1171 lines
32 KiB
C
1171 lines
32 KiB
C
#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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#ifdef _MSC_VER
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static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
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static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
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static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
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static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
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#else
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#endif
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#ifdef _MSC_VER
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#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
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#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
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#else
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#endif
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimagf(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#ifdef _MSC_VER
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static _Fcomplex cpow_ui(complex x, integer n) {
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complex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
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for(u = n; ; ) {
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if(u & 01) pow.r *= x.r, pow.i *= x.i;
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if(u >>= 1) x.r *= x.r, x.i *= x.i;
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else break;
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}
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}
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_Fcomplex p={pow.r, pow.i};
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return p;
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}
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#else
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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#ifdef _MSC_VER
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static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
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_Dcomplex pow={1.0,0.0}; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
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for(u = n; ; ) {
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if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
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if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
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else break;
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}
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}
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_Dcomplex p = {pow._Val[0], pow._Val[1]};
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return p;
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}
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#else
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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#endif
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Fcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
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zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
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}
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}
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pCf(z) = zdotc;
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}
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#else
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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#endif
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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#ifdef _MSC_VER
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_Dcomplex zdotc = {0.0, 0.0};
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
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zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
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}
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} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Fcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex float zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i]) * Cf(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
|
|
}
|
|
}
|
|
pCf(z) = zdotc;
|
|
}
|
|
#endif
|
|
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
|
|
integer n = *n_, incx = *incx_, incy = *incy_, i;
|
|
#ifdef _MSC_VER
|
|
_Dcomplex zdotc = {0.0, 0.0};
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
|
|
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#else
|
|
_Complex double zdotc = 0.0;
|
|
if (incx == 1 && incy == 1) {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i]) * Cd(&y[i]);
|
|
}
|
|
} else {
|
|
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
|
|
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
|
|
}
|
|
}
|
|
pCd(z) = zdotc;
|
|
}
|
|
#endif
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
/* -- translated by f2c (version 20000121).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
|
|
|
|
/* -- 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 complex c_b1 = {1.f,0.f};
|
|
static integer c__1 = 1;
|
|
static integer c__65 = 65;
|
|
|
|
/* > \brief \b CGBTRF */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* > \htmlonly */
|
|
/* > Download CGBTRF + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbtrf.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbtrf.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbtrf.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE CGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO ) */
|
|
|
|
/* INTEGER INFO, KL, KU, LDAB, M, N */
|
|
/* INTEGER IPIV( * ) */
|
|
/* COMPLEX AB( LDAB, * ) */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > CGBTRF computes an LU factorization of a complex m-by-n band matrix A */
|
|
/* > using partial pivoting with row interchanges. */
|
|
/* > */
|
|
/* > This is the blocked version of the algorithm, calling Level 3 BLAS. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] M */
|
|
/* > \verbatim */
|
|
/* > M is INTEGER */
|
|
/* > The number of rows of the matrix A. M >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > The number of columns of the matrix A. N >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KL */
|
|
/* > \verbatim */
|
|
/* > KL is INTEGER */
|
|
/* > The number of subdiagonals within the band of A. KL >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] KU */
|
|
/* > \verbatim */
|
|
/* > KU is INTEGER */
|
|
/* > The number of superdiagonals within the band of A. KU >= 0. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] AB */
|
|
/* > \verbatim */
|
|
/* > AB is COMPLEX array, dimension (LDAB,N) */
|
|
/* > On entry, the matrix A in band storage, in rows KL+1 to */
|
|
/* > 2*KL+KU+1; rows 1 to KL of the array need not be set. */
|
|
/* > The j-th column of A is stored in the j-th column of the */
|
|
/* > array AB as follows: */
|
|
/* > AB(kl+ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl) */
|
|
/* > */
|
|
