Use f2c translations of LAPACK when no Fortran compiler is available (#3539)
* Add C equivalents of the Fortran routines from Reference-LAPACK as fallbacks, and C_LAPACK variable to trigger their use
This commit is contained in:
Martin Kroeker
GitHub
885
lapack-netlib/SRC/cunbdb4.c
Normal file
885
lapack-netlib/SRC/cunbdb4.c
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@@ -0,0 +1,885 @@
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/* f2c.h -- Standard Fortran to C header file */
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/** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
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- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
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#ifndef F2C_INCLUDE
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#define F2C_INCLUDE
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#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimag(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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_Complex double zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
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}
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}
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pCd(z) = zdotc;
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}
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static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += Cf(&x[i]) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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_Complex double zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += Cd(&x[i]) * Cd(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
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}
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}
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pCd(z) = zdotc;
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}
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#endif
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/* -- translated by f2c (version 20000121).
|
||||
You must link the resulting object file with the libraries:
|
||||
-lf2c -lm (in that order)
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*/
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||||
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||||
|
||||
/* Table of constant values */
|
||||
|
||||
static complex c_b1 = {-1.f,0.f};
|
||||
static integer c__1 = 1;
|
||||
|
||||
/* > \brief \b CUNBDB4 */
|
||||
|
||||
/* =========== DOCUMENTATION =========== */
|
||||
|
||||
/* Online html documentation available at */
|
||||
/* http://www.netlib.org/lapack/explore-html/ */
|
||||
|
||||
/* > \htmlonly */
|
||||
/* > Download CUNBDB4 + dependencies */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb4
|
||||
.f"> */
|
||||
/* > [TGZ]</a> */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb4
|
||||
.f"> */
|
||||
/* > [ZIP]</a> */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb4
|
||||
.f"> */
|
||||
/* > [TXT]</a> */
|
||||
/* > \endhtmlonly */
|
||||
|
||||
/* Definition: */
|
||||
/* =========== */
|
||||
|
||||
/* SUBROUTINE CUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, */
|
||||
/* TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK, */
|
||||
/* INFO ) */
|
||||
|
||||
/* INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21 */
|
||||
/* REAL PHI(*), THETA(*) */
|
||||
/* COMPLEX PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*), */
|
||||
/* $ WORK(*), X11(LDX11,*), X21(LDX21,*) */
|
||||
|
||||
|
||||
/* > \par Purpose: */
|
||||
/* ============= */
|
||||
/* > */
|
||||
/* >\verbatim */
|
||||
/* > */
|
||||
/* > CUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny */
|
||||
/* > matrix X with orthonomal columns: */
|
||||
/* > */
|
||||
/* > [ B11 ] */
|
||||
/* > [ X11 ] [ P1 | ] [ 0 ] */
|
||||
/* > [-----] = [---------] [-----] Q1**T . */
|
||||
/* > [ X21 ] [ | P2 ] [ B21 ] */
|
||||
/* > [ 0 ] */
|
||||
/* > */
|
||||
/* > X11 is P-by-Q, and X21 is (M-P)-by-Q. M-Q must be no larger than P, */
|
||||
/* > M-P, or Q. Routines CUNBDB1, CUNBDB2, and CUNBDB3 handle cases in */
|
||||
/* > which M-Q is not the minimum dimension. */
|
||||
/* > */
|
||||
/* > The unitary matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P), */
|
||||
/* > and (M-Q)-by-(M-Q), respectively. They are represented implicitly by */
|
||||
/* > Householder vectors. */
|
||||
/* > */
|
||||
/* > B11 and B12 are (M-Q)-by-(M-Q) bidiagonal matrices represented */
|
||||
/* > implicitly by angles THETA, PHI. */
|
||||
/* > */
|
||||
/* >\endverbatim */
|
||||
|
||||
/* Arguments: */
|
||||
/* ========== */
|
||||
|
||||
/* > \param[in] M */
|
||||
/* > \verbatim */
|
||||
/* > M is INTEGER */
|
||||
/* > The number of rows X11 plus the number of rows in X21. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] P */
|
||||
/* > \verbatim */
|
||||
/* > P is INTEGER */
|
||||
/* > The number of rows in X11. 0 <= P <= M. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] Q */
|
||||
/* > \verbatim */
|
||||
/* > Q is INTEGER */
|
||||
/* > The number of columns in X11 and X21. 0 <= Q <= M and */
|
||||
/* > M-Q <= f2cmin(P,M-P,Q). */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in,out] X11 */
|
||||
/* > \verbatim */
|
||||
/* > X11 is COMPLEX array, dimension (LDX11,Q) */
|
||||
/* > On entry, the top block of the matrix X to be reduced. On */
|
||||
/* > exit, the columns of tril(X11) specify reflectors for P1 and */
|
||||
/* > the rows of triu(X11,1) specify reflectors for Q1. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] LDX11 */
|
||||
/* > \verbatim */
|
||||
/* > LDX11 is INTEGER */
|
||||
/* > The leading dimension of X11. LDX11 >= P. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in,out] X21 */
|
||||
/* > \verbatim */
|
||||
/* > X21 is COMPLEX array, dimension (LDX21,Q) */
|
||||
/* > On entry, the bottom block of the matrix X to be reduced. On */
|
||||
/* > exit, the columns of tril(X21) specify reflectors for P2. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] LDX21 */
|
||||
/* > \verbatim */
|
||||
/* > LDX21 is INTEGER */
|
||||
/* > The leading dimension of X21. LDX21 >= M-P. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] THETA */
|
||||
/* > \verbatim */
|
||||
/* > THETA is REAL array, dimension (Q) */
|
||||
/* > The entries of the bidiagonal blocks B11, B21 are defined by */
|
||||
/* > THETA and PHI. See Further Details. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] PHI */
