floraachy
/
OpenBLAS
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
OpenBLAS/lapack-netlib/SRC/strsyl3.c

2067 lines
60 KiB
C
Raw Permalink Blame History

#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]/Cd(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)
#define myexp_(w) my_expfunc(w)
static int my_expfunc(float *x) {int e; (void)frexpf(*x,&e); return e;}
/* 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__1 = 1;
static integer c_n1 = -1;
static real c_b19 = 2.f;
static real c_b31 = -1.f;
static real c_b32 = 1.f;
/* > \brief \b STRSYL3 */
/* Definition: */
/* =========== */
/* > \par Purpose */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > STRSYL3 solves the real Sylvester matrix equation: */
/* > */
/* > op(A)*X + X*op(B) = scale*C or */
/* > op(A)*X - X*op(B) = scale*C, */
/* > */
/* > where op(A) = A or A**T, and A and B are both upper quasi- */
/* > triangular. A is M-by-M and B is N-by-N; the right hand side C and */
/* > the solution X are M-by-N; and scale is an output scale factor, set */
/* > <= 1 to avoid overflow in X. */
/* > */
/* > A and B must be in Schur canonical form (as returned by SHSEQR), that */
/* > is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; */
/* > each 2-by-2 diagonal block has its diagonal elements equal and its */
/* > off-diagonal elements of opposite sign. */
/* > */
/* > This is the block version of the algorithm. */
/* > \endverbatim */
/* Arguments */
/* ========= */
/* > \param[in] TRANA */
/* > \verbatim */
/* > TRANA is CHARACTER*1 */
/* > Specifies the option op(A): */
/* > = 'N': op(A) = A (No transpose) */
/* > = 'T': op(A) = A**T (Transpose) */
/* > = 'C': op(A) = A**H (Conjugate transpose = Transpose) */
/* > \endverbatim */
/* > */
/* > \param[in] TRANB */
/* > \verbatim */
/* > TRANB is CHARACTER*1 */
/* > Specifies the option op(B): */
/* > = 'N': op(B) = B (No transpose) */
/* > = 'T': op(B) = B**T (Transpose) */
/* > = 'C': op(B) = B**H (Conjugate transpose = Transpose) */
/* > \endverbatim */
/* > */
/* > \param[in] ISGN */
/* > \verbatim */
/* > ISGN is INTEGER */
/* > Specifies the sign in the equation: */
/* > = +1: solve op(A)*X + X*op(B) = scale*C */
/* > = -1: solve op(A)*X - X*op(B) = scale*C */
/* > \endverbatim */
/* > */
/* > \param[in] M */
/* > \verbatim */
/* > M is INTEGER */
/* > The order of the matrix A, and the number of rows in the */
/* > matrices X and C. M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrix B, and the number of columns in the */
/* > matrices X and C. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] A */
/* > \verbatim */
/* > A is REAL array, dimension (LDA,M) */
/* > The upper quasi-triangular matrix A, in Schur canonical form. */
/* > \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, in Schur canonical form. */
/* > \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, the M-by-N right hand side matrix C. */
/* > On exit, C is overwritten by the solution matrix X. */
/* > \endverbatim */
/* > */
/* > \param[in] LDC */
/* > \verbatim */
/* > LDC is INTEGER */
/* > The leading dimension of the array C. LDC >= f2cmax(1,M) */
/* > \endverbatim */
/* > */
/* > \param[out] SCALE */
/* > \verbatim */
/* > SCALE is REAL */
/* > The scale factor, scale, set <= 1 to avoid overflow in X. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LIWORK */
/* > \verbatim */
/* > IWORK is INTEGER */
/* > The dimension of the array IWORK. LIWORK >= ((M + NB - 1) / NB + 1) */
/* > + ((N + NB - 1) / NB + 1), where NB is the optimal block size. */
/* > */
/* > If LIWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal dimension of the IWORK array, */
/* > returns this value as the first entry of the IWORK array, and */
/* > no error message related to LIWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] SWORK */
/* > \verbatim */
/* > SWORK is REAL array, dimension (MAX(2, ROWS), */
/* > MAX(1,COLS)). */
/* > On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS */
/* > and SWORK(2) returns the optimal COLS. */
/* > \endverbatim */
/* > */
/* > \param[in] LDSWORK */
/* > \verbatim */
/* > LDSWORK is INTEGER */
/* > LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1) */
/* > and NB is the optimal block size. */
/* > */
/* > If LDSWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal dimensions of the SWORK matrix, */
/* > returns these values as the first and second entry of the SWORK */
/* > matrix, and no error message related LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit */
/* > < 0: if INFO = -i, the i-th argument had an illegal value */
/* > = 1: A and B have common or very close eigenvalues; perturbed */
/* > values were used to solve the equation (but the matrices */
/* > A and B are unchanged). */
/* > \endverbatim */
/* ===================================================================== */
/* References: */
