1589 lines
44 KiB
C
1589 lines
44 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]/Cd(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle_() continue;
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#define myceiling_(w) {ceil(w)}
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#define myhuge_(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc_(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Table of constant values */
|
|
|
|
static doublecomplex c_b1 = {1.,0.};
|
|
|
|
/* > \brief \b ZTFSM solves a matrix equation (one operand is a triangular matrix in RFP format). */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download ZTFSM + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztfsm.f
|
|
"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztfsm.f
|
|
"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztfsm.f
|
|
"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, */
|
|
/* B, LDB ) */
|
|
|
|
/* CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO */
|
|
/* INTEGER LDB, M, N */
|
|
/* COMPLEX*16 ALPHA */
|
|
/* COMPLEX*16 A( 0: * ), B( 0: LDB-1, 0: * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Level 3 BLAS like routine for A in RFP Format. */
|
|
/* > */
|
|
/* > ZTFSM solves the matrix equation */
|
|
/* > */
|
|
/* > op( A )*X = alpha*B or X*op( A ) = alpha*B */
|
|
/* > */
|
|
/* > where alpha is a scalar, X and B are m by n matrices, A is a unit, or */
|
|
/* > non-unit, upper or lower triangular matrix and op( A ) is one of */
|
|
/* > */
|
|
/* > op( A ) = A or op( A ) = A**H. */
|
|
/* > */
|
|
/* > A is in Rectangular Full Packed (RFP) Format. */
|
|
/* > */
|
|
/* > The matrix X is overwritten on B. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] TRANSR */
|
|
/* > \verbatim */
|
|
/* > TRANSR is CHARACTER*1 */
|
|
/* > = 'N': The Normal Form of RFP A is stored; */
|
|
/* > = 'C': The Conjugate-transpose Form of RFP A is stored. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] SIDE */
|
|
/* > \verbatim */
|
|
/* > SIDE is CHARACTER*1 */
|
|
/* > On entry, SIDE specifies whether op( A ) appears on the left */
|
|
/* > or right of X as follows: */
|
|
/* > */
|
|
/* > SIDE = 'L' or 'l' op( A )*X = alpha*B. */
|
|
/* > */
|
|
/* > SIDE = 'R' or 'r' X*op( A ) = alpha*B. */
|
|
/* > */
|
|
/* > Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > On entry, UPLO specifies whether the RFP matrix A came from */
|
|
/* > an upper or lower triangular matrix as follows: */
|
|
/* > UPLO = 'U' or 'u' RFP A came from an upper triangular matrix */
|
|
/* > UPLO = 'L' or 'l' RFP A came from a lower triangular matrix */
|
|
/* > */
|
|
/* > Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] TRANS */
|
|
/* > \verbatim */
|
|
/* > TRANS is CHARACTER*1 */
|
|
/* > On entry, TRANS specifies the form of op( A ) to be used */
|
|
/* > in the matrix multiplication as follows: */
|
|
/* > */
|
|
/* > TRANS = 'N' or 'n' op( A ) = A. */
|
|
/* > */
|
|
/* > TRANS = 'C' or 'c' op( A ) = conjg( A' ). */
|
|
/* > */
|
|
/* > Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] DIAG */
|
|
/* > \verbatim */
|
|
/* > DIAG is CHARACTER*1 */
|
|
/* > On entry, DIAG specifies whether or not RFP A is unit */
|
|
/* > triangular as follows: */
|
|
/* > */
|
|
/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */
|
|
/* > */
|
|
/* > DIAG = 'N' or 'n' A is not assumed to be unit */
|
|
/* > triangular. */
|
|
/* > */
|
|
/* > Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > On entry, M specifies the number of rows of B. M must be at */
|
|
/* > least zero. */
|
|
/* > Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > On entry, N specifies the number of columns of B. N must be */
|
|
/* > at least zero. */
|
|
/* > Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is COMPLEX*16 */
|
|
/* > On entry, ALPHA specifies the scalar alpha. When alpha is */
|
|
/* > zero then A is not referenced and B need not be set before */
|
|
/* > entry. */
|
|
/* > Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension (N*(N+1)/2) */
|
|
/* > NT = N*(N+1)/2. On entry, the matrix A in RFP Format. */
|
|
/* > RFP Format is described by TRANSR, UPLO and N as follows: */
|
|
/* > If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; */
|
|
/* > K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If */
|
|
/* > TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as */
|
|
/* > defined when TRANSR = 'N'. The contents of RFP A are defined */
|
|
/* > by UPLO as follows: If UPLO = 'U' the RFP A contains the NT */
|
|
/* > elements of upper packed A either in normal or */
|
|
/* > conjugate-transpose Format. If UPLO = 'L' the RFP A contains */
|
|
/* > the NT elements of lower packed A either in normal or */
|
|
/* > conjugate-transpose Format. The LDA of RFP A is (N+1)/2 when */
|
|
/* > TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is */
|
|
/* > even and is N when is odd. */
|
|
/* > See the Note below for more details. Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] B */
|
|
/* > \verbatim */
|
|
/* > B is COMPLEX*16 array, dimension (LDB,N) */
|
|
/* > Before entry, the leading m by n part of the array B must */
|
|
/* > contain the right-hand side matrix B, and on exit is */
|
|
/* > overwritten by the solution matrix X. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDB */
|
|
/* > \verbatim */
|
|
/* > LDB is INTEGER */
|
|
/* > On entry, LDB specifies the first dimension of B as declared */
|
|
/* > in the calling (sub) program. LDB must be at least */
|
|
/* > f2cmax( 1, m ). */
|
|
/* > Unchanged on exit. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complex16OTHERcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > We first consider Standard Packed Format when N is even. */
|
|
/* > We give an example where N = 6. */
|
|
/* > */
|
|
/* > AP is Upper AP is Lower */
|
|
/* > */
|
|
/* > 00 01 02 03 04 05 00 */
|
|
/* > 11 12 13 14 15 10 11 */
|
|
/* > 22 23 24 25 20 21 22 */
|
|
/* > 33 34 35 30 31 32 33 */
|
|
/* > 44 45 40 41 42 43 44 */
|
|
/* > 55 50 51 52 53 54 55 */
|
|
/* > */
|
|
/* > */
|
|
/* > Let TRANSR = 'N'. RFP holds AP as follows: */
|
|
/* > For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
|
|
/* > three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
|
|
/* > conjugate-transpose of the first three columns of AP upper. */
|
|
/* > For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
|
|
/* > three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
|
|
/* > conjugate-transpose of the last three columns of AP lower. */
|
|
/* > To denote conjugate we place -- above the element. This covers the */
|
|
/* > case N even and TRANSR = 'N'. */
|
|
/* > */
|
|
/* > RFP A RFP A */
|
|
/* > */
|
|
/* > -- -- -- */
|
|
/* > 03 04 05 33 43 53 */
|
|
/* > -- -- */
|
|
/* > 13 14 15 00 44 54 */
|
|
/* > -- */
|
|
/* > 23 24 25 10 11 55 */
|
|
/* > */
|
|
/* > 33 34 35 20 21 22 */
|
|
/* > -- */
|
|
