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OpenBLAS/lapack-netlib/TESTING/MATGEN/claghe.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 complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__3 = 3;
static integer c__1 = 1;
/* > \brief \b CLAGHE */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* Definition: */
/* =========== */
/* SUBROUTINE CLAGHE( N, K, D, A, LDA, ISEED, WORK, INFO ) */
/* INTEGER INFO, K, LDA, N */
/* INTEGER ISEED( 4 ) */
/* REAL D( * ) */
/* COMPLEX A( LDA, * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > CLAGHE generates a complex hermitian matrix A, by pre- and post- */
/* > multiplying a real diagonal matrix D with a random unitary matrix: */
/* > A = U*D*U'. The semi-bandwidth may then be reduced to k by additional */
/* > unitary transformations. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix A. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] K */
/* > \verbatim */
/* > K is INTEGER */
/* > The number of nonzero subdiagonals within the band of A. */
/* > 0 <= K <= N-1. */
/* > \endverbatim */
/* > */
/* > \param[in] D */
/* > \verbatim */
/* > D is REAL array, dimension (N) */
/* > The diagonal elements of the diagonal matrix D. */
/* > \endverbatim */
/* > */
/* > \param[out] A */
/* > \verbatim */
/* > A is COMPLEX array, dimension (LDA,N) */
/* > The generated n by n hermitian matrix A (the full matrix is */
/* > stored). */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= N. */
/* > \endverbatim */
/* > */
/* > \param[in,out] ISEED */
/* > \verbatim */
/* > ISEED is INTEGER array, dimension (4) */
/* > On entry, the seed of the random number generator; the array */
/* > elements must be between 0 and 4095, and ISEED(4) must be */
/* > odd. */
/* > On exit, the seed is updated. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is COMPLEX array, dimension (2*N) */
/* > \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 December 2016 */
/* > \ingroup complex_matgen */
/* ===================================================================== */
/* Subroutine */ void claghe_(integer *n, integer *k, real *d__, complex *a,
integer *lda, integer *iseed, complex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1;
complex q__1, q__2, q__3, q__4;
/* Local variables */
extern /* Subroutine */ void cher2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, integer *);
integer i__, j;
extern /* Subroutine */ void cgerc_(integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *);
complex alpha;
extern /* Subroutine */ void cscal_(integer *, complex *, complex *,
integer *);
extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer
*, complex *, integer *);
extern /* Subroutine */ void cgemv_(char *, integer *, integer *, complex *
, complex *, integer *, complex *, integer *, complex *, complex *
, integer *), chemv_(char *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, complex *,
integer *), caxpy_(integer *, complex *, complex *,
integer *, complex *, integer *);
extern real scnrm2_(integer *, complex *, integer *);
complex wa, wb;
real wn;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern void clarnv_(
integer *, integer *, integer *, complex *);
complex tau;
/* -- 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 arguments */
/* Parameter adjustments */
--d__;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--iseed;
--work;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*k < 0 || *k > *n - 1) {
*info = -2;
} else if (*lda < f2cmax(1,*n)) {
*info = -5;
}
if (*info < 0) {
i__1 = -(*info);
xerbla_("CLAGHE", &i__1, 6);
return;
}
/* initialize lower triangle of A to diagonal matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L10: */
}
/* L20: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
i__3 = i__;
a[i__2].r = d__[i__3], a[i__2].i = 0.f;
/* L30: */
}
/* Generate lower triangle of hermitian matrix */
for (i__ = *n - 1; i__ >= 1; --i__) {
/* generate random reflection */
i__1 = *n - i__ + 1;
clarnv_(&c__3, &iseed[1], &i__1, &work[1]);
i__1 = *n - i__ + 1;
