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OpenBLAS/lapack-netlib/TESTING/MATGEN/clahilb.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 int logical;
typedef short int shortlogical;
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 pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(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)}
/* procedure parameter types for -A and -C++ */
#define F2C_proc_par_types 1
/* Table of constant values */
static integer c__2 = 2;
static complex c_b6 = {0.f,0.f};
/* > \brief \b CLAHILB */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* Definition: */
/* =========== */
/* SUBROUTINE CLAHILB( N, NRHS, A, LDA, X, LDX, B, LDB, WORK, */
/* INFO, PATH) */
/* INTEGER N, NRHS, LDA, LDX, LDB, INFO */
/* REAL WORK(N) */
/* COMPLEX A(LDA,N), X(LDX, NRHS), B(LDB, NRHS) */
/* CHARACTER*3 PATH */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CLAHILB generates an N by N scaled Hilbert matrix in A along with */
/* > NRHS right-hand sides in B and solutions in X such that A*X=B. */
/* > */
/* > The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all */
/* > entries are integers. The right-hand sides are the first NRHS */
/* > columns of M * the identity matrix, and the solutions are the */
/* > first NRHS columns of the inverse Hilbert matrix. */
/* > */
/* > The condition number of the Hilbert matrix grows exponentially with */
/* > its size, roughly as O(e ** (3.5*N)). Additionally, the inverse */
/* > Hilbert matrices beyond a relatively small dimension cannot be */
/* > generated exactly without extra precision. Precision is exhausted */
/* > when the largest entry in the inverse Hilbert matrix is greater than */
/* > 2 to the power of the number of bits in the fraction of the data type */
/* > used plus one, which is 24 for single precision. */
/* > */
/* > In single, the generated solution is exact for N <= 6 and has */
/* > small componentwise error for 7 <= N <= 11. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The dimension of the matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] NRHS */
/* > \verbatim */
/* > NRHS is INTEGER */
/* > The requested number of right-hand sides. */
/* > \endverbatim */
/* > */
/* > \param[out] A */
/* > \verbatim */
/* > A is COMPLEX array, dimension (LDA, N) */
/* > The generated scaled Hilbert matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] X */
/* > \verbatim */
/* > X is COMPLEX array, dimension (LDX, NRHS) */
/* > The generated exact solutions. Currently, the first NRHS */
/* > columns of the inverse Hilbert matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] LDX */
/* > \verbatim */
/* > LDX is INTEGER */
/* > The leading dimension of the array X. LDX >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] B */
/* > \verbatim */
/* > B is REAL array, dimension (LDB, NRHS) */
/* > The generated right-hand sides. Currently, the first NRHS */
/* > columns of LCM(1, 2, ..., 2*N-1) * the identity matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > = 1: N is too large; the data is still generated but may not */
/* > be not exact. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > \endverbatim */
/* > */
/* > \param[in] PATH */
/* > \verbatim */
/* > PATH is CHARACTER*3 */
/* > The LAPACK path name. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date November 2017 */
/* > \ingroup complex_matgen */
/* ===================================================================== */
/* Subroutine */ void clahilb_(integer *n, integer *nrhs, complex *a, integer *
lda, complex *x, integer *ldx, complex *b, integer *ldb, real *work,
integer *info, char *path)
{
/* Initialized data */
static complex d1[8] = { {-1.f,0.f},{0.f,1.f},{-1.f,-1.f},{0.f,-1.f},{1.f,
0.f},{-1.f,1.f},{1.f,1.f},{1.f,-1.f} };
static complex d2[8] = { {-1.f,0.f},{0.f,-1.f},{-1.f,1.f},{0.f,1.f},{1.f,
0.f},{-1.f,-1.f},{1.f,-1.f},{1.f,1.f} };
static complex invd1[8] = { {-1.f,0.f},{0.f,-1.f},{-.5f,.5f},{0.f,1.f},{
1.f,0.f},{-.5f,-.5f},{.5f,-.5f},{.5f,.5f} };
