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OpenBLAS/lapack-netlib/TESTING/MATGEN/slatm6.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 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++ */
/* Table of constant values */
static integer c__1 = 1;
static integer c__4 = 4;
static integer c__12 = 12;
static integer c__8 = 8;
static integer c__40 = 40;
static integer c__2 = 2;
static integer c__3 = 3;
static integer c__60 = 60;
/* > \brief \b SLATM6 */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* Definition: */
/* =========== */
/* SUBROUTINE SLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA, */
/* BETA, WX, WY, S, DIF ) */
/* INTEGER LDA, LDX, LDY, N, TYPE */
/* REAL ALPHA, BETA, WX, WY */
/* REAL A( LDA, * ), B( LDA, * ), DIF( * ), S( * ), */
/* $ X( LDX, * ), Y( LDY, * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SLATM6 generates test matrices for the generalized eigenvalue */
/* > problem, their corresponding right and left eigenvector matrices, */
/* > and also reciprocal condition numbers for all eigenvalues and */
/* > the reciprocal condition numbers of eigenvectors corresponding to */
/* > the 1th and 5th eigenvalues. */
/* > */
/* > Test Matrices */
/* > ============= */
/* > */
/* > Two kinds of test matrix pairs */
/* > */
/* > (A, B) = inverse(YH) * (Da, Db) * inverse(X) */
/* > */
/* > are used in the tests: */
/* > */
/* > Type 1: */
/* > Da = 1+a 0 0 0 0 Db = 1 0 0 0 0 */
/* > 0 2+a 0 0 0 0 1 0 0 0 */
/* > 0 0 3+a 0 0 0 0 1 0 0 */
/* > 0 0 0 4+a 0 0 0 0 1 0 */
/* > 0 0 0 0 5+a , 0 0 0 0 1 , and */
/* > */
/* > Type 2: */
/* > Da = 1 -1 0 0 0 Db = 1 0 0 0 0 */
/* > 1 1 0 0 0 0 1 0 0 0 */
/* > 0 0 1 0 0 0 0 1 0 0 */
/* > 0 0 0 1+a 1+b 0 0 0 1 0 */
/* > 0 0 0 -1-b 1+a , 0 0 0 0 1 . */
/* > */
/* > In both cases the same inverse(YH) and inverse(X) are used to compute */
/* > (A, B), giving the exact eigenvectors to (A,B) as (YH, X): */
/* > */
/* > YH: = 1 0 -y y -y X = 1 0 -x -x x */
/* > 0 1 -y y -y 0 1 x -x -x */
/* > 0 0 1 0 0 0 0 1 0 0 */
/* > 0 0 0 1 0 0 0 0 1 0 */
/* > 0 0 0 0 1, 0 0 0 0 1 , */
/* > */
/* > where a, b, x and y will have all values independently of each other. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] TYPE */
/* > \verbatim */
/* > TYPE is INTEGER */
/* > Specifies the problem type (see further details). */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > Size of the matrices A and B. */
/* > \endverbatim */
/* > */
/* > \param[out] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA, N). */
/* > On exit A N-by-N is initialized according to TYPE. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of A and of B. */
/* > \endverbatim */
/* > */
/* > \param[out] B */
/* > \verbatim */
/* > B is REAL array, dimension (LDA, N). */
/* > On exit B N-by-N is initialized according to TYPE. */
/* > \endverbatim */
/* > */
/* > \param[out] X */
/* > \verbatim */
/* > X is REAL array, dimension (LDX, N). */
/* > On exit X is the N-by-N matrix of right eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] LDX */
/* > \verbatim */
/* > LDX is INTEGER */
/* > The leading dimension of X. */