|
||||
/* > \verbatim */
|
||||
/* > PHI is REAL array, dimension (Q-1) */
|
||||
/* > The entries of the bidiagonal blocks B11, B21 are defined by */
|
||||
/* > THETA and PHI. See Further Details. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] TAUP1 */
|
||||
/* > \verbatim */
|
||||
/* > TAUP1 is COMPLEX array, dimension (P) */
|
||||
/* > The scalar factors of the elementary reflectors that define */
|
||||
/* > P1. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] TAUP2 */
|
||||
/* > \verbatim */
|
||||
/* > TAUP2 is COMPLEX array, dimension (M-P) */
|
||||
/* > The scalar factors of the elementary reflectors that define */
|
||||
/* > P2. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] TAUQ1 */
|
||||
/* > \verbatim */
|
||||
/* > TAUQ1 is COMPLEX array, dimension (Q) */
|
||||
/* > The scalar factors of the elementary reflectors that define */
|
||||
/* > Q1. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] PHANTOM */
|
||||
/* > \verbatim */
|
||||
/* > PHANTOM is COMPLEX array, dimension (M) */
|
||||
/* > The routine computes an M-by-1 column vector Y that is */
|
||||
/* > orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and */
|
||||
/* > PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and */
|
||||
/* > Y(P+1:M), respectively. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] WORK */
|
||||
/* > \verbatim */
|
||||
/* > WORK is COMPLEX array, dimension (LWORK) */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] LWORK */
|
||||
/* > \verbatim */
|
||||
/* > LWORK is INTEGER */
|
||||
/* > The dimension of the array WORK. LWORK >= M-Q. */
|
||||
/* > */
|
||||
/* > If LWORK = -1, then a workspace query is assumed; the routine */
|
||||
/* > only calculates the optimal size of the WORK array, returns */
|
||||
/* > this value as the first entry of the WORK array, and no error */
|
||||
/* > message related to LWORK is issued by XERBLA. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] INFO */
|
||||
/* > \verbatim */
|
||||
/* > INFO is INTEGER */
|
||||
/* > = 0: successful exit. */
|
||||
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
||||
/* > \endverbatim */
|
||||
|
||||
/* Authors: */
|
||||
/* ======== */
|
||||
|
||||
/* > \author Univ. of Tennessee */
|
||||
/* > \author Univ. of California Berkeley */
|
||||
/* > \author Univ. of Colorado Denver */
|
||||
/* > \author NAG Ltd. */
|
||||
|
||||
/* > \date July 2012 */
|
||||
|
||||
/* > \ingroup complexOTHERcomputational */
|
||||
|
||||
/* > \par Further Details: */
|
||||
/* ===================== */
|
||||
/* > \verbatim */
|
||||
/* > */
|
||||
/* > The upper-bidiagonal blocks B11, B21 are represented implicitly by */
|
||||
/* > angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry */
|
||||
/* > in each bidiagonal band is a product of a sine or cosine of a THETA */
|
||||
/* > with a sine or cosine of a PHI. See [1] or CUNCSD for details. */
|
||||
/* > */
|
||||
/* > P1, P2, and Q1 are represented as products of elementary reflectors. */
|
||||
/* > See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR */
|
||||
/* > and CUNGLQ. */
|
||||
/* > \endverbatim */
|
||||
|
||||
/* > \par References: */
|
||||
/* ================ */
|
||||
/* > */
|
||||
/* > [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. */