static complex invd2[8] = { {-1.f,0.f},{0.f,1.f},{-.5f,-.5f},{0.f,-1.f},{
1.f,0.f},{-.5f,.5f},{.5f,.5f},{.5f,-.5f} };
/* System generated locals */
integer a_dim1, a_offset, x_dim1, x_offset, b_dim1, b_offset, i__1, i__2,
i__3, i__4, i__5;
real r__1;
complex q__1, q__2;
/* Local variables */
integer i__, j, m, r__;
char c2[2];
integer ti, tm;
extern /* Subroutine */ void claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *);
extern int xerbla_(char *, integer *, ftnlen);
extern logical lsamen_(integer *, char *, char *);
complex tmp;
/* -- LAPACK test 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..-- */
/* November 2017 */
/* ===================================================================== */
/* NMAX_EXACT the largest dimension where the generated data is */
/* exact. */
/* NMAX_APPROX the largest dimension where the generated data has */
/* a small componentwise relative error. */
/* ??? complex uses how many bits ??? */
/* d's are generated from random permutation of those eight elements. */
/* Parameter adjustments */
--work;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Test the input arguments */
*info = 0;
if (*n < 0 || *n > 11) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*lda < *n) {
*info = -4;
} else if (*ldx < *n) {
*info = -6;
} else if (*ldb < *n) {
*info = -8;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLAHILB", &i__1, 7);
return;
}
if (*n > 6) {
*info = 1;
}
/* Compute M = the LCM of the integers [1, 2*N-1]. The largest */
/* reasonable N is small enough that integers suffice (up to N = 11). */
m = 1;
i__1 = (*n << 1) - 1;
for (i__ = 2; i__ <= i__1; ++i__) {
tm = m;
ti = i__;
r__ = tm % ti;
while(r__ != 0) {
tm = ti;
ti = r__;
r__ = tm % ti;
}
m = m / ti * i__;
}
/* Generate the scaled Hilbert matrix in A */
/* If we are testing SY routines, take */
/* D1_i = D2_i, else, D1_i = D2_i* */
if (lsamen_(&c__2, c2, "SY")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = j % 8;
r__1 = (real) m / (i__ + j - 1);
q__2.r = r__1 * d1[i__4].r, q__2.i = r__1 * d1[i__4].i;
i__5 = i__ % 8;
q__1.r = q__2.r * d1[i__5].r - q__2.i * d1[i__5].i, q__1.i =
q__2.r * d1[i__5].i + q__2.i * d1[i__5].r;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
}
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
i__4 = j % 8;
r__1 = (real) m / (i__ + j - 1);
q__2.r = r__1 * d1[i__4].r, q__2.i = r__1 * d1[i__4].i;
i__5 = i__ % 8;
q__1.r = q__2.r * d2[i__5].r - q__2.i * d2[i__5].i, q__1.i =
q__2.r * d2[i__5].i + q__2.i * d2[i__5].r;
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
}
}
}
/* Generate matrix B as simply the first NRHS columns of M * the */
/* identity. */
r__1 = (real) m;
tmp.r = r__1, tmp.i = 0.f;
claset_("Full", n, nrhs, &c_b6, &tmp, &b[b_offset], ldb);
/* Generate the true solutions in X. Because B = the first NRHS */
/* columns of M*I, the true solutions are just the first NRHS columns */
/* of the inverse Hilbert matrix. */
work[1] = (real) (*n);
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
work[j] = work[j - 1] / (j - 1) * (j - 1 - *n) / (j - 1) * (*n + j -
1);
}
/* If we are testing SY routines, */
/* take D1_i = D2_i, else, D1_i = D2_i* */
if (lsamen_(&c__2, c2, "SY")) {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * x_dim1;
i__4 = j % 8;
r__1 = work[i__] * work[j] / (i__ + j - 1);
q__2.r = r__1 * invd1[i__4].r, q__2.i = r__1 * invd1[i__4].i;
i__5 = i__ % 8;
q__1.r = q__2.r * invd1[i__5].r - q__2.i * invd1[i__5].i,
q__1.i = q__2.r * invd1[i__5].i + q__2.i * invd1[i__5]
.r;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
}
}
} else {
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * x_dim1;
i__4 = j % 8;
r__1 = work[i__] * work[j] / (i__ + j - 1);
q__2.r = r__1 * invd2[i__4].r, q__2.i = r__1 * invd2[i__4].i;
i__5 = i__ % 8;
q__1.r = q__2.r * invd1[i__5].r - q__2.i * invd1[i__5].i,
q__1.i = q__2.r * invd1[i__5].i + q__2.i * invd1[i__5]
.r;
x[i__3].r = q__1.r, x[i__3].i = q__1.i;
}
}
}
return;
} /* clahilb_ */
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