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
988
lapack-netlib/SRC/slasda.c
Normal file
988
lapack-netlib/SRC/slasda.c
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@@ -0,0 +1,988 @@
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/* f2c.h -- Standard Fortran to C header file */
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/** barf [ba:rf] 2. "He suggested using FORTRAN, and everybody barfed."
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- From The Shogakukan DICTIONARY OF NEW ENGLISH (Second edition) */
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#ifndef F2C_INCLUDE
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#define F2C_INCLUDE
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#include <math.h>
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#include <stdlib.h>
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#include <string.h>
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#include <stdio.h>
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#include <complex.h>
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#ifdef complex
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#undef complex
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#endif
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#ifdef I
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#undef I
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#endif
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#if defined(_WIN64)
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typedef long long BLASLONG;
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typedef unsigned long long BLASULONG;
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#else
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typedef long BLASLONG;
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typedef unsigned long BLASULONG;
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#endif
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#ifdef LAPACK_ILP64
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typedef BLASLONG blasint;
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#if defined(_WIN64)
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#define blasabs(x) llabs(x)
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#else
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#define blasabs(x) labs(x)
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#endif
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#else
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typedef int blasint;
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#define blasabs(x) abs(x)
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#endif
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typedef blasint integer;
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typedef unsigned int uinteger;
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typedef char *address;
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typedef short int shortint;
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typedef float real;
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typedef double doublereal;
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typedef struct { real r, i; } complex;
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typedef struct { doublereal r, i; } doublecomplex;
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static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
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static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
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static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
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#define pCf(z) (*_pCf(z))
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#define pCd(z) (*_pCd(z))
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typedef int logical;
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typedef short int shortlogical;
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typedef char logical1;
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typedef char integer1;
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#define TRUE_ (1)
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#define FALSE_ (0)
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/* Extern is for use with -E */
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#ifndef Extern
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#define Extern extern
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#endif
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/* I/O stuff */
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typedef int flag;
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typedef int ftnlen;
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typedef int ftnint;
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/*external read, write*/
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typedef struct
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{ flag cierr;
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ftnint ciunit;
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flag ciend;
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char *cifmt;
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ftnint cirec;
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} cilist;
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/*internal read, write*/
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typedef struct
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{ flag icierr;
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char *iciunit;
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flag iciend;
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char *icifmt;
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ftnint icirlen;
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ftnint icirnum;
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} icilist;
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/*open*/
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typedef struct
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{ flag oerr;
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ftnint ounit;
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char *ofnm;
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ftnlen ofnmlen;
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char *osta;
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char *oacc;
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char *ofm;
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ftnint orl;
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char *oblnk;
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} olist;
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/*close*/
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typedef struct
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{ flag cerr;
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ftnint cunit;
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char *csta;
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} cllist;
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/*rewind, backspace, endfile*/
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typedef struct
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{ flag aerr;
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ftnint aunit;
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} alist;
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/* inquire */
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typedef struct
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{ flag inerr;
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ftnint inunit;
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char *infile;
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ftnlen infilen;
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ftnint *inex; /*parameters in standard's order*/
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ftnint *inopen;
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ftnint *innum;
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ftnint *innamed;
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char *inname;
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ftnlen innamlen;
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char *inacc;
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ftnlen inacclen;
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char *inseq;
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ftnlen inseqlen;
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char *indir;
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ftnlen indirlen;
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char *infmt;
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ftnlen infmtlen;
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char *inform;
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ftnint informlen;
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char *inunf;
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ftnlen inunflen;
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ftnint *inrecl;
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ftnint *innrec;
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char *inblank;
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ftnlen inblanklen;
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} inlist;
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#define VOID void
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union Multitype { /* for multiple entry points */
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integer1 g;
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shortint h;
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integer i;
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/* longint j; */
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real r;
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doublereal d;
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complex c;
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doublecomplex z;
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};
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typedef union Multitype Multitype;
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struct Vardesc { /* for Namelist */
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char *name;
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char *addr;
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ftnlen *dims;
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int type;
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};
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typedef struct Vardesc Vardesc;
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struct Namelist {
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char *name;
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Vardesc **vars;
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int nvars;
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};
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typedef struct Namelist Namelist;
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (fabs(x))
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#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
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#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
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#define dmin(a,b) (f2cmin(a,b))
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#define dmax(a,b) (f2cmax(a,b))
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#define bit_test(a,b) ((a) >> (b) & 1)
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#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
