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OpenBLAS/lapack-netlib/SRC/stgsyl.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 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++ */
#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__2 = 2;
static integer c_n1 = -1;
static integer c__5 = 5;
static real c_b14 = 0.f;
static integer c__1 = 1;
static real c_b51 = -1.f;
static real c_b52 = 1.f;
/* > \brief \b STGSYL */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download STGSYL + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stgsyl.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stgsyl.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stgsyl.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE STGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, */
/* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, */
/* IWORK, INFO ) */
/* CHARACTER TRANS */
/* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, */
/* $ LWORK, M, N */
/* REAL DIF, SCALE */
/* INTEGER IWORK( * ) */
/* REAL A( LDA, * ), B( LDB, * ), C( LDC, * ), */
/* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), */
/* $ WORK( * ) */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > STGSYL solves the generalized Sylvester equation: */
/* > */
/* > A * R - L * B = scale * C (1) */
/* > D * R - L * E = scale * F */
/* > */
/* > where R and L are unknown m-by-n matrices, (A, D), (B, E) and */
/* > (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n, */
/* > respectively, with real entries. (A, D) and (B, E) must be in */
/* > generalized (real) Schur canonical form, i.e. A, B are upper quasi */
/* > triangular and D, E are upper triangular. */
/* > */
/* > The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output */
/* > scaling factor chosen to avoid overflow. */
/* > */
/* > In matrix notation (1) is equivalent to solve Zx = scale b, where */
/* > Z is defined as */
/* > */
/* > Z = [ kron(In, A) -kron(B**T, Im) ] (2) */
/* > [ kron(In, D) -kron(E**T, Im) ]. */
/* > */
/* > Here Ik is the identity matrix of size k and X**T is the transpose of */
/* > X. kron(X, Y) is the Kronecker product between the matrices X and Y. */
/* > */
/* > If TRANS = 'T', STGSYL solves the transposed system Z**T*y = scale*b, */
/* > which is equivalent to solve for R and L in */
/* > */
/* > A**T * R + D**T * L = scale * C (3) */
/* > R * B**T + L * E**T = scale * -F */
/* > */
/* > This case (TRANS = 'T') is used to compute an one-norm-based estimate */
/* > of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) */
/* > and (B,E), using SLACON. */
/* > */
/* > If IJOB >= 1, STGSYL computes a Frobenius norm-based estimate */
/* > of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the */
/* > reciprocal of the smallest singular value of Z. See [1-2] for more */
/* > information. */
/* > */
/* > This is a level 3 BLAS algorithm. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] TRANS */
/* > \verbatim */
/* > TRANS is CHARACTER*1 */
/* > = 'N': solve the generalized Sylvester equation (1). */
/* > = 'T': solve the 'transposed' system (3). */
/* > \endverbatim */
/* > */
/* > \param[in] IJOB */
/* > \verbatim */
/* > IJOB is INTEGER */
/* > Specifies what kind of functionality to be performed. */
/* > = 0: solve (1) only. */
/* > = 1: The functionality of 0 and 3. */
/* > = 2: The functionality of 0 and 4. */
/* > = 3: Only an estimate of Dif[(A,D), (B,E)] is computed. */
/* > (look ahead strategy IJOB = 1 is used). */
/* > = 4: Only an estimate of Dif[(A,D), (B,E)] is computed. */
/* > ( SGECON on sub-systems is used ). */
/* > Not referenced if TRANS = 'T'. */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The order of the matrices A and D, and the row dimension of */
