_INCLUDE
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#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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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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#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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#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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#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) = conj(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) (cimag(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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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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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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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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_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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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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_Complex double 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 += conj(Cd(&x[i])) * Cd(&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 += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
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}
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}
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pCd(z) = zdotc;
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}
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static inline void cdotu_(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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_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 += 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 += 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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static inline void zdotu_(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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_Complex double 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 += Cd(&x[i]) * Cd(&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 += Cd(&x[i*incx]) * Cd(&y[i*incy]);
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}
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}
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pCd(z) = zdotc;
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}
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#endif
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/* -- translated by f2c (version 20000121).
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You must link the resulting object file with the libraries:
|
||||
-lf2c -lm (in that order)
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*/
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||||
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||||
|
||||
/* Table of constant values */
|
||||
|
||||
static integer c__9 = 9;
|
||||
static integer c__0 = 0;
|
||||
static real c_b15 = 1.f;
|
||||
static integer c__1 = 1;
|
||||
static real c_b29 = 0.f;
|
||||
|
||||
/* > \brief \b SBDSDC */
|
||||
|
||||
/* =========== DOCUMENTATION =========== */
|
||||
|
||||
/* Online html documentation available at */
|
||||
/* http://www.netlib.org/lapack/explore-html/ */
|
||||
|
||||
/* > \htmlonly */
|
||||
/* > Download SBDSDC + dependencies */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sbdsdc.