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#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
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#define abort_() { sig_die("Fortran abort routine called", 1); }
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#define c_abs(z) (cabsf(Cf(z)))
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#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
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#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
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#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
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#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
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#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
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#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
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//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
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#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
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#define d_abs(x) (fabs(*(x)))
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#define d_acos(x) (acos(*(x)))
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#define d_asin(x) (asin(*(x)))
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#define d_atan(x) (atan(*(x)))
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#define d_atn2(x, y) (atan2(*(x),*(y)))
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#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
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#define r_cnjg(R, Z) { pCf(R) = conj(Cf(Z)); }
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#define d_cos(x) (cos(*(x)))
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#define d_cosh(x) (cosh(*(x)))
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#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
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#define d_exp(x) (exp(*(x)))
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#define d_imag(z) (cimag(Cd(z)))
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#define r_imag(z) (cimag(Cf(z)))
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#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
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#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
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#define d_log(x) (log(*(x)))
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#define d_mod(x, y) (fmod(*(x), *(y)))
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#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
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#define d_nint(x) u_nint(*(x))
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#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
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#define d_sign(a,b) u_sign(*(a),*(b))
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#define r_sign(a,b) u_sign(*(a),*(b))
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#define d_sin(x) (sin(*(x)))
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#define d_sinh(x) (sinh(*(x)))
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#define d_sqrt(x) (sqrt(*(x)))
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#define d_tan(x) (tan(*(x)))
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#define d_tanh(x) (tanh(*(x)))
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#define i_abs(x) abs(*(x))
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#define i_dnnt(x) ((integer)u_nint(*(x)))
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#define i_len(s, n) (n)
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#define i_nint(x) ((integer)u_nint(*(x)))
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#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
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#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
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#define pow_si(B,E) spow_ui(*(B),*(E))
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#define pow_ri(B,E) spow_ui(*(B),*(E))
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#define pow_di(B,E) dpow_ui(*(B),*(E))
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#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
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#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
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#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
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#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }
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#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
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#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
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#define sig_die(s, kill) { exit(1); }
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#define s_stop(s, n) {exit(0);}
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static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
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#define z_abs(z) (cabs(Cd(z)))
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#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
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#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
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#define myexit_() break;
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#define mycycle() continue;
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#define myceiling(w) {ceil(w)}
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#define myhuge(w) {HUGE_VAL}
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//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
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#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
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/* procedure parameter types for -A and -C++ */
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#define F2C_proc_par_types 1
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#ifdef __cplusplus
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typedef logical (*L_fp)(...);
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#else
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typedef logical (*L_fp)();
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#endif
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static float spow_ui(float x, integer n) {
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float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static double dpow_ui(double x, integer n) {
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double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static _Complex float cpow_ui(_Complex float x, integer n) {
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_Complex float pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static _Complex double zpow_ui(_Complex double x, integer n) {
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_Complex double pow=1.0; unsigned long int u;
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if(n != 0) {
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if(n < 0) n = -n, x = 1/x;
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for(u = n; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer pow_ii(integer x, integer n) {
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integer pow; unsigned long int u;
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if (n <= 0) {
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if (n == 0 || x == 1) pow = 1;
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else if (x != -1) pow = x == 0 ? 1/x : 0;
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else n = -n;
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}
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if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
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u = n;
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for(pow = 1; ; ) {
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if(u & 01) pow *= x;
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if(u >>= 1) x *= x;
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else break;
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}
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}
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return pow;
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}
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static integer dmaxloc_(double *w, integer s, integer e, integer *n)
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{
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double m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static integer smaxloc_(float *w, integer s, integer e, integer *n)
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{
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float m; integer i, mi;
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for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
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if (w[i-1]>m) mi=i ,m=w[i-1];
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return mi-s+1;
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}
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static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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_Complex double zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
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}
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}
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pCd(z) = zdotc;
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}
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static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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_Complex float zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += Cf(&x[i]) * Cf(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
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}
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}
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pCf(z) = zdotc;
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}
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static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
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integer n = *n_, incx = *incx_, incy = *incy_, i;
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_Complex double zdotc = 0.0;
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if (incx == 1 && incy == 1) {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += Cd(&x[i]) * Cd(&y[i]);
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}
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} else {
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for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
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zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
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}
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}
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pCd(z) = zdotc;
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}
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#endif
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/* -- translated by f2c (version 20000121).