/* > \endverbatim */
/* > */
/* > \param[out] Y */
/* > \verbatim */
/* > Y is REAL array, dimension (LDY, N). */
/* > On exit Y is the N-by-N matrix of left eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] LDY */
/* > \verbatim */
/* > LDY is INTEGER */
/* > The leading dimension of Y. */
/* > \endverbatim */
/* > */
/* > \param[in] ALPHA */
/* > \verbatim */
/* > ALPHA is REAL */
/* > \endverbatim */
/* > */
/* > \param[in] BETA */
/* > \verbatim */
/* > BETA is REAL */
/* > */
/* > Weighting constants for matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] WX */
/* > \verbatim */
/* > WX is REAL */
/* > Constant for right eigenvector matrix. */
/* > \endverbatim */
/* > */
/* > \param[in] WY */
/* > \verbatim */
/* > WY is REAL */
/* > Constant for left eigenvector matrix. */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* > S is REAL array, dimension (N) */
/* > S(i) is the reciprocal condition number for eigenvalue i. */
/* > \endverbatim */
/* > */
/* > \param[out] DIF */
/* > \verbatim */
/* > DIF is REAL array, dimension (N) */
/* > DIF(i) is the reciprocal condition number for eigenvector i. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup real_matgen */
/* ===================================================================== */
/* Subroutine */ void slatm6_(integer *type__, integer *n, real *a, integer *
lda, real *b, real *x, integer *ldx, real *y, integer *ldy, real *
alpha, real *beta, real *wx, real *wy, real *s, real *dif)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, y_dim1,
y_offset, i__1, i__2;
/* Local variables */
integer info;
real work[100];
integer i__, j;
real z__[144] /* was [12][12] */;
extern /* Subroutine */ void slakf2_(integer *, integer *, real *, integer
*, real *, real *, real *, real *, integer *), sgesvd_(char *,
char *, integer *, integer *, real *, integer *, real *, real *,
integer *, real *, integer *, real *, integer *, integer *), slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *);
/* -- 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 */
/* ===================================================================== */
/* Generate test problem ... */
/* (Da, Db) ... */
/* Parameter adjustments */
b_dim1 = *lda;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
y_dim1 = *ldy;
y_offset = 1 + y_dim1 * 1;
y -= y_offset;
--s;
--dif;
/* Function Body */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
if (i__ == j) {
a[i__ + i__ * a_dim1] = (real) i__ + *alpha;
b[i__ + i__ * b_dim1] = 1.f;
} else {
a[i__ + j * a_dim1] = 0.f;
b[i__ + j * b_dim1] = 0.f;
}
/* L10: */
}
/* L20: */
}
/* Form X and Y */
slacpy_("F", n, n, &b[b_offset], lda, &y[y_offset], ldy);
y[y_dim1 + 3] = -(*wy);
y[y_dim1 + 4] = *wy;
y[y_dim1 + 5] = -(*wy);
y[(y_dim1 << 1) + 3] = -(*wy);
y[(y_dim1 << 1) + 4] = *wy;
y[(y_dim1 << 1) + 5] = -(*wy);
slacpy_("F", n, n, &b[b_offset], lda, &x[x_offset], ldx);
x[x_dim1 * 3 + 1] = -(*wx);
x[(x_dim1 << 2) + 1] = -(*wx);
x[x_dim1 * 5 + 1] = *wx;
x[x_dim1 * 3 + 2] = *wx;
x[(x_dim1 << 2) + 2] = -(*wx);
x[x_dim1 * 5 + 2] = -(*wx);
/* Form (A, B) */
b[b_dim1 * 3 + 1] = *wx + *wy;
