#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 DTRSYL */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DTRSYL + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, */ /* LDC, SCALE, INFO ) */ /* CHARACTER TRANA, TRANB */ /* INTEGER INFO, ISGN, LDA, LDB, LDC, M, N */ /* DOUBLE PRECISION SCALE */ /* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > DTRSYL 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. */ /* > \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] 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 */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup doubleSYcomputational */ /* ===================================================================== */ /* Subroutine */ int dtrsyl_(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 *info) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2; /* Local variables */ extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, integer *); integer ierr; doublereal smin, suml, sumr; integer j, k, l; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *); doublereal x[4] /* was [2][2] */; extern logical lsame_(char *, char *); integer knext, lnext, k1, k2, l1, l2; doublereal xnorm; extern /* Subroutine */ int dlaln2_(logical *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, doublereal * , doublereal *, integer *, doublereal *, doublereal *, integer *), dlasy2_(logical *, logical *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); doublereal a11, db; extern /* Subroutine */ int dlabad_(doublereal *, doublereal *); extern doublereal dlamch_(char *), dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *); doublereal scaloc; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); doublereal bignum; logical notrna, notrnb; doublereal smlnum, da11, vec[4] /* was [2][2] */, dum[1], eps, sgn; /* -- 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 */ /* ===================================================================== */ /* 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; /* Function Body */ notrna = lsame_(trana, "N"); notrnb = lsame_(tranb, "N"); *info = 0; 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_("DTRSYL", &i__1, (ftnlen)6); return 0; } /* Quick return if possible */ *scale = 1.; if (*m == 0 || *n == 0) { return 0; } /* Set constants to control overflow */ eps = dlamch_("P"); smlnum = dlamch_("S"); bignum = 1. / smlnum; dlabad_(&smlnum, &bignum); smlnum = smlnum * (doublereal) (*m * *n) / eps; bignum = 1. / smlnum; /* Computing MAX */ d__1 = smlnum, d__2 = eps * dlange_("M", m, m, &a[a_offset], lda, dum), d__1 = f2cmax(d__1,d__2), d__2 = eps * dlange_("M", n, n, &b[b_offset], ldb, dum); smin = f2cmax(d__1,d__2); 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 column loop (index = L) */ /* L1 (L2) : column index of the first (first) row of X(K,L). */ lnext = 1; i__1 = *n; for (l = 1; l <= i__1; ++l) { if (l < lnext) { goto L60; } if (l == *n) { l1 = l; l2 = l; } else { if (b[l + 1 + l * b_dim1] != 0.) { l1 = l; l2 = l + 1; lnext = l + 2; } else { l1 = l; l2 = l; lnext = l + 1; } } /* Start row loop (index = K) */ /* K1 (K2): row index of the first (last) row of X(K,L). */ knext = *m; for (k = *m; k >= 1; --k) { if (k > knext) { goto L50; } if (k == 1) { k1 = k; k2 = k; } else { if (a[k + (k - 1) * a_dim1] != 0.) { k1 = k - 1; k2 = k; knext = k - 2; } else { k1 = k; k2 = k; knext = k - 1; } } if (l1 == l2 && k1 == k2) { i__2 = *m - k1; /* Computing MIN */ i__3 = k1 + 1; /* Computing MIN */ i__4 = k1 + 1; suml = ddot_(&i__2