/* E. S. Quintana-Orti and R. A. Van De Geijn (2003). Formal derivation of */
/* algorithms: The triangular Sylvester equation, ACM Transactions */
/* on Mathematical Software (TOMS), volume 29, pages 218--243. */
/* A. Schwarz and C. C. Kjelgaard Mikkelsen (2020). Robust Task-Parallel */
/* Solution of the Triangular Sylvester Equation. Lecture Notes in */
/* Computer Science, vol 12043, pages 82--92, Springer. */
/* Contributor: */
/* Angelika Schwarz, Umea University, Sweden. */
/* ===================================================================== */
/* Subroutine */ void strsyl3_(char *trana, char *tranb, integer *isgn,
integer *m, integer *n, real *a, integer *lda, real *b, integer *ldb,
real *c__, integer *ldc, real *scale, integer *iwork, integer *liwork,
real *swork, integer *ldswork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, swork_dim1,
swork_offset, i__1, i__2, i__3, i__4, i__5, i__6;
real r__1, r__2, r__3;
/* Local variables */
real scal, anrm, bnrm, cnrm;
integer awrk, bwrk;
logical skip;
real *wnrm, xnrm;
integer i__, j, k, l;
extern logical lsame_(char *, char *);
integer iinfo;
extern /* Subroutine */ void sscal_(integer *, real *, real *, integer *),
sgemm_(char *, char *, integer *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *);
integer i1, i2, j1, j2, k1, k2, l1;
// extern integer myexp_(real *);
integer l2, nb, pc, jj, ll;
real scaloc;
extern real slamch_(char *), slange_(char *, integer *, integer *,
real *, integer *, real *);
real scamin;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
real bignum;
extern /* Subroutine */ void slascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, real *, integer *, integer *);
extern real slarmm_(real *, real *, real *);
logical notrna, notrnb;
real smlnum;
logical lquery;
extern /* Subroutine */ void strsyl_(char *, char *, integer *, integer *,
integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *);
integer nba, nbb;
real buf, sgn;
/* 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;
--iwork;
swork_dim1 = *ldswork;
swork_offset = 1 + swork_dim1 * 1;
swork -= swork_offset;
/* Function Body */
notrna = lsame_(trana, "N");
notrnb = lsame_(tranb, "N");
/* Use the same block size for all matrices. */
/* Computing MAX */
i__1 = 8, i__2 = ilaenv_(&c__1, "STRSYL", "", m, n, &c_n1, &c_n1, (ftnlen)
6, (ftnlen)0);
nb = f2cmax(i__1,i__2);
/* Compute number of blocks in A and B */
/* Computing MAX */
i__1 = 1, i__2 = (*m + nb - 1) / nb;
nba = f2cmax(i__1,i__2);
/* Computing MAX */
i__1 = 1, i__2 = (*n + nb - 1) / nb;
nbb = f2cmax(i__1,i__2);
/* Compute workspace */
*info = 0;
lquery = *liwork == -1 || *ldswork == -1;
iwork[1] = nba + nbb + 2;
if (lquery) {
*ldswork = 2;
swork[swork_dim1 + 1] = (real) f2cmax(nba,nbb);
swork[swork_dim1 + 2] = (real) ((nbb << 1) + nba);
}
/* Test the input arguments */
if (! notrna && ! lsame_(trana, "T") && ! lsame_(
trana, "C")) {
*info = -1;
} else if (! notrnb && ! lsame_(tranb, "T") && !
lsame_(tranb, "C")) {
*info = -2;
} else if (*isgn != 1 && *isgn != -1) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < f2cmax(1,*m)) {
*info = -7;
} else if (*ldb < f2cmax(1,*n)) {
*info = -9;
} else if (*ldc < f2cmax(1,*m)) {
*info = -11;
} else if (! lquery && *liwork < iwork[1]) {
*info = -14;
} else if (! lquery && *ldswork < f2cmax(nba,nbb)) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STRSYL3", &i__1, 7);
return;
} else if (lquery) {
return;
}
/* Quick return if possible */
*scale = 1.f;
if (*m == 0 || *n == 0) {
return;
}
/* Use unblocked code for small problems or if insufficient */
/* workspaces are provided */
if (f2cmin(nba,nbb) == 1 || *ldswork < f2cmax(nba,nbb) || *liwork < iwork[1]) {
strsyl_(trana, tranb, isgn, m, n, &a[a_offset], lda, &b[b_offset],
ldb, &c__[c_offset], ldc, scale, info);
return;
}
/* REAL WNRM( MAX( M, N ) ) */
wnrm=(real*)malloc (f2cmax(*m,*n)*sizeof(real));
/* Set constants to control overflow */
smlnum = slamch_("S");
bignum = 1.f / smlnum;
/* Partition A such that 2-by-2 blocks on the diagonal are not split */
skip = FALSE_;
i__1 = nba;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = (i__ - 1) * nb + 1;
}
iwork[nba + 1] = *m + 1;
i__1 = nba;
for (k = 1; k <= i__1; ++k) {
l1 = iwork[k];
l2 = iwork[k + 1] - 1;
i__2 = l2;
for (l = l1; l <= i__2; ++l) {
if (skip) {
skip = FALSE_;
mycycle_();
}
if (l >= *m) {
/* A( M, M ) is a 1-by-1 block */
mycycle_();
}
if (a[l + (l + 1) * a_dim1] != 0.f && a[l + 1 + l * a_dim1] !=
0.f) {
/* Check if 2-by-2 block is split */
if (l + 1 == iwork[k + 1]) {
++iwork[k + 1];
mycycle_();
}
skip = TRUE_;
}
}
}
iwork[nba + 1] = *m + 1;
if (iwork[nba] >= iwork[nba + 1]) {
iwork[nba] = iwork[nba + 1];
--nba;
}
/* Partition B such that 2-by-2 blocks on the diagonal are not split */
pc = nba + 1;
skip = FALSE_;
i__1 = nbb;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[pc + i__] = (i__ - 1) * nb + 1;
}
iwork[pc + nbb + 1] = *n + 1;