|
||||
f"> */
|
||||
/* > [TGZ]</a> */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sbdsdc.
|
||||
f"> */
|
||||
/* > [ZIP]</a> */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sbdsdc.
|
||||
f"> */
|
||||
/* > [TXT]</a> */
|
||||
/* > \endhtmlonly */
|
||||
|
||||
/* Definition: */
|
||||
/* =========== */
|
||||
|
||||
/* SUBROUTINE SBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, */
|
||||
/* WORK, IWORK, INFO ) */
|
||||
|
||||
/* CHARACTER COMPQ, UPLO */
|
||||
/* INTEGER INFO, LDU, LDVT, N */
|
||||
/* INTEGER IQ( * ), IWORK( * ) */
|
||||
/* REAL D( * ), E( * ), Q( * ), U( LDU, * ), */
|
||||
/* $ VT( LDVT, * ), WORK( * ) */
|
||||
|
||||
|
||||
/* > \par Purpose: */
|
||||
/* ============= */
|
||||
/* > */
|
||||
/* > \verbatim */
|
||||
/* > */
|
||||
/* > SBDSDC computes the singular value decomposition (SVD) of a real */
|
||||
/* > N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT, */
|
||||
/* > using a divide and conquer method, where S is a diagonal matrix */
|
||||
/* > with non-negative diagonal elements (the singular values of B), and */
|
||||
/* > U and VT are orthogonal matrices of left and right singular vectors, */
|
||||
/* > respectively. SBDSDC can be used to compute all singular values, */
|
||||
/* > and optionally, singular vectors or singular vectors in compact form. */
|
||||
/* > */
|
||||
/* > 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 X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
|
||||
/* > It could conceivably fail on hexadecimal or decimal machines */
|
||||
/* > without guard digits, but we know of none. See SLASD3 for details. */
|
||||
/* > */
|
||||
/* > The code currently calls SLASDQ if singular values only are desired. */
|
||||
/* > However, it can be slightly modified to compute singular values */
|
||||
/* > using the divide and conquer method. */
|
||||
/* > \endverbatim */
|
||||
|
||||
/* Arguments: */
|
||||
/* ========== */
|
||||
|
||||
/* > \param[in] UPLO */
|
||||
/* > \verbatim */
|
||||
/* > UPLO is CHARACTER*1 */
|
||||
/* > = 'U': B is upper bidiagonal. */
|
||||
/* > = 'L': B is lower bidiagonal. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] COMPQ */
|
||||
/* > \verbatim */
|
||||
/* > COMPQ is CHARACTER*1 */
|
||||
/* > Specifies whether singular vectors are to be computed */
|
||||
/* > as follows: */
|
||||
/* > = 'N': Compute singular values only; */
|
||||
/* > = 'P': Compute singular values and compute singular */
|
||||
/* > vectors in compact form; */
|
||||
/* > = 'I': Compute singular values and singular vectors. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] N */
|
||||
/* > \verbatim */
|
||||
/* > N is INTEGER */
|
||||
/* > The order of the matrix B. N >= 0. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in,out] D */
|
||||
/* > \verbatim */
|
||||
/* > D is REAL array, dimension (N) */
|
||||
/* > On entry, the n diagonal elements of the bidiagonal matrix B. */
|
||||
/* > On exit, if INFO=0, the singular values of B. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in,out] E */
|
||||
/* > \verbatim */
|
||||
/* > E is REAL array, dimension (N-1) */
|
||||
/* > On entry, the elements of E contain the offdiagonal */
|
||||
/* > elements of the bidiagonal matrix whose SVD is desired. */
|
||||
/* > On exit, E has been destroyed. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] U */
|
||||
/* > \verbatim */
|
||||
/* > U is REAL array, dimension (LDU,N) */
|
||||
/* > If COMPQ = 'I', then: */
|
||||
/* > On exit, if INFO = 0, U contains the left singular vectors */
|
||||