/* > the matrices C, F, R and L. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrices B and E, and the column dimension */
/* > of the matrices C, F, R and L. */
/* > \endverbatim */
/* > */
/* > \param[in] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA, M) */
/* > The upper quasi triangular matrix A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= f2cmax(1, M). */
/* > \endverbatim */
/* > */
/* > \param[in] B */
/* > \verbatim */
/* > B is REAL array, dimension (LDB, N) */
/* > The upper quasi triangular matrix B. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= f2cmax(1, N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] C */
/* > \verbatim */
/* > C is REAL array, dimension (LDC, N) */
/* > On entry, C contains the right-hand-side of the first matrix */
/* > equation in (1) or (3). */
/* > On exit, if IJOB = 0, 1 or 2, C has been overwritten by */
/* > the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R, */
/* > the solution achieved during the computation of the */
/* > Dif-estimate. */
/* > \endverbatim */
/* > */
/* > \param[in] LDC */
/* > \verbatim */
/* > LDC is INTEGER */
/* > The leading dimension of the array C. LDC >= f2cmax(1, M). */
/* > \endverbatim */
/* > */
/* > \param[in] D */
/* > \verbatim */
/* > D is REAL array, dimension (LDD, M) */
/* > The upper triangular matrix D. */
/* > \endverbatim */
/* > */
/* > \param[in] LDD */
/* > \verbatim */
/* > LDD is INTEGER */
/* > The leading dimension of the array D. LDD >= f2cmax(1, M). */
/* > \endverbatim */
/* > */
/* > \param[in] E */
/* > \verbatim */
/* > E is REAL array, dimension (LDE, N) */
/* > The upper triangular matrix E. */
/* > \endverbatim */
/* > */
/* > \param[in] LDE */
/* > \verbatim */
/* > LDE is INTEGER */
/* > The leading dimension of the array E. LDE >= f2cmax(1, N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] F */
/* > \verbatim */
/* > F is REAL array, dimension (LDF, N) */
/* > On entry, F contains the right-hand-side of the second matrix */
/* > equation in (1) or (3). */
/* > On exit, if IJOB = 0, 1 or 2, F has been overwritten by */
/* > the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L, */
/* > the solution achieved during the computation of the */
/* > Dif-estimate. */
/* > \endverbatim */
/* > */
/* > \param[in] LDF */
/* > \verbatim */
/* > LDF is INTEGER */
/* > The leading dimension of the array F. LDF >= f2cmax(1, M). */
/* > \endverbatim */
/* > */
/* > \param[out] DIF */
/* > \verbatim */
/* > DIF is REAL */
/* > On exit DIF is the reciprocal of a lower bound of the */
/* > reciprocal of the Dif-function, i.e. DIF is an upper bound of */
/* > Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2). */
/* > IF IJOB = 0 or TRANS = 'T', DIF is not touched. */
/* > \endverbatim */
/* > */
/* > \param[out] SCALE */
/* > \verbatim */
/* > SCALE is REAL */
/* > On exit SCALE is the scaling factor in (1) or (3). */
/* > If 0 < SCALE < 1, C and F hold the solutions R and L, resp., */
/* > to a slightly perturbed system but the input matrices A, B, D */
/* > and E have not been changed. If SCALE = 0, C and F hold the */
/* > solutions R and L, respectively, to the homogeneous system */
/* > with C = F = 0. Normally, SCALE = 1. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is REAL array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. LWORK > = 1. */
/* > If IJOB = 1 or 2 and TRANS = 'N', LWORK >= f2cmax(1,2*M*N). */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (M+N+6) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > =0: successful exit */
/* > <0: If INFO = -i, the i-th argument had an illegal value. */
/* > >0: (A, D) and (B, E) have common or close eigenvalues. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date December 2016 */