|
||||
/* > Algorithms, 50(1):33-65, 2009. */
|
||||
/* > */
|
||||
/* ===================================================================== */
|
||||
/* Subroutine */ int cunbdb4_(integer *m, integer *p, integer *q, complex *
|
||||
x11, integer *ldx11, complex *x21, integer *ldx21, real *theta, real *
|
||||
phi, complex *taup1, complex *taup2, complex *tauq1, complex *phantom,
|
||||
complex *work, integer *lwork, integer *info)
|
||||
{
|
||||
/* System generated locals */
|
||||
integer x11_dim1, x11_offset, x21_dim1, x21_offset, i__1, i__2, i__3,
|
||||
i__4;
|
||||
real r__1, r__2;
|
||||
complex q__1;
|
||||
|
||||
/* Local variables */
|
||||
integer lworkmin, lworkopt;
|
||||
real c__;
|
||||
integer i__, j;
|
||||
real s;
|
||||
extern /* Subroutine */ int cscal_(integer *, complex *, complex *,
|
||||
integer *), clarf_(char *, integer *, integer *, complex *,
|
||||
integer *, complex *, complex *, integer *, complex *);
|
||||
integer ilarf, llarf, childinfo;
|
||||
extern /* Subroutine */ int csrot_(integer *, complex *, integer *,
|
||||
complex *, integer *, real *, real *);
|
||||
extern real scnrm2_(integer *, complex *, integer *);
|
||||
extern /* Subroutine */ int clacgv_(integer *, complex *, integer *),
|
||||
xerbla_(char *, integer *, ftnlen);
|
||||
logical lquery;
|
||||
extern /* Subroutine */ int cunbdb5_(integer *, integer *, integer *,
|
||||
complex *, integer *, complex *, integer *, complex *, integer *,
|
||||
complex *, integer *, complex *, integer *, integer *);
|
||||
integer iorbdb5, lorbdb5;
|
||||
extern /* Subroutine */ int clarfgp_(integer *, complex *, complex *,
|
||||
integer *, complex *);
|
||||
|
||||
|
||||
/* -- LAPACK computational routine (version 3.8.0) -- */
|
||||
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
||||
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
||||
/* July 2012 */
|
||||
|
||||
|
||||
/* ==================================================================== */
|
||||
|
||||
|
||||
/* Test input arguments */
|
||||
|
||||
/* Parameter adjustments */
|
||||
x11_dim1 = *ldx11;
|
||||
x11_offset = 1 + x11_dim1 * 1;
|
||||
x11 -= x11_offset;
|
||||
x21_dim1 = *ldx21;
|
||||
x21_offset = 1 + x21_dim1 * 1;
|
||||
x21 -= x21_offset;
|
||||
--theta;
|
||||
--phi;
|
||||
--taup1;
|
||||
--taup2;
|
||||
--tauq1;
|
||||
--phantom;
|
||||
--work;
|
||||
|
||||
/* Function Body */
|
||||
*info = 0;
|
||||
lquery = *lwork == -1;
|
||||
|
||||
if (*m < 0) {
|
||||
*info = -1;
|
||||
} else if (*p < *m - *q || *m - *p < *m - *q) {
|
||||
*info = -2;
|
||||
} else if (*q < *m - *q || *q > *m) {
|
||||
*info = -3;
|
||||
} else if (*ldx11 < f2cmax(1,*p)) {
|
||||
*info = -5;
|
||||
} else /* if(complicated condition) */ {
|
||||
/* Computing MAX */
|
||||
i__1 = 1, i__2 = *m - *p;
|
||||
if (*ldx21 < f2cmax(i__1,i__2)) {
|
||||
*info = -7;
|
||||
}
|
||||
}
|
||||
|
||||
/* Compute workspace */
|
||||
|
||||
if (*info == 0) {
|
||||
ilarf = 2;
|
||||
/* Computing MAX */
|
||||
i__1 = *q - 1, i__2 = *p - 1, i__1 = f2cmax(i__1,i__2), i__2 = *m - *p -
|
||||
1;
|
||||
llarf = f2cmax(i__1,i__2);
|
||||
iorbdb5 = 2;
|
||||
lorbdb5 = *q;
|
||||
lworkopt = ilarf + llarf - 1;
|
||||
/* Computing MAX */
|
||||
i__1 = lworkopt, i__2 = iorbdb5 + lorbdb5 - 1;
|
||||
lworkopt = f2cmax(i__1,i__2);