/* > 00 44 45 30 31 32 */
|
|
/* > -- -- */
|
|
/* > 01 11 55 40 41 42 */
|
|
/* > -- -- -- */
|
|
/* > 02 12 22 50 51 52 */
|
|
/* > */
|
|
/* > Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- */
|
|
/* > transpose of RFP A above. One therefore gets: */
|
|
/* > */
|
|
/* > */
|
|
/* > RFP A RFP A */
|
|
/* > */
|
|
/* > -- -- -- -- -- -- -- -- -- -- */
|
|
/* > 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */
|
|
/* > -- -- -- -- -- -- -- -- -- -- */
|
|
/* > 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */
|
|
/* > -- -- -- -- -- -- -- -- -- -- */
|
|
/* > 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */
|
|
/* > */
|
|
/* > */
|
|
/* > We next consider Standard Packed Format when N is odd. */
|
|
/* > We give an example where N = 5. */
|
|
/* > */
|
|
/* > AP is Upper AP is Lower */
|
|
/* > */
|
|
/* > 00 01 02 03 04 00 */
|
|
/* > 11 12 13 14 10 11 */
|
|
/* > 22 23 24 20 21 22 */
|
|
/* > 33 34 30 31 32 33 */
|
|
/* > 44 40 41 42 43 44 */
|
|
/* > */
|
|
/* > */
|
|
/* > Let TRANSR = 'N'. RFP holds AP as follows: */
|
|
/* > For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
|
|
/* > three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
|
|
/* > conjugate-transpose of the first two columns of AP upper. */
|
|
/* > For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
|
|
/* > three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
|
|
/* > conjugate-transpose of the last two columns of AP lower. */
|
|
/* > To denote conjugate we place -- above the element. This covers the */
|
|
/* > case N odd and TRANSR = 'N'. */
|
|
/* > */
|
|
/* > RFP A RFP A */
|
|
/* > */
|
|
/* > -- -- */
|
|
/* > 02 03 04 00 33 43 */
|
|
/* > -- */
|
|
/* > 12 13 14 10 11 44 */
|
|
/* > */
|
|
/* > 22 23 24 20 21 22 */
|
|
/* > -- */
|
|
/* > 00 33 34 30 31 32 */
|
|
/* > -- -- */
|
|
/* > 01 11 44 40 41 42 */
|
|
/* > */
|
|
/* > Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- */
|
|
/* > transpose of RFP A above. One therefore gets: */
|
|
/* > */
|
|
/* > */
|
|
/* > RFP A RFP A */
|
|
/* > */
|
|
/* > -- -- -- -- -- -- -- -- -- */
|
|
/* > 02 12 22 00 01 00 10 20 30 40 50 */
|
|
/* > -- -- -- -- -- -- -- -- -- */
|
|
/* > 03 13 23 33 11 33 11 21 31 41 51 */
|
|
/* > -- -- -- -- -- -- -- -- -- */
|
|
/* > 04 14 24 34 44 43 44 22 32 42 52 */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void ztfsm_(char *transr, char *side, char *uplo, char *trans,
|
|
char *diag, integer *m, integer *n, doublecomplex *alpha,
|
|
doublecomplex *a, doublecomplex *b, integer *ldb)
|
|
{
|
|
/* System generated locals */
|
|
integer b_dim1, b_offset, i__1, i__2, i__3;
|
|
doublecomplex z__1;
|
|
|
|
/* Local variables */
|
|
integer info, i__, j, k;
|
|
logical normaltransr, lside;
|
|
extern logical lsame_(char *, char *);
|
|
extern /* Subroutine */ void zgemm_(char *, char *, integer *, integer *,
|
|
integer *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
|
|
integer *);
|
|
logical lower;
|
|
integer m1, m2, n1, n2;
|
|
extern /* Subroutine */ void ztrsm_(char *, char *, char *, char *,
|
|
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
|
|
doublecomplex *, integer *);
|
|
extern int xerbla_(char *, integer *, ftnlen);
|
|
logical misodd, nisodd, notrans;
|
|
|
|
|
|
/* -- 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 */
|
|
b_dim1 = *ldb - 1 - 0 + 1;
|
|
b_offset = 0 + b_dim1 * 0;
|
|
b -= b_offset;
|
|
|
|
/* Function Body */
|
|
info = 0;
|
|