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You must link the resulting object file with the libraries:
|
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-lf2c -lm (in that order)
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*/
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|
||||
/* Table of constant values */
|
||||
|
||||
static integer c__0 = 0;
|
||||
static real c_b11 = 0.f;
|
||||
static real c_b12 = 1.f;
|
||||
static integer c__1 = 1;
|
||||
static integer c__2 = 2;
|
||||
|
||||
/* > \brief \b SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with d
|
||||
iagonal d and off-diagonal e. Used by sbdsdc. */
|
||||
|
||||
/* =========== DOCUMENTATION =========== */
|
||||
|
||||
/* Online html documentation available at */
|
||||
/* http://www.netlib.org/lapack/explore-html/ */
|
||||
|
||||
/* > \htmlonly */
|
||||
/* > Download SLASDA + dependencies */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slasda.
|
||||
f"> */
|
||||
/* > [TGZ]</a> */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slasda.
|
||||
f"> */
|
||||
/* > [ZIP]</a> */
|
||||
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasda.
|
||||
f"> */
|
||||
/* > [TXT]</a> */
|
||||
/* > \endhtmlonly */
|
||||
|
||||
/* Definition: */
|
||||
/* =========== */
|
||||
|
||||
/* SUBROUTINE SLASDA( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, */
|
||||
/* DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, */
|
||||
/* PERM, GIVNUM, C, S, WORK, IWORK, INFO ) */
|
||||
|
||||
/* INTEGER ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE */
|
||||
/* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */
|
||||
/* $ K( * ), PERM( LDGCOL, * ) */
|
||||
/* REAL C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ), */
|
||||
/* $ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), */
|
||||
/* $ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ), */
|
||||
/* $ Z( LDU, * ) */
|
||||
|
||||
|
||||
/* > \par Purpose: */
|
||||
/* ============= */
|
||||
/* > */
|
||||
/* > \verbatim */
|
||||
/* > */
|
||||
/* > Using a divide and conquer approach, SLASDA computes the singular */
|
||||
/* > value decomposition (SVD) of a real upper bidiagonal N-by-M matrix */
|
||||
/* > B with diagonal D and offdiagonal E, where M = N + SQRE. The */
|
||||
/* > algorithm computes the singular values in the SVD B = U * S * VT. */
|
||||
/* > The orthogonal matrices U and VT are optionally computed in */
|
||||
/* > compact form. */
|
||||
/* > */
|
||||
/* > A related subroutine, SLASD0, computes the singular values and */
|
||||
/* > the singular vectors in explicit form. */
|
||||
/* > \endverbatim */
|
||||
|
||||
/* Arguments: */
|
||||
/* ========== */
|
||||
|
||||
/* > \param[in] ICOMPQ */
|
||||
/* > \verbatim */
|
||||
/* > ICOMPQ is INTEGER */
|
||||
/* > Specifies whether singular vectors are to be computed */
|
||||
/* > in compact form, as follows */
|
||||
/* > = 0: Compute singular values only. */
|
||||
/* > = 1: Compute singular vectors of upper bidiagonal */
|
||||
/* > matrix in compact form. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] SMLSIZ */
|
||||
/* > \verbatim */
|
||||
/* > SMLSIZ is INTEGER */
|
||||
/* > The maximum size of the subproblems at the bottom of the */
|
||||
/* > computation tree. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] N */
|
||||
/* > \verbatim */
|
||||
/* > N is INTEGER */
|
||||
/* > The row dimension of the upper bidiagonal matrix. This is */
|
||||