i__1 = nbb;
for (k = 1; k <= i__1; ++k) {
l1 = iwork[pc + k];
l2 = iwork[pc + k + 1] - 1;
i__2 = l2;
for (l = l1; l <= i__2; ++l) {
if (skip) {
skip = FALSE_;
mycycle_();
}
if (l >= *n) {
/* B( N, N ) is a 1-by-1 block */
mycycle_();
}
if (b[l + (l + 1) * b_dim1] != 0.f && b[l + 1 + l * b_dim1] !=
0.f) {
/* Check if 2-by-2 block is split */
if (l + 1 == iwork[pc + k + 1]) {
++iwork[pc + k + 1];
mycycle_();
}
skip = TRUE_;
}
}
}
iwork[pc + nbb + 1] = *n + 1;
if (iwork[pc + nbb] >= iwork[pc + nbb + 1]) {
iwork[pc + nbb] = iwork[pc + nbb + 1];
--nbb;
}
/* Set local scaling factors - must never attain zero. */
i__1 = nbb;
for (l = 1; l <= i__1; ++l) {
i__2 = nba;
for (k = 1; k <= i__2; ++k) {
swork[k + l * swork_dim1] = 1.f;
}
}
/* Fallback scaling factor to prevent flushing of SWORK( K, L ) to zero. */
/* This scaling is to ensure compatibility with TRSYL and may get flushed. */
buf = 1.f;
/* Compute upper bounds of blocks of A and B */
awrk = nbb;
i__1 = nba;
for (k = 1; k <= i__1; ++k) {
k1 = iwork[k];
k2 = iwork[k + 1];
i__2 = nba;
for (l = k; l <= i__2; ++l) {
l1 = iwork[l];
l2 = iwork[l + 1];
if (notrna) {
i__3 = k2 - k1;
i__4 = l2 - l1;
swork[k + (awrk + l) * swork_dim1] = slange_("I", &i__3, &
i__4, &a[k1 + l1 * a_dim1], lda, wnrm);
} else {
i__3 = k2 - k1;
i__4 = l2 - l1;
swork[l + (awrk + k) * swork_dim1] = slange_("1", &i__3, &
i__4, &a[k1 + l1 * a_dim1], lda, wnrm);
}
}
}
bwrk = nbb + nba;
i__1 = nbb;
for (k = 1; k <= i__1; ++k) {
k1 = iwork[pc + k];
k2 = iwork[pc + k + 1];
i__2 = nbb;
for (l = k; l <= i__2; ++l) {
l1 = iwork[pc + l];
l2 = iwork[pc + l + 1];
if (notrnb) {
i__3 = k2 - k1;
i__4 = l2 - l1;
swork[k + (bwrk + l) * swork_dim1] = slange_("I", &i__3, &
i__4, &b[k1 + l1 * b_dim1], ldb, wnrm);
} else {
i__3 = k2 - k1;
i__4 = l2 - l1;
swork[l + (bwrk + k) * swork_dim1] = slange_("1", &i__3, &
i__4, &b[k1 + l1 * b_dim1], ldb, wnrm);
}
}
}
sgn = (real) (*isgn);
if (notrna && notrnb) {
/* Solve A*X + ISGN*X*B = scale*C. */
/* The (K,L)th block of X is determined starting from */
/* bottom-left corner column by column by */
/* A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L) */
/* Where */
/* M L-1 */
/* R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]. */
/* I=K+1 J=1 */
/* Start loop over block rows (index = K) and block columns (index = L) */
for (k = nba; k >= 1; --k) {
/* K1: row index of the first row in X( K, L ) */
/* K2: row index of the first row in X( K+1, L ) */
/* so the K2 - K1 is the column count of the block X( K, L ) */
k1 = iwork[k];
k2 = iwork[k + 1];
i__1 = nbb;
for (l = 1; l <= i__1; ++l) {
/* L1: column index of the first column in X( K, L ) */
/* L2: column index of the first column in X( K, L + 1) */
/* so that L2 - L1 is the row count of the block X( K, L ) */
l1 = iwork[pc + l];
l2 = iwork[pc + l + 1];
i__2 = k2 - k1;
i__3 = l2 - l1;
strsyl_(trana, tranb, isgn, &i__2, &i__3, &a[k1 + k1 * a_dim1]
, lda, &b[l1 + l1 * b_dim1], ldb, &c__[k1 + l1 *
c_dim1], ldc, &scaloc, &iinfo);
*info = f2cmax(*info,iinfo);
if (scaloc * swork[k + l * swork_dim1] == 0.f) {
if (scaloc == 0.f) {
/* The magnitude of the largest entry of X(K1:K2-1, L1:L2-1) */
/* is larger than the product of BIGNUM**2 and cannot be */
/* represented in the form (1/SCALE)*X(K1:K2-1, L1:L2-1). */
/* Mark the computation as pointless. */
buf = 0.f;
} else {
/* Use second scaling factor to prevent flushing to zero. */
i__2 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__2);
}
i__2 = nbb;
for (jj = 1; jj <= i__2; ++jj) {
i__3 = nba;
for (ll = 1; ll <= i__3; ++ll) {
/* Bound by BIGNUM to not introduce Inf. The value */
/* is irrelevant; corresponding entries of the */
/* solution will be flushed in consistency scaling. */
/* Computing MIN */
i__4 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj * swork_dim1]
/ pow_ri(&c_b19, &i__4);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
}
swork[k + l * swork_dim1] = scaloc * swork[k + l * swork_dim1]
;
i__2 = k2 - k1;
i__3 = l2 - l1;
xnrm = slange_("I", &i__2, &i__3, &c__[k1 + l1 * c_dim1], ldc,
wnrm);
for (i__ = k - 1; i__ >= 1; --i__) {
/* C( I, L ) := C( I, L ) - A( I, K ) * C( K, L ) */
i1 = iwork[i__];
i2 = iwork[i__ + 1];
/* Compute scaling factor to survive the linear update */
/* simulating consistent scaling. */
i__2 = i2 - i1;
i__3 = l2 - l1;
cnrm = slange_("I", &i__2, &i__3, &c__[i1 + l1 * c_dim1],
ldc, wnrm);
/* Computing MIN */
r__1 = swork[i__ + l * swork_dim1], r__2 = swork[k + l *
swork_dim1];
scamin = f2cmin(r__1,r__2);
cnrm *= scamin / swork[i__ + l * swork_dim1];
xnrm *= scamin / swork[k + l * swork_dim1];
anrm = swork[i__ + (awrk + k) * swork_dim1];
scaloc = slarmm_(&anrm, &xnrm, &cnrm);
if (scaloc * scamin == 0.f) {
/* Use second scaling factor to prevent flushing to zero. */
i__2 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__2);
i__2 = nbb;
for (jj = 1; jj <= i__2; ++jj) {
i__3 = nba;
for (ll = 1; ll <= i__3; ++ll) {