|
||||
lworkmin = lworkopt;
|
||||
work[1].r = (real) lworkopt, work[1].i = 0.f;
|
||||
if (*lwork < lworkmin && ! lquery) {
|
||||
*info = -14;
|
||||
}
|
||||
}
|
||||
if (*info != 0) {
|
||||
i__1 = -(*info);
|
||||
xerbla_("CUNBDB4", &i__1, (ftnlen)7);
|
||||
return 0;
|
||||
} else if (lquery) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Reduce columns 1, ..., M-Q of X11 and X21 */
|
||||
|
||||
i__1 = *m - *q;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
|
||||
if (i__ == 1) {
|
||||
i__2 = *m;
|
||||
for (j = 1; j <= i__2; ++j) {
|
||||
i__3 = j;
|
||||
phantom[i__3].r = 0.f, phantom[i__3].i = 0.f;
|
||||
}
|
||||
i__2 = *m - *p;
|
||||
cunbdb5_(p, &i__2, q, &phantom[1], &c__1, &phantom[*p + 1], &c__1,
|
||||
&x11[x11_offset], ldx11, &x21[x21_offset], ldx21, &work[
|
||||
iorbdb5], &lorbdb5, &childinfo);
|
||||
cscal_(p, &c_b1, &phantom[1], &c__1);
|
||||
clarfgp_(p, &phantom[1], &phantom[2], &c__1, &taup1[1]);
|
||||
i__2 = *m - *p;
|
||||
clarfgp_(&i__2, &phantom[*p + 1], &phantom[*p + 2], &c__1, &taup2[
|
||||
1]);
|
||||
theta[i__] = atan2((real) phantom[1].r, (real) phantom[*p + 1].r);
|
||||
c__ = cos(theta[i__]);
|
||||
s = sin(theta[i__]);
|
||||
phantom[1].r = 1.f, phantom[1].i = 0.f;
|
||||
i__2 = *p + 1;
|
||||
phantom[i__2].r = 1.f, phantom[i__2].i = 0.f;
|
||||
r_cnjg(&q__1, &taup1[1]);
|
||||
clarf_("L", p, q, &phantom[1], &c__1, &q__1, &x11[x11_offset],
|
||||
ldx11, &work[ilarf]);
|
||||
i__2 = *m - *p;
|
||||
r_cnjg(&q__1, &taup2[1]);
|
||||
clarf_("L", &i__2, q, &phantom[*p + 1], &c__1, &q__1, &x21[
|
||||
x21_offset], ldx21, &work[ilarf]);
|
||||
} else {
|
||||
i__2 = *p - i__ + 1;
|
||||
i__3 = *m - *p - i__ + 1;
|
||||
i__4 = *q - i__ + 1;
|
||||
cunbdb5_(&i__2, &i__3, &i__4, &x11[i__ + (i__ - 1) * x11_dim1], &
|
||||
c__1, &x21[i__ + (i__ - 1) * x21_dim1], &c__1, &x11[i__ +
|
||||
i__ * x11_dim1], ldx11, &x21[i__ + i__ * x21_dim1], ldx21,
|
||||
&work[iorbdb5], &lorbdb5, &childinfo);
|
||||
i__2 = *p - i__ + 1;
|
||||
cscal_(&i__2, &c_b1, &x11[i__ + (i__ - 1) * x11_dim1], &c__1);
|
||||
i__2 = *p - i__ + 1;
|
||||
clarfgp_(&i__2, &x11[i__ + (i__ - 1) * x11_dim1], &x11[i__ + 1 + (
|
||||
i__ - 1) * x11_dim1], &c__1, &taup1[i__]);
|
||||
i__2 = *m - *p - i__ + 1;
|
||||
clarfgp_(&i__2, &x21[i__ + (i__ - 1) * x21_dim1], &x21[i__ + 1 + (
|
||||
i__ - 1) * x21_dim1], &c__1, &taup2[i__]);
|
||||
theta[i__] = atan2((real) x11[i__ + (i__ - 1) * x11_dim1].r, (
|
||||
real) x21[i__ + (i__ - 1) * x21_dim1].r);
|
||||
c__ = cos(theta[i__]);
|
||||
s = sin(theta[i__]);
|
||||
i__2 = i__ + (i__ - 1) * x11_dim1;
|
||||
x11[i__2].r = 1.f, x11[i__2].i = 0.f;
|
||||
i__2 = i__ + (i__ - 1) * x21_dim1;
|
||||
x21[i__2].r = 1.f, x21[i__2].i = 0.f;
|
||||
i__2 = *p - i__ + 1;
|
||||
i__3 = *q - i__ + 1;
|
||||
r_cnjg(&q__1, &taup1[i__]);
|
||||
clarf_("L", &i__2, &i__3, &x11[i__ + (i__ - 1) * x11_dim1], &c__1,
|
||||
&q__1, &x11[i__ + i__ * x11_dim1], ldx11, &work[ilarf]);
|
||||
i__2 = *m - *p - i__ + 1;
|
||||
i__3 = *q - i__ + 1;
|
||||
r_cnjg(&q__1, &taup2[i__]);
|
||||
clarf_("L", &i__2, &i__3, &x21[i__ + (i__ - 1) * x21_dim1], &c__1,
|
||||
&q__1, &x21[i__ + i__ * x21_dim1], ldx21, &work[ilarf]);
|
||||
}
|
||||
|
||||
i__2 = *q - i__ + 1;
|
||||
r__1 = -c__;
|
||||
