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OpenBLAS/lapack-netlib/SRC/sgbequ.c

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#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif
#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif
#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif
typedef blasint integer;
typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef blasint logical;
typedef char logical1;
typedef char integer1;
#define TRUE_ (1)
#define FALSE_ (0)
/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif
/* I/O stuff */
typedef int flag;
typedef int ftnlen;
typedef int ftnint;
/*external read, write*/
typedef struct
{ flag cierr;
ftnint ciunit;
flag ciend;
char *cifmt;
ftnint cirec;
} cilist;
/*internal read, write*/
typedef struct
{ flag icierr;
char *iciunit;
flag iciend;
char *icifmt;
ftnint icirlen;
ftnint icirnum;
} icilist;
/*open*/
typedef struct
{ flag oerr;
ftnint ounit;
char *ofnm;
ftnlen ofnmlen;
char *osta;
char *oacc;
char *ofm;
ftnint orl;
char *oblnk;
} olist;
/*close*/
typedef struct
{ flag cerr;
ftnint cunit;
char *csta;
} cllist;
/*rewind, backspace, endfile*/
typedef struct
{ flag aerr;
ftnint aunit;
} alist;
/* inquire */
typedef struct
{ flag inerr;
ftnint inunit;
char *infile;
ftnlen infilen;
ftnint *inex; /*parameters in standard's order*/
ftnint *inopen;
ftnint *innum;
ftnint *innamed;
char *inname;
ftnlen innamlen;
char *inacc;
ftnlen inacclen;
char *inseq;
ftnlen inseqlen;
char *indir;
ftnlen indirlen;
char *infmt;
ftnlen infmtlen;
char *inform;
ftnint informlen;
char *inunf;
ftnlen inunflen;
ftnint *inrecl;
ftnint *innrec;
char *inblank;
ftnlen inblanklen;
} inlist;
#define VOID void
union Multitype { /* for multiple entry points */
integer1 g;
shortint h;
integer i;
/* longint j; */
real r;
doublereal d;
complex c;
doublecomplex z;
};
typedef union Multitype Multitype;
struct Vardesc { /* for Namelist */
char *name;
char *addr;
ftnlen *dims;
int type;
};
typedef struct Vardesc Vardesc;
struct Namelist {
char *name;
Vardesc **vars;
int nvars;
};
typedef struct Namelist Namelist;
#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b) ((a) >> (b) & 1)
#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))
#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#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++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#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]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* > \brief \b SGBEQU */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download SGBEQU + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgbequ.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgbequ.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgbequ.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE SGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, */
/* AMAX, INFO ) */
/* INTEGER INFO, KL, KU, LDAB, M, N */
/* REAL AMAX, COLCND, ROWCND */
/* REAL AB( LDAB, * ), C( * ), R( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SGBEQU computes row and column scalings intended to equilibrate an */
/* > M-by-N band matrix A and reduce its condition number. R returns the */
/* > row scale factors and C the column scale factors, chosen to try to */
/* > make the largest element in each row and column of the matrix B with */
/* > elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. */
/* > */
/* > R(i) and C(j) are restricted to be between SMLNUM = smallest safe */
/* > number and BIGNUM = largest safe number. Use of these scaling */
/* > factors is not guaranteed to reduce the condition number of A but */
/* > works well in practice. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The number of rows of the matrix A. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KL */
/* > \verbatim */
/* > KL is INTEGER */
/* > The number of subdiagonals within the band of A. KL >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] KU */
/* > \verbatim */
/* > KU is INTEGER */
/* > The number of superdiagonals within the band of A. KU >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] AB */
/* > \verbatim */
/* > AB is REAL array, dimension (LDAB,N) */
/* > The band matrix A, stored in rows 1 to KL+KU+1. The j-th */
/* > column of A is stored in the j-th column of the array AB as */
/* > follows: */
/* > AB(ku+1+i-j,j) = A(i,j) for f2cmax(1,j-ku)<=i<=f2cmin(m,j+kl). */
/* > \endverbatim */
/* > */
/* > \param[in] LDAB */
/* > \verbatim */
/* > LDAB is INTEGER */
/* > The leading dimension of the array AB. LDAB >= KL+KU+1. */
/* > \endverbatim */
/* > */
/* > \param[out] R */
/* > \verbatim */
/* > R is REAL array, dimension (M) */
/* > If INFO = 0, or INFO > M, R contains the row scale factors */
/* > for A. */
/* > \endverbatim */
/* > */
/* > \param[out] C */
/* > \verbatim */
/* > C is REAL array, dimension (N) */
/* > If INFO = 0, C contains the column scale factors for A. */
/* > \endverbatim */
/* > */
/* > \param[out] ROWCND */
