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OpenBLAS/lapack-netlib/TESTING/MATGEN/slatme.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);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#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
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif
static float spow_ui(float x, integer n) {
float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static double dpow_ui(double x, integer n) {
double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
complex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
for(u = n; ; ) {
if(u & 01) pow.r *= x.r, pow.i *= x.i;
if(u >>= 1) x.r *= x.r, x.i *= x.i;
else break;
}
}
_Fcomplex p={pow.r, pow.i};
return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
_Complex float pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
_Dcomplex pow={1.0,0.0}; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
for(u = n; ; ) {
if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
else break;
}
}
_Dcomplex p = {pow._Val[0], pow._Val[1]};
return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
_Complex double pow=1.0; unsigned long int u;
if(n != 0) {
if(n < 0) n = -n, x = 1/x;
for(u = n; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
integer pow; unsigned long int u;
if (n <= 0) {
if (n == 0 || x == 1) pow = 1;
else if (x != -1) pow = x == 0 ? 1/x : 0;
else n = -n;
}
if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
u = n;
for(pow = 1; ; ) {
if(u & 01) pow *= x;
if(u >>= 1) x *= x;
else break;
}
}
return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
double m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
float m; integer i, mi;
for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
if (w[i-1]>m) mi=i ,m=w[i-1];
return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Fcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
}
}
pCf(z) = zdotc;
}
#else
_Complex float zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i]) * Cf(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
}
}
pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
_Dcomplex zdotc = {0.0, 0.0};
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
}
}
pCd(z) = zdotc;
}
#else
_Complex double zdotc = 0.0;
if (incx == 1 && incy == 1) {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i]) * Cd(&y[i]);
}
} else {
for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
}
}
pCd(z) = zdotc;
}
#endif
/* -- translated by f2c (version 20000121).
You must link the resulting object file with the libraries:
-lf2c -lm (in that order)
*/
/* Table of constant values */
static integer c__1 = 1;
static real c_b23 = 0.f;
static integer c__0 = 0;
static real c_b39 = 1.f;
/* > \brief \b SLATME */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* Definition: */
/* =========== */
/* SUBROUTINE SLATME( N, DIST, ISEED, D, MODE, COND, DMAX, EI, */
/* RSIGN, */
/* UPPER, SIM, DS, MODES, CONDS, KL, KU, ANORM, */
/* A, */
/* LDA, WORK, INFO ) */
/* CHARACTER DIST, RSIGN, SIM, UPPER */
/* INTEGER INFO, KL, KU, LDA, MODE, MODES, N */
/* REAL ANORM, COND, CONDS, DMAX */
/* CHARACTER EI( * ) */
/* INTEGER ISEED( 4 ) */
/* REAL A( LDA, * ), D( * ), DS( * ), WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > SLATME generates random non-symmetric square matrices with */
/* > specified eigenvalues for testing LAPACK programs. */
/* > */
/* > SLATME operates by applying the following sequence of */
/* > operations: */
/* > */
/* > 1. Set the diagonal to D, where D may be input or */
/* > computed according to MODE, COND, DMAX, and RSIGN */
/* > as described below. */
/* > */
/* > 2. If complex conjugate pairs are desired (MODE=0 and EI(1)='R', */
/* > or MODE=5), certain pairs of adjacent elements of D are */
/* > interpreted as the real and complex parts of a complex */
/* > conjugate pair; A thus becomes block diagonal, with 1x1 */
/* > and 2x2 blocks. */
/* > */
/* > 3. If UPPER='T', the upper triangle of A is set to random values */
/* > out of distribution DIST. */
/* > */
/* > 4. If SIM='T', A is multiplied on the left by a random matrix */
/* > X, whose singular values are specified by DS, MODES, and */
/* > CONDS, and on the right by X inverse. */
/* > */
/* > 5. If KL < N-1, the lower bandwidth is reduced to KL using */
/* > Householder transformations. If KU < N-1, the upper */
/* > bandwidth is reduced to KU. */
/* > */
/* > 6. If ANORM is not negative, the matrix is scaled to have */
/* > maximum-element-norm ANORM. */
/* > */
/* > (Note: since the matrix cannot be reduced beyond Hessenberg form, */
/* > no packing options are available.) */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The number of columns (or rows) of A. Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] DIST */
/* > \verbatim */
/* > DIST is CHARACTER*1 */
/* > On entry, DIST specifies the type of distribution to be used */
/* > to generate the random eigen-/singular values, and for the */
/* > upper triangle (see UPPER). */
/* > 'U' => UNIFORM( 0, 1 ) ( 'U' for uniform ) */
/* > 'S' => UNIFORM( -1, 1 ) ( 'S' for symmetric ) */
/* > 'N' => NORMAL( 0, 1 ) ( 'N' for normal ) */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in,out] ISEED */
/* > \verbatim */
/* > ISEED is INTEGER array, dimension ( 4 ) */
/* > On entry ISEED specifies the seed of the random number */
/* > generator. They should lie between 0 and 4095 inclusive, */
/* > and ISEED(4) should be odd. The random number generator */
/* > uses a linear congruential sequence limited to small */
/* > integers, and so should produce machine independent */
/* > random numbers. The values of ISEED are changed on */
/* > exit, and can be used in the next call to SLATME */
/* > to continue the same random number sequence. */
/* > Changed on exit. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* > D is REAL array, dimension ( N ) */
/* > This array is used to specify the eigenvalues of A. If */
/* > MODE=0, then D is assumed to contain the eigenvalues (but */
/* > see the description of EI), otherwise they will be */
/* > computed according to MODE, COND, DMAX, and RSIGN and */
/* > placed in D. */
/* > Modified if MODE is nonzero. */
/* > \endverbatim */
/* > */
/* > \param[in] MODE */
/* > \verbatim */
/* > MODE is INTEGER */
/* > On entry this describes how the eigenvalues are to */
/* > be specified: */
/* > MODE = 0 means use D (with EI) as input */
/* > MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND */
/* > MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND */
/* > MODE = 3 sets D(I)=COND**(-(I-1)/(N-1)) */
/* > MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) */
/* > MODE = 5 sets D to random numbers in the range */
/* > ( 1/COND , 1 ) such that their logarithms */
/* > are uniformly distributed. Each odd-even pair */
/* > of elements will be either used as two real */
/* > eigenvalues or as the real and imaginary part */
/* > of a complex conjugate pair of eigenvalues; */
/* > the choice of which is done is random, with */
/* > 50-50 probability, for each pair. */
/* > MODE = 6 set D to random numbers from same distribution */
/* > as the rest of the matrix. */
/* > MODE < 0 has the same meaning as ABS(MODE), except that */
/* > the order of the elements of D is reversed. */
/* > Thus if MODE is between 1 and 4, D has entries ranging */
/* > from 1 to 1/COND, if between -1 and -4, D has entries */
/* > ranging from 1/COND to 1, */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] COND */
/* > \verbatim */
/* > COND is REAL */
/* > On entry, this is used as described under MODE above. */
/* > If used, it must be >= 1. Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] DMAX */
/* > \verbatim */
/* > DMAX is REAL */
/* > If MODE is neither -6, 0 nor 6, the contents of D, as */
/* > computed according to MODE and COND, will be scaled by */
/* > DMAX / f2cmax(abs(D(i))). Note that DMAX need not be */
/* > positive: if DMAX is negative (or zero), D will be */
/* > scaled by a negative number (or zero). */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] EI */
/* > \verbatim */
/* > EI is CHARACTER*1 array, dimension ( N ) */
/* > If MODE is 0, and EI(1) is not ' ' (space character), */
/* > this array specifies which elements of D (on input) are */
/* > real eigenvalues and which are the real and imaginary parts */
/* > of a complex conjugate pair of eigenvalues. The elements */
/* > of EI may then only have the values 'R' and 'I'. If */
/* > EI(j)='R' and EI(j+1)='I', then the j-th eigenvalue is */
/* > CMPLX( D(j) , D(j+1) ), and the (j+1)-th is the complex */
/* > conjugate thereof. If EI(j)=EI(j+1)='R', then the j-th */
/* > eigenvalue is D(j) (i.e., real). EI(1) may not be 'I', */
/* > nor may two adjacent elements of EI both have the value 'I'. */
/* > If MODE is not 0, then EI is ignored. If MODE is 0 and */
/* > EI(1)=' ', then the eigenvalues will all be real. */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] RSIGN */
/* > \verbatim */
/* > RSIGN is CHARACTER*1 */
/* > If MODE is not 0, 6, or -6, and RSIGN='T', then the */
/* > elements of D, as computed according to MODE and COND, will */
/* > be multiplied by a random sign (+1 or -1). If RSIGN='F', */
/* > they will not be. RSIGN may only have the values 'T' or */
/* > 'F'. */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] UPPER */
/* > \verbatim */
/* > UPPER is CHARACTER*1 */
/* > If UPPER='T', then the elements of A above the diagonal */
/* > (and above the 2x2 diagonal blocks, if A has complex */
/* > eigenvalues) will be set to random numbers out of DIST. */
/* > If UPPER='F', they will not. UPPER may only have the */
/* > values 'T' or 'F'. */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] SIM */
/* > \verbatim */
/* > SIM is CHARACTER*1 */
/* > If SIM='T', then A will be operated on by a "similarity */
/* > transform", i.e., multiplied on the left by a matrix X and */
/* > on the right by X inverse. X = U S V, where U and V are */
/* > random unitary matrices and S is a (diagonal) matrix of */
/* > singular values specified by DS, MODES, and CONDS. If */
/* > SIM='F', then A will not be transformed. */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in,out] DS */
/* > \verbatim */
/* > DS is REAL array, dimension ( N ) */
/* > This array is used to specify the singular values of X, */
/* > in the same way that D specifies the eigenvalues of A. */
/* > If MODE=0, the DS contains the singular values, which */
/* > may not be zero. */
/* > Modified if MODE is nonzero. */
/* > \endverbatim */
/* > */
/* > \param[in] MODES */
/* > \verbatim */
/* > MODES is INTEGER */
/* > \endverbatim */
/* > */
/* > \param[in] CONDS */
/* > \verbatim */
/* > CONDS is REAL */
/* > Same as MODE and COND, but for specifying the diagonal */
/* > of S. MODES=-6 and +6 are not allowed (since they would */
/* > result in randomly ill-conditioned eigenvalues.) */
/* > \endverbatim */
/* > */
/* > \param[in] KL */
/* > \verbatim */
/* > KL is INTEGER */
/* > This specifies the lower bandwidth of the matrix. KL=1 */
/* > specifies upper Hessenberg form. If KL is at least N-1, */
/* > then A will have full lower bandwidth. KL must be at */
/* > least 1. */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] KU */
/* > \verbatim */
/* > KU is INTEGER */
/* > This specifies the upper bandwidth of the matrix. KU=1 */
/* > specifies lower Hessenberg form. If KU is at least N-1, */
/* > then A will have full upper bandwidth; if KU and KL */
/* > are both at least N-1, then A will be dense. Only one of */
/* > KU and KL may be less than N-1. KU must be at least 1. */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[in] ANORM */
/* > \verbatim */
/* > ANORM is REAL */
/* > If ANORM is not negative, then A will be scaled by a non- */
/* > negative real number to make the maximum-element-norm of A */
/* > to be ANORM. */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[out] A */
/* > \verbatim */
/* > A is REAL array, dimension ( LDA, N ) */
/* > On exit A is the desired test matrix. */
/* > Modified. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > LDA specifies the first dimension of A as declared in the */
/* > calling program. LDA must be at least N. */
/* > Not modified. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension ( 3*N ) */
/* > Workspace. */
/* > Modified. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > Error code. On exit, INFO will be set to one of the */
/* > following values: */
/* > 0 => normal return */
/* > -1 => N negative */
/* > -2 => DIST illegal string */
/* > -5 => MODE not in range -6 to 6 */
/* > -6 => COND less than 1.0, and MODE neither -6, 0 nor 6 */
/* > -8 => EI(1) is not ' ' or 'R', EI(j) is not 'R' or 'I', or */
/* > two adjacent elements of EI are 'I'. */
/* > -9 => RSIGN is not 'T' or 'F' */
/* > -10 => UPPER is not 'T' or 'F' */
/* > -11 => SIM is not 'T' or 'F' */
/* > -12 => MODES=0 and DS has a zero singular value. */
/* > -13 => MODES is not in the range -5 to 5. */
/* > -14 => MODES is nonzero and CONDS is less than 1. */
/* > -15 => KL is less than 1. */
/* > -16 => KU is less than 1, or KL and KU are both less than */
/* > N-1. */
/* > -19 => LDA is less than N. */
/* > 1 => Error return from SLATM1 (computing D) */
/* > 2 => Cannot scale to DMAX (f2cmax. eigenvalue is 0) */
/* > 3 => Error return from SLATM1 (computing DS) */
/* > 4 => Error return from SLARGE */
/* > 5 => Zero singular value from SLATM1. */
/* > \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 */ int slatme_(integer *n, char *dist, integer *iseed, real *
d__, integer *mode, real *cond, real *dmax__, char *ei, char *rsign,
char *upper, char *sim, real *ds, integer *modes, real *conds,
integer *kl, integer *ku, real *anorm, real *a, integer *lda, real *
work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
real r__1, r__2, r__3;
/* Local variables */
logical bads;
extern /* Subroutine */ int sger_(integer *, integer *, real *, real *,
integer *, real *, integer *, real *, integer *);
integer isim;
real temp;
logical badei;
integer i__, j;
real alpha;
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
real tempa[1];
integer icols;
logical useei;
integer idist;
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *);
integer irows;
extern /* Subroutine */ int slatm1_(integer *, real *, integer *, integer
*, integer *, real *, integer *, integer *);
integer ic, jc, ir, jr;
extern real slange_(char *, integer *, integer *, real *, integer *, real
*);
extern /* Subroutine */ int slarge_(integer *, real *, integer *, integer
*, real *, integer *), slarfg_(integer *, real *, real *, integer
*, real *), xerbla_(char *, integer *);
extern real slaran_(integer *);
integer irsign;
extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *,
real *, real *, integer *);
integer iupper;
extern /* Subroutine */ int slarnv_(integer *, integer *, integer *, real
*);
real xnorms;
integer jcr;
real tau;
/* -- 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 */
/* ===================================================================== */
/* 1) Decode and Test the input parameters. */
/* Initialize flags & seed. */
/* Parameter adjustments */
--iseed;
--d__;
--ei;
--ds;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--work;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Decode DIST */
if (lsame_(dist, "U")) {
idist = 1;
} else if (lsame_(dist, "S")) {
idist = 2;
} else if (lsame_(dist, "N")) {
idist = 3;
} else {
idist = -1;
}
/* Check EI */
useei = TRUE_;
badei = FALSE_;
if (lsame_(ei + 1, " ") || *mode != 0) {
useei = FALSE_;
} else {
if (lsame_(ei + 1, "R")) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
if (lsame_(ei + j, "I")) {
if (lsame_(ei + (j - 1), "I")) {
badei = TRUE_;
}
} else {
if (! lsame_(ei + j, "R")) {
badei = TRUE_;
}
}
/* L10: */
}
} else {
badei = TRUE_;
}
}
/* Decode RSIGN */
if (lsame_(rsign, "T")) {
irsign = 1;
} else if (lsame_(rsign, "F")) {
irsign = 0;
} else {
irsign = -1;
}
/* Decode UPPER */
if (lsame_(upper, "T")) {
iupper = 1;
} else if (lsame_(upper, "F")) {
iupper = 0;
} else {
iupper = -1;
}
/* Decode SIM */
if (lsame_(sim, "T")) {
isim = 1;
} else if (lsame_(sim, "F")) {
isim = 0;
} else {
isim = -1;
}
/* Check DS, if MODES=0 and ISIM=1 */
bads = FALSE_;
if (*modes == 0 && isim == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (ds[j] == 0.f) {
bads = TRUE_;
}
/* L20: */
}
}
/* Set INFO if an error */
if (*n < 0) {
*info = -1;
} else if (idist == -1) {
*info = -2;
} else if (abs(*mode) > 6) {
*info = -5;
} else if (*mode != 0 && abs(*mode) != 6 && *cond < 1.f) {
*info = -6;
} else if (badei) {
*info = -8;
} else if (irsign == -1) {
*info = -9;
} else if (iupper == -1) {
*info = -10;
} else if (isim == -1) {
*info = -11;
} else if (bads) {
*info = -12;
} else if (isim == 1 && abs(*modes) > 5) {
*info = -13;
} else if (isim == 1 && *modes != 0 && *conds < 1.f) {
*info = -14;
} else if (*kl < 1) {
*info = -15;
} else if (*ku < 1 || *ku < *n - 1 && *kl < *n - 1) {
*info = -16;
} else if (*lda < f2cmax(1,*n)) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SLATME", &i__1);
return 0;
}
/* Initialize random number generator */
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__] = (i__1 = iseed[i__], abs(i__1)) % 4096;
/* L30: */
}
if (iseed[4] % 2 != 1) {
++iseed[4];
}
/* 2) Set up diagonal of A */
/* Compute D according to COND and MODE */
slatm1_(mode, cond, &irsign, &idist, &iseed[1], &d__[1], n, &iinfo);
if (iinfo != 0) {
*info = 1;
return 0;
}
if (*mode != 0 && abs(*mode) != 6) {
/* Scale by DMAX */
temp = abs(d__[1]);
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
/* Computing MAX */
r__2 = temp, r__3 = (r__1 = d__[i__], abs(r__1));
temp = f2cmax(r__2,r__3);
/* L40: */
}
if (temp > 0.f) {
alpha = *dmax__ / temp;
} else if (*dmax__ != 0.f) {
*info = 2;
return 0;
} else {
alpha = 0.f;
}
sscal_(n, &alpha, &d__[1], &c__1);
}
slaset_("Full", n, n, &c_b23, &c_b23, &a[a_offset], lda);
i__1 = *lda + 1;
scopy_(n, &d__[1], &c__1, &a[a_offset], &i__1);
/* Set up complex conjugate pairs */
if (*mode == 0) {
if (useei) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
if (lsame_(ei + j, "I")) {
a[j - 1 + j * a_dim1] = a[j + j * a_dim1];
a[j + (j - 1) * a_dim1] = -a[j + j * a_dim1];
a[j + j * a_dim1] = a[j - 1 + (j - 1) * a_dim1];
}
/* L50: */
}
}
} else if (abs(*mode) == 5) {
i__1 = *n;
for (j = 2; j <= i__1; j += 2) {
if (slaran_(&iseed[1]) > .5f) {
a[j - 1 + j * a_dim1] = a[j + j * a_dim1];
a[j + (j - 1) * a_dim1] = -a[j + j * a_dim1];
a[j + j * a_dim1] = a[j - 1 + (j - 1) * a_dim1];
}
/* L60: */
}
}
/* 3) If UPPER='T', set upper triangle of A to random numbers. */
/* (but don't modify the corners of 2x2 blocks.) */
if (iupper != 0) {
i__1 = *n;
for (jc = 2; jc <= i__1; ++jc) {
if (a[jc - 1 + jc * a_dim1] != 0.f) {
jr = jc - 2;
} else {
jr = jc - 1;
}
slarnv_(&idist, &iseed[1], &jr, &a[jc * a_dim1 + 1]);
/* L70: */
}
}
/* 4) If SIM='T', apply similarity transformation. */
/* -1 */
/* Transform is X A X , where X = U S V, thus */
/* it is U S V A V' (1/S) U' */
if (isim != 0) {
/* Compute S (singular values of the eigenvector matrix) */
/* according to CONDS and MODES */
slatm1_(modes, conds, &c__0, &c__0, &iseed[1], &ds[1], n, &iinfo);
if (iinfo != 0) {
*info = 3;
return 0;
}
/* Multiply by V and V' */
slarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo);
if (iinfo != 0) {
*info = 4;
return 0;
}
/* Multiply by S and (1/S) */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sscal_(n, &ds[j], &a[j + a_dim1], lda);
if (ds[j] != 0.f) {
r__1 = 1.f / ds[j];
sscal_(n, &r__1, &a[j * a_dim1 + 1], &c__1);
} else {
*info = 5;
return 0;
}
/* L80: */
}
/* Multiply by U and U' */
slarge_(n, &a[a_offset], lda, &iseed[1], &work[1], &iinfo);
if (iinfo != 0) {
*info = 4;
return 0;
}
}
/* 5) Reduce the bandwidth. */
if (*kl < *n - 1) {
/* Reduce bandwidth -- kill column */
i__1 = *n - 1;
for (jcr = *kl + 1; jcr <= i__1; ++jcr) {
ic = jcr - *kl;
irows = *n + 1 - jcr;
icols = *n + *kl - jcr;
scopy_(&irows, &a[jcr + ic * a_dim1], &c__1, &work[1], &c__1);
xnorms = work[1];
slarfg_(&irows, &xnorms, &work[2], &c__1, &tau);
work[1] = 1.f;
sgemv_("T", &irows, &icols, &c_b39, &a[jcr + (ic + 1) * a_dim1],
lda, &work[1], &c__1, &c_b23, &work[irows + 1], &c__1);
r__1 = -tau;
sger_(&irows, &icols, &r__1, &work[1], &c__1, &work[irows + 1], &
c__1, &a[jcr + (ic + 1) * a_dim1], lda);
sgemv_("N", n, &irows, &c_b39, &a[jcr * a_dim1 + 1], lda, &work[1]
, &c__1, &c_b23, &work[irows + 1], &c__1);
r__1 = -tau;
sger_(n, &irows, &r__1, &work[irows + 1], &c__1, &work[1], &c__1,
&a[jcr * a_dim1 + 1], lda);
a[jcr + ic * a_dim1] = xnorms;
i__2 = irows - 1;
slaset_("Full", &i__2, &c__1, &c_b23, &c_b23, &a[jcr + 1 + ic *
a_dim1], lda);
/* L90: */
}
} else if (*ku < *n - 1) {
/* Reduce upper bandwidth -- kill a row at a time. */
i__1 = *n - 1;
for (jcr = *ku + 1; jcr <= i__1; ++jcr) {
ir = jcr - *ku;
irows = *n + *ku - jcr;
icols = *n + 1 - jcr;
scopy_(&icols, &a[ir + jcr * a_dim1], lda, &work[1], &c__1);
xnorms = work[1];
slarfg_(&icols, &xnorms, &work[2], &c__1, &tau);
work[1] = 1.f;
sgemv_("N", &irows, &icols, &c_b39, &a[ir + 1 + jcr * a_dim1],
lda, &work[1], &c__1, &c_b23, &work[icols + 1], &c__1);
r__1 = -tau;
sger_(&irows, &icols, &r__1, &work[icols + 1], &c__1, &work[1], &
c__1, &a[ir + 1 + jcr * a_dim1], lda);
sgemv_("C", &icols, n, &c_b39, &a[jcr + a_dim1], lda, &work[1], &
c__1, &c_b23, &work[icols + 1], &c__1);
r__1 = -tau;
sger_(&icols, n, &r__1, &work[1], &c__1, &work[icols + 1], &c__1,
&a[jcr + a_dim1], lda);
a[ir + jcr * a_dim1] = xnorms;
i__2 = icols - 1;
slaset_("Full", &c__1, &i__2, &c_b23, &c_b23, &a[ir + (jcr + 1) *
a_dim1], lda);
/* L100: */
}
}
/* Scale the matrix to have norm ANORM */
if (*anorm >= 0.f) {
temp = slange_("M", n, n, &a[a_offset], lda, tempa);
if (temp > 0.f) {
alpha = *anorm / temp;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sscal_(n, &alpha, &a[j * a_dim1 + 1], &c__1);
/* L110: */
}
}
}
return 0;
/* End of SLATME */
} /* slatme_ */
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