#include #include #include #include #include #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(double *x) {int e; (void)frexp(*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 \brief \b DTRSYL3 */ /* Definition: */ /* =========== */ /* > \par Purpose */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DTRSYL3 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 DHSEQR), 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION */ /* > 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 DOUBLE PRECISION 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 dtrsyl3_(char *trana, char *tranb, integer *isgn, integer *m, integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *c__, integer *ldc, doublereal *scale, integer *iwork, integer *liwork, doublereal *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; doublereal d__1, d__2, d__3; /* Local variables */ doublereal scal, anrm, bnrm, cnrm; integer awrk, bwrk; logical skip; doublereal *wnrm, xnrm; integer i__, j, k, l; extern /* Subroutine */ void dscal_(integer *, doublereal *, doublereal *, integer *), dgemm_(char *, char *, integer *, integer *, integer * , doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); integer iinfo, i1, i2, j1, j2, k1, k2, l1; // extern integer myexp_(doublereal *); integer l2, nb, pc, jj, ll; extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); extern /* Subroutine */ void dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); doublereal scaloc, scamin; extern doublereal dlarmm_(doublereal *, doublereal *, doublereal *); extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen ); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); doublereal bignum; logical notrna, notrnb; doublereal smlnum; logical lquery; extern /* Subroutine */ void dtrsyl_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *); integer nba, nbb; doublereal 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, "DTRSYL", "", 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] = (doublereal) f2cmax(nba,nbb); swork[swork_dim1 + 2] = (doublereal) ((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; } if (*info != 0) { i__1 = -(*info); xerbla_("DTRSYL3", &i__1, 7); return; } else if (lquery) { return; } /* Quick return if possible */ *scale = 1.; if (*m == 0 || *n == 0) { return; } wnrm = (doublereal*)malloc(f2cmax(*m,*n)*sizeof(doublereal)); /* Use unblocked code for small problems or if insufficient */ /* workspaces are provided */ if (f2cmin(nba,nbb) == 1 || *ldswork < f2cmax(nba,nbb) || *liwork < iwork[1]) { dtrsyl_(trana, tranb, isgn, m, n, &a[a_offset], lda, &b[b_offset], ldb, &c__[c_offset], ldc, scale, info); return; } /* Set constants to control overflow */ smlnum = dlamch_("S"); bignum = 1. / 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. && a[l + 1 + l * a_dim1] != 0.) { /* 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. && b[l + 1 + l * b_dim1] != 0.) { /* 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.; } } /* 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.; /* 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] = dlange_("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] = dlange_("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] = dlange_("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] = dlange_("1", &i__3, & i__4, &b[k1 + l1 * b_dim1], ldb, wnrm); } } } sgn = (doublereal) (*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; dtrsyl_(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.) { if (scaloc == 0.) { /* 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.; } else { /* Use second scaling factor to prevent flushing to zero. */ i__2 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__4); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } } swork[k + l * swork_dim1] = scaloc * swork[k + l * swork_dim1] ; i__2 = k2 - k1; i__3 = l2 - l1; xnrm = dlange_("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 = dlange_("I", &i__2, &i__3, &c__[i1 + l1 * c_dim1], ldc, wnrm); /* Computing MIN */ d__1 = swork[i__ + l * swork_dim1], d__2 = swork[k + l * swork_dim1]; scamin = f2cmin(d__1,d__2); cnrm *= scamin / swork[i__ + l * swork_dim1]; xnrm *= scamin / swork[k + l * swork_dim1]; anrm = swork[i__ + (awrk + k) * swork_dim1]; scaloc = dlarmm_(&anrm, &xnrm, &cnrm); if (scaloc * scamin == 0.) { /* Use second scaling factor to prevent flushing to zero. */ i__2 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__4); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } i__2 = myexp_(&scaloc); scamin /= pow_di(&c_b19, &i__2); i__2 = myexp_(&scaloc); scaloc /= pow_di(&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.) { i__2 = l2 - 1; for (jj = l1; jj <= i__2; ++jj) { i__3 = k2 - k1; dscal_(&i__3, &scal, &c__[k1 + jj * c_dim1], & c__1); } } scal = scamin / swork[i__ + l * swork_dim1] * scaloc; if (scal != 1.) { i__2 = l2 - 1; for (ll = l1; ll <= i__2; ++ll) { i__3 = i2 - i1; dscal_(&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; dgemm_("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 = dlange_("I", &i__3, &i__4, &c__[k1 + j1 * c_dim1], ldc, wnrm); /* Computing MIN */ d__1 = swork[k + j * swork_dim1], d__2 = swork[k + l * swork_dim1]; scamin = f2cmin(d__1,d__2); cnrm *= scamin / swork[k + j * swork_dim1]; xnrm *= scamin / swork[k + l * swork_dim1]; bnrm = swork[l + (bwrk + j) * swork_dim1]; scaloc = dlarmm_(&bnrm, &xnrm, &cnrm); if (scaloc * scamin == 0.) { /* Use second scaling factor to prevent flushing to zero. */ i__3 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__5); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } i__3 = myexp_(&scaloc); scamin /= pow_di(&c_b19, &i__3); i__3 = myexp_(&scaloc); scaloc /= pow_di(&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.) { i__3 = l2 - 1; for (ll = l1; ll <= i__3; ++ll) { i__4 = k2 - k1; dscal_(&i__4, &scal, &c__[k1 + ll * c_dim1], & c__1); } } scal = scamin / swork[k + j * swork_dim1] * scaloc; if (scal != 1.) { i__3 = j2 - 1; for (jj = j1; jj <= i__3; ++jj) { i__4 = k2 - k1; dscal_(&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; d__1 = -sgn; dgemm_("N", "N", &i__3, &i__4, &i__5, &d__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; dtrsyl_(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.) { if (scaloc == 0.) { /* 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.; } else { /* Use second scaling factor to prevent flushing to zero. */ i__3 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__5); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } } swork[k + l * swork_dim1] = scaloc * swork[k + l * swork_dim1] ; i__3 = k2 - k1; i__4 = l2 - l1; xnrm = dlange_("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 = dlange_("I", &i__4, &i__5, &c__[i1 + l1 * c_dim1], ldc, wnrm); /* Computing MIN */ d__1 = swork[i__ + l * swork_dim1], d__2 = swork[k + l * swork_dim1]; scamin = f2cmin(d__1,d__2); cnrm *= scamin / swork[i__ + l * swork_dim1]; xnrm *= scamin / swork[k + l * swork_dim1]; anrm = swork[i__ + (awrk + k) * swork_dim1]; scaloc = dlarmm_(&anrm, &xnrm, &cnrm); if (scaloc * scamin == 0.) { /* Use second scaling factor to prevent flushing to zero. */ i__4 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__6); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } i__4 = myexp_(&scaloc); scamin /= pow_di(&c_b19, &i__4); i__4 = myexp_(&scaloc); scaloc /= pow_di(&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.) { i__4 = l2 - 1; for (ll = l1; ll <= i__4; ++ll) { i__5 = k2 - k1; dscal_(&i__5, &scal, &c__[k1 + ll * c_dim1], & c__1); } } scal = scamin / swork[i__ + l * swork_dim1] * scaloc; if (scal != 1.) { i__4 = l2 - 1; for (ll = l1; ll <= i__4; ++ll) { i__5 = i2 - i1; dscal_(&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; dgemm_("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 = dlange_("I", &i__4, &i__5, &c__[k1 + j1 * c_dim1], ldc, wnrm); /* Computing MIN */ d__1 = swork[k + j * swork_dim1], d__2 = swork[k + l * swork_dim1]; scamin = f2cmin(d__1,d__2); cnrm *= scamin / swork[k + j * swork_dim1]; xnrm *= scamin / swork[k + l * swork_dim1]; bnrm = swork[l + (bwrk + j) * swork_dim1]; scaloc = dlarmm_(&bnrm, &xnrm, &cnrm); if (scaloc * scamin == 0.) { /* Use second scaling factor to prevent flushing to zero. */ i__4 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__6); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } i__4 = myexp_(&scaloc); scamin /= pow_di(&c_b19, &i__4); i__4 = myexp_(&scaloc); scaloc /= pow_di(&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.) { i__4 = l2 - 1; for (ll = l1; ll <= i__4; ++ll) { i__5 = k2 - k1; dscal_(&i__5, &scal, &c__[k1 + ll * c_dim1], & c__1); } } scal = scamin / swork[k + j * swork_dim1] * scaloc; if (scal != 1.) { i__4 = j2 - 1; for (jj = j1; jj <= i__4; ++jj) { i__5 = k2 - k1; dscal_(&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; d__1 = -sgn; dgemm_("N", "N", &i__4, &i__5, &i__6, &d__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; dtrsyl_(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); swork[k + l * swork_dim1] = scaloc * swork[k + l * swork_dim1] ; if (scaloc * swork[k + l * swork_dim1] == 0.) { if (scaloc == 0.) { /* 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.; } else { /* Use second scaling factor to prevent flushing to zero. */ i__2 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__4); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } } i__2 = k2 - k1; i__3 = l2 - l1; xnrm = dlange_("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 = dlange_("I", &i__3, &i__4, &c__[i1 + l1 * c_dim1], ldc, wnrm); /* Computing MIN */ d__1 = swork[i__ + l * swork_dim1], d__2 = swork[k + l * swork_dim1]; scamin = f2cmin(d__1,d__2); cnrm *= scamin / swork[i__ + l * swork_dim1]; xnrm *= scamin / swork[k + l * swork_dim1]; anrm = swork[i__ + (awrk + k) * swork_dim1]; scaloc = dlarmm_(&anrm, &xnrm, &cnrm); if (scaloc * scamin == 0.) { /* Use second scaling factor to prevent flushing to zero. */ i__3 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__5); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } i__3 = myexp_(&scaloc); scamin /= pow_di(&c_b19, &i__3); i__3 = myexp_(&scaloc); scaloc /= pow_di(&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.) { i__3 = l2 - 1; for (ll = l1; ll <= i__3; ++ll) { i__4 = k2 - k1; dscal_(&i__4, &scal, &c__[k1 + ll * c_dim1], & c__1); } } scal = scamin / swork[i__ + l * swork_dim1] * scaloc; if (scal != 1.) { i__3 = l2 - 1; for (ll = l1; ll <= i__3; ++ll) { i__4 = i2 - i1; dscal_(&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; dgemm_("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 = dlange_("I", &i__3, &i__4, &c__[k1 + j1 * c_dim1], ldc, wnrm); /* Computing MIN */ d__1 = swork[k + j * swork_dim1], d__2 = swork[k + l * swork_dim1]; scamin = f2cmin(d__1,d__2); cnrm *= scamin / swork[k + j * swork_dim1]; xnrm *= scamin / swork[k + l * swork_dim1]; bnrm = swork[l + (bwrk + j) * swork_dim1]; scaloc = dlarmm_(&bnrm, &xnrm, &cnrm); if (scaloc * scamin == 0.) { /* Use second scaling factor to prevent flushing to zero. */ i__3 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__5); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } i__3 = myexp_(&scaloc); scamin /= pow_di(&c_b19, &i__3); i__3 = myexp_(&scaloc); scaloc /= pow_di(&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.) { i__3 = l2 - 1; for (ll = l1; ll <= i__3; ++ll) { i__4 = k2 - k1; dscal_(&i__4, &scal, &c__[k1 + ll * c_dim1], & c__1); } } scal = scamin / swork[k + j * swork_dim1] * scaloc; if (scal != 1.) { i__3 = j2 - 1; for (jj = j1; jj <= i__3; ++jj) { i__4 = k2 - k1; dscal_(&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; d__1 = -sgn; dgemm_("N", "T", &i__3, &i__4, &i__5, &d__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; dtrsyl_(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.) { if (scaloc == 0.) { /* 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.; } else { /* Use second scaling factor to prevent flushing to zero. */ i__1 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__3); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } } swork[k + l * swork_dim1] = scaloc * swork[k + l * swork_dim1] ; i__1 = k2 - k1; i__2 = l2 - l1; xnrm = dlange_("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 = dlange_("I", &i__2, &i__3, &c__[i1 + l1 * c_dim1], ldc, wnrm); /* Computing MIN */ d__1 = swork[i__ + l * swork_dim1], d__2 = swork[k + l * swork_dim1]; scamin = f2cmin(d__1,d__2); cnrm *= scamin / swork[i__ + l * swork_dim1]; xnrm *= scamin / swork[k + l * swork_dim1]; anrm = swork[i__ + (awrk + k) * swork_dim1]; scaloc = dlarmm_(&anrm, &xnrm, &cnrm); if (scaloc * scamin == 0.) { /* Use second scaling factor to prevent flushing to zero. */ i__2 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__4); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } i__2 = myexp_(&scaloc); scamin /= pow_di(&c_b19, &i__2); i__2 = myexp_(&scaloc); scaloc /= pow_di(&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.) { i__2 = l2 - 1; for (ll = l1; ll <= i__2; ++ll) { i__3 = k2 - k1; dscal_(&i__3, &scal, &c__[k1 + ll * c_dim1], & c__1); } } scal = scamin / swork[i__ + l * swork_dim1] * scaloc; if (scal != 1.) { i__2 = l2 - 1; for (ll = l1; ll <= i__2; ++ll) { i__3 = i2 - i1; dscal_(&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; dgemm_("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 = dlange_("I", &i__2, &i__3, &c__[k1 + j1 * c_dim1], ldc, wnrm); /* Computing MIN */ d__1 = swork[k + j * swork_dim1], d__2 = swork[k + l * swork_dim1]; scamin = f2cmin(d__1,d__2); cnrm *= scamin / swork[k + j * swork_dim1]; xnrm *= scamin / swork[k + l * swork_dim1]; bnrm = swork[l + (bwrk + j) * swork_dim1]; scaloc = dlarmm_(&bnrm, &xnrm, &cnrm); if (scaloc * scamin == 0.) { /* Use second scaling factor to prevent flushing to zero. */ i__2 = myexp_(&scaloc); buf *= pow_di(&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); d__1 = bignum, d__2 = swork[ll + jj * swork_dim1] / pow_di(&c_b19, &i__4); swork[ll + jj * swork_dim1] = f2cmin(d__1,d__2); } } i__2 = myexp_(&scaloc); scamin /= pow_di(&c_b19, &i__2); i__2 = myexp_(&scaloc); scaloc /= pow_di(&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.) { i__2 = l2 - 1; for (jj = l1; jj <= i__2; ++jj) { i__3 = k2 - k1; dscal_(&i__3, &scal, &c__[k1 + jj * c_dim1], & c__1); } } scal = scamin / swork[k + j * swork_dim1] * scaloc; if (scal != 1.) { i__2 = j2 - 1; for (jj = j1; jj <= i__2; ++jj) { i__3 = k2 - k1; dscal_(&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; d__1 = -sgn; dgemm_("N", "T", &i__2, &i__3, &i__4, &d__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 */ d__1 = *scale, d__2 = swork[k + l * swork_dim1]; *scale = f2cmin(d__1,d__2); } } if (*scale == 0.) { /* 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 DOUBLE PRECISION. Set SCALE to */ /* zero and give up. */ iwork[1] = nba + nbb + 2; swork[swork_dim1 + 1] = (doublereal) f2cmax(nba,nbb); swork[swork_dim1 + 2] = (doublereal) ((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.) { i__3 = l2 - 1; for (ll = l1; ll <= i__3; ++ll) { i__4 = k2 - k1; dscal_(&i__4, &scal, &c__[k1 + ll * c_dim1], &c__1); } } } } if (buf != 1. && buf > 0.) { /* Decrease SCALE as much as possible. */ /* Computing MIN */ d__1 = *scale / smlnum, d__2 = 1. / buf; scaloc = f2cmin(d__1,d__2); buf *= scaloc; *scale /= scaloc; } if (buf != 1. && buf > 0.) { /* 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 */ d__2 = scal, d__3 = (d__1 = c__[k + l * c_dim1], abs(d__1)); scal = f2cmax(d__2,d__3); } } /* Increase BUF as close to 1 as possible and apply scaling. */ /* Computing MIN */ d__1 = bignum / scal, d__2 = 1. / buf; scaloc = f2cmin(d__1,d__2); buf *= scaloc; dlascl_("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] = (doublereal) f2cmax(nba,nbb); swork[swork_dim1 + 2] = (doublereal) ((nbb << 1) + nba); return; /* End of DTRSYL3 */ } /* dtrsyl3_ */