/* > also the dimension of the main diagonal array D. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] SQRE */
|
||||
/* > \verbatim */
|
||||
/* > SQRE is INTEGER */
|
||||
/* > Specifies the column dimension of the bidiagonal matrix. */
|
||||
/* > = 0: The bidiagonal matrix has column dimension M = N; */
|
||||
/* > = 1: The bidiagonal matrix has column dimension M = N + 1. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in,out] D */
|
||||
/* > \verbatim */
|
||||
/* > D is REAL array, dimension ( N ) */
|
||||
/* > On entry D contains the main diagonal of the bidiagonal */
|
||||
/* > matrix. On exit D, if INFO = 0, contains its singular values. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] E */
|
||||
/* > \verbatim */
|
||||
/* > E is REAL array, dimension ( M-1 ) */
|
||||
/* > Contains the subdiagonal entries of the bidiagonal matrix. */
|
||||
/* > On exit, E has been destroyed. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] U */
|
||||
/* > \verbatim */
|
||||
/* > U is REAL array, */
|
||||
/* > dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced */
|
||||
/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left */
|
||||
/* > singular vector matrices of all subproblems at the bottom */
|
||||
/* > level. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] LDU */
|
||||
/* > \verbatim */
|
||||
/* > LDU is INTEGER, LDU = > N. */
|
||||
/* > The leading dimension of arrays U, VT, DIFL, DIFR, POLES, */
|
||||
/* > GIVNUM, and Z. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] VT */
|
||||
/* > \verbatim */
|
||||
/* > VT is REAL array, */
|
||||
/* > dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced */
|
||||
/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right */
|
||||
/* > singular vector matrices of all subproblems at the bottom */
|
||||
/* > level. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] K */
|
||||
/* > \verbatim */
|
||||
/* > K is INTEGER array, dimension ( N ) */
|
||||
/* > if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. */
|
||||
/* > If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th */
|
||||
/* > secular equation on the computation tree. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] DIFL */
|
||||
/* > \verbatim */
|
||||
/* > DIFL is REAL array, dimension ( LDU, NLVL ), */
|
||||
/* > where NLVL = floor(log_2 (N/SMLSIZ))). */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] DIFR */
|
||||
/* > \verbatim */
|
||||
/* > DIFR is REAL array, */
|
||||
/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and */
|
||||
/* > dimension ( N ) if ICOMPQ = 0. */
|
||||
/* > If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1) */
|
||||
/* > record distances between singular values on the I-th */
|
||||
/* > level and singular values on the (I -1)-th level, and */
|
||||
/* > DIFR(1:N, 2 * I ) contains the normalizing factors for */
|
||||
/* > the right singular vector matrix. See SLASD8 for details. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] Z */
|
||||
/* > \verbatim */
|
||||
/* > Z is REAL array, */
|
||||
/* > dimension ( LDU, NLVL ) if ICOMPQ = 1 and */
|
||||
/* > dimension ( N ) if ICOMPQ = 0. */
|
||||
/* > The first K elements of Z(1, I) contain the components of */
|
||||
/* > the deflation-adjusted updating row vector for subproblems */
|
||||
/* > on the I-th level. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] POLES */
|
||||
/* > \verbatim */
|
||||
/* > POLES is REAL array, */
|
||||
/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced */
|
||||
/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and */
|
||||
/* > POLES(1, 2*I) contain the new and old singular values */
|
||||
/* > involved in the secular equations on the I-th level. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] GIVPTR */
|
||||
/* > \verbatim */
|
||||
/* > GIVPTR is INTEGER array, */
|
||||
/* > dimension ( N ) if ICOMPQ = 1, and not referenced if */
|
||||
/* > ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records */
|
||||
/* > the number of Givens rotations performed on the I-th */
|
||||
/* > problem on the computation tree. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] GIVCOL */
|
||||
/* > \verbatim */
|
||||
/* > GIVCOL is INTEGER array, */
|
||||
/* > dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not */
|
||||
/* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
|
||||
/* > GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations */
|
||||
/* > of Givens rotations performed on the I-th level on the */
|
||||
/* > computation tree. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[in] LDGCOL */
|
||||
/* > \verbatim */
|
||||
/* > LDGCOL is INTEGER, LDGCOL = > N. */
|
||||
/* > The leading dimension of arrays GIVCOL and PERM. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] PERM */
|
||||
/* > \verbatim */
|
||||
/* > PERM is INTEGER array, dimension ( LDGCOL, NLVL ) */
|
||||
/* > if ICOMPQ = 1, and not referenced */
|
||||
/* > if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records */
|
||||
/* > permutations done on the I-th level of the computation tree. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] GIVNUM */
|
||||
/* > \verbatim */
|
||||
/* > GIVNUM is REAL array, */
|
||||
/* > dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not */
|
||||
/* > referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, */
|
||||
/* > GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S- */
|
||||
/* > values of Givens rotations performed on the I-th level on */
|
||||
/* > the computation tree. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] C */
|
||||
/* > \verbatim */
|
||||
/* > C is REAL array, */
|
||||
/* > dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. */
|
||||
/* > If ICOMPQ = 1 and the I-th subproblem is not square, on exit, */
|
||||
/* > C( I ) contains the C-value of a Givens rotation related to */
|
||||
/* > the right null space of the I-th subproblem. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] S */
|
||||
/* > \verbatim */
|
||||
/* > S is REAL array, dimension ( N ) if */
|
||||
/* > ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 */
|
||||
/* > and the I-th subproblem is not square, on exit, S( I ) */
|
||||
/* > contains the S-value of a Givens rotation related to */
|
||||
/* > the right null space of the I-th subproblem. */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] WORK */
|
||||
/* > \verbatim */
|
||||
/* > WORK is REAL array, dimension */
|
||||
/* > (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)). */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] IWORK */
|
||||
/* > \verbatim */
|
||||
/* > IWORK is INTEGER array, dimension (7*N). */
|
||||
/* > \endverbatim */
|
||||
/* > */
|
||||
/* > \param[out] INFO */
|
||||
/* > \verbatim */
|
||||
/* > INFO is INTEGER */
|
||||
/* > = 0: successful exit. */
|
||||
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
|
||||
/* > > 0: if INFO = 1, a singular value did not converge */
|
||||