/* > On exit, details of the factorization: U is stored as an */
|
|
/* > upper triangular band matrix with KL+KU superdiagonals in */
|
|
/* > rows 1 to KL+KU+1, and the multipliers used during the */
|
|
/* > factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */
|
|
/* > See below for further details. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDAB */
|
|
/* > \verbatim */
|
|
/* > LDAB is INTEGER */
|
|
/* > The leading dimension of the array AB. LDAB >= 2*KL+KU+1. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] IPIV */
|
|
/* > \verbatim */
|
|
/* > IPIV is INTEGER array, dimension (f2cmin(M,N)) */
|
|
/* > The pivot indices; for 1 <= i <= f2cmin(M,N), row i of the */
|
|
/* > matrix was interchanged with row IPIV(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[out] INFO */
|
|
/* > \verbatim */
|
|
/* > INFO is INTEGER */
|
|
/* > = 0: successful exit */
|
|
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
|
|
/* > > 0: if INFO = +i, U(i,i) is exactly zero. The factorization */
|
|
/* > has been completed, but the factor U is exactly */
|
|
/* > singular, and division by zero will occur if it is used */
|
|
/* > to solve a system of equations. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \date December 2016 */
|
|
|
|
/* > \ingroup complexGBcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The band storage scheme is illustrated by the following example, when */
|
|
/* > M = N = 6, KL = 2, KU = 1: */
|
|
/* > */
|
|
/* > On entry: On exit: */
|
|
/* > */
|
|
/* > * * * + + + * * * u14 u25 u36 */
|
|
/* > * * + + + + * * u13 u24 u35 u46 */
|
|
/* > * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 */
|
|
/* > a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 */
|
|
/* > a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * */
|
|
/* > a31 a42 a53 a64 * * m31 m42 m53 m64 * * */
|
|
/* > */
|
|
/* > Array elements marked * are not used by the routine; elements marked */
|
|
/* > + need not be set on entry, but are required by the routine to store */
|
|
/* > elements of U because of fill-in resulting from the row interchanges. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ void cgbtrf_(integer *m, integer *n, integer *kl, integer *ku,
|
|
complex *ab, integer *ldab, integer *ipiv, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5, i__6;
|
|
complex q__1;
|
|
|
|
/* Local variables */
|
|
complex temp;
|
|
integer i__, j;
|
|
extern /* Subroutine */ void cscal_(integer *, complex *, complex *,
|
|
integer *), cgemm_(char *, char *, integer *, integer *, integer *
|
|
, complex *, complex *, integer *, complex *, integer *, complex *
|
|
, complex *, integer *), cgeru_(integer *,
|
|
integer *, complex *, complex *, integer *, complex *, integer *,
|
|
complex *, integer *), ccopy_(integer *, complex *, integer *,
|
|
complex *, integer *), cswap_(integer *, complex *, integer *,
|
|
complex *, integer *);
|
|
complex work13[4160] /* was [65][64] */, work31[4160] /*
|
|
was [65][64] */;
|
|
extern /* Subroutine */ void ctrsm_(char *, char *, char *, char *,
|
|
integer *, integer *, complex *, complex *, integer *, complex *,
|
|
integer *);
|
|
integer i2, i3, j2, j3, k2;
|
|
extern /* Subroutine */ void cgbtf2_(integer *, integer *, integer *,
|
|
integer *, complex *, integer *, integer *, integer *);
|
|
integer jb, nb, ii, jj, jm, ip, jp, km, ju, kv;
|
|
extern integer icamax_(integer *, complex *, integer *);
|
|
integer nw;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ int claswp_(integer *, complex *, integer *,
|
|
integer *, integer *, integer *, integer *);
|
|
|
|
|
|
/* -- 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 */
|
|
|
|
|
|
/* ===================================================================== */
|
|
|
|
|
|