/* Computing MIN */
i__4 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj *
swork_dim1] / pow_ri(&c_b19, &i__4);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
i__2 = myexp_(&scaloc);
scamin /= pow_ri(&c_b19, &i__2);
i__2 = myexp_(&scaloc);
scaloc /= pow_ri(&c_b19, &i__2);
}
cnrm *= scaloc;
xnrm *= scaloc;
/* Simultaneously apply the robust update factor and the */
/* consistency scaling factor to C( I, L ) and C( K, L ). */
scal = scamin / swork[k + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__2 = l2 - 1;
for (jj = l1; jj <= i__2; ++jj) {
i__3 = k2 - k1;
sscal_(&i__3, &scal, &c__[k1 + jj * c_dim1], &
c__1);
}
}
scal = scamin / swork[i__ + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__2 = l2 - 1;
for (ll = l1; ll <= i__2; ++ll) {
i__3 = i2 - i1;
sscal_(&i__3, &scal, &c__[i1 + ll * c_dim1], &
c__1);
}
}
/* Record current scaling factor */
swork[k + l * swork_dim1] = scamin * scaloc;
swork[i__ + l * swork_dim1] = scamin * scaloc;
i__2 = i2 - i1;
i__3 = l2 - l1;
i__4 = k2 - k1;
sgemm_("N", "N", &i__2, &i__3, &i__4, &c_b31, &a[i1 + k1 *
a_dim1], lda, &c__[k1 + l1 * c_dim1], ldc, &
c_b32, &c__[i1 + l1 * c_dim1], ldc);
}
i__2 = nbb;
for (j = l + 1; j <= i__2; ++j) {
/* C( K, J ) := C( K, J ) - SGN * C( K, L ) * B( L, J ) */
j1 = iwork[pc + j];
j2 = iwork[pc + j + 1];
/* Compute scaling factor to survive the linear update */
/* simulating consistent scaling. */
i__3 = k2 - k1;
i__4 = j2 - j1;
cnrm = slange_("I", &i__3, &i__4, &c__[k1 + j1 * c_dim1],
ldc, wnrm);
/* Computing MIN */
r__1 = swork[k + j * swork_dim1], r__2 = swork[k + l *
swork_dim1];
scamin = f2cmin(r__1,r__2);
cnrm *= scamin / swork[k + j * swork_dim1];
xnrm *= scamin / swork[k + l * swork_dim1];
bnrm = swork[l + (bwrk + j) * swork_dim1];
scaloc = slarmm_(&bnrm, &xnrm, &cnrm);
if (scaloc * scamin == 0.f) {
/* Use second scaling factor to prevent flushing to zero. */
i__3 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__3);
i__3 = nbb;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = nba;
for (ll = 1; ll <= i__4; ++ll) {
/* Computing MIN */
i__5 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj *
swork_dim1] / pow_ri(&c_b19, &i__5);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
i__3 = myexp_(&scaloc);
scamin /= pow_ri(&c_b19, &i__3);
i__3 = myexp_(&scaloc);
scaloc /= pow_ri(&c_b19, &i__3);
}
cnrm *= scaloc;
xnrm *= scaloc;
/* Simultaneously apply the robust update factor and the */
/* consistency scaling factor to C( K, J ) and C( K, L). */
scal = scamin / swork[k + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__3 = l2 - 1;
for (ll = l1; ll <= i__3; ++ll) {
i__4 = k2 - k1;
sscal_(&i__4, &scal, &c__[k1 + ll * c_dim1], &
c__1);
}
}
scal = scamin / swork[k + j * swork_dim1] * scaloc;
if (scal != 1.f) {
i__3 = j2 - 1;
for (jj = j1; jj <= i__3; ++jj) {
i__4 = k2 - k1;
sscal_(&i__4, &scal, &c__[k1 + jj * c_dim1], &
c__1);
}
}
/* Record current scaling factor */
swork[k + l * swork_dim1] = scamin * scaloc;
swork[k + j * swork_dim1] = scamin * scaloc;
i__3 = k2 - k1;
i__4 = j2 - j1;
i__5 = l2 - l1;
r__1 = -sgn;
sgemm_("N", "N", &i__3, &i__4, &i__5, &r__1, &c__[k1 + l1
* c_dim1], ldc, &b[l1 + j1 * b_dim1], ldb, &c_b32,
&c__[k1 + j1 * c_dim1], ldc);
}
}
}
} else if (! notrna && notrnb) {
/* Solve A**T*X + ISGN*X*B = scale*C. */
/* The (K,L)th block of X is determined starting from */
/* upper-left corner column by column by */
/* A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L) */
/* Where */
/* K-1 L-1 */
/* R(K,L) = SUM [A(I,K)**T*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)] */
/* I=1 J=1 */
/* Start loop over block rows (index = K) and block columns (index = L) */
i__1 = nba;
for (k = 1; k <= i__1; ++k) {
/* K1: row index of the first row in X( K, L ) */
/* K2: row index of the first row in X( K+1, L ) */
/* so the K2 - K1 is the column count of the block X( K, L ) */
k1 = iwork[k];
k2 = iwork[k + 1];
i__2 = nbb;
for (l = 1; l <= i__2; ++l) {
/* L1: column index of the first column in X( K, L ) */
/* L2: column index of the first column in X( K, L + 1) */
/* so that L2 - L1 is the row count of the block X( K, L ) */
l1 = iwork[pc + l];
l2 = iwork[pc + l + 1];
i__3 = k2 - k1;
i__4 = l2 - l1;
strsyl_(trana, tranb, isgn, &i__3, &i__4, &a[k1 + k1 * a_dim1]
, lda, &b[l1 + l1 * b_dim1], ldb, &c__[k1 + l1 *
c_dim1], ldc, &scaloc, &iinfo);
*info = f2cmax(*info,iinfo);
if (scaloc * swork[k + l * swork_dim1] == 0.f) {
if (scaloc == 0.f) {
/* The magnitude of the largest entry of X(K1:K2-1, L1:L2-1) */
/* is larger than the product of BIGNUM**2 and cannot be */
/* represented in the form (1/SCALE)*X(K1:K2-1, L1:L2-1). */
/* Mark the computation as pointless. */
buf = 0.f;
} else {
/* Use second scaling factor to prevent flushing to zero. */
i__3 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__3);
}
i__3 = nbb;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = nba;