/* > \endverbatim */
|
||||
|
||||
/* Authors: */
|
||||
/* ======== */
|
||||
|
||||
/* > \author Univ. of Tennessee */
|
||||
/* > \author Univ. of California Berkeley */
|
||||
/* > \author Univ. of Colorado Denver */
|
||||
/* > \author NAG Ltd. */
|
||||
|
||||
/* > \date December 2016 */
|
||||
|
||||
/* > \ingroup OTHERauxiliary */
|
||||
|
||||
/* > \par Contributors: */
|
||||
/* ================== */
|
||||
/* > */
|
||||
/* > Ming Gu and Huan Ren, Computer Science Division, University of */
|
||||
/* > California at Berkeley, USA */
|
||||
/* > */
|
||||
/* ===================================================================== */
|
||||
/* Subroutine */ int slasda_(integer *icompq, integer *smlsiz, integer *n,
|
||||
integer *sqre, real *d__, real *e, real *u, integer *ldu, real *vt,
|
||||
integer *k, real *difl, real *difr, real *z__, real *poles, integer *
|
||||
givptr, integer *givcol, integer *ldgcol, integer *perm, real *givnum,
|
||||
real *c__, real *s, real *work, integer *iwork, integer *info)
|
||||
{
|
||||
/* System generated locals */
|
||||
integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, difl_dim1,
|
||||
difl_offset, difr_dim1, difr_offset, givnum_dim1, givnum_offset,
|
||||
poles_dim1, poles_offset, u_dim1, u_offset, vt_dim1, vt_offset,
|
||||
z_dim1, z_offset, i__1, i__2;
|
||||
|
||||
/* Local variables */
|
||||
real beta;
|
||||
integer idxq, nlvl, i__, j, m;
|
||||
real alpha;
|
||||
integer inode, ndiml, ndimr, idxqi, itemp, sqrei, i1;
|
||||
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
|
||||
integer *), slasd6_(integer *, integer *, integer *, integer *,
|
||||
real *, real *, real *, real *, real *, integer *, integer *,
|
||||
integer *, integer *, integer *, real *, integer *, real *, real *
|
||||
, real *, real *, integer *, real *, real *, real *, integer *,
|
||||
integer *);
|
||||
integer ic, nwork1, lf, nd, nwork2, ll, nl, vf, nr, vl;
|
||||
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), slasdq_(
|
||||
char *, integer *, integer *, integer *, integer *, integer *,
|
||||
real *, real *, real *, integer *, real *, integer *, real *,
|
||||
integer *, real *, integer *), slasdt_(integer *, integer
|
||||
*, integer *, integer *, integer *, integer *, integer *),
|
||||
slaset_(char *, integer *, integer *, real *, real *, real *,
|
||||
integer *);
|
||||
integer im1, smlszp, ncc, nlf, nrf, vfi, iwk, vli, lvl, nru, ndb1, nlp1,
|
||||
lvl2, nrp1;
|
||||
|
||||
|
||||
/* -- LAPACK auxiliary routine (version 3.7.0) -- */
|
||||
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
||||
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
||||
/* December 2016 */
|
||||
|
||||
|
||||
/* ===================================================================== */
|
||||
|
||||
|
||||
/* Test the input parameters. */
|
||||
|
||||
/* Parameter adjustments */
|
||||
--d__;
|
||||
--e;
|
||||
givnum_dim1 = *ldu;
|
||||
givnum_offset = 1 + givnum_dim1 * 1;
|
||||
givnum -= givnum_offset;
|
||||
poles_dim1 = *ldu;
|
||||
poles_offset = 1 + poles_dim1 * 1;
|
||||
poles -= poles_offset;
|
||||
z_dim1 = *ldu;
|
||||
z_offset = 1 + z_dim1 * 1;
|
||||
z__ -= z_offset;
|
||||
difr_dim1 = *ldu;
|
||||
difr_offset = 1 + difr_dim1 * 1;
|
||||
difr -= difr_offset;
|
||||
difl_dim1 = *ldu;
|
||||
difl_offset = 1 + difl_dim1 * 1;
|
||||
difl -= difl_offset;
|
||||
vt_dim1 = *ldu;
|
||||
vt_offset = 1 + vt_dim1 * 1;
|
||||
vt -= vt_offset;
|
||||
u_dim1 = *ldu;
|
||||
u_offset = 1 + u_dim1 * 1;
|
||||