/* > \ingroup realSYcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* > Umea University, S-901 87 Umea, Sweden. */
/* > \par References: */
/* ================ */
/* > */
/* > \verbatim */
/* > */
/* > [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
/* > for Solving the Generalized Sylvester Equation and Estimating the */
/* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
/* > Department of Computing Science, Umea University, S-901 87 Umea, */
/* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
/* > Note 75. To appear in ACM Trans. on Math. Software, Vol 22, */
/* > No 1, 1996. */
/* > */
/* > [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester */
/* > Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. */
/* > Appl., 15(4):1045-1060, 1994 */
/* > */
/* > [3] B. Kagstrom and L. Westin, Generalized Schur Methods with */
/* > Condition Estimators for Solving the Generalized Sylvester */
/* > Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, */
/* > July 1989, pp 745-751. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* Subroutine */ void stgsyl_(char *trans, integer *ijob, integer *m, integer *
n, real *a, integer *lda, real *b, integer *ldb, real *c__, integer *
ldc, real *d__, integer *ldd, real *e, integer *lde, real *f, integer
*ldf, real *scale, real *dif, real *work, integer *lwork, integer *
iwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1,
d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3,
i__4;
/* Local variables */
real dsum;
integer ppqq, i__, j, k, p, q;
extern logical lsame_(char *, char *);
integer ifunc;
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *);
integer linfo;
extern /* Subroutine */ void sgemm_(char *, char *, integer *, integer *,
integer *, real *, real *, integer *, real *, integer *, real *,
real *, integer *);
integer lwmin;
real scale2;
integer ie, je, mb, nb;
real dscale;
integer is, js;
extern /* Subroutine */ void stgsy2_(char *, integer *, integer *, integer
*, real *, integer *, real *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *, real *, real *,
real *, integer *, integer *, integer *);
integer pq;
real scaloc;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ void slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *);
integer iround;
logical notran;
integer isolve;
logical lquery;
/* -- 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 */
/* ===================================================================== */
/* Replaced various illegal calls to SCOPY by calls to SLASET. */
/* Sven Hammarling, 1/5/02. */
/* Decode and test input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
d_dim1 = *ldd;
d_offset = 1 + d_dim1 * 1;
d__ -= d_offset;
e_dim1 = *lde;
e_offset = 1 + e_dim1 * 1;
e -= e_offset;
f_dim1 = *ldf;
f_offset = 1 + f_dim1 * 1;
f -= f_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
notran = lsame_(trans, "N");
lquery = *lwork == -1;
if (! notran && ! lsame_(trans, "T")) {
*info = -1;
} else if (notran) {
if (*ijob < 0 || *ijob > 4) {
*info = -2;
}
}
if (*info == 0) {
if (*m <= 0) {
*info = -3;
} else if (*n <= 0) {
*info = -4;
} else if (*lda < f2cmax(1,*m)) {
*info = -6;
} else if (*ldb < f2cmax(1,*n)) {
*info = -8;
} else if (*ldc < f2cmax(1,*m)) {
*info = -10;
} else if (*ldd < f2cmax(1,*m)) {
*info = -12;
} else if (*lde < f2cmax(1,*n)) {
*info = -14;
} else if (*ldf < f2cmax(1,*m)) {
*info = -16;
}
}
if (*info == 0) {
if (notran) {
if (*ijob == 1 || *ijob == 2) {
/* Computing MAX */
i__1 = 1, i__2 = (*m << 1) * *n;
lwmin = f2cmax(i__1,i__2);
} else {
lwmin = 1;
}
} else {
lwmin = 1;
}
work[1] = (real) lwmin;
if (*lwork < lwmin && ! lquery) {