normaltransr = lsame_(transr, "N");
|
|
lside = lsame_(side, "L");
|
|
lower = lsame_(uplo, "L");
|
|
notrans = lsame_(trans, "N");
|
|
if (! normaltransr && ! lsame_(transr, "C")) {
|
|
info = -1;
|
|
} else if (! lside && ! lsame_(side, "R")) {
|
|
info = -2;
|
|
} else if (! lower && ! lsame_(uplo, "U")) {
|
|
info = -3;
|
|
} else if (! notrans && ! lsame_(trans, "C")) {
|
|
info = -4;
|
|
} else if (! lsame_(diag, "N") && ! lsame_(diag,
|
|
"U")) {
|
|
info = -5;
|
|
} else if (*m < 0) {
|
|
info = -6;
|
|
} else if (*n < 0) {
|
|
info = -7;
|
|
} else if (*ldb < f2cmax(1,*m)) {
|
|
info = -11;
|
|
}
|
|
if (info != 0) {
|
|
i__1 = -info;
|
|
xerbla_("ZTFSM ", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return when ( (N.EQ.0).OR.(M.EQ.0) ) */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Quick return when ALPHA.EQ.(0D+0,0D+0) */
|
|
|
|
if (alpha->r == 0. && alpha->i == 0.) {
|
|
i__1 = *n - 1;
|
|
for (j = 0; j <= i__1; ++j) {
|
|
i__2 = *m - 1;
|
|
for (i__ = 0; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * b_dim1;
|
|
b[i__3].r = 0., b[i__3].i = 0.;
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
return;
|
|
}
|
|
|
|
if (lside) {
|
|
|
|
/* SIDE = 'L' */
|
|
|
|
/* A is M-by-M. */
|
|
/* If M is odd, set NISODD = .TRUE., and M1 and M2. */
|
|
/* If M is even, NISODD = .FALSE., and M. */
|
|
|
|
if (*m % 2 == 0) {
|
|
misodd = FALSE_;
|
|
k = *m / 2;
|
|
} else {
|
|
misodd = TRUE_;
|
|
if (lower) {
|
|
m2 = *m / 2;
|
|
m1 = *m - m2;
|
|
} else {
|
|
m1 = *m / 2;
|
|
m2 = *m - m1;
|
|
}
|
|
}
|
|
|
|
if (misodd) {
|
|
|
|
/* SIDE = 'L' and N is odd */
|
|
|
|
if (normaltransr) {
|
|
|
|
/* SIDE = 'L', N is odd, and TRANSR = 'N' */
|
|
|
|
if (lower) {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'L' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and */
|
|
/* TRANS = 'N' */
|
|
|
|
if (*m == 1) {
|
|
ztrsm_("L", "L", "N", diag, &m1, n, alpha, a, m, &
|
|
b[b_offset], ldb);
|
|
} else {
|
|
ztrsm_("L", "L", "N", diag, &m1, n, alpha, a, m, &
|
|
b[b_offset], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", &m2, n, &m1, &z__1, &a[m1], m, &
|
|
b[b_offset], ldb, alpha, &b[m1], ldb);
|
|
ztrsm_("L", "U", "C", diag, &m2, n, &c_b1, &a[*m],
|
|
m, &b[m1], ldb);
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and */
|
|
/* TRANS = 'C' */
|
|
|
|
if (*m == 1) {
|
|
ztrsm_("L", "L", "C", diag, &m1, n, alpha, a, m, &
|
|
b[b_offset], ldb);
|
|
} else {
|
|
ztrsm_("L", "U", "N", diag, &m2, n, alpha, &a[*m],
|
|
m, &b[m1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("C", "N", &m1, n, &m2, &z__1, &a[m1], m, &
|
|
b[m1], ldb, alpha, &b[b_offset], ldb);
|
|
ztrsm_("L", "L", "C", diag, &m1, n, &c_b1, a, m, &
|
|
b[b_offset], ldb);
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'U' */
|
|
|
|
if (! notrans) {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and */
|
|
/* TRANS = 'N' */
|
|
|
|
ztrsm_("L", "L", "N", diag, &m1, n, alpha, &a[m2], m,
|
|
&b[b_offset], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("C", "N", &m2, n, &m1, &z__1, a, m, &b[
|
|
b_offset], ldb, alpha, &b[m1], ldb);
|
|
ztrsm_("L", "U", "C", diag, &m2, n, &c_b1, &a[m1], m,
|
|
&b[m1], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and */
|
|
/* TRANS = 'C' */
|
|
|
|
ztrsm_("L", "U", "N", diag, &m2, n, alpha, &a[m1], m,
|
|
&b[m1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", &m1, n, &m2, &z__1, a, m, &b[m1],
|
|
ldb, alpha, &b[b_offset], ldb);
|
|
