#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 int logical; typedef short int shortlogical; typedef char logical1; typedef char integer1; #define TRUE_ (1) #define FALSE_ (0) /* Extern is for use with -E */ #ifndef Extern #define Extern extern #endif /* I/O stuff */ typedef int flag; typedef int ftnlen; typedef int ftnint; /*external read, write*/ typedef struct { flag cierr; ftnint ciunit; flag ciend; char *cifmt; ftnint cirec; } cilist; /*internal read, write*/ typedef struct { flag icierr; char *iciunit; flag iciend; char *icifmt; ftnint icirlen; ftnint icirnum; } icilist; /*open*/ typedef struct { flag oerr; ftnint ounit; char *ofnm; ftnlen ofnmlen; char *osta; char *oacc; char *ofm; ftnint orl; char *oblnk; } olist; /*close*/ typedef struct { flag cerr; ftnint cunit; char *csta; } cllist; /*rewind, backspace, endfile*/ typedef struct { flag aerr; ftnint aunit; } alist; /* inquire */ typedef struct { flag inerr; ftnint inunit; char *infile; ftnlen infilen; ftnint *inex; /*parameters in standard's order*/ ftnint *inopen; ftnint *innum; ftnint *innamed; char *inname; ftnlen innamlen; char *inacc; ftnlen inacclen; char *inseq; ftnlen inseqlen; char *indir; ftnlen indirlen; char *infmt; ftnlen infmtlen; char *inform; ftnint informlen; char *inunf; ftnlen inunflen; ftnint *inrecl; ftnint *innrec; char *inblank; ftnlen inblanklen; } inlist; #define VOID void union Multitype { /* for multiple entry points */ integer1 g; shortint h; integer i; /* longint j; */ real r; doublereal d; complex c; doublecomplex z; }; typedef union Multitype Multitype; struct Vardesc { /* for Namelist */ char *name; char *addr; ftnlen *dims; int type; }; typedef struct Vardesc Vardesc; struct Namelist { char *name; Vardesc **vars; int nvars; }; typedef struct Namelist Namelist; #define abs(x) ((x) >= 0 ? (x) : -(x)) #define dabs(x) (fabs(x)) #define f2cmin(a,b) ((a) <= (b) ? (a) : (b)) #define f2cmax(a,b) ((a) >= (b) ? (a) : (b)) #define dmin(a,b) (f2cmin(a,b)) #define dmax(a,b) (f2cmax(a,b)) #define bit_test(a,b) ((a) >> (b) & 1) #define bit_clear(a,b) ((a) & ~((uinteger)1 << (b))) #define bit_set(a,b) ((a) | ((uinteger)1 << (b))) #define abort_() { sig_die("Fortran abort routine called", 1); } #define c_abs(z) (cabsf(Cf(z))) #define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); } #ifdef _MSC_VER #define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);} #define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);} #else #define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);} #define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);} #endif #define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));} #define c_log(R, Z) {pCf(R) = clogf(Cf(Z));} #define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));} //#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));} #define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));} #define d_abs(x) (fabs(*(x))) #define d_acos(x) (acos(*(x))) #define d_asin(x) (asin(*(x))) #define d_atan(x) (atan(*(x))) #define d_atn2(x, y) (atan2(*(x),*(y))) #define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); } #define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); } #define d_cos(x) (cos(*(x))) #define d_cosh(x) (cosh(*(x))) #define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 ) #define d_exp(x) (exp(*(x))) #define d_imag(z) (cimag(Cd(z))) #define r_imag(z) (cimagf(Cf(z))) #define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x))) #define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) ) #define d_log(x) (log(*(x))) #define d_mod(x, y) (fmod(*(x), *(y))) #define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x))) #define d_nint(x) u_nint(*(x)) #define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a))) #define d_sign(a,b) u_sign(*(a),*(b)) #define r_sign(a,b) u_sign(*(a),*(b)) #define