/* > of the bidiagonal matrix. */
|
||||
/* > For other values of COMPQ, U is not referenced. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] LDU */
|
||||
/* > \verbatim */
|
||||
/* > LDU is INTEGER */
|
||||
/* > The leading dimension of the array U. LDU >= 1. */
|
||||
/* > If singular vectors are desired, then LDU >= f2cmax( 1, N ). */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] VT */
|
||||
/* > \verbatim */
|
||||
/* > VT is REAL array, dimension (LDVT,N) */
|
||||
/* > If COMPQ = 'I', then: */
|
||||
/* > On exit, if INFO = 0, VT**T contains the right singular */
|
||||
/* > vectors of the bidiagonal matrix. */
|
||||
/* > For other values of COMPQ, VT is not referenced. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] LDVT */
|
||||
/* > \verbatim */
|
||||
/* > LDVT is INTEGER */
|
||||
/* > The leading dimension of the array VT. LDVT >= 1. */
|
||||
/* > If singular vectors are desired, then LDVT >= f2cmax( 1, N ). */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] Q */
|
||||
/* > \verbatim */
|
||||
/* > Q is REAL array, dimension (LDQ) */
|
||||
/* > If COMPQ = 'P', then: */
|
||||
/* > On exit, if INFO = 0, Q and IQ contain the left */
|
||||
/* > and right singular vectors in a compact form, */
|
||||
/* > requiring O(N log N) space instead of 2*N**2. */
|
||||
/* > In particular, Q contains all the REAL data in */
|
||||
/* > LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1)))) */
|
||||
/* > words of memory, where SMLSIZ is returned by ILAENV and */
|
||||
/* > is equal to the maximum size of the subproblems at the */
|
||||
/* > bottom of the computation tree (usually about 25). */
|
||||
/* > For other values of COMPQ, Q is not referenced. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] IQ */
|
||||
/* > \verbatim */
|
||||
/* > IQ is INTEGER array, dimension (LDIQ) */
|
||||
/* > If COMPQ = 'P', then: */
|
||||
/* > On exit, if INFO = 0, Q and IQ contain the left */
|
||||
/* > and right singular vectors in a compact form, */
|
||||
/* > requiring O(N log N) space instead of 2*N**2. */
|
||||
/* > In particular, IQ contains all INTEGER data in */
|
||||
/* > LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1)))) */
|
||||
/* > words of memory, where SMLSIZ is returned by ILAENV and */
|
||||
/* > is equal to the maximum size of the subproblems at the */
|
||||
/* > bottom of the computation tree (usually about 25). */
|
||||
/* > For other values of COMPQ, IQ is not referenced. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] WORK */
|
||||
/* > \verbatim */
|
||||
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
|
||||
/* > If COMPQ = 'N' then LWORK >= (4 * N). */
|
||||
/* > If COMPQ = 'P' then LWORK >= (6 * N). */
|
||||
/* > If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N). */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] IWORK */
|
||||
/* > \verbatim */
|
||||
/* > IWORK is INTEGER array, dimension (8*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. */
|
||||
/* > The update process of divide and conquer failed. */
|
||||
/* > \endverbatim */
|
||||
|
||||
/* Authors: */
|
||||
/* ======== */
|
||||
|
||||
/* > \author Univ. of Tennessee */
|
||||
/* > \author Univ. of California Berkeley */
|
||||
/* > \author Univ. of Colorado Denver */
|
||||
/* > \author NAG Ltd. */
|
||||
|
||||
/* > \date June 2016 */
|
||||
|
||||
/* > \ingroup auxOTHERcomputational */
|
||||
|
||||
/* > \par Contributors: */
|
||||
/* ================== */
|
||||
/* > */
|
||||
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
|
||||
/* > California at Berkeley, USA */
|
||||
/* > */