u -= u_offset;
|
||||
--k;
|
||||
--givptr;
|
||||
perm_dim1 = *ldgcol;
|
||||
perm_offset = 1 + perm_dim1 * 1;
|
||||
perm -= perm_offset;
|
||||
givcol_dim1 = *ldgcol;
|
||||
givcol_offset = 1 + givcol_dim1 * 1;
|
||||
givcol -= givcol_offset;
|
||||
--c__;
|
||||
--s;
|
||||
--work;
|
||||
--iwork;
|
||||
|
||||
/* Function Body */
|
||||
*info = 0;
|
||||
|
||||
if (*icompq < 0 || *icompq > 1) {
|
||||
*info = -1;
|
||||
} else if (*smlsiz < 3) {
|
||||
*info = -2;
|
||||
} else if (*n < 0) {
|
||||
*info = -3;
|
||||
} else if (*sqre < 0 || *sqre > 1) {
|
||||
*info = -4;
|
||||
} else if (*ldu < *n + *sqre) {
|
||||
*info = -8;
|
||||
} else if (*ldgcol < *n) {
|
||||
*info = -17;
|
||||
}
|
||||
if (*info != 0) {
|
||||
i__1 = -(*info);
|
||||
xerbla_("SLASDA", &i__1, (ftnlen)6);
|
||||
return 0;
|
||||
}
|
||||
|
||||
m = *n + *sqre;
|
||||
|
||||
/* If the input matrix is too small, call SLASDQ to find the SVD. */
|
||||
|
||||
if (*n <= *smlsiz) {
|
||||
if (*icompq == 0) {
|
||||
slasdq_("U", sqre, n, &c__0, &c__0, &c__0, &d__[1], &e[1], &vt[
|
||||
vt_offset], ldu, &u[u_offset], ldu, &u[u_offset], ldu, &
|
||||
work[1], info);
|
||||
} else {
|
||||
slasdq_("U", sqre, n, &m, n, &c__0, &d__[1], &e[1], &vt[vt_offset]
|
||||
, ldu, &u[u_offset], ldu, &u[u_offset], ldu, &work[1],
|
||||
info);
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Book-keeping and set up the computation tree. */
|
||||
|
||||
inode = 1;
|
||||
ndiml = inode + *n;
|
||||
ndimr = ndiml + *n;
|
||||
idxq = ndimr + *n;
|
||||
iwk = idxq + *n;
|
||||
|
||||
ncc = 0;
|
||||
nru = 0;
|
||||
|
||||
smlszp = *smlsiz + 1;
|
||||
vf = 1;
|
||||
vl = vf + m;
|
||||
nwork1 = vl + m;
|
||||
nwork2 = nwork1 + smlszp * smlszp;
|
||||
|
||||
slasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
|
||||
smlsiz);
|
||||
|
||||
/* for the nodes on bottom level of the tree, solve */
|
||||
/* their subproblems by SLASDQ. */
|
||||
|
||||
ndb1 = (nd + 1) / 2;
|
||||
i__1 = nd;
|
||||
for (i__ = ndb1; i__ <= i__1; ++i__) {
|
||||
|
||||
/* IC : center row of each node */
|
||||
/* NL : number of rows of left subproblem */
|
||||
/* NR : number of rows of right subproblem */
|
||||
/* NLF: starting row of the left subproblem */
|
||||
/* NRF: starting row of the right subproblem */
|
||||
|
||||
i1 = i__ - 1;
|
||||
ic = iwork[inode + i1];
|
||||
nl = iwork[ndiml + i1];
|
||||
nlp1 = nl + 1;
|
||||
nr = iwork[ndimr + i1];
|
||||
nlf = ic - nl;
|
||||
nrf = ic + 1;
|
||||
idxqi = idxq + nlf - 2;
|
||||
vfi = vf + nlf - 1;
|
||||
vli = vl + nlf - 1;
|
||||
sqrei = 1;
|
||||
if (*icompq == 0) {
|
||||
slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
|
||||
slasdq_("U", &sqrei, &nl, &nlp1, &nru, &ncc, &d__[nlf], &e[nlf], &
|
||||
work[nwork1], &smlszp, &work[nwork2], &nl, &work[nwork2],
|
||||
&nl, &work[nwork2], info);
|
||||
itemp = nwork1 + nl * smlszp;
|
||||
scopy_(&nlp1, &work[nwork1], &c__1, &work[vfi], &c__1);
|
||||
scopy_(&nlp1, &work[itemp], &c__1, &work[vli], &c__1);
|
||||
} else {
|
||||
slaset_("A", &nl, &nl, &c_b11, &c_b12, &u[nlf + u_dim1], ldu);
|
||||
slaset_("A", &nlp1, &nlp1, &c_b11, &c_b12, &vt[nlf + vt_dim1],
|
||||
ldu);
|
||||
slasdq_("U", &sqrei, &nl, &nlp1, &nl, &ncc, &d__[nlf], &e[nlf], &
|
||||
vt[nlf + vt_dim1], ldu, &u[nlf + u_dim1], ldu, &u[nlf +
|
||||
u_dim1], ldu, &work[nwork1], info);
|
||||
scopy_(&nlp1, &vt[nlf + vt_dim1], &c__1, &work[vfi], &c__1);
|
||||
scopy_(&nlp1, &vt[nlf + nlp1 * vt_dim1], &c__1, &work[vli], &c__1)
|
||||
;
|
||||
}