wn = scnrm2_(&i__1, &work[1], &c__1);
r__1 = wn / c_abs(&work[1]);
q__1.r = r__1 * work[1].r, q__1.i = r__1 * work[1].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
q__1.r = work[1].r + wa.r, q__1.i = work[1].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__1 = *n - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__1, &q__1, &work[2], &c__1);
work[1].r = 1.f, work[1].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply random reflection to A(i:n,i:n) from the left */
/* and the right */
/* compute y := tau * A * u */
i__1 = *n - i__ + 1;
chemv_("Lower", &i__1, &tau, &a[i__ + i__ * a_dim1], lda, &work[1], &
c__1, &c_b1, &work[*n + 1], &c__1);
/* compute v := y - 1/2 * tau * ( y, u ) * u */
q__3.r = -.5f, q__3.i = 0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__1 = *n - i__ + 1;
cdotc_(&q__4, &i__1, &work[*n + 1], &c__1, &work[1], &c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__1 = *n - i__ + 1;
caxpy_(&i__1, &alpha, &work[1], &c__1, &work[*n + 1], &c__1);
/* apply the transformation as a rank-2 update to A(i:n,i:n) */
i__1 = *n - i__ + 1;
q__1.r = -1.f, q__1.i = 0.f;
cher2_("Lower", &i__1, &q__1, &work[1], &c__1, &work[*n + 1], &c__1, &
a[i__ + i__ * a_dim1], lda);
/* L40: */
}
/* Reduce number of subdiagonals to K */
i__1 = *n - 1 - *k;
for (i__ = 1; i__ <= i__1; ++i__) {
/* generate reflection to annihilate A(k+i+1:n,i) */
i__2 = *n - *k - i__ + 1;
wn = scnrm2_(&i__2, &a[*k + i__ + i__ * a_dim1], &c__1);
r__1 = wn / c_abs(&a[*k + i__ + i__ * a_dim1]);
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = r__1 * a[i__2].r, q__1.i = r__1 * a[i__2].i;
wa.r = q__1.r, wa.i = q__1.i;
if (wn == 0.f) {
tau.r = 0.f, tau.i = 0.f;
} else {
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = a[i__2].r + wa.r, q__1.i = a[i__2].i + wa.i;
wb.r = q__1.r, wb.i = q__1.i;
i__2 = *n - *k - i__;
c_div(&q__1, &c_b2, &wb);
cscal_(&i__2, &q__1, &a[*k + i__ + 1 + i__ * a_dim1], &c__1);
i__2 = *k + i__ + i__ * a_dim1;
a[i__2].r = 1.f, a[i__2].i = 0.f;
c_div(&q__1, &wb, &wa);
r__1 = q__1.r;
tau.r = r__1, tau.i = 0.f;
}
/* apply reflection to A(k+i:n,i+1:k+i-1) from the left */
i__2 = *n - *k - i__ + 1;
i__3 = *k - 1;
cgemv_("Conjugate transpose", &i__2, &i__3, &c_b2, &a[*k + i__ + (i__
+ 1) * a_dim1], lda, &a[*k + i__ + i__ * a_dim1], &c__1, &
c_b1, &work[1], &c__1);
i__2 = *n - *k - i__ + 1;
i__3 = *k - 1;
q__1.r = -tau.r, q__1.i = -tau.i;
cgerc_(&i__2, &i__3, &q__1, &a[*k + i__ + i__ * a_dim1], &c__1, &work[
1], &c__1, &a[*k + i__ + (i__ + 1) * a_dim1], lda);
/* apply reflection to A(k+i:n,k+i:n) from the left and the right */
/* compute y := tau * A * u */
i__2 = *n - *k - i__ + 1;
chemv_("Lower", &i__2, &tau, &a[*k + i__ + (*k + i__) * a_dim1], lda,
&a[*k + i__ + i__ * a_dim1], &c__1, &c_b1, &work[1], &c__1);
/* compute v := y - 1/2 * tau * ( y, u ) * u */
q__3.r = -.5f, q__3.i = 0.f;
q__2.r = q__3.r * tau.r - q__3.i * tau.i, q__2.i = q__3.r * tau.i +
q__3.i * tau.r;
i__2 = *n - *k - i__ + 1;
cdotc_(&q__4, &i__2, &work[1], &c__1, &a[*k + i__ + i__ * a_dim1], &
c__1);
q__1.r = q__2.r * q__4.r - q__2.i * q__4.i, q__1.i = q__2.r * q__4.i
+ q__2.i * q__4.r;
alpha.r = q__1.r, alpha.i = q__1.i;
i__2 = *n - *k - i__ + 1;
caxpy_(&i__2, &alpha, &a[*k + i__ + i__ * a_dim1], &c__1, &work[1], &
c__1);
/* apply hermitian rank-2 update to A(k+i:n,k+i:n) */
i__2 = *n - *k - i__ + 1;
q__1.r = -1.f, q__1.i = 0.f;
cher2_("Lower", &i__2, &q__1, &a[*k + i__ + i__ * a_dim1], &c__1, &
work[1], &c__1, &a[*k + i__ + (*k + i__) * a_dim1], lda);
i__2 = *k + i__ + i__ * a_dim1;
q__1.r = -wa.r, q__1.i = -wa.i;
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
i__2 = *n;
for (j = *k + i__ + 1; j <= i__2; ++j) {
i__3 = j + i__ * a_dim1;
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L50: */
}
/* L60: */
}
/* Store full hermitian matrix */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * a_dim1;
r_cnjg(&q__1, &a[i__ + j * a_dim1]);
a[i__3].r = q__1.r, a[i__3].i = q__1.i;
/* L70: */
}
/* L80: */
}
return;
/* End of CLAGHE */
} /* claghe_ */
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