d_sin(x) (sin(*(x))) #define d_sinh(x) (sinh(*(x))) #define d_sqrt(x) (sqrt(*(x))) #define d_tan(x) (tan(*(x))) #define d_tanh(x) (tanh(*(x))) #define i_abs(x) abs(*(x)) #define i_dnnt(x) ((integer)u_nint(*(x))) #define i_len(s, n) (n) #define i_nint(x) ((integer)u_nint(*(x))) #define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b))) #define pow_dd(ap, bp) ( pow(*(ap), *(bp))) #define pow_si(B,E) spow_ui(*(B),*(E)) #define pow_ri(B,E) spow_ui(*(B),*(E)) #define pow_di(B,E) dpow_ui(*(B),*(E)) #define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));} #define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));} #define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));} #define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; } #define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d)))) #define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; } #define sig_die(s, kill) { exit(1); } #define s_stop(s, n) {exit(0);} static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n"; #define z_abs(z) (cabs(Cd(z))) #define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));} #define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));} #define myexit_() break; #define mycycle() continue; #define myceiling(w) {ceil(w)} #define myhuge(w) {HUGE_VAL} //#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);} #define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)} /* procedure parameter types for -A and -C++ */ #define F2C_proc_par_types 1 #ifdef __cplusplus typedef logical (*L_fp)(...); #else typedef logical (*L_fp)(); #endif static float spow_ui(float x, integer n) { float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static double dpow_ui(double x, integer n) { double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #ifdef _MSC_VER static _Fcomplex cpow_ui(complex x, integer n) { complex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i; for(u = n; ; ) { if(u & 01) pow.r *= x.r, pow.i *= x.i; if(u >>= 1) x.r *= x.r, x.i *= x.i; else break; } } _Fcomplex p={pow.r, pow.i}; return p; } #else static _Complex float cpow_ui(_Complex float x, integer n) { _Complex float pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif #ifdef _MSC_VER static _Dcomplex zpow_ui(_Dcomplex x, integer n) { _Dcomplex pow={1.0,0.0}; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1]; for(u = n; ; ) { if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1]; if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1]; else break; } } _Dcomplex p = {pow._Val[0], pow._Val[1]}; return p; } #else static _Complex double zpow_ui(_Complex double x, integer n) { _Complex double pow=1.0; unsigned long int u; if(n != 0) { if(n < 0) n = -n, x = 1/x; for(u = n; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } #endif static integer pow_ii(integer x, integer n) { integer pow; unsigned long int u; if (n <= 0) { if (n == 0 || x == 1) pow = 1; else if (x != -1) pow = x == 0 ? 1/x : 0; else n = -n; } if ((n > 0) || !(n == 0 || x == 1 || x != -1)) { u = n; for(pow = 1; ; ) { if(u & 01) pow *= x; if(u >>= 1) x *= x; else break; } } return pow; } static integer dmaxloc_(double *w, integer s, integer e, integer *n) { double m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static integer smaxloc_(float *w, integer s, integer e, integer *n) { float m; integer i, mi; for(m=w[s-1], mi=s, i=s+1; i<=e; i++) if (w[i-1]>m) mi=i ,m=w[i-1]; return mi-s+1; } static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) { integer n = *n_, incx = *incx_, incy = *incy_, i; #ifdef _MSC_VER _Fcomplex zdotc = {0.0, 0.0}; if (incx == 1 && incy == 1) { for (i=0;i \brief \b CTGSYL */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download CTGSYL + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE CTGSYL( TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, */ /* LDD, E, LDE, F, LDF, SCALE, DIF, WORK, LWORK, */ /* IWORK, INFO ) */ /* CHARACTER TRANS */ /* INTEGER IJOB, INFO, LDA, LDB, LDC, LDD, LDE, LDF, */ /* $ LWORK, M, N */ /* REAL DIF, SCALE */ /* INTEGER IWORK( * ) */ /* COMPLEX A( LDA, * ), B( LDB, * ), C( LDC, * ), */ /* $ D( LDD, * ), E( LDE, * ), F( LDF, * ), */ /* $ WORK( * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > CTGSYL solves the generalized Sylvester equation: */ /* > */ /* > A * R - L * B = scale * C (1) */ /* > D * R - L * E = scale * F */ /* > */ /* > where R and L are unknown m-by-n matrices, (A, D), (B, E) and */ /* > (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n, */ /* > respectively, with complex entries. A, B, D and E are upper */ /* > triangular (i.e., (A,D) and (B,E) in generalized Schur form). */ /* > */ /* > The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 */ /* > is an output scaling factor chosen to avoid overflow. */ /* > */ /* > In matrix notation (1) is equivalent to solve Zx = scale*b, where Z */ /* > is defined as */ /* > */ /* > Z = [ kron(In, A) -kron(B**H, Im) ] (2) */ /* > [ kron(In, D) -kron(E**H, Im) ], */ /* > */ /* > Here Ix is the identity matrix of size x and X**H is the conjugate */ /* > transpose of X. Kron(X, Y) is the Kronecker product between the */ /* > matrices X and Y. */ /* > */ /* > If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b */ /* > is solved for, which is equivalent to solve for R and L in */ /* > */ /* > A**H * R + D**H * L = scale * C (3) */ /* > R * B**H + L * E**H = scale * -F */ /* > */ /* > This case (TRANS = 'C') is used to compute an one-norm-based estimate */ /* > of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D) */ /* > and (B,E), using CLACON. */ /* > */ /* > If IJOB >= 1, CTGSYL computes a Frobenius norm-based estimate of */ /* > Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the */ /* > reciprocal of the smallest singular value of Z. */ /* > */ /* > This is a level-3 BLAS algorithm. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] TRANS */ /* > \verbatim */ /* > TRANS is CHARACTER*1 */ /* > = 'N': solve the generalized sylvester equation (1). */ /* > = 'C': solve the "conjugate transposed" system (3). */ /* > \endverbatim */ /* > */ /* > \param[in] IJOB */ /* > \verbatim */ /* > IJOB is INTEGER */ /* > Specifies what kind of functionality to be performed. */ /* > =0: solve (1) only. */ /* > =1: The functionality of 0 and 3. */ /* > =2: The functionality of 0 and 4. */ /* > =3: Only an estimate of Dif[(A,D), (B,E)] is computed. */ /* > (look ahead strategy is used). */ /* > =4: Only an estimate of Dif[(A,D), (B,E)] is computed. */ /* > (CGECON on sub-systems is used). */ /* > Not referenced if TRANS = 'C'. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > The order of the matrices A and D, and the row dimension of */ /* > the matrices C, F, R and L. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > The order of the matrices B and E, and the column dimension */ /* > of the matrices C, F, R and L. */ /* > \endverbatim */ /* > */ /* > \param[in] A */ /* > \verbatim */ /* > A is COMPLEX array, dimension (LDA, M) */ /* > The upper triangular matrix A. */ /* > \endverbatim */ /* > */ /* > \param[in] LDA */ /* > \verbatim */ /* > LDA is INTEGER */ /* > The leading dimension of the array A. LDA >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] B */ /* > \verbatim */ /* > B is COMPLEX array, dimension (LDB, N) */ /* > The upper triangular matrix B. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > The leading dimension of the array B. LDB >= f2cmax(1, N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] C */ /* > \verbatim */ /* > C is COMPLEX array, dimension (LDC, N) */ /* > On entry, C contains the right-hand-side of the first matrix */ /* > equation in (1) or (3). */ /* > On exit, if IJOB = 0, 1 or 2, C has been overwritten by */ /* > the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R, */ /* > the solution achieved during the computation of the */ /* > Dif-estimate. */ /* > \endverbatim */ /* > */ /* > \param[in] LDC */ /* > \verbatim */ /* > LDC is INTEGER */ /* > The leading dimension of the array C. LDC >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] D */ /* > \verbatim */ /* > D is COMPLEX array, dimension (LDD, M) */ /* > The upper triangular matrix D. */ /* > \endverbatim */ /* > */ /* > \param[in] LDD */ /* > \verbatim */ /* > LDD is INTEGER */ /* > The leading dimension of the array D. LDD >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[in] E */ /* > \verbatim */ /* > E is COMPLEX array, dimension (LDE, N) */ /* > The upper triangular matrix E. */ /* > \endverbatim */ /* > */ /* > \param[in] LDE */ /* > \verbatim */ /* > LDE is INTEGER */ /* > The leading dimension of the array E. LDE >= f2cmax(1, N). */ /* > \endverbatim */ /* > */ /* > \param[in,out] F */ /* > \verbatim */ /* > F is COMPLEX array, dimension (LDF, N) */ /* > On entry, F contains the right-hand-side of the second matrix */ /* > equation in (1) or (3). */ /* > On exit, if IJOB = 0, 1 or 2, F has been overwritten by */ /* > the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L, */ /* > the solution achieved during the computation of the */ /* > Dif-estimate. */ /* > \endverbatim */ /* > */ /* > \param[in] LDF */ /* > \verbatim */ /* > LDF is INTEGER */ /* > The leading dimension of the array F. LDF >= f2cmax(1, M). */ /* > \endverbatim */ /* > */ /* > \param[out] DIF */ /* > \verbatim */ /* > DIF is REAL */ /* > On exit DIF is the reciprocal of a lower bound of the */ /* > reciprocal of the Dif-function, i.e. DIF is an upper bound of */ /* > Dif[(A,D), (B,E)] = sigma-f2cmin(Z), where Z as in (2). */ /* > IF IJOB = 0 or TRANS = 'C', DIF is not referenced. */ /* > \endverbatim */ /* > */ /* > \param[out] SCALE */ /* > \verbatim */ /* > SCALE is REAL */ /* > On exit SCALE is the scaling factor in (1) or (3). */ /* > If 0 < SCALE < 1, C and F hold the solutions R and L, resp., */ /* > to a slightly perturbed system but the input matrices A, B, */ /* > D and E have not been changed. If SCALE = 0, R and L will */ /* > hold the solutions to the homogenious system with C = F = 0. */ /* > \endverbatim */ /* > */ /* > \param[out] WORK */ /* > \verbatim */ /* > WORK is COMPLEX array, dimension (MAX(1,LWORK)) */ /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* > \endverbatim */ /* > */ /* > \param[in] LWORK */ /* > \verbatim */ /* > LWORK is INTEGER */ /* > The dimension of the array WORK. LWORK > = 1. */ /* > If IJOB = 1 or 2 and TRANS = 'N', LWORK >= f2cmax(1,2*M*N). */ /* > */ /* > If LWORK = -1, then a workspace query is assumed; the routine */ /* > only calculates the optimal size of the WORK array, returns */ /* > this value as the first entry of the WORK array, and no error */ /* > message related to LWORK is issued by XERBLA. */ /* > \endverbatim */ /* > */ /* > \param[out] IWORK */ /* > \verbatim */ /* > IWORK is INTEGER array, dimension (M+N+2) */ /* > \endverbatim */ /* > */ /* > \param[out] INFO */ /* > \verbatim */ /* > INFO is INTEGER */ /* > =0: successful exit */ /* > <0: If INFO = -i, the i-th argument had an illegal value. */ /* > >0: (A, D) and (B, E) have common or very close */ /* > eigenvalues. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup complexSYcomputational */ /* > \par Contributors: */ /* ================== */ /* > */ /* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */ /* > Umea University, S-901 87 Umea, Sweden. */ /* > \par References: */ /* ================ */ /* > */ /* > [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */ /* > for Solving the Generalized Sylvester Equation and Estimating the */ /* > Separation between Regular Matrix Pairs, Report UMINF - 93.23, */ /* > Department of Computing Science, Umea University, S-901 87 Umea, */ /* > Sweden, December 1993, Revised April 1994, Also as LAPACK Working */ /* > Note 75. To appear in ACM Trans. on Math. Software, Vol 22, */ /* > No 1, 1996. */ /* > \n */ /* > [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester */ /* > Equation (AR - LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. */ /* > Appl., 15(4):1045-1060, 1994. */ /* > \n */ /* > [3] B. Kagstrom and L. Westin, Generalized Schur Methods with */ /* > Condition Estimators for Solving the Generalized Sylvester */ /* > Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7, */ /* > July 1989, pp 745-751. */ /* > */ /* ===================================================================== */ /* Subroutine */ int ctgsyl_(char *trans, integer *ijob, integer *m, integer * n, complex *a, integer *lda, complex *b, integer *ldb, complex *c__, integer *ldc, complex *d__, integer *ldd, complex *e, integer *lde, complex *f, integer *ldf, real *scale, real *dif, complex *work, integer *lwork, integer *iwork, integer *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, d_dim1, d_offset, e_dim1, e_offset, f_dim1, f_offset, i__1, i__2, i__3, i__4; complex q__1; /* Local variables */ real dsum; integer i__, j, k, p, q; extern /* Subroutine */ int cscal_(integer *, complex *, complex *, integer *), cgemm_(char *, char *, integer *, integer *, integer * , complex *, complex *, integer *, complex *, integer *, complex * , complex *, integer *); extern logical lsame_(char *, char *); integer ifunc, linfo, lwmin; real scale2; extern /* Subroutine */ int ctgsy2_(char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, real *, integer *); integer ie, je, mb, nb; real dscale; integer is, js, pq; real scaloc; extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *, ftnlen); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); integer iround; logical notran; integer isolve; logical lquery; /* -- LAPACK computational routine (version 3.7.0) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* December 2016 */ /* ===================================================================== */ /* Replaced various illegal calls to CCOPY by calls to CLASET. */ /* Sven Hammarling, 1/5/02. */ /* Decode and test input parameters */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; c_dim1 = *ldc; c_offset = 1 + c_dim1 * 1; c__ -= c_offset; d_dim1 = *ldd; d_offset = 1 + d_dim1 * 1; d__ -= d_offset; e_dim1 = *lde; e_offset = 1 + e_dim1 * 1; e -= e_offset; f_dim1 = *ldf; f_offset = 1 + f_dim1 * 1; f -= f_offset; --work; --iwork; /* Function Body */ *info = 0; notran = lsame_(trans, "N"); lquery = *lwork == -1; if (! notran && ! lsame_(trans, "C")) { *info = -1; } else if (notran) { if (*ijob < 0 || *ijob > 4) { *info = -2; } } if (*info == 0) { if (*m <= 0) { *info = -3; } else if (*n <= 0) { *info = -4; } else if (*lda < f2cmax(1,*m)) { *info = -6; } else if (*ldb < f2cmax(1,*n)) { *info = -8; } else if (*ldc < f2cmax(1,*m)) { *info = -10; } else if (*ldd < f2cmax(1,*m)) { *info = -12; } else if (*lde < f2cmax(1,*n)) { *info = -14; } else if (*ldf < f2cmax(1,*m)) { *info = -16; } } if (*info == 0) { if (notran) { if (*ijob == 1 || *ijob == 2) { /* Computing MAX */ i__1 = 1, i__2 = (*m << 1) * *n; lwmin = f2cmax(i__1,i__2); } else { lwmin = 1; } } else { lwmin = 1; } work[1].r = (real) lwmin, work[1].i = 0.f; if (*lwork < lwmin && ! lquery) { *info = -20; } } if (*info != 0) { i__1 = -(*info); xerbla_("CTGSYL", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*m == 0 || *n == 0) { *scale = 1.f; if (notran) { if (*ijob != 0) { *dif = 0.f; } } return 0; } /* Determine optimal block sizes MB and NB */ mb = ilaenv_(&c__2, "CTGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); nb = ilaenv_(&c__5, "CTGSYL", trans, m, n, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); isolve = 1; ifunc = 0; if (notran) { if (*ijob >= 3) { ifunc = *ijob - 2; claset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc); claset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf); } else if (*ijob >= 1 && notran) { isolve = 2; } } if (mb <= 1 && nb <= 1 || mb >= *m && nb >= *n) { /* Use unblocked Level 2 solver */ i__1 = isolve; for (iround = 1; iround <= i__1; ++iround) { *scale = 1.f; dscale = 0.f; dsum = 1.f; pq = *m * *n; ctgsy2_(trans, &ifunc, m, n, &a[a_offset], lda, &b[b_offset], ldb, &c__[c_offset], ldc, &d__[d_offset], ldd, &e[e_offset], lde, &f[f_offset], ldf, scale, &dsum, &dscale, info); if (dscale != 0.f) { if (*ijob == 1 || *ijob == 3) { *dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt( dsum)); } else { *dif = sqrt((real) pq) / (dscale * sqrt(dsum)); } } if (isolve == 2 && iround == 1) { if (notran) { ifunc = *ijob; } scale2 = *scale; clacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m); clacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m); claset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc); claset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf) ; } else if (isolve == 2 && iround == 2) { clacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc); clacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf); *scale = scale2; } /* L30: */ } return 0; } /* Determine block structure of A */ p = 0; i__ = 1; L40: if (i__ > *m) { goto L50; } ++p; iwork[p] = i__; i__ += mb; if (i__ >= *m) { goto L50; } goto L40; L50: iwork[p + 1] = *m + 1; if (iwork[p] == iwork[p + 1]) { --p; } /* Determine block structure of B */ q = p + 1; j = 1; L60: if (j > *n) { goto L70; } ++q; iwork[q] = j; j += nb; if (j >= *n) { goto L70; } goto L60; L70: iwork[q + 1] = *n + 1; if (iwork[q] == iwork[q + 1]) { --q; } if (notran) { i__1 = isolve; for (iround = 1; iround <= i__1; ++iround) { /* Solve (I, J) - subsystem */ /* A(I, I) * R(I, J) - L(I, J) * B(J, J) = C(I, J) */ /* D(I, I) * R(I, J) - L(I, J) * E(J, J) = F(I, J) */ /* for I = P, P - 1, ..., 1; J = 1, 2, ..., Q */ pq = 0; *scale = 1.f; dscale = 0.f; dsum = 1.f; i__2 = q; for (j = p + 2; j <= i__2; ++j) { js = iwork[j]; je = iwork[j + 1] - 1; nb = je - js + 1; for (i__ = p; i__ >= 1; --i__) { is = iwork[i__]; ie = iwork[i__ + 1] - 1; mb = ie - is + 1; ctgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1], lda, &b[js + js * b_dim1], ldb, &c__[is + js * c_dim1], ldc, &d__[is + is * d_dim1], ldd, &e[js + js * e_dim1], lde, &f[is + js * f_dim1], ldf, & scaloc, &dsum, &dscale, &linfo); if (linfo > 0) { *info = linfo; } pq += mb * nb; if (scaloc != 1.f) { i__3 = js - 1; for (k = 1; k <= i__3; ++k) { q__1.r = scaloc, q__1.i = 0.f; cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1); q__1.r = scaloc, q__1.i = 0.f; cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1); /* L80: */ } i__3 = je; for (k = js; k <= i__3; ++k) { i__4 = is - 1; q__1.r = scaloc, q__1.i = 0.f; cscal_(&i__4, &q__1, &c__[k * c_dim1 + 1], &c__1); i__4 = is - 1; q__1.r = scaloc, q__1.i = 0.f; cscal_(&i__4, &q__1, &f[k * f_dim1 + 1], &c__1); /* L90: */ } i__3 = je; for (k = js; k <= i__3; ++k) { i__4 = *m - ie; q__1.r = scaloc, q__1.i = 0.f; cscal_(&i__4, &q__1, &c__[ie + 1 + k * c_dim1], & c__1); i__4 = *m - ie; q__1.r = scaloc, q__1.i = 0.f; cscal_(&i__4, &q__1, &f[ie + 1 + k * f_dim1], & c__1); /* L100: */ } i__3 = *n; for (k = je + 1; k <= i__3; ++k) { q__1.r = scaloc, q__1.i = 0.f; cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1); q__1.r = scaloc, q__1.i = 0.f; cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1); /* L110: */ } *scale *= scaloc; } /* Substitute R(I,J) and L(I,J) into remaining equation. */ if (i__ > 1) { i__3 = is - 