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
i__2 = nl;
|
||||
for (j = 1; j <= i__2; ++j) {
|
||||
iwork[idxqi + j] = j;
|
||||
/* L10: */
|
||||
}
|
||||
if (i__ == nd && *sqre == 0) {
|
||||
sqrei = 0;
|
||||
} else {
|
||||
sqrei = 1;
|
||||
}
|
||||
idxqi += nlp1;
|
||||
vfi += nlp1;
|
||||
vli += nlp1;
|
||||
nrp1 = nr + sqrei;
|
||||
if (*icompq == 0) {
|
||||
slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &work[nwork1], &smlszp);
|
||||
slasdq_("U", &sqrei, &nr, &nrp1, &nru, &ncc, &d__[nrf], &e[nrf], &
|
||||
work[nwork1], &smlszp, &work[nwork2], &nr, &work[nwork2],
|
||||
&nr, &work[nwork2], info);
|
||||
itemp = nwork1 + (nrp1 - 1) * smlszp;
|
||||
scopy_(&nrp1, &work[nwork1], &c__1, &work[vfi], &c__1);
|
||||
scopy_(&nrp1, &work[itemp], &c__1, &work[vli], &c__1);
|
||||
} else {
|
||||
slaset_("A", &nr, &nr, &c_b11, &c_b12, &u[nrf + u_dim1], ldu);
|
||||
slaset_("A", &nrp1, &nrp1, &c_b11, &c_b12, &vt[nrf + vt_dim1],
|
||||
ldu);
|
||||
slasdq_("U", &sqrei, &nr, &nrp1, &nr, &ncc, &d__[nrf], &e[nrf], &
|
||||
vt[nrf + vt_dim1], ldu, &u[nrf + u_dim1], ldu, &u[nrf +
|
||||
u_dim1], ldu, &work[nwork1], info);
|
||||
scopy_(&nrp1, &vt[nrf + vt_dim1], &c__1, &work[vfi], &c__1);
|
||||
scopy_(&nrp1, &vt[nrf + nrp1 * vt_dim1], &c__1, &work[vli], &c__1)
|
||||
;
|
||||
}
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
i__2 = nr;
|
||||
for (j = 1; j <= i__2; ++j) {
|
||||
iwork[idxqi + j] = j;
|
||||
/* L20: */
|
||||
}
|
||||
/* L30: */
|
||||
}
|
||||
|
||||
/* Now conquer each subproblem bottom-up. */
|
||||
|
||||
j = pow_ii(&c__2, &nlvl);
|
||||
for (lvl = nlvl; lvl >= 1; --lvl) {
|
||||
lvl2 = (lvl << 1) - 1;
|
||||
|
||||
/* Find the first node LF and last node LL on */
|
||||
/* the current level LVL. */
|
||||
|
||||
if (lvl == 1) {
|
||||
lf = 1;
|
||||
ll = 1;
|
||||
} else {
|
||||
i__1 = lvl - 1;
|
||||
lf = pow_ii(&c__2, &i__1);
|
||||
ll = (lf << 1) - 1;
|
||||
}
|
||||
i__1 = ll;
|
||||
for (i__ = lf; i__ <= i__1; ++i__) {
|
||||
im1 = i__ - 1;
|
||||
ic = iwork[inode + im1];
|
||||
nl = iwork[ndiml + im1];
|
||||
nr = iwork[ndimr + im1];
|
||||
nlf = ic - nl;
|
||||
nrf = ic + 1;
|
||||
if (i__ == ll) {
|
||||
sqrei = *sqre;
|
||||
} else {
|
||||
sqrei = 1;
|
||||
}
|
||||
vfi = vf + nlf - 1;
|
||||
vli = vl + nlf - 1;
|
||||
idxqi = idxq + nlf - 1;
|
||||
alpha = d__[ic];
|
||||
beta = e[ic];
|
||||
if (*icompq == 0) {
|
||||
slasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
|
||||
work[vli], &alpha, &beta, &iwork[idxqi], &perm[
|
||||
perm_offset], &givptr[1], &givcol[givcol_offset],
|
||||
ldgcol, &givnum[givnum_offset], ldu, &poles[
|
||||
poles_offset], &difl[difl_offset], &difr[difr_offset],
|
||||
&z__[z_offset], &k[1], &c__[1], &s[1], &work[nwork1],
|
||||
&iwork[iwk], info);
|
||||
} else {
|
||||
--j;
|
||||
slasd6_(icompq, &nl, &nr, &sqrei, &d__[nlf], &work[vfi], &
|
||||
work[vli], &alpha, &beta, &iwork[idxqi], &perm[nlf +
|
||||
lvl * perm_dim1], &givptr[j], &givcol[nlf + lvl2 *
|
||||
givcol_dim1], ldgcol, &givnum[nlf + lvl2 *
|
||||
givnum_dim1], ldu, &poles[nlf + lvl2 * poles_dim1], &
|
||||
difl[nlf + lvl * difl_dim1], &difr[nlf + lvl2 *
|
||||
difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[j],
|
||||
&s[j], &work[nwork1], &iwork[iwk], info);
|
||||
}
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
/* L40: */
|
||||
}
|
||||
/* L50: */
|
||||
}
|
||||
|
||||
return 0;
|
||||
|
||||
/* End of SLASDA */
|
||||
|
||||
} /* slasda_ */
|
||||
|
||||
Reference in New Issue
Block a user