|
||||
/* ===================================================================== */
|
||||
/* Subroutine */ int sbdsdc_(char *uplo, char *compq, integer *n, real *d__,
|
||||
real *e, real *u, integer *ldu, real *vt, integer *ldvt, real *q,
|
||||
integer *iq, real *work, integer *iwork, integer *info)
|
||||
{
|
||||
/* System generated locals */
|
||||
integer u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2;
|
||||
real r__1;
|
||||
|
||||
/* Local variables */
|
||||
integer difl, difr, ierr, perm, mlvl, sqre, i__, j, k;
|
||||
real p, r__;
|
||||
integer z__;
|
||||
extern logical lsame_(char *, char *);
|
||||
integer poles;
|
||||
extern /* Subroutine */ int slasr_(char *, char *, char *, integer *,
|
||||
integer *, real *, real *, real *, integer *);
|
||||
integer iuplo, nsize, start;
|
||||
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
|
||||
integer *), sswap_(integer *, real *, integer *, real *, integer *
|
||||
), slasd0_(integer *, integer *, real *, real *, real *, integer *
|
||||
, real *, integer *, integer *, integer *, real *, integer *);
|
||||
integer ic, ii, kk;
|
||||
real cs;
|
||||
integer is, iu;
|
||||
real sn;
|
||||
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 *),
|
||||
xerbla_(char *, integer *, ftnlen);
|
||||
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
||||
integer *, integer *, ftnlen, ftnlen);
|
||||
extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *,
|
||||
real *, integer *, integer *, real *, integer *, integer *);
|
||||
integer givcol;
|
||||
extern /* Subroutine */ int slasdq_(char *, integer *, integer *, integer
|
||||
*, integer *, integer *, real *, real *, real *, integer *, real *
|
||||
, integer *, real *, integer *, real *, integer *);
|
||||
integer icompq;
|
||||
extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *,
|
||||
real *, real *, integer *), slartg_(real *, real *, real *
|
||||
, real *, real *);
|
||||
real orgnrm;
|
||||
integer givnum;
|
||||
extern real slanst_(char *, integer *, real *, real *);
|
||||
integer givptr, nm1, qstart, smlsiz, wstart, smlszp;
|
||||
real eps;
|
||||
integer ivt;
|
||||
|
||||
|
||||
/* -- 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 2016 */
|
||||
|
||||
|
||||
/* ===================================================================== */
|
||||
/* Changed dimension statement in comment describing E from (N) to */
|
||||
/* (N-1). Sven, 17 Feb 05. */
|
||||
/* ===================================================================== */
|
||||
|
||||
|
||||
/* Test the input parameters. */
|
||||
|
||||
/* Parameter adjustments */
|
||||
--d__;
|
||||
--e;
|
||||
u_dim1 = *ldu;
|
||||
u_offset = 1 + u_dim1 * 1;
|
||||
u -= u_offset;
|
||||
vt_dim1 = *ldvt;
|
||||
vt_offset = 1 + vt_dim1 * 1;
|
||||
vt -= vt_offset;
|
||||
--q;
|
||||
--iq;
|
||||
--work;
|
||||
--iwork;
|
||||
|
||||
/* Function Body */
|
||||
*info = 0;
|
||||
|
||||
iuplo = 0;
|
||||
if (lsame_(uplo, "U")) {
|
||||
iuplo = 1;
|
||||
}
|
||||
if (lsame_(uplo, "L")) {
|
||||
iuplo = 2;
|
||||
}
|
||||
if (lsame_(compq, "N")) {
|
||||
icompq = 0;
|
||||
} else if (lsame_(compq, "P")) {
|
||||
icompq = 1;
|
||||
} else if (lsame_(compq, "I")) {
|
||||
icompq = 2;
|
||||
} else {
|
||||
icompq = -1;
|
||||
}
|
||||
if (iuplo == 0) {
|
||||
*info = -1;
|
||||
} else if (icompq < 0) {
|
||||
*info = -2;
|
||||
} else if (*n < 0) {
|
||||
*info = -3;
|
||||
} else if (*ldu < 1 || icompq == 2 && *ldu < *n) {
|
||||
*info = -7;
|
||||
} else if (*ldvt < 1 || icompq == 2 && *ldvt < *n) {
|
||||
*info = -9;
|
||||
}
|
||||
if (*info != 0) {
|
||||
i__1 = -(*info);