for (ll = 1; ll <= i__4; ++ll) {
/* Bound by BIGNUM to not introduce Inf. The value */
/* is irrelevant; corresponding entries of the */
/* solution will be flushed in consistency scaling. */
/* Computing MIN */
i__5 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj * swork_dim1]
/ pow_ri(&c_b19, &i__5);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
}
swork[k + l * swork_dim1] = scaloc * swork[k + l * swork_dim1]
;
i__3 = k2 - k1;
i__4 = l2 - l1;
xnrm = slange_("I", &i__3, &i__4, &c__[k1 + l1 * c_dim1], ldc,
wnrm);
i__3 = nba;
for (i__ = k + 1; i__ <= i__3; ++i__) {
/* C( I, L ) := C( I, L ) - A( K, I )**T * C( K, L ) */
i1 = iwork[i__];
i2 = iwork[i__ + 1];
/* Compute scaling factor to survive the linear update */
/* simulating consistent scaling. */
i__4 = i2 - i1;
i__5 = l2 - l1;
cnrm = slange_("I", &i__4, &i__5, &c__[i1 + l1 * c_dim1],
ldc, wnrm);
/* Computing MIN */
r__1 = swork[i__ + l * swork_dim1], r__2 = swork[k + l *
swork_dim1];
scamin = f2cmin(r__1,r__2);
cnrm *= scamin / swork[i__ + l * swork_dim1];
xnrm *= scamin / swork[k + l * swork_dim1];
anrm = swork[i__ + (awrk + k) * swork_dim1];
scaloc = slarmm_(&anrm, &xnrm, &cnrm);
if (scaloc * scamin == 0.f) {
/* Use second scaling factor to prevent flushing to zero. */
i__4 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__4);
i__4 = nbb;
for (jj = 1; jj <= i__4; ++jj) {
i__5 = nba;
for (ll = 1; ll <= i__5; ++ll) {
/* Computing MIN */
i__6 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj *
swork_dim1] / pow_ri(&c_b19, &i__6);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
i__4 = myexp_(&scaloc);
scamin /= pow_ri(&c_b19, &i__4);
i__4 = myexp_(&scaloc);
scaloc /= pow_ri(&c_b19, &i__4);
}
cnrm *= scaloc;
xnrm *= scaloc;
/* Simultaneously apply the robust update factor and the */
/* consistency scaling factor to to C( I, L ) and C( K, L ). */
scal = scamin / swork[k + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__4 = l2 - 1;
for (ll = l1; ll <= i__4; ++ll) {
i__5 = k2 - k1;
sscal_(&i__5, &scal, &c__[k1 + ll * c_dim1], &
c__1);
}
}
scal = scamin / swork[i__ + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__4 = l2 - 1;
for (ll = l1; ll <= i__4; ++ll) {
i__5 = i2 - i1;
sscal_(&i__5, &scal, &c__[i1 + ll * c_dim1], &
c__1);
}
}
/* Record current scaling factor */
swork[k + l * swork_dim1] = scamin * scaloc;
swork[i__ + l * swork_dim1] = scamin * scaloc;
i__4 = i2 - i1;
i__5 = l2 - l1;
i__6 = k2 - k1;
sgemm_("T", "N", &i__4, &i__5, &i__6, &c_b31, &a[k1 + i1 *
a_dim1], lda, &c__[k1 + l1 * c_dim1], ldc, &
c_b32, &c__[i1 + l1 * c_dim1], ldc);
}
i__3 = nbb;
for (j = l + 1; j <= i__3; ++j) {
/* C( K, J ) := C( K, J ) - SGN * C( K, L ) * B( L, J ) */
j1 = iwork[pc + j];
j2 = iwork[pc + j + 1];
/* Compute scaling factor to survive the linear update */
/* simulating consistent scaling. */
i__4 = k2 - k1;
i__5 = j2 - j1;
cnrm = slange_("I", &i__4, &i__5, &c__[k1 + j1 * c_dim1],
ldc, wnrm);
/* Computing MIN */
r__1 = swork[k + j * swork_dim1], r__2 = swork[k + l *
swork_dim1];
scamin = f2cmin(r__1,r__2);
cnrm *= scamin / swork[k + j * swork_dim1];
xnrm *= scamin / swork[k + l * swork_dim1];
bnrm = swork[l + (bwrk + j) * swork_dim1];
scaloc = slarmm_(&bnrm, &xnrm, &cnrm);
if (scaloc * scamin == 0.f) {
/* Use second scaling factor to prevent flushing to zero. */
i__4 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__4);
i__4 = nbb;
for (jj = 1; jj <= i__4; ++jj) {
i__5 = nba;
for (ll = 1; ll <= i__5; ++ll) {
/* Computing MIN */
i__6 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj *
swork_dim1] / pow_ri(&c_b19, &i__6);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
i__4 = myexp_(&scaloc);
scamin /= pow_ri(&c_b19, &i__4);
i__4 = myexp_(&scaloc);
scaloc /= pow_ri(&c_b19, &i__4);
}
cnrm *= scaloc;
xnrm *= scaloc;
/* Simultaneously apply the robust update factor and the */
/* consistency scaling factor to to C( K, J ) and C( K, L ). */
scal = scamin / swork[k + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__4 = l2 - 1;
for (ll = l1; ll <= i__4; ++ll) {
i__5 = k2 - k1;
sscal_(&i__5, &scal, &c__[k1 + ll * c_dim1], &
c__1);
}
}
scal = scamin / swork[k + j * swork_dim1] * scaloc;
if (scal != 1.f) {
i__4 = j2 - 1;
for (jj = j1; jj <= i__4; ++jj) {
i__5 = k2 - k1;
sscal_(&i__5, &scal, &c__[k1 + jj * c_dim1], &
c__1);
}
}
/* Record current scaling factor */
swork[k + l * swork_dim1] = scamin * scaloc;
swork[k + j * swork_dim1] = scamin * scaloc;
i__4 = k2 - k1;
i__5 = j2 - j1;
i__6 = l2 - l1;
r__1 = -sgn;
sgemm_("N", "N", &i__4, &i__5, &i__6, &r__1, &c__[k1 + l1
* c_dim1], ldc, &b[l1 + j1 * b_dim1], ldb, &c_b32,
&c__[k1 + j1 * c_dim1], ldc);
}
}
}
} else if (! notrna && ! notrnb) {
/* Solve A**T*X + ISGN*X*B**T = scale*C. */
/* The (K,L)th block of X is determined starting from */
/* top-right corner column by column by */
/* A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L) */
/* Where */
/* K-1 N */