ztrsm_("L", "L", "C", diag, &m1, n, &c_b1, &a[m2], m,
|
|
&b[b_offset], ldb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE = 'L', N is odd, and TRANSR = 'C' */
|
|
|
|
if (lower) {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'C', and UPLO = 'L' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'L', and */
|
|
/* TRANS = 'N' */
|
|
|
|
if (*m == 1) {
|
|
ztrsm_("L", "U", "C", diag, &m1, n, alpha, a, &m1,
|
|
&b[b_offset], ldb);
|
|
} else {
|
|
ztrsm_("L", "U", "C", diag, &m1, n, alpha, a, &m1,
|
|
&b[b_offset], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("C", "N", &m2, n, &m1, &z__1, &a[m1 * m1],
|
|
&m1, &b[b_offset], ldb, alpha, &b[m1],
|
|
ldb);
|
|
ztrsm_("L", "L", "N", diag, &m2, n, &c_b1, &a[1],
|
|
&m1, &b[m1], ldb);
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'L', and */
|
|
/* TRANS = 'C' */
|
|
|
|
if (*m == 1) {
|
|
ztrsm_("L", "U", "N", diag, &m1, n, alpha, a, &m1,
|
|
&b[b_offset], ldb);
|
|
} else {
|
|
ztrsm_("L", "L", "C", diag, &m2, n, alpha, &a[1],
|
|
&m1, &b[m1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", &m1, n, &m2, &z__1, &a[m1 * m1],
|
|
&m1, &b[m1], ldb, alpha, &b[b_offset],
|
|
ldb);
|
|
ztrsm_("L", "U", "N", diag, &m1, n, &c_b1, a, &m1,
|
|
&b[b_offset], ldb);
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'C', and UPLO = 'U' */
|
|
|
|
if (! notrans) {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'U', and */
|
|
/* TRANS = 'N' */
|
|
|
|
ztrsm_("L", "U", "C", diag, &m1, n, alpha, &a[m2 * m2]
|
|
, &m2, &b[b_offset], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", &m2, n, &m1, &z__1, a, &m2, &b[
|
|
b_offset], ldb, alpha, &b[m1], ldb);
|
|
ztrsm_("L", "L", "N", diag, &m2, n, &c_b1, &a[m1 * m2]
|
|
, &m2, &b[m1], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is odd, TRANSR = 'C', UPLO = 'U', and */
|
|
/* TRANS = 'C' */
|
|
|
|
ztrsm_("L", "L", "C", diag, &m2, n, alpha, &a[m1 * m2]
|
|
, &m2, &b[m1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("C", "N", &m1, n, &m2, &z__1, a, &m2, &b[m1],
|
|
ldb, alpha, &b[b_offset], ldb);
|
|
ztrsm_("L", "U", "N", diag, &m1, n, &c_b1, &a[m2 * m2]
|
|
, &m2, &b[b_offset], ldb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE = 'L' and N is even */
|
|
|
|
if (normaltransr) {
|
|
|
|
/* SIDE = 'L', N is even, and TRANSR = 'N' */
|
|
|
|
if (lower) {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'L' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L', */
|
|
/* and TRANS = 'N' */
|
|
|
|
i__1 = *m + 1;
|
|
ztrsm_("L", "L", "N", diag, &k, n, alpha, &a[1], &
|
|
i__1, &b[b_offset], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
i__1 = *m + 1;
|
|
zgemm_("N", "N", &k, n, &k, &z__1, &a[k + 1], &i__1, &
|
|
b[b_offset], ldb, alpha, &b[k], ldb);
|
|
i__1 = *m + 1;
|
|
ztrsm_("L", "U", "C", diag, &k, n, &c_b1, a, &i__1, &
|
|
b[k], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L', */
|
|
/* and TRANS = 'C' */
|
|
|
|
i__1 = *m + 1;
|
|
ztrsm_("L", "U", "N", diag, &k, n, alpha, a, &i__1, &
|
|
b[k], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
i__1 = *m + 1;
|
|
zgemm_("C", "N", &k, n, &k, &z__1, &a[k + 1], &i__1, &
|
|
b[k], ldb, alpha, &b[b_offset], ldb);
|
|
i__1 = *m + 1;
|
|
ztrsm_("L", "L", "C", diag, &k, n, &c_b1, &a[1], &
|
|
i__1, &b[b_offset], ldb);
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'U' */
|
|
|
|
if (! notrans) {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U', */
|
|
/* and TRANS = 'N' */
|
|
|
|
i__1 = *m + 1;
|
|