/* KV is the number of superdiagonals in the factor U, allowing for */
|
|
/* fill-in */
|
|
|
|
/* Parameter adjustments */
|
|
ab_dim1 = *ldab;
|
|
ab_offset = 1 + ab_dim1 * 1;
|
|
ab -= ab_offset;
|
|
--ipiv;
|
|
|
|
/* Function Body */
|
|
kv = *ku + *kl;
|
|
|
|
/* Test the input parameters. */
|
|
|
|
*info = 0;
|
|
if (*m < 0) {
|
|
*info = -1;
|
|
} else if (*n < 0) {
|
|
*info = -2;
|
|
} else if (*kl < 0) {
|
|
*info = -3;
|
|
} else if (*ku < 0) {
|
|
*info = -4;
|
|
} else if (*ldab < *kl + kv + 1) {
|
|
*info = -6;
|
|
}
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("CGBTRF", &i__1, (ftnlen)6);
|
|
return;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
return;
|
|
}
|
|
|
|
/* Determine the block size for this environment */
|
|
|
|
nb = ilaenv_(&c__1, "CGBTRF", " ", m, n, kl, ku, (ftnlen)6, (ftnlen)1);
|
|
|
|
/* The block size must not exceed the limit set by the size of the */
|
|
/* local arrays WORK13 and WORK31. */
|
|
|
|
nb = f2cmin(nb,64);
|
|
|
|
if (nb <= 1 || nb > *kl) {
|
|
|
|
/* Use unblocked code */
|
|
|
|
cgbtf2_(m, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info);
|
|
} else {
|
|
|
|
/* Use blocked code */
|
|
|
|
/* Zero the superdiagonal elements of the work array WORK13 */
|
|
|
|
i__1 = nb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * 65 - 66;
|
|
work13[i__3].r = 0.f, work13[i__3].i = 0.f;
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
|
|
/* Zero the subdiagonal elements of the work array WORK31 */
|
|
|
|
i__1 = nb;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = nb;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * 65 - 66;
|
|
work31[i__3].r = 0.f, work31[i__3].i = 0.f;
|
|
/* L30: */
|
|
}
|
|
/* L40: */
|
|
}
|
|
|
|
/* Gaussian elimination with partial pivoting */
|
|
|
|
/* Set fill-in elements in columns KU+2 to KV to zero */
|
|
|
|
i__1 = f2cmin(kv,*n);
|
|
for (j = *ku + 2; j <= i__1; ++j) {
|
|
i__2 = *kl;
|
|
for (i__ = kv - j + 2; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * ab_dim1;
|
|
ab[i__3].r = 0.f, ab[i__3].i = 0.f;
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
|
|
/* JU is the index of the last column affected by the current */
|
|
/* stage of the factorization */
|
|
|
|
ju = 1;
|
|
|
|
i__1 = f2cmin(*m,*n);
|
|
i__2 = nb;
|
|
for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
|
|
/* Computing MIN */
|
|
i__3 = nb, i__4 = f2cmin(*m,*n) - j + 1;
|
|
jb = f2cmin(i__3,i__4);
|
|
|
|
/* The active part of the matrix is partitioned */
|
|
|
|
/* A11 A12 A13 */
|
|
/* A21 A22 A23 */
|
|
/* A31 A32 A33 */
|
|
|
|
/* Here A11, A21 and A31 denote the current block of JB columns */
|
|
/* which is about to be factorized. The number of rows in the */
|
|
/* partitioning are JB, I2, I3 respectively, and the numbers */
|
|
/* of columns are JB, J2, J3. The superdiagonal elements of A13 */
|
|
/* and the subdiagonal elements of A31 lie outside the band. */
|
|
|
|
/* Computing MIN */
|
|
i__3 = *kl - jb, i__4 = *m - j - jb + 1;
|
|
i2 = f2cmin(i__3,i__4);
|
|
/* Computing MIN */
|
|
i__3 = jb, i__4 = *m - j - *kl + 1;
|
|
i3 = f2cmin(i__3,i__4);
|
|
|
|
/* J2 and J3 are computed after JU has been updated. */
|
|
|
|
/* Factorize the current block of JB columns */
|
|
|
|
i__3 = j + jb - 1;
|
|
for (jj = j; jj <= i__3; ++jj) {
|
|
|
|
/* Set fill-in elements in column JJ+KV to zero */
|
|
|
|
if (jj + kv <= *n) {
|
|
i__4 = *kl;
|
|
for (i__ = 1; i__ <= i__4; ++i__) {
|
|
i__5 = i__ + (jj + kv) * ab_dim1;
|
|
ab[i__5].r = 0.f, ab[i__5].i = 0.f;
|
|
/* L70: */
|
|
}
|
|
}
|
|
|
|
/* Find pivot and test for singularity. KM is the number of */
|
|
/* subdiagonal elements in the current column. */
|
|
|
|
/* Computing MIN */
|
|
i__4 = *kl, i__5 = *m - jj;
|
|
km = f2cmin(i__4,i__5);
|
|
i__4 = km + 1;
|
|