|
||||
xerbla_("SBDSDC", &i__1, (ftnlen)6);
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Quick return if possible */
|
||||
|
||||
if (*n == 0) {
|
||||
return 0;
|
||||
}
|
||||
smlsiz = ilaenv_(&c__9, "SBDSDC", " ", &c__0, &c__0, &c__0, &c__0, (
|
||||
ftnlen)6, (ftnlen)1);
|
||||
if (*n == 1) {
|
||||
if (icompq == 1) {
|
||||
q[1] = r_sign(&c_b15, &d__[1]);
|
||||
q[smlsiz * *n + 1] = 1.f;
|
||||
} else if (icompq == 2) {
|
||||
u[u_dim1 + 1] = r_sign(&c_b15, &d__[1]);
|
||||
vt[vt_dim1 + 1] = 1.f;
|
||||
}
|
||||
d__[1] = abs(d__[1]);
|
||||
return 0;
|
||||
}
|
||||
nm1 = *n - 1;
|
||||
|
||||
/* If matrix lower bidiagonal, rotate to be upper bidiagonal */
|
||||
/* by applying Givens rotations on the left */
|
||||
|
||||
wstart = 1;
|
||||
qstart = 3;
|
||||
if (icompq == 1) {
|
||||
scopy_(n, &d__[1], &c__1, &q[1], &c__1);
|
||||
i__1 = *n - 1;
|
||||
scopy_(&i__1, &e[1], &c__1, &q[*n + 1], &c__1);
|
||||
}
|
||||
if (iuplo == 2) {
|
||||
qstart = 5;
|
||||
if (icompq == 2) {
|
||||
wstart = (*n << 1) - 1;
|
||||
}
|
||||
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 (icompq == 1) {
|
||||
q[i__ + (*n << 1)] = cs;
|
||||
q[i__ + *n * 3] = sn;
|
||||
} else if (icompq == 2) {
|
||||
work[i__] = cs;
|
||||
work[nm1 + i__] = -sn;
|
||||
}
|
||||
/* L10: */
|
||||
}
|
||||
}
|
||||
|
||||
/* If ICOMPQ = 0, use SLASDQ to compute the singular values. */
|
||||
|
||||
if (icompq == 0) {
|
||||
/* Ignore WSTART, instead using WORK( 1 ), since the two vectors */
|
||||
/* for CS and -SN above are added only if ICOMPQ == 2, */
|
||||
/* and adding them exceeds documented WORK size of 4*n. */
|
||||
slasdq_("U", &c__0, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
|
||||
vt_offset], ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[
|
||||
1], info);
|
||||
goto L40;
|
||||
}
|
||||
|
||||
/* If N is smaller than the minimum divide size SMLSIZ, then solve */
|
||||
/* the problem with another solver. */
|
||||
|
||||
if (*n <= smlsiz) {
|
||||
if (icompq == 2) {
|
||||
slaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu);
|
||||
slaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt);
|
||||
slasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
|
||||
, ldvt, &u[u_offset], ldu, &u[u_offset], ldu, &work[
|
||||
wstart], info);
|
||||
} else if (icompq == 1) {
|
||||
iu = 1;
|
||||
ivt = iu + *n;
|
||||
slaset_("A", n, n, &c_b29, &c_b15, &q[iu + (qstart - 1) * *n], n);
|
||||
slaset_("A", n, n, &c_b29, &c_b15, &q[ivt + (qstart - 1) * *n], n);
|
||||
slasdq_("U", &c__0, n, n, n, &c__0, &d__[1], &e[1], &q[ivt + (
|
||||
qstart - 1) * *n], n, &q[iu + (qstart - 1) * *n], n, &q[
|
||||
iu + (qstart - 1) * *n], n, &work[wstart], info);
|
||||
}
|
||||
goto L40;
|
||||
}
|
||||
|
||||
if (icompq == 2) {
|
||||
slaset_("A", n, n, &c_b29, &c_b15, &u[u_offset], ldu);
|
||||
slaset_("A", n, n, &c_b29, &c_b15, &vt[vt_offset], ldvt);
|
||||
}
|
||||
|
||||
/* Scale. */
|
||||
|
||||
orgnrm = slanst_("M", n, &d__[1], &e[1]);
|
||||
if (orgnrm == 0.f) {
|
||||
return 0;
|
||||
}
|
||||
slascl_("G", &c__0, &c__0, &orgnrm, &c_b15, n, &c__1, &d__[1], n, &ierr);
|
||||
slascl_("G", &c__0, &c__0, &orgnrm, &c_b15, &nm1, &c__1, &e[1], &nm1, &
|
||||
ierr);
|
||||
|
||||
eps = slamch_("Epsilon");
|
||||
|
||||
mlvl = (integer) (log((real) (*n) / (real) (smlsiz + 1)) / log(2.f)) + 1;
|
||||
smlszp = smlsiz + 1;
|
||||
|
||||
if (icompq == 1) {
|
||||
iu = 1;
|
||||
ivt = smlsiz + 1;
|
||||
difl = ivt + smlszp;
|
||||
difr = difl + mlvl;
|
||||
z__ = difr + (mlvl << 1);
|
||||
ic = z__ + mlvl;
|
||||
is = ic + 1;
|
||||
poles = is + 1;
|
||||