/* R(K,L) = SUM [A(I,K)**T*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T]. */
/* I=1 J=L+1 */
/* Start loop over block rows (index = K) and block columns (index = L) */
i__1 = nba;
for (k = 1; k <= i__1; ++k) {
/* K1: row index of the first row in X( K, L ) */
/* K2: row index of the first row in X( K+1, L ) */
/* so the K2 - K1 is the column count of the block X( K, L ) */
k1 = iwork[k];
k2 = iwork[k + 1];
for (l = nbb; l >= 1; --l) {
/* L1: column index of the first column in X( K, L ) */
/* L2: column index of the first column in X( K, L + 1) */
/* so that L2 - L1 is the row count of the block X( K, L ) */
l1 = iwork[pc + l];
l2 = iwork[pc + l + 1];
i__2 = k2 - k1;
i__3 = l2 - l1;
strsyl_(trana, tranb, isgn, &i__2, &i__3, &a[k1 + k1 * a_dim1]
, lda, &b[l1 + l1 * b_dim1], ldb, &c__[k1 + l1 *
c_dim1], ldc, &scaloc, &iinfo);
*info = f2cmax(*info,iinfo);
if (scaloc * swork[k + l * swork_dim1] == 0.f) {
if (scaloc == 0.f) {
/* The magnitude of the largest entry of X(K1:K2-1, L1:L2-1) */
/* is larger than the product of BIGNUM**2 and cannot be */
/* represented in the form (1/SCALE)*X(K1:K2-1, L1:L2-1). */
/* Mark the computation as pointless. */
buf = 0.f;
} else {
/* Use second scaling factor to prevent flushing to zero. */
i__2 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__2);
}
i__2 = nbb;
for (jj = 1; jj <= i__2; ++jj) {
i__3 = nba;
for (ll = 1; ll <= i__3; ++ll) {
/* Bound by BIGNUM to not introduce Inf. The value */
/* is irrelevant; corresponding entries of the */
/* solution will be flushed in consistency scaling. */
/* Computing MIN */
i__4 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj * swork_dim1]
/ pow_ri(&c_b19, &i__4);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
}
swork[k + l * swork_dim1] = scaloc * swork[k + l * swork_dim1]
;
i__2 = k2 - k1;
i__3 = l2 - l1;
xnrm = slange_("I", &i__2, &i__3, &c__[k1 + l1 * c_dim1], ldc,
wnrm);
i__2 = nba;
for (i__ = k + 1; i__ <= i__2; ++i__) {
/* C( I, L ) := C( I, L ) - A( K, I )**T * C( K, L ) */
i1 = iwork[i__];
i2 = iwork[i__ + 1];
/* Compute scaling factor to survive the linear update */
/* simulating consistent scaling. */
i__3 = i2 - i1;
i__4 = l2 - l1;
cnrm = slange_("I", &i__3, &i__4, &c__[i1 + l1 * c_dim1],
ldc, wnrm);
/* Computing MIN */
r__1 = swork[i__ + l * swork_dim1], r__2 = swork[k + l *
swork_dim1];
scamin = f2cmin(r__1,r__2);
cnrm *= scamin / swork[i__ + l * swork_dim1];
xnrm *= scamin / swork[k + l * swork_dim1];
anrm = swork[i__ + (awrk + k) * swork_dim1];
scaloc = slarmm_(&anrm, &xnrm, &cnrm);
if (scaloc * scamin == 0.f) {
/* Use second scaling factor to prevent flushing to zero. */
i__3 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__3);
i__3 = nbb;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = nba;
for (ll = 1; ll <= i__4; ++ll) {
/* Computing MIN */
i__5 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj *
swork_dim1] / pow_ri(&c_b19, &i__5);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
i__3 = myexp_(&scaloc);
scamin /= pow_ri(&c_b19, &i__3);
i__3 = myexp_(&scaloc);
scaloc /= pow_ri(&c_b19, &i__3);
}
cnrm *= scaloc;
xnrm *= scaloc;
/* Simultaneously apply the robust update factor and the */
/* consistency scaling factor to C( I, L ) and C( K, L ). */
scal = scamin / swork[k + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__3 = l2 - 1;
for (ll = l1; ll <= i__3; ++ll) {
i__4 = k2 - k1;
sscal_(&i__4, &scal, &c__[k1 + ll * c_dim1], &
c__1);
}
}
scal = scamin / swork[i__ + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__3 = l2 - 1;
for (ll = l1; ll <= i__3; ++ll) {
i__4 = i2 - i1;
sscal_(&i__4, &scal, &c__[i1 + ll * c_dim1], &
c__1);
}
}
/* Record current scaling factor */
swork[k + l * swork_dim1] = scamin * scaloc;
swork[i__ + l * swork_dim1] = scamin * scaloc;
i__3 = i2 - i1;
i__4 = l2 - l1;
i__5 = k2 - k1;
sgemm_("T", "N", &i__3, &i__4, &i__5, &c_b31, &a[k1 + i1 *
a_dim1], lda, &c__[k1 + l1 * c_dim1], ldc, &
c_b32, &c__[i1 + l1 * c_dim1], ldc);
}
i__2 = l - 1;
for (j = 1; j <= i__2; ++j) {
/* C( K, J ) := C( K, J ) - SGN * C( K, L ) * B( J, L )**T */
j1 = iwork[pc + j];
j2 = iwork[pc + j + 1];
/* Compute scaling factor to survive the linear update */
/* simulating consistent scaling. */
i__3 = k2 - k1;
i__4 = j2 - j1;
cnrm = slange_("I", &i__3, &i__4, &c__[k1 + j1 * c_dim1],
ldc, wnrm);
/* Computing MIN */
r__1 = swork[k + j * swork_dim1], r__2 = swork[k + l *
swork_dim1];
scamin = f2cmin(r__1,r__2);
cnrm *= scamin / swork[k + j * swork_dim1];
xnrm *= scamin / swork[k + l * swork_dim1];
bnrm = swork[l + (bwrk + j) * swork_dim1];
scaloc = slarmm_(&bnrm, &xnrm, &cnrm);
if (scaloc * scamin == 0.f) {
/* Use second scaling factor to prevent flushing to zero. */
i__3 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__3);
i__3 = nbb;
for (jj = 1; jj <= i__3; ++jj) {
i__4 = nba;
for (ll = 1; ll <= i__4; ++ll) {
/* Computing MIN */
i__5 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj *
swork_dim1] / pow_ri(&c_b19, &i__5);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
i__3 = myexp_(&scaloc);
scamin /= pow_ri(&c_b19, &i__3);
i__3 = myexp_(&scaloc);
scaloc /= pow_ri(&c_b19, &i__3);
}
cnrm *= scaloc;
xnrm *= scaloc;
/* Simultaneously apply the robust update factor and the */
/* consistency scaling factor to C( K, J ) and C( K, L ). */
scal = scamin / swork[k + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__3 = l2 - 1;
for (ll = l1; ll <= i__3; ++ll) {
i__4 = k2 - k1;
sscal_(&i__4, &scal, &c__[k1 + ll * c_dim1], &
c__1);
}
}
scal = scamin / swork[k + j * swork_dim1] * scaloc;
if (scal != 1.f) {
i__3 = j2 - 1;
for (jj = j1; jj <= i__3; ++jj) {
i__4 = k2 - k1;
sscal_(&i__4, &scal, &c__[k1 + jj * c_dim1], &
c__1);
}
}
/* Record current scaling factor */
swork[k + l * swork_dim1] = scamin * scaloc;
swork[k + j * swork_dim1] = scamin * scaloc;
i__3 = k2 - k1;
i__4 = j2 - j1;
i__5 = l2 - l1;
r__1 = -sgn;
sgemm_("N", "T", &i__3, &i__4, &i__5, &r__1, &c__[k1 + l1
* c_dim1], ldc, &b[j1 + l1 * b_dim1], ldb, &c_b32,
&c__[k1 + j1 * c_dim1], ldc);
}
}
}
} else if (notrna && ! notrnb) {
/* Solve A*X + ISGN*X*B**T = scale*C. */
/* The (K,L)th block of X is determined starting from */
/* bottom-right corner column by column by */
/* A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L) */
/* Where */
/* M N */
/* R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T]. */
/* I=K+1 J=L+1 */
/* Start loop over block rows (index = K) and block columns (index = L) */
for (k = nba; k >= 1; --k) {
/* K1: row index of the first row in X( K, L ) */
/* K2: row index of the first row in X( K+1, L ) */
/* so the K2 - K1 is the column count of the block X( K, L ) */
k1 = iwork[k];
k2 = iwork[k + 1];
for (l = nbb; l >= 1; --l) {
/* L1: column index of the first column in X( K, L ) */
/* L2: column index of the first column in X( K, L + 1) */
/* so that L2 - L1 is the row count of the block X( K, L ) */
l1 = iwork[pc + l];
l2 = iwork[pc + l + 1];
i__1 = k2 - k1;
i__2 = l2 - l1;
strsyl_(trana, tranb, isgn, &i__1, &i__2, &a[k1 + k1 * a_dim1]
, lda, &b[l1 + l1 * b_dim1], ldb, &c__[k1 + l1 *
c_dim1], ldc, &scaloc, &iinfo);
*info = f2cmax(*info,iinfo);
if (scaloc * swork[k + l * swork_dim1] == 0.f) {
if (scaloc == 0.f) {
/* The magnitude of the largest entry of X(K1:K2-1, L1:L2-1) */
/* is larger than the product of BIGNUM**2 and cannot be */
/* represented in the form (1/SCALE)*X(K1:K2-1, L1:L2-1). */
/* Mark the computation as pointless. */
buf = 0.f;
} else {
/* Use second scaling factor to prevent flushing to zero. */
i__1 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__1);
}
i__1 = nbb;
for (jj = 1; jj <= i__1; ++jj) {
i__2 = nba;
for (ll = 1; ll <= i__2; ++ll) {
/* Bound by BIGNUM to not introduce Inf. The value */
/* is irrelevant; corresponding entries of the */
/* solution will be flushed in consistency scaling. */
/* Computing MIN */
i__3 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj * swork_dim1]
/ pow_ri(&c_b19, &i__3);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
}
swork[k + l * swork_dim1] = scaloc * swork[k + l * swork_dim1]
;
i__1 = k2 - k1;
i__2 = l2 - l1;
xnrm = slange_("I", &i__1, &i__2, &c__[k1 + l1 * c_dim1], ldc,
wnrm);
i__1 = k - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/* C( I, L ) := C( I, L ) - A( I, K ) * C( K, L ) */
i1 = iwork[i__];
i2 = iwork[i__ + 1];
/* Compute scaling factor to survive the linear update */
/* simulating consistent scaling. */
i__2 = i2 - i1;
i__3 = l2 - l1;
cnrm = slange_("I", &i__2, &i__3, &c__[i1 + l1 * c_dim1],
ldc, wnrm);
/* Computing MIN */
r__1 = swork[i__ + l * swork_dim1], r__2 = swork[k + l *
swork_dim1];
scamin = f2cmin(r__1,r__2);
cnrm *= scamin / swork[i__ + l * swork_dim1];
xnrm *= scamin / swork[k + l * swork_dim1];
anrm = swork[i__ + (awrk + k) * swork_dim1];
scaloc = slarmm_(&anrm, &xnrm, &cnrm);
if (scaloc * scamin == 0.f) {
/* Use second scaling factor to prevent flushing to zero. */
i__2 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__2);
i__2 = nbb;
for (jj = 1; jj <= i__2; ++jj) {
i__3 = nba;
for (ll = 1; ll <= i__3; ++ll) {
/* Computing MIN */
i__4 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj *
swork_dim1] / pow_ri(&c_b19, &i__4);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
i__2 = myexp_(&scaloc);
scamin /= pow_ri(&c_b19, &i__2);
i__2 = myexp_(&scaloc);
scaloc /= pow_ri(&c_b19, &i__2);
}
cnrm *= scaloc;
xnrm *= scaloc;
/* Simultaneously apply the robust update factor and the */
/* consistency scaling factor to C( I, L ) and C( K, L ). */
scal = scamin / swork[k + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__2 = l2 - 1;
for (ll = l1; ll <= i__2; ++ll) {
i__3 = k2 - k1;
sscal_(&i__3, &scal, &c__[k1 + ll * c_dim1], &
c__1);
}
}
scal = scamin / swork[i__ + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__2 = l2 - 1;