csrot_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11, &x21[i__ + i__ *
|
||||
x21_dim1], ldx21, &s, &r__1);
|
||||
i__2 = *q - i__ + 1;
|
||||
clacgv_(&i__2, &x21[i__ + i__ * x21_dim1], ldx21);
|
||||
i__2 = *q - i__ + 1;
|
||||
clarfgp_(&i__2, &x21[i__ + i__ * x21_dim1], &x21[i__ + (i__ + 1) *
|
||||
x21_dim1], ldx21, &tauq1[i__]);
|
||||
i__2 = i__ + i__ * x21_dim1;
|
||||
c__ = x21[i__2].r;
|
||||
i__2 = i__ + i__ * x21_dim1;
|
||||
x21[i__2].r = 1.f, x21[i__2].i = 0.f;
|
||||
i__2 = *p - i__;
|
||||
i__3 = *q - i__ + 1;
|
||||
clarf_("R", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], ldx21, &tauq1[
|
||||
i__], &x11[i__ + 1 + i__ * x11_dim1], ldx11, &work[ilarf]);
|
||||
i__2 = *m - *p - i__;
|
||||
i__3 = *q - i__ + 1;
|
||||
clarf_("R", &i__2, &i__3, &x21[i__ + i__ * x21_dim1], ldx21, &tauq1[
|
||||
i__], &x21[i__ + 1 + i__ * x21_dim1], ldx21, &work[ilarf]);
|
||||
i__2 = *q - i__ + 1;
|
||||
clacgv_(&i__2, &x21[i__ + i__ * x21_dim1], ldx21);
|
||||
if (i__ < *m - *q) {
|
||||
i__2 = *p - i__;
|
||||
/* Computing 2nd power */
|
||||
r__1 = scnrm2_(&i__2, &x11[i__ + 1 + i__ * x11_dim1], &c__1);
|
||||
i__3 = *m - *p - i__;
|
||||
/* Computing 2nd power */
|
||||
r__2 = scnrm2_(&i__3, &x21[i__ + 1 + i__ * x21_dim1], &c__1);
|
||||
s = sqrt(r__1 * r__1 + r__2 * r__2);
|
||||
phi[i__] = atan2(s, c__);
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
/* Reduce the bottom-right portion of X11 to [ I 0 ] */
|
||||
|
||||
i__1 = *p;
|
||||
for (i__ = *m - *q + 1; i__ <= i__1; ++i__) {
|
||||
i__2 = *q - i__ + 1;
|
||||
clacgv_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11);
|
||||
i__2 = *q - i__ + 1;
|
||||
clarfgp_(&i__2, &x11[i__ + i__ * x11_dim1], &x11[i__ + (i__ + 1) *
|
||||
x11_dim1], ldx11, &tauq1[i__]);
|
||||
i__2 = i__ + i__ * x11_dim1;
|
||||
x11[i__2].r = 1.f, x11[i__2].i = 0.f;
|
||||
i__2 = *p - i__;
|
||||
i__3 = *q - i__ + 1;
|
||||
clarf_("R", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], ldx11, &tauq1[
|
||||
i__], &x11[i__ + 1 + i__ * x11_dim1], ldx11, &work[ilarf]);
|
||||
i__2 = *q - *p;
|
||||
i__3 = *q - i__ + 1;
|
||||
clarf_("R", &i__2, &i__3, &x11[i__ + i__ * x11_dim1], ldx11, &tauq1[
|
||||
i__], &x21[*m - *q + 1 + i__ * x21_dim1], ldx21, &work[ilarf]);
|
||||
i__2 = *q - i__ + 1;
|
||||
clacgv_(&i__2, &x11[i__ + i__ * x11_dim1], ldx11);
|
||||
}
|
||||
|
||||
/* Reduce the bottom-right portion of X21 to [ 0 I ] */
|
||||
|
||||
i__1 = *q;
|
||||
for (i__ = *p + 1; i__ <= i__1; ++i__) {
|
||||
i__2 = *q - i__ + 1;
|
||||
clacgv_(&i__2, &x21[*m - *q + i__ - *p + i__ * x21_dim1], ldx21);
|
||||
i__2 = *q - i__ + 1;
|
||||
clarfgp_(&i__2, &x21[*m - *q + i__ - *p + i__ * x21_dim1], &x21[*m - *
|
||||
q + i__ - *p + (i__ + 1) * x21_dim1], ldx21, &tauq1[i__]);
|
||||
i__2 = *m - *q + i__ - *p + i__ * x21_dim1;
|
||||
x21[i__2].r = 1.f, x21[i__2].i = 0.f;
|
||||
i__2 = *q - i__;
|
||||
i__3 = *q - i__ + 1;
|
||||
clarf_("R", &i__2, &i__3, &x21[*m - *q + i__ - *p + i__ * x21_dim1],
|
||||
ldx21, &tauq1[i__], &x21[*m - *q + i__ - *p + 1 + i__ *
|
||||
x21_dim1], ldx21, &work[ilarf]);
|
||||
i__2 = *q - i__ + 1;
|
||||
clacgv_(&i__2, &x21[*m - *q + i__ - *p + i__ * x21_dim1], ldx21);
|
||||
}
|
||||
|
||||
return 0;
|
||||
|
||||
/* End of CUNBDB4 */
|
||||
|
||||
} /* cunbdb4_ */
|
||||
|
||||
Reference in New Issue
Block a user