givnum = poles + (mlvl << 1);
|
||||
|
||||
k = 1;
|
||||
givptr = 2;
|
||||
perm = 3;
|
||||
givcol = perm + mlvl;
|
||||
}
|
||||
|
||||
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__]);
|
||||
}
|
||||
/* L20: */
|
||||
}
|
||||
|
||||
start = 1;
|
||||
sqre = 0;
|
||||
|
||||
i__1 = nm1;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
if ((r__1 = e[i__], abs(r__1)) < eps || i__ == nm1) {
|
||||
|
||||
/* 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__ - start + 1;
|
||||
} else if ((r__1 = e[i__], abs(r__1)) >= eps) {
|
||||
|
||||
/* A subproblem with E(NM1) not too small but I = NM1. */
|
||||
|
||||
nsize = *n - start + 1;
|
||||
} else {
|
||||
|
||||
/* A subproblem with E(NM1) small. This implies an */
|
||||
/* 1-by-1 subproblem at D(N). Solve this 1-by-1 problem */
|
||||
/* first. */
|
||||
|
||||
nsize = i__ - start + 1;
|
||||
if (icompq == 2) {
|
||||
u[*n + *n * u_dim1] = r_sign(&c_b15, &d__[*n]);
|
||||
vt[*n + *n * vt_dim1] = 1.f;
|
||||
} else if (icompq == 1) {
|
||||
q[*n + (qstart - 1) * *n] = r_sign(&c_b15, &d__[*n]);
|
||||
q[*n + (smlsiz + qstart - 1) * *n] = 1.f;
|
||||
}
|
||||
d__[*n] = (r__1 = d__[*n], abs(r__1));
|
||||
}
|
||||
if (icompq == 2) {
|
||||
slasd0_(&nsize, &sqre, &d__[start], &e[start], &u[start +
|
||||
start * u_dim1], ldu, &vt[start + start * vt_dim1],
|
||||
ldvt, &smlsiz, &iwork[1], &work[wstart], info);
|
||||
} else {
|
||||
slasda_(&icompq, &smlsiz, &nsize, &sqre, &d__[start], &e[
|
||||
start], &q[start + (iu + qstart - 2) * *n], n, &q[
|
||||
start + (ivt + qstart - 2) * *n], &iq[start + k * *n],
|
||||
&q[start + (difl + qstart - 2) * *n], &q[start + (
|
||||
difr + qstart - 2) * *n], &q[start + (z__ + qstart -
|
||||
2) * *n], &q[start + (poles + qstart - 2) * *n], &iq[
|
||||
start + givptr * *n], &iq[start + givcol * *n], n, &
|
||||
iq[start + perm * *n], &q[start + (givnum + qstart -
|
||||
2) * *n], &q[start + (ic + qstart - 2) * *n], &q[
|
||||
start + (is + qstart - 2) * *n], &work[wstart], &
|
||||
iwork[1], info);
|
||||
}
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
start = i__ + 1;
|
||||
}
|
||||
/* L30: */
|
||||
}
|
||||
|
||||
/* Unscale */
|
||||
|
||||
slascl_("G", &c__0, &c__0, &c_b15, &orgnrm, n, &c__1, &d__[1], n, &ierr);
|
||||
L40:
|
||||
|
||||
/* Use Selection Sort to minimize swaps of singular vectors */
|
||||
|
||||
i__1 = *n;
|
||||
for (ii = 2; ii <= i__1; ++ii) {
|
||||
i__ = ii - 1;
|
||||
kk = i__;
|
||||
p = d__[i__];
|
||||
i__2 = *n;
|
||||
for (j = ii; j <= i__2; ++j) {
|
||||
if (d__[j] > p) {
|
||||
kk = j;
|
||||
p = d__[j];
|
||||
}
|
||||
/* L50: */
|
||||
}
|
||||
if (kk != i__) {
|
||||
d__[kk] = d__[i__];
|
||||
d__[i__] = p;
|
||||
if (icompq == 1) {
|
||||
iq[i__] = kk;
|
||||
} else if (icompq == 2) {
|
||||
sswap_(n, &u[i__ * u_dim1 + 1], &c__1, &u[kk * u_dim1 + 1], &
|
||||
c__1);
|
||||
sswap_(n, &vt[i__ + vt_dim1], ldvt, &vt[kk + vt_dim1], ldvt);
|
||||
}
|
||||
} else if (icompq == 1) {
|
||||
iq[i__] = i__;
|
||||
}
|
||||
/* L60: */
|
||||
}
|
||||
|
||||
/* If ICOMPQ = 1, use IQ(N,1) as the indicator for UPLO */
|
||||
|
||||
if (icompq == 1) {
|
||||
if (iuplo == 1) {
|
||||
iq[*n] = 1;
|
||||
} else {
|
||||
iq[*n] = 0;
|
||||
}
|
||||
}
|
||||
|
||||
/* If B is lower bidiagonal, update U by those Givens rotations */
|
||||
/* which rotated B to be upper bidiagonal */
|
||||
|
||||
if (iuplo == 2 && icompq == 2) {
|
||||
slasr_("L", "V", "B", n, n, &work[1], &work[*n], &u[u_offset], ldu);
|
||||
}
|
||||
|
||||
return 0;
|
||||
|
||||
/* End of SBDSDC */
|
||||
|
||||
} /* sbdsdc_ */
|
||||
|
||||
Reference in New Issue
Block a user