*info = -20;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STGSYL", &i__1, (ftnlen)6);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
if (*m == 0 || *n == 0) {
*scale = 1.f;
if (notran) {
if (*ijob != 0) {
*dif = 0.f;
}
}
return;
}
/* Determine optimal block sizes MB and NB */
mb = ilaenv_(&c__2, "STGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb = ilaenv_(&c__5, "STGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
isolve = 1;
ifunc = 0;
if (notran) {
if (*ijob >= 3) {
ifunc = *ijob - 2;
slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc)
;
slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
} else if (*ijob >= 1 && notran) {
isolve = 2;
}
}
if (mb <= 1 && nb <= 1 || mb >= *m && nb >= *n) {
i__1 = isolve;
for (iround = 1; iround <= i__1; ++iround) {
/* Use unblocked Level 2 solver */
dscale = 0.f;
dsum = 1.f;
pq = 0;
stgsy2_(trans, &ifunc, m, n, &a[a_offset], lda, &b[b_offset], ldb,
&c__[c_offset], ldc, &d__[d_offset], ldd, &e[e_offset],
lde, &f[f_offset], ldf, scale, &dsum, &dscale, &iwork[1],
&pq, info);
if (dscale != 0.f) {
if (*ijob == 1 || *ijob == 3) {
*dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt(
dsum));
} else {
*dif = sqrt((real) pq) / (dscale * sqrt(dsum));
}
}
if (isolve == 2 && iround == 1) {
if (notran) {
ifunc = *ijob;
}
scale2 = *scale;
slacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
slacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc);
slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
} else if (isolve == 2 && iround == 2) {
slacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
slacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
*scale = scale2;
}
/* L30: */
}
return;
}
/* Determine block structure of A */
p = 0;
i__ = 1;
L40:
if (i__ > *m) {
goto L50;
}
++p;
iwork[p] = i__;
i__ += mb;
if (i__ >= *m) {
goto L50;
}
if (a[i__ + (i__ - 1) * a_dim1] != 0.f) {
++i__;
}
goto L40;
L50:
iwork[p + 1] = *m + 1;
if (iwork[p] == iwork[p + 1]) {
--p;
}
/* Determine block structure of B */
q = p + 1;
j = 1;
L60:
if (j > *n) {
goto L70;
}
++q;
iwork[q] = j;
j += nb;
if (j >= *n) {
goto L70;
}
if (b[j + (j - 1) * b_dim1] != 0.f) {
++j;
}
goto L60;
L70:
iwork[q + 1] = *n + 1;
if (iwork[q] == iwork[q + 1]) {
--q;
}
if (notran) {
i__1 = isolve;
for (iround = 1; iround <= i__1; ++iround) {
/* Solve (I, J)-subsystem */
/* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */
/* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */
/* for I = P, P - 1,..., 1; J = 1, 2,..., Q */
dscale = 0.f;
dsum = 1.f;
pq = 0;
*scale = 1.f;
i__2 = q;
for (j = p + 2; j <= i__2; ++j) {
js = iwork[j];
je = iwork[j + 1] - 1;
nb = je - js + 1;
for (i__ = p; i__ >= 1; --i__) {
is = iwork[i__];
ie = iwork[i__ + 1] - 1;
mb = ie - is + 1;
ppqq = 0;
stgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1],
lda, &b[js + js * b_dim1], ldb, &c__[is + js *
c_dim1], ldc, &d__[is + is * d_dim1], ldd, &e[js
+ js * e_dim1], lde, &f[is + js * f_dim1], ldf, &
scaloc, &dsum, &dscale, &iwork[q + 2], &ppqq, &
linfo);
if (linfo > 0) {
*info = linfo;
}
pq += ppqq;
if (scaloc != 1.f) {
i__3 = js - 1;
for (k = 1; k <= i__3; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L80: */
}
i__3 = je;
for (k = js; k <= i__3; ++k) {
i__4 = is - 1;
sscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &
c__1);
i__4 = is - 1;
sscal_(&i__4, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L90: */
}
i__3 = je;
for (k = js; k <= i__3; ++k) {
i__4 = *m - ie;
sscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1],
&c__1);
i__4 = *m - ie;
sscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &
c__1);
/* L100: */
}
i__3 = *n;
for (k = je + 1; k <= i__3; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L110: */
}
*scale *= scaloc;
}