b[b_dim1 * 3 + 2] = -(*wx) + *wy;
b[(b_dim1 << 2) + 1] = *wx - *wy;
b[(b_dim1 << 2) + 2] = *wx - *wy;
b[b_dim1 * 5 + 1] = -(*wx) + *wy;
b[b_dim1 * 5 + 2] = *wx + *wy;
if (*type__ == 1) {
a[a_dim1 * 3 + 1] = *wx * a[a_dim1 + 1] + *wy * a[a_dim1 * 3 + 3];
a[a_dim1 * 3 + 2] = -(*wx) * a[(a_dim1 << 1) + 2] + *wy * a[a_dim1 *
3 + 3];
a[(a_dim1 << 2) + 1] = *wx * a[a_dim1 + 1] - *wy * a[(a_dim1 << 2) +
4];
a[(a_dim1 << 2) + 2] = *wx * a[(a_dim1 << 1) + 2] - *wy * a[(a_dim1 <<
2) + 4];
a[a_dim1 * 5 + 1] = -(*wx) * a[a_dim1 + 1] + *wy * a[a_dim1 * 5 + 5];
a[a_dim1 * 5 + 2] = *wx * a[(a_dim1 << 1) + 2] + *wy * a[a_dim1 * 5 +
5];
} else if (*type__ == 2) {
a[a_dim1 * 3 + 1] = *wx * 2.f + *wy;
a[a_dim1 * 3 + 2] = *wy;
a[(a_dim1 << 2) + 1] = -(*wy) * (*alpha + 2.f + *beta);
a[(a_dim1 << 2) + 2] = *wx * 2.f - *wy * (*alpha + 2.f + *beta);
a[a_dim1 * 5 + 1] = *wx * -2.f + *wy * (*alpha - *beta);
a[a_dim1 * 5 + 2] = *wy * (*alpha - *beta);
a[a_dim1 + 1] = 1.f;
a[(a_dim1 << 1) + 1] = -1.f;
a[a_dim1 + 2] = 1.f;
a[(a_dim1 << 1) + 2] = a[a_dim1 + 1];
a[a_dim1 * 3 + 3] = 1.f;
a[(a_dim1 << 2) + 4] = *alpha + 1.f;
a[a_dim1 * 5 + 4] = *beta + 1.f;
a[(a_dim1 << 2) + 5] = -a[a_dim1 * 5 + 4];
a[a_dim1 * 5 + 5] = a[(a_dim1 << 2) + 4];
}
/* Compute condition numbers */
if (*type__ == 1) {
s[1] = 1.f / sqrt((*wy * 3.f * *wy + 1.f) / (a[a_dim1 + 1] * a[a_dim1
+ 1] + 1.f));
s[2] = 1.f / sqrt((*wy * 3.f * *wy + 1.f) / (a[(a_dim1 << 1) + 2] * a[
(a_dim1 << 1) + 2] + 1.f));
s[3] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[a_dim1 * 3 + 3] * a[
a_dim1 * 3 + 3] + 1.f));
s[4] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[(a_dim1 << 2) + 4] * a[
(a_dim1 << 2) + 4] + 1.f));
s[5] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / (a[a_dim1 * 5 + 5] * a[
a_dim1 * 5 + 5] + 1.f));
slakf2_(&c__1, &c__4, &a[a_offset], lda, &a[(a_dim1 << 1) + 2], &b[
b_offset], &b[(b_dim1 << 1) + 2], z__, &c__12);
sgesvd_("N", "N", &c__8, &c__8, z__, &c__12, work, &work[8], &c__1, &
work[9], &c__1, &work[10], &c__40, &info);
dif[1] = work[7];
slakf2_(&c__4, &c__1, &a[a_offset], lda, &a[a_dim1 * 5 + 5], &b[
b_offset], &b[b_dim1 * 5 + 5], z__, &c__12);
sgesvd_("N", "N", &c__8, &c__8, z__, &c__12, work, &work[8], &c__1, &
work[9], &c__1, &work[10], &c__40, &info);
dif[5] = work[7];
} else if (*type__ == 2) {
s[1] = 1.f / sqrt(*wy * *wy + .33333333333333331f);
s[2] = s[1];
s[3] = 1.f / sqrt(*wx * *wx + .5f);
s[4] = 1.f / sqrt((*wx * 2.f * *wx + 1.f) / ((*alpha + 1.f) * (*alpha
+ 1.f) + 1.f + (*beta + 1.f) * (*beta + 1.f)));
s[5] = s[4];
slakf2_(&c__2, &c__3, &a[a_offset], lda, &a[a_dim1 * 3 + 3], &b[
b_offset], &b[b_dim1 * 3 + 3], z__, &c__12);
sgesvd_("N", "N", &c__12, &c__12, z__, &c__12, work, &work[12], &c__1,
&work[13], &c__1, &work[14], &c__60, &info);
dif[1] = work[11];
slakf2_(&c__3, &c__2, &a[a_offset], lda, &a[(a_dim1 << 2) + 4], &b[
b_offset], &b[(b_dim1 << 2) + 4], z__, &c__12);
sgesvd_("N", "N", &c__12, &c__12, z__, &c__12, work, &work[12], &c__1,
&work[13], &c__1, &work[14], &c__60, &info);
dif[5] = work[11];
}
return;
/* End of SLATM6 */
} /* slatm6_ */
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