ztrsm_("L", "L", "N", diag, &k, n, alpha, &a[k + 1], &
|
|
i__1, &b[b_offset], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
i__1 = *m + 1;
|
|
zgemm_("C", "N", &k, n, &k, &z__1, a, &i__1, &b[
|
|
b_offset], ldb, alpha, &b[k], ldb);
|
|
i__1 = *m + 1;
|
|
ztrsm_("L", "U", "C", diag, &k, n, &c_b1, &a[k], &
|
|
i__1, &b[k], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U', */
|
|
/* and TRANS = 'C' */
|
|
i__1 = *m + 1;
|
|
ztrsm_("L", "U", "N", diag, &k, n, alpha, &a[k], &
|
|
i__1, &b[k], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
i__1 = *m + 1;
|
|
zgemm_("N", "N", &k, n, &k, &z__1, a, &i__1, &b[k],
|
|
ldb, alpha, &b[b_offset], ldb);
|
|
i__1 = *m + 1;
|
|
ztrsm_("L", "L", "C", diag, &k, n, &c_b1, &a[k + 1], &
|
|
i__1, &b[b_offset], ldb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE = 'L', N is even, and TRANSR = 'C' */
|
|
|
|
if (lower) {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'C', and UPLO = 'L' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'L', */
|
|
/* and TRANS = 'N' */
|
|
|
|
ztrsm_("L", "U", "C", diag, &k, n, alpha, &a[k], &k, &
|
|
b[b_offset], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("C", "N", &k, n, &k, &z__1, &a[k * (k + 1)], &
|
|
k, &b[b_offset], ldb, alpha, &b[k], ldb);
|
|
ztrsm_("L", "L", "N", diag, &k, n, &c_b1, a, &k, &b[k]
|
|
, ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'L', */
|
|
/* and TRANS = 'C' */
|
|
|
|
ztrsm_("L", "L", "C", diag, &k, n, alpha, a, &k, &b[k]
|
|
, ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", &k, n, &k, &z__1, &a[k * (k + 1)], &
|
|
k, &b[k], ldb, alpha, &b[b_offset], ldb);
|
|
ztrsm_("L", "U", "N", diag, &k, n, &c_b1, &a[k], &k, &
|
|
b[b_offset], ldb);
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'C', and UPLO = 'U' */
|
|
|
|
if (! notrans) {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'U', */
|
|
/* and TRANS = 'N' */
|
|
|
|
ztrsm_("L", "U", "C", diag, &k, n, alpha, &a[k * (k +
|
|
1)], &k, &b[b_offset], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", &k, n, &k, &z__1, a, &k, &b[b_offset]
|
|
, ldb, alpha, &b[k], ldb);
|
|
ztrsm_("L", "L", "N", diag, &k, n, &c_b1, &a[k * k], &
|
|
k, &b[k], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='L', N is even, TRANSR = 'C', UPLO = 'U', */
|
|
/* and TRANS = 'C' */
|
|
|
|
ztrsm_("L", "L", "C", diag, &k, n, alpha, &a[k * k], &
|
|
k, &b[k], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("C", "N", &k, n, &k, &z__1, a, &k, &b[k], ldb,
|
|
alpha, &b[b_offset], ldb);
|
|
ztrsm_("L", "U", "N", diag, &k, n, &c_b1, &a[k * (k +
|
|
1)], &k, &b[b_offset], ldb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE = 'R' */
|
|
|
|
/* A is N-by-N. */
|
|
/* If N is odd, set NISODD = .TRUE., and N1 and N2. */
|
|
/* If N is even, NISODD = .FALSE., and K. */
|
|
|
|
if (*n % 2 == 0) {
|
|
nisodd = FALSE_;
|
|
k = *n / 2;
|
|
} else {
|
|
nisodd = TRUE_;
|
|
if (lower) {
|
|
n2 = *n / 2;
|
|
n1 = *n - n2;
|
|
} else {
|
|
n1 = *n / 2;
|
|
n2 = *n - n1;
|
|
}
|
|
}
|
|
|
|
if (nisodd) {
|
|
|
|
/* SIDE = 'R' and N is odd */
|
|
|
|
if (normaltransr) {
|
|
|
|
/* SIDE = 'R', N is odd, and TRANSR = 'N' */
|
|
|
|
if (lower) {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'L' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and */
|
|
/* TRANS = 'N' */
|
|
|
|
ztrsm_("R", "U", "C", diag, m, &n2, alpha, &a[*n], n,
|
|
&b[n1 * b_dim1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", m, &n1, &n2, &z__1, &b[n1 * b_dim1],
|