jp = icamax_(&i__4, &ab[kv + 1 + jj * ab_dim1], &c__1);
|
|
ipiv[jj] = jp + jj - j;
|
|
i__4 = kv + jp + jj * ab_dim1;
|
|
if (ab[i__4].r != 0.f || ab[i__4].i != 0.f) {
|
|
/* Computing MAX */
|
|
/* Computing MIN */
|
|
i__6 = jj + *ku + jp - 1;
|
|
i__4 = ju, i__5 = f2cmin(i__6,*n);
|
|
ju = f2cmax(i__4,i__5);
|
|
if (jp != 1) {
|
|
|
|
/* Apply interchange to columns J to J+JB-1 */
|
|
|
|
if (jp + jj - 1 < j + *kl) {
|
|
|
|
i__4 = *ldab - 1;
|
|
i__5 = *ldab - 1;
|
|
cswap_(&jb, &ab[kv + 1 + jj - j + j * ab_dim1], &
|
|
i__4, &ab[kv + jp + jj - j + j * ab_dim1],
|
|
&i__5);
|
|
} else {
|
|
|
|
/* The interchange affects columns J to JJ-1 of A31 */
|
|
/* which are stored in the work array WORK31 */
|
|
|
|
i__4 = jj - j;
|
|
i__5 = *ldab - 1;
|
|
cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1],
|
|
&i__5, &work31[jp + jj - j - *kl - 1], &
|
|
c__65);
|
|
i__4 = j + jb - jj;
|
|
i__5 = *ldab - 1;
|
|
i__6 = *ldab - 1;
|
|
cswap_(&i__4, &ab[kv + 1 + jj * ab_dim1], &i__5, &
|
|
ab[kv + jp + jj * ab_dim1], &i__6);
|
|
}
|
|
}
|
|
|
|
/* Compute multipliers */
|
|
|
|
c_div(&q__1, &c_b1, &ab[kv + 1 + jj * ab_dim1]);
|
|
cscal_(&km, &q__1, &ab[kv + 2 + jj * ab_dim1], &c__1);
|
|
|
|
/* Update trailing submatrix within the band and within */
|
|
/* the current block. JM is the index of the last column */
|
|
/* which needs to be updated. */
|
|
|
|
/* Computing MIN */
|
|
i__4 = ju, i__5 = j + jb - 1;
|
|
jm = f2cmin(i__4,i__5);
|
|
if (jm > jj) {
|
|
i__4 = jm - jj;
|
|
q__1.r = -1.f, q__1.i = 0.f;
|
|
i__5 = *ldab - 1;
|
|
i__6 = *ldab - 1;
|
|
cgeru_(&km, &i__4, &q__1, &ab[kv + 2 + jj * ab_dim1],
|
|
&c__1, &ab[kv + (jj + 1) * ab_dim1], &i__5, &
|
|
ab[kv + 1 + (jj + 1) * ab_dim1], &i__6);
|
|
}
|
|
} else {
|
|
|
|
/* If pivot is zero, set INFO to the index of the pivot */
|
|
/* unless a zero pivot has already been found. */
|
|
|
|
if (*info == 0) {
|
|
*info = jj;
|
|
}
|
|
}
|
|
|
|
/* Copy current column of A31 into the work array WORK31 */
|
|
|
|
/* Computing MIN */
|
|
i__4 = jj - j + 1;
|
|
nw = f2cmin(i__4,i3);
|
|
if (nw > 0) {
|
|
ccopy_(&nw, &ab[kv + *kl + 1 - jj + j + jj * ab_dim1], &
|
|
c__1, &work31[(jj - j + 1) * 65 - 65], &c__1);
|
|
}
|
|
/* L80: */
|
|
}
|
|
if (j + jb <= *n) {
|
|
|
|
/* Apply the row interchanges to the other blocks. */
|
|
|
|
/* Computing MIN */
|
|
i__3 = ju - j + 1;
|
|
j2 = f2cmin(i__3,kv) - jb;
|
|
/* Computing MAX */
|
|
i__3 = 0, i__4 = ju - j - kv + 1;
|
|
j3 = f2cmax(i__3,i__4);
|
|
|
|
/* Use CLASWP to apply the row interchanges to A12, A22, and */
|
|
/* A32. */
|
|
|
|
i__3 = *ldab - 1;
|
|
claswp_(&j2, &ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__3, &
|
|
c__1, &jb, &ipiv[j], &c__1);
|
|
|
|
/* Adjust the pivot indices. */
|
|
|
|
i__3 = j + jb - 1;
|
|
for (i__ = j; i__ <= i__3; ++i__) {
|
|
ipiv[i__] = ipiv[i__] + j - 1;
|
|
/* L90: */
|
|
}
|
|
|
|
/* Apply the row interchanges to A13, A23, and A33 */
|
|
/* columnwise. */
|
|
|
|
k2 = j - 1 + jb + j2;
|
|
i__3 = j3;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
jj = k2 + i__;
|
|
i__4 = j + jb - 1;
|
|
for (ii = j + i__ - 1; ii <= i__4; ++ii) {
|
|
ip = ipiv[ii];
|
|
if (ip != ii) {
|
|
i__5 = kv + 1 + ii - jj + jj * ab_dim1;
|
|
temp.r = ab[i__5].r, temp.i = ab[i__5].i;
|
|
i__5 = kv + 1 + ii - jj + jj * ab_dim1;
|
|
i__6 = kv + 1 + ip - jj + jj * ab_dim1;
|
|
ab[i__5].r = ab[i__6].r, ab[i__5].i = ab[i__6].i;
|
|
i__5 = kv + 1 + ip - jj + jj * ab_dim1;
|
|
ab[i__5].r = temp.r, ab[i__5].i = temp.i;
|
|
}
|
|
/* L100: */
|
|
}
|
|
/* L110: */
|
|
}
|
|
|
|
/* Update the relevant part of the trailing submatrix */
|
|
|
|
if (j2 > 0) {
|
|
|
|
/* Update A12 */
|
|
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &j2,
|
|
&c_b1, &ab[kv + 1 + j * ab_dim1], &i__3, &ab[kv +
|
|