1; cgemm_("N", "N", &i__3, &nb, &mb, &c_b44, &a[is * a_dim1 + 1], lda, &c__[is + js * c_dim1], ldc, &c_b45, &c__[js * c_dim1 + 1], ldc); i__3 = is - 1; cgemm_("N", "N", &i__3, &nb, &mb, &c_b44, &d__[is * d_dim1 + 1], ldd, &c__[is + js * c_dim1], ldc, &c_b45, &f[js * f_dim1 + 1], ldf); } if (j < q) { i__3 = *n - je; cgemm_("N", "N", &mb, &i__3, &nb, &c_b45, &f[is + js * f_dim1], ldf, &b[js + (je + 1) * b_dim1], ldb, &c_b45, &c__[is + (je + 1) * c_dim1], ldc); i__3 = *n - je; cgemm_("N", "N", &mb, &i__3, &nb, &c_b45, &f[is + js * f_dim1], ldf, &e[js + (je + 1) * e_dim1], lde, &c_b45, &f[is + (je + 1) * f_dim1], ldf); } /* L120: */ } /* L130: */ } if (dscale != 0.f) { if (*ijob == 1 || *ijob == 3) { *dif = sqrt((real) ((*m << 1) * *n)) / (dscale * sqrt( dsum)); } else { *dif = sqrt((real) pq) / (dscale * sqrt(dsum)); } } if (isolve == 2 && iround == 1) { if (notran) { ifunc = *ijob; } scale2 = *scale; clacpy_("F", m, n, &c__[c_offset], ldc, &work[1], m); clacpy_("F", m, n, &f[f_offset], ldf, &work[*m * *n + 1], m); claset_("F", m, n, &c_b1, &c_b1, &c__[c_offset], ldc); claset_("F", m, n, &c_b1, &c_b1, &f[f_offset], ldf) ; } else if (isolve == 2 && iround == 2) { clacpy_("F", m, n, &work[1], m, &c__[c_offset], ldc); clacpy_("F", m, n, &work[*m * *n + 1], m, &f[f_offset], ldf); *scale = scale2; } /* L150: */ } } else { /* Solve transposed (I, J)-subsystem */ /* A(I, I)**H * R(I, J) + D(I, I)**H * L(I, J) = C(I, J) */ /* R(I, J) * B(J, J) + L(I, J) * E(J, J) = -F(I, J) */ /* for I = 1,2,..., P; J = Q, Q-1,..., 1 */ *scale = 1.f; i__1 = p; for (i__ = 1; i__ <= i__1; ++i__) { is = iwork[i__]; ie = iwork[i__ + 1] - 1; mb = ie - is + 1; i__2 = p + 2; for (j = q; j >= i__2; --j) { js = iwork[j]; je = iwork[j + 1] - 1; nb = je - js + 1; ctgsy2_(trans, &ifunc, &mb, &nb, &a[is + is * a_dim1], lda, & b[js + js * b_dim1], ldb, &c__[is + js * c_dim1], ldc, &d__[is + is * d_dim1], ldd, &e[js + js * e_dim1], lde, &f[is + js * f_dim1], ldf, &scaloc, &dsum, & dscale, &linfo); if (linfo > 0) { *info = linfo; } if (scaloc != 1.f) { i__3 = js - 1; for (k = 1; k <= i__3; ++k) { q__1.r = scaloc, q__1.i = 0.f; cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1); q__1.r = scaloc, q__1.i = 0.f; cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1); /* L160: */ } i__3 = je; for (k = js; k <= i__3; ++k) { i__4 = is - 1; q__1.r = scaloc, q__1.i = 0.f; cscal_(&i__4, &q__1, &c__[k * c_dim1 + 1], &c__1); i__4 = is - 1; q__1.r = scaloc, q__1.i = 0.f; cscal_(&i__4, &q__1, &f[k * f_dim1 + 1], &c__1); /* L170: */ } i__3 = je; for (k = js; k <= i__3; ++k) { i__4 = *m - ie; q__1.r = scaloc, q__1.i = 0.f; cscal_(&i__4, &q__1, &c__[ie + 1 + k * c_dim1], &c__1) ; i__4 = *m - ie; q__1.r = scaloc, q__1.i = 0.f; cscal_(&i__4, &q__1, &f[ie + 1 + k * f_dim1], &c__1); /* L180: */ } i__3 = *n; for (k = je + 1; k <= i__3; ++k) { q__1.r = scaloc, q__1.i = 0.f; cscal_(m, &q__1, &c__[k * c_dim1 + 1], &c__1); q__1.r = scaloc, q__1.i = 0.f; cscal_(m, &q__1, &f[k * f_dim1 + 1], &c__1); /* L190: */ } *scale *= scaloc; } /* Substitute R(I,J) and L(I,J) into remaining equation. */ if (j > p + 2) { i__3 = js - 1; cgemm_("N", "C", &mb, &i__3, &nb, &c_b45, &c__[is + js * c_dim1], ldc, &b[js * b_dim1 + 1], ldb, &c_b45, & f[is + f_dim1], ldf); i__3 = js - 1; cgemm_("N", "C", &mb, &i__3, &nb, &c_b45, &f[is + js * f_dim1], ldf, &e[js * e_dim1 + 1], lde, &c_b45, & f[is + f_dim1], ldf); } if (i__ < p) { i__3 = *m - ie; cgemm_("C", "N", &i__3, &nb, &mb, &c_b44, &a[is + (ie + 1) * a_dim1], lda, &c__[is + js * c_dim1], ldc, & c_b45, &c__[ie + 1 + js * c_dim1], ldc); i__3 = *m - ie; cgemm_("C", "N", &i__3, &nb, &mb, &c_b44, &d__[is + (ie + 1) * d_dim1], ldd, &f[is + js * f_dim1], ldf, & c_b45, &c__[ie + 1 + js * c_dim1], ldc); } /* L200: */ } /* L210: */ } } work[1].r = (real) lwmin, work[1].i = 0.f; return 0; /* End of CTGSYL */ } /* ctgsyl_ */