|
ldb, &a[n1], n, alpha, b, ldb);
|
|
ztrsm_("R", "L", "N", diag, m, &n1, &c_b1, a, n, b,
|
|
ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and */
|
|
/* TRANS = 'C' */
|
|
|
|
ztrsm_("R", "L", "C", diag, m, &n1, alpha, a, n, b,
|
|
ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "C", m, &n2, &n1, &z__1, b, ldb, &a[n1],
|
|
n, alpha, &b[n1 * b_dim1], ldb);
|
|
ztrsm_("R", "U", "N", diag, m, &n2, &c_b1, &a[*n], n,
|
|
&b[n1 * b_dim1], ldb);
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'U' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and */
|
|
/* TRANS = 'N' */
|
|
|
|
ztrsm_("R", "L", "C", diag, m, &n1, alpha, &a[n2], n,
|
|
b, ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", m, &n2, &n1, &z__1, b, ldb, a, n,
|
|
alpha, &b[n1 * b_dim1], ldb);
|
|
ztrsm_("R", "U", "N", diag, m, &n2, &c_b1, &a[n1], n,
|
|
&b[n1 * b_dim1], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and */
|
|
/* TRANS = 'C' */
|
|
|
|
ztrsm_("R", "U", "C", diag, m, &n2, alpha, &a[n1], n,
|
|
&b[n1 * b_dim1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "C", m, &n1, &n2, &z__1, &b[n1 * b_dim1],
|
|
ldb, a, n, alpha, b, ldb);
|
|
ztrsm_("R", "L", "N", diag, m, &n1, &c_b1, &a[n2], n,
|
|
b, ldb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE = 'R', N is odd, and TRANSR = 'C' */
|
|
|
|
if (lower) {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'C', and UPLO = 'L' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'L', and */
|
|
/* TRANS = 'N' */
|
|
|
|
ztrsm_("R", "L", "N", diag, m, &n2, alpha, &a[1], &n1,
|
|
&b[n1 * b_dim1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "C", m, &n1, &n2, &z__1, &b[n1 * b_dim1],
|
|
ldb, &a[n1 * n1], &n1, alpha, b, ldb);
|
|
ztrsm_("R", "U", "C", diag, m, &n1, &c_b1, a, &n1, b,
|
|
ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'L', and */
|
|
/* TRANS = 'C' */
|
|
|
|
ztrsm_("R", "U", "N", diag, m, &n1, alpha, a, &n1, b,
|
|
ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", m, &n2, &n1, &z__1, b, ldb, &a[n1 *
|
|
n1], &n1, alpha, &b[n1 * b_dim1], ldb);
|
|
ztrsm_("R", "L", "C", diag, m, &n2, &c_b1, &a[1], &n1,
|
|
&b[n1 * b_dim1], ldb);
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'C', and UPLO = 'U' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'U', and */
|
|
/* TRANS = 'N' */
|
|
|
|
ztrsm_("R", "U", "N", diag, m, &n1, alpha, &a[n2 * n2]
|
|
, &n2, b, ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "C", m, &n2, &n1, &z__1, b, ldb, a, &n2,
|
|
alpha, &b[n1 * b_dim1], ldb);
|
|
ztrsm_("R", "L", "C", diag, m, &n2, &c_b1, &a[n1 * n2]
|
|
, &n2, &b[n1 * b_dim1], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is odd, TRANSR = 'C', UPLO = 'U', and */
|
|
/* TRANS = 'C' */
|
|
|
|
ztrsm_("R", "L", "N", diag, m, &n2, alpha, &a[n1 * n2]
|
|
, &n2, &b[n1 * b_dim1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", m, &n1, &n2, &z__1, &b[n1 * b_dim1],
|
|
ldb, a, &n2, alpha, b, ldb);
|
|
ztrsm_("R", "U", "C", diag, m, &n1, &c_b1, &a[n2 * n2]
|
|
, &n2, b, ldb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE = 'R' and N is even */
|
|
|
|
if (normaltransr) {
|
|
|
|
/* SIDE = 'R', N is even, and TRANSR = 'N' */
|
|
|
|
if (lower) {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'L' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L', */
|
|
/* and TRANS = 'N' */
|
|
|
|
i__1 = *n + 1;
|
|
ztrsm_("R", "U", "C", diag, m, &k, alpha, a, &i__1, &
|
|
b[k * b_dim1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