1 - jb + (j + jb) * ab_dim1], &i__4);
|
|
|
|
if (i2 > 0) {
|
|
|
|
/* Update A22 */
|
|
|
|
q__1.r = -1.f, q__1.i = 0.f;
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
i__5 = *ldab - 1;
|
|
cgemm_("No transpose", "No transpose", &i2, &j2, &jb,
|
|
&q__1, &ab[kv + 1 + jb + j * ab_dim1], &i__3,
|
|
&ab[kv + 1 - jb + (j + jb) * ab_dim1], &i__4,
|
|
&c_b1, &ab[kv + 1 + (j + jb) * ab_dim1], &
|
|
i__5);
|
|
}
|
|
|
|
if (i3 > 0) {
|
|
|
|
/* Update A32 */
|
|
|
|
q__1.r = -1.f, q__1.i = 0.f;
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
cgemm_("No transpose", "No transpose", &i3, &j2, &jb,
|
|
&q__1, work31, &c__65, &ab[kv + 1 - jb + (j +
|
|
jb) * ab_dim1], &i__3, &c_b1, &ab[kv + *kl +
|
|
1 - jb + (j + jb) * ab_dim1], &i__4);
|
|
}
|
|
}
|
|
|
|
if (j3 > 0) {
|
|
|
|
/* Copy the lower triangle of A13 into the work array */
|
|
/* WORK13 */
|
|
|
|
i__3 = j3;
|
|
for (jj = 1; jj <= i__3; ++jj) {
|
|
i__4 = jb;
|
|
for (ii = jj; ii <= i__4; ++ii) {
|
|
i__5 = ii + jj * 65 - 66;
|
|
i__6 = ii - jj + 1 + (jj + j + kv - 1) * ab_dim1;
|
|
work13[i__5].r = ab[i__6].r, work13[i__5].i = ab[
|
|
i__6].i;
|
|
/* L120: */
|
|
}
|
|
/* L130: */
|
|
}
|
|
|
|
/* Update A13 in the work array */
|
|
|
|
i__3 = *ldab - 1;
|
|
ctrsm_("Left", "Lower", "No transpose", "Unit", &jb, &j3,
|
|
&c_b1, &ab[kv + 1 + j * ab_dim1], &i__3, work13, &
|
|
c__65);
|
|
|
|
if (i2 > 0) {
|
|
|
|
/* Update A23 */
|
|
|
|
q__1.r = -1.f, q__1.i = 0.f;
|
|
i__3 = *ldab - 1;
|
|
i__4 = *ldab - 1;
|
|
cgemm_("No transpose", "No transpose", &i2, &j3, &jb,
|
|
&q__1, &ab[kv + 1 + jb + j * ab_dim1], &i__3,
|
|
work13, &c__65, &c_b1, &ab[jb + 1 + (j + kv) *
|
|
ab_dim1], &i__4);
|
|
}
|
|
|
|
if (i3 > 0) {
|
|
|
|
/* Update A33 */
|
|
|
|
q__1.r = -1.f, q__1.i = 0.f;
|
|
i__3 = *ldab - 1;
|
|
cgemm_("No transpose", "No transpose", &i3, &j3, &jb,
|
|
&q__1, work31, &c__65, work13, &c__65, &c_b1,
|
|
&ab[*kl + 1 + (j + kv) * ab_dim1], &i__3);
|
|
}
|
|
|
|
/* Copy the lower triangle of A13 back into place */
|
|
|
|
i__3 = j3;
|
|
for (jj = 1; jj <= i__3; ++jj) {
|
|
i__4 = jb;
|
|
for (ii = jj; ii <= i__4; ++ii) {
|
|
i__5 = ii - jj + 1 + (jj + j + kv - 1) * ab_dim1;
|
|
i__6 = ii + jj * 65 - 66;
|
|
ab[i__5].r = work13[i__6].r, ab[i__5].i = work13[
|
|
i__6].i;
|
|
/* L140: */
|
|
}
|
|
/* L150: */
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* Adjust the pivot indices. */
|
|
|
|
i__3 = j + jb - 1;
|
|
for (i__ = j; i__ <= i__3; ++i__) {
|
|
ipiv[i__] = ipiv[i__] + j - 1;
|
|
/* L160: */
|
|
}
|
|
}
|
|
|
|
/* Partially undo the interchanges in the current block to */
|
|
/* restore the upper triangular form of A31 and copy the upper */
|
|
/* triangle of A31 back into place */
|
|
|
|
i__3 = j;
|
|
for (jj = j + jb - 1; jj >= i__3; --jj) {
|
|
jp = ipiv[jj] - jj + 1;
|
|
if (jp != 1) {
|
|
|
|
/* Apply interchange to columns J to JJ-1 */
|
|
|
|
if (jp + jj - 1 < j + *kl) {
|
|
|
|
/* The interchange does not affect A31 */
|
|
|
|
i__4 = jj - j;
|
|
i__5 = *ldab - 1;
|
|
i__6 = *ldab - 1;
|
|
cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], &
|
|
i__5, &ab[kv + jp + jj - j + j * ab_dim1], &
|
|
i__6);
|
|
} else {
|
|
|
|
/* The interchange does affect A31 */
|
|
|
|
i__4 = jj - j;
|
|
i__5 = *ldab - 1;
|
|
cswap_(&i__4, &ab[kv + 1 + jj - j + j * ab_dim1], &
|
|
i__5, &work31[jp + jj - j - *kl - 1], &c__65);
|
|
}
|
|
}
|
|
|
|
/* Copy the current column of A31 back into place */
|
|
|
|
/* Computing MIN */
|
|
i__4 = i3, i__5 = jj - j + 1;
|
|
nw = f2cmin(i__4,i__5);
|
|
if (nw > 0) {
|
|
ccopy_(&nw, &work31[(jj - j + 1) * 65 - 65], &c__1, &ab[
|
|
kv + *kl + 1 - jj + j + jj * ab_dim1], &c__1);
|
|
}
|
|
/* L170: */
|
|
}
|
|
/* L180: */
|
|
}
|
|
}
|
|
|
|
return;
|
|
|
|
/* End of CGBTRF */
|
|
|
|
} /* cgbtrf_ */
|
|
|