for (ll = l1; ll <= i__2; ++ll) {
i__3 = i2 - i1;
sscal_(&i__3, &scal, &c__[i1 + ll * c_dim1], &
c__1);
}
}
/* Record current scaling factor */
swork[k + l * swork_dim1] = scamin * scaloc;
swork[i__ + l * swork_dim1] = scamin * scaloc;
i__2 = i2 - i1;
i__3 = l2 - l1;
i__4 = k2 - k1;
sgemm_("N", "N", &i__2, &i__3, &i__4, &c_b31, &a[i1 + k1 *
a_dim1], lda, &c__[k1 + l1 * c_dim1], ldc, &
c_b32, &c__[i1 + l1 * c_dim1], ldc);
}
i__1 = l - 1;
for (j = 1; j <= i__1; ++j) {
/* C( K, J ) := C( K, J ) - SGN * C( K, L ) * B( J, L )**T */
j1 = iwork[pc + j];
j2 = iwork[pc + j + 1];
/* Compute scaling factor to survive the linear update */
/* simulating consistent scaling. */
i__2 = k2 - k1;
i__3 = j2 - j1;
cnrm = slange_("I", &i__2, &i__3, &c__[k1 + j1 * c_dim1],
ldc, wnrm);
/* Computing MIN */
r__1 = swork[k + j * swork_dim1], r__2 = swork[k + l *
swork_dim1];
scamin = f2cmin(r__1,r__2);
cnrm *= scamin / swork[k + j * swork_dim1];
xnrm *= scamin / swork[k + l * swork_dim1];
bnrm = swork[l + (bwrk + j) * swork_dim1];
scaloc = slarmm_(&bnrm, &xnrm, &cnrm);
if (scaloc * scamin == 0.f) {
/* Use second scaling factor to prevent flushing to zero. */
i__2 = myexp_(&scaloc);
buf *= pow_ri(&c_b19, &i__2);
i__2 = nbb;
for (jj = 1; jj <= i__2; ++jj) {
i__3 = nba;
for (ll = 1; ll <= i__3; ++ll) {
/* Computing MIN */
i__4 = myexp_(&scaloc);
r__1 = bignum, r__2 = swork[ll + jj *
swork_dim1] / pow_ri(&c_b19, &i__4);
swork[ll + jj * swork_dim1] = f2cmin(r__1,r__2);
}
}
i__2 = myexp_(&scaloc);
scamin /= pow_ri(&c_b19, &i__2);
i__2 = myexp_(&scaloc);
scaloc /= pow_ri(&c_b19, &i__2);
}
cnrm *= scaloc;
xnrm *= scaloc;
/* Simultaneously apply the robust update factor and the */
/* consistency scaling factor to C( K, J ) and C( K, L ). */
scal = scamin / swork[k + l * swork_dim1] * scaloc;
if (scal != 1.f) {
i__2 = l2 - 1;
for (jj = l1; jj <= i__2; ++jj) {
i__3 = k2 - k1;
sscal_(&i__3, &scal, &c__[k1 + jj * c_dim1], &
c__1);
}
}
scal = scamin / swork[k + j * swork_dim1] * scaloc;
if (scal != 1.f) {
i__2 = j2 - 1;
for (jj = j1; jj <= i__2; ++jj) {
i__3 = k2 - k1;
sscal_(&i__3, &scal, &c__[k1 + jj * c_dim1], &
c__1);
}
}
/* Record current scaling factor */
swork[k + l * swork_dim1] = scamin * scaloc;
swork[k + j * swork_dim1] = scamin * scaloc;
i__2 = k2 - k1;
i__3 = j2 - j1;
i__4 = l2 - l1;
r__1 = -sgn;
sgemm_("N", "T", &i__2, &i__3, &i__4, &r__1, &c__[k1 + l1
* c_dim1], ldc, &b[j1 + l1 * b_dim1], ldb, &c_b32,
&c__[k1 + j1 * c_dim1], ldc);
}
}
}
}
free(wnrm);
/* Reduce local scaling factors */
*scale = swork[swork_dim1 + 1];
i__1 = nba;
for (k = 1; k <= i__1; ++k) {
i__2 = nbb;
for (l = 1; l <= i__2; ++l) {
/* Computing MIN */
r__1 = *scale, r__2 = swork[k + l * swork_dim1];
*scale = f2cmin(r__1,r__2);
}
}
if (*scale == 0.f) {
/* The magnitude of the largest entry of the solution is larger */
/* than the product of BIGNUM**2 and cannot be represented in the */
/* form (1/SCALE)*X if SCALE is REAL. Set SCALE to zero and give up. */
iwork[1] = nba + nbb + 2;
swork[swork_dim1 + 1] = (real) f2cmax(nba,nbb);
swork[swork_dim1 + 2] = (real) ((nbb << 1) + nba);
return;
}
/* Realize consistent scaling */
i__1 = nba;
for (k = 1; k <= i__1; ++k) {
k1 = iwork[k];
k2 = iwork[k + 1];
i__2 = nbb;
for (l = 1; l <= i__2; ++l) {
l1 = iwork[pc + l];
l2 = iwork[pc + l + 1];
scal = *scale / swork[k + l * swork_dim1];
if (scal != 1.f) {
i__3 = l2 - 1;
for (ll = l1; ll <= i__3; ++ll) {
i__4 = k2 - k1;
sscal_(&i__4, &scal, &c__[k1 + ll * c_dim1], &c__1);
}
}
}
}
if (buf != 1.f && buf > 0.f) {
/* Decrease SCALE as much as possible. */
/* Computing MIN */
r__1 = *scale / smlnum, r__2 = 1.f / buf;
scaloc = f2cmin(r__1,r__2);
buf *= scaloc;
*scale /= scaloc;
}
if (buf != 1.f && buf > 0.f) {
/* In case of overly aggressive scaling during the computation, */
/* flushing of the global scale factor may be prevented by */
/* undoing some of the scaling. This step is to ensure that */
/* this routine flushes only scale factors that TRSYL also */
/* flushes and be usable as a drop-in replacement. */
/* How much can the normwise largest entry be upscaled? */
scal = c__[c_dim1 + 1];
i__1 = *m;
for (k = 1; k <= i__1; ++k) {
i__2 = *n;
for (l = 1; l <= i__2; ++l) {
/* Computing MAX */
r__2 = scal, r__3 = (r__1 = c__[k + l * c_dim1], abs(r__1));
scal = f2cmax(r__2,r__3);
}
}
/* Increase BUF as close to 1 as possible and apply scaling. */
/* Computing MIN */
r__1 = bignum / scal, r__2 = 1.f / buf;
scaloc = f2cmin(r__1,r__2);
buf *= scaloc;
slascl_("G", &c_n1, &c_n1, &c_b32, &scaloc, m, n, &c__[c_offset], ldc,
&iwork[1]);
}
/* Combine with buffer scaling factor. SCALE will be flushed if */
/* BUF is less than one here. */
*scale *= buf;
/* Restore workspace dimensions */
iwork[1] = nba + nbb + 2;
swork[swork_dim1 + 1] = (real) f2cmax(nba,nbb);
swork[swork_dim1 + 2] = (real) ((nbb << 1) + nba);
return;
/* End of STRSYL3 */
} /* strsyl3_ */
Reference in New Issue View Git Blame Copy Permalink