i__1 = *n + 1;
|
|
zgemm_("N", "N", m, &k, &k, &z__1, &b[k * b_dim1],
|
|
ldb, &a[k + 1], &i__1, alpha, b, ldb);
|
|
i__1 = *n + 1;
|
|
ztrsm_("R", "L", "N", diag, m, &k, &c_b1, &a[1], &
|
|
i__1, b, ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L', */
|
|
/* and TRANS = 'C' */
|
|
|
|
i__1 = *n + 1;
|
|
ztrsm_("R", "L", "C", diag, m, &k, alpha, &a[1], &
|
|
i__1, b, ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
i__1 = *n + 1;
|
|
zgemm_("N", "C", m, &k, &k, &z__1, b, ldb, &a[k + 1],
|
|
&i__1, alpha, &b[k * b_dim1], ldb);
|
|
i__1 = *n + 1;
|
|
ztrsm_("R", "U", "N", diag, m, &k, &c_b1, a, &i__1, &
|
|
b[k * b_dim1], ldb);
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'U' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U', */
|
|
/* and TRANS = 'N' */
|
|
|
|
i__1 = *n + 1;
|
|
ztrsm_("R", "L", "C", diag, m, &k, alpha, &a[k + 1], &
|
|
i__1, b, ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
i__1 = *n + 1;
|
|
zgemm_("N", "N", m, &k, &k, &z__1, b, ldb, a, &i__1,
|
|
alpha, &b[k * b_dim1], ldb);
|
|
i__1 = *n + 1;
|
|
ztrsm_("R", "U", "N", diag, m, &k, &c_b1, &a[k], &
|
|
i__1, &b[k * b_dim1], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U', */
|
|
/* and TRANS = 'C' */
|
|
|
|
i__1 = *n + 1;
|
|
ztrsm_("R", "U", "C", diag, m, &k, alpha, &a[k], &
|
|
i__1, &b[k * b_dim1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
i__1 = *n + 1;
|
|
zgemm_("N", "C", m, &k, &k, &z__1, &b[k * b_dim1],
|
|
ldb, a, &i__1, alpha, b, ldb);
|
|
i__1 = *n + 1;
|
|
ztrsm_("R", "L", "N", diag, m, &k, &c_b1, &a[k + 1], &
|
|
i__1, b, ldb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE = 'R', N is even, and TRANSR = 'C' */
|
|
|
|
if (lower) {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'C', and UPLO = 'L' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'L', */
|
|
/* and TRANS = 'N' */
|
|
|
|
ztrsm_("R", "L", "N", diag, m, &k, alpha, a, &k, &b[k
|
|
* b_dim1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "C", m, &k, &k, &z__1, &b[k * b_dim1],
|
|
ldb, &a[(k + 1) * k], &k, alpha, b, ldb);
|
|
ztrsm_("R", "U", "C", diag, m, &k, &c_b1, &a[k], &k,
|
|
b, ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'L', */
|
|
/* and TRANS = 'C' */
|
|
|
|
ztrsm_("R", "U", "N", diag, m, &k, alpha, &a[k], &k,
|
|
b, ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", m, &k, &k, &z__1, b, ldb, &a[(k + 1)
|
|
* k], &k, alpha, &b[k * b_dim1], ldb);
|
|
ztrsm_("R", "L", "C", diag, m, &k, &c_b1, a, &k, &b[k
|
|
* b_dim1], ldb);
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'C', and UPLO = 'U' */
|
|
|
|
if (notrans) {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'U', */
|
|
/* and TRANS = 'N' */
|
|
|
|
ztrsm_("R", "U", "N", diag, m, &k, alpha, &a[(k + 1) *
|
|
k], &k, b, ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "C", m, &k, &k, &z__1, b, ldb, a, &k,
|
|
alpha, &b[k * b_dim1], ldb);
|
|
ztrsm_("R", "L", "C", diag, m, &k, &c_b1, &a[k * k], &
|
|
k, &b[k * b_dim1], ldb);
|
|
|
|
} else {
|
|
|
|
/* SIDE ='R', N is even, TRANSR = 'C', UPLO = 'U', */
|
|
/* and TRANS = 'C' */
|
|
|
|
ztrsm_("R", "L", "N", diag, m, &k, alpha, &a[k * k], &
|
|
k, &b[k * b_dim1], ldb);
|
|
z__1.r = -1., z__1.i = 0.;
|
|
zgemm_("N", "N", m, &k, &k, &z__1, &b[k * b_dim1],
|
|
ldb, a, &k, alpha, b, ldb);
|
|
ztrsm_("R", "U", "C", diag, m, &k, &c_b1, &a[(k + 1) *
|
|
k], &k, b, ldb);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of ZTFSM */
|
|
|
|
} /* ztfsm_ */
|
|
|