/* > \verbatim */
/* > ROWCND is REAL */
/* > If INFO = 0 or INFO > M, ROWCND contains the ratio of the */
/* > smallest R(i) to the largest R(i). If ROWCND >= 0.1 and */
/* > AMAX is neither too large nor too small, it is not worth */
/* > scaling by R. */
/* > \endverbatim */
/* > */
/* > \param[out] COLCND */
/* > \verbatim */
/* > COLCND is REAL */
/* > If INFO = 0, COLCND contains the ratio of the smallest */
/* > C(i) to the largest C(i). If COLCND >= 0.1, it is not */
/* > worth scaling by C. */
/* > \endverbatim */
/* > */
/* > \param[out] AMAX */
/* > \verbatim */
/* > AMAX is REAL */
/* > Absolute value of largest matrix element. If AMAX is very */
/* > close to overflow or very close to underflow, the matrix */
/* > should be scaled. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > > 0: if INFO = i, and i is */
/* > <= M: the i-th row of A is exactly zero */
/* > > M: the (i-M)-th column of A is exactly zero */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup realGBcomputational */
/* ===================================================================== */
/* Subroutine */ void sgbequ_(integer *m, integer *n, integer *kl, integer *ku,
real *ab, integer *ldab, real *r__, real *c__, real *rowcnd, real *
colcnd, real *amax, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4;
real r__1, r__2, r__3;
/* Local variables */
integer i__, j;
real rcmin, rcmax;
integer kd;
extern real slamch_(char *);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
real bignum, smlnum;
/* -- LAPACK computational routine (version 3.7.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* December 2016 */
/* ===================================================================== */
/* Test the input parameters */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1 * 1;
ab -= ab_offset;
--r__;
--c__;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*kl < 0) {
*info = -3;
} else if (*ku < 0) {
*info = -4;
} else if (*ldab < *kl + *ku + 1) {
*info = -6;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SGBEQU", &i__1, (ftnlen)6);
return;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
*rowcnd = 1.f;
*colcnd = 1.f;
*amax = 0.f;
return;
}
/* Get machine constants. */
smlnum = slamch_("S");
bignum = 1.f / smlnum;
/* Compute row scale factors. */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
r__[i__] = 0.f;
/* L10: */
}
/* Find the maximum element in each row. */
kd = *ku + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = j - *ku;
/* Computing MIN */
i__4 = j + *kl;
i__3 = f2cmin(i__4,*m);
for (i__ = f2cmax(i__2,1); i__ <= i__3; ++i__) {
/* Computing MAX */
r__2 = r__[i__], r__3 = (r__1 = ab[kd + i__ - j + j * ab_dim1],
abs(r__1));
r__[i__] = f2cmax(r__2,r__3);
/* L20: */
}
/* L30: */
}
/* Find the maximum and minimum scale factors. */
rcmin = bignum;
rcmax = 0.f;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
r__1 = rcmax, r__2 = r__[i__];
rcmax = f2cmax(r__1,r__2);
/* Computing MIN */
r__1 = rcmin, r__2 = r__[i__];
rcmin = f2cmin(r__1,r__2);
/* L40: */
}
*amax = rcmax;
if (rcmin == 0.f) {
/* Find the first zero scale factor and return an error code. */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
if (r__[i__] == 0.f) {
*info = i__;
return;
}
/* L50: */
}
} else {
/* Invert the scale factors. */
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MIN */
/* Computing MAX */
r__2 = r__[i__];
r__1 = f2cmax(r__2,smlnum);
r__[i__] = 1.f / f2cmin(r__1,bignum);
/* L60: */
}
/* Compute ROWCND = f2cmin(R(I)) / f2cmax(R(I)) */
*rowcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
}
/* Compute column scale factors */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
c__[j] = 0.f;
/* L70: */
}
/* Find the maximum element in each column, */
/* assuming the row scaling computed above. */
kd = *ku + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__3 = j - *ku;
/* Computing MIN */
i__4 = j + *kl;
i__2 = f2cmin(i__4,*m);
for (i__ = f2cmax(i__3,1); i__ <= i__2; ++i__) {
/* Computing MAX */
r__2 = c__[j], r__3 = (r__1 = ab[kd + i__ - j + j * ab_dim1], abs(
r__1)) * r__[i__];
c__[j] = f2cmax(r__2,r__3);
/* L80: */
}
/* L90: */
}
/* Find the maximum and minimum scale factors. */
rcmin = bignum;
rcmax = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
r__1 = rcmin, r__2 = c__[j];
rcmin = f2cmin(r__1,r__2);
/* Computing MAX */
r__1 = rcmax, r__2 = c__[j];
rcmax = f2cmax(r__1,r__2);
/* L100: */
}
if (rcmin == 0.f) {
/* Find the first zero scale factor and return an error code. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (c__[j] == 0.f) {
*info = *m + j;
return;
}
/* L110: */
}
} else {
/* Invert the scale factors. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
/* Computing MAX */
r__2 = c__[j];
r__1 = f2cmax(r__2,smlnum);
c__[j] = 1.f / f2cmin(r__1,bignum);
/* L120: */
}
/* Compute COLCND = f2cmin(C(J)) / f2cmax(C(J)) */
*colcnd = f2cmax(rcmin,smlnum) / f2cmin(rcmax,bignum);
}
return;
/* End of SGBEQU */
} /* sgbequ_ */
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