/* Substitute R(I, J) and L(I, J) into remaining */
/* equation. */
if (i__ > 1) {
i__3 = is - 1;
sgemm_("N", "N", &i__3, &nb, &mb, &c_b51, &a[is *
a_dim1 + 1], lda, &c__[is + js * c_dim1], ldc,
&c_b52, &c__[js * c_dim1 + 1], ldc);
i__3 = is - 1;
sgemm_("N", "N", &i__3, &nb, &mb, &c_b51, &d__[is *
d_dim1 + 1], ldd, &c__[is + js * c_dim1], ldc,
&c_b52, &f[js * f_dim1 + 1], ldf);
}
if (j < q) {
i__3 = *n - je;
sgemm_("N", "N", &mb, &i__3, &nb, &c_b52, &f[is + js *
f_dim1], ldf, &b[js + (je + 1) * b_dim1],
ldb, &c_b52, &c__[is + (je + 1) * c_dim1],
ldc);
i__3 = *n - je;
sgemm_("N", "N", &mb, &i__3, &nb, &c_b52, &f[is + js *
f_dim1], ldf, &e[js + (je + 1) * e_dim1],
lde, &c_b52, &f[is + (je + 1) * f_dim1], ldf);
}
/* L120: */
}
/* L130: */
}
if (dscale != 0.f) {
if (*ijob == 1 || *ijob == 3) {
*dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt(
dsum));
} else {
*dif = sqrt((real) pq) / (dscale * sqrt(dsum));
}
}
if (isolve == 2 && iround == 1) {
if (notran) {
ifunc = *ijob;
}
scale2 = *scale;
slacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m);
slacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m);
slaset_("F", m, n, &c_b14, &c_b14, &c__[c_offset], ldc);
slaset_("F", m, n, &c_b14, &c_b14, &f[f_offset], ldf);
} else if (isolve == 2 && iround == 2) {
slacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc);
slacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf);
*scale = scale2;
}
/* L150: */
}
} else {
/* Solve transposed (I, J)-subsystem */
/* A(I, I)**T * R(I, J) + D(I, I)**T * L(I, J) = C(I, J) */
/* R(I, J) * B(J, J)**T + L(I, J) * E(J, J)**T = -F(I, J) */
/* for I = 1,2,..., P; J = Q, Q-1,..., 1 */
*scale = 1.f;
i__1 = p;
for (i__ = 1; i__ <= i__1; ++i__) {
is = iwork[i__];
ie = iwork[i__ + 1] - 1;
mb = ie - is + 1;
i__2 = p + 2;
for (j = q; j >= i__2; --j) {
js = iwork[j];
je = iwork[j + 1] - 1;
nb = je - js + 1;
stgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1], lda, &
b[js + js * b_dim1], ldb, &c__[is + js * c_dim1], ldc,
&d__[is + is * d_dim1], ldd, &e[js + js * e_dim1],
lde, &f[is + js * f_dim1], ldf, &scaloc, &dsum, &
dscale, &iwork[q + 2], &ppqq, &linfo);
if (linfo > 0) {
*info = linfo;
}
if (scaloc != 1.f) {
i__3 = js - 1;
for (k = 1; k <= i__3; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L160: */
}
i__3 = je;
for (k = js; k <= i__3; ++k) {
i__4 = is - 1;
sscal_(&i__4, &scaloc, &c__[k * c_dim1 + 1], &c__1);
i__4 = is - 1;
sscal_(&i__4, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L170: */
}
i__3 = je;
for (k = js; k <= i__3; ++k) {
i__4 = *m - ie;
sscal_(&i__4, &scaloc, &c__[ie + 1 + k * c_dim1], &
c__1);
i__4 = *m - ie;
sscal_(&i__4, &scaloc, &f[ie + 1 + k * f_dim1], &c__1)
;
/* L180: */
}
i__3 = *n;
for (k = je + 1; k <= i__3; ++k) {
sscal_(m, &scaloc, &c__[k * c_dim1 + 1], &c__1);
sscal_(m, &scaloc, &f[k * f_dim1 + 1], &c__1);
/* L190: */
}
*scale *= scaloc;
}
/* Substitute R(I, J) and L(I, J) into remaining equation. */
if (j > p + 2) {
i__3 = js - 1;
sgemm_("N", "T", &mb, &i__3, &nb, &c_b52, &c__[is + js *
c_dim1], ldc, &b[js * b_dim1 + 1], ldb, &c_b52, &
f[is + f_dim1], ldf);
i__3 = js - 1;
sgemm_("N", "T", &mb, &i__3, &nb, &c_b52, &f[is + js *
f_dim1], ldf, &e[js * e_dim1 + 1], lde, &c_b52, &
f[is + f_dim1], ldf);
}
if (i__ < p) {
i__3 = *m - ie;
sgemm_("T", "N", &i__3, &nb, &mb, &c_b51, &a[is + (ie + 1)
* a_dim1], lda, &c__[is + js * c_dim1], ldc, &
c_b52, &c__[ie + 1 + js * c_dim1], ldc);
i__3 = *m - ie;
sgemm_("T", "N", &i__3, &nb, &mb, &c_b51, &d__[is + (ie +
1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, &
c_b52, &c__[ie + 1 + js * c_dim1], ldc);
}
/* L200: */
}
/* L210: */
}
}
work[1] = (real) lwmin;
return;
/* End of STGSYL */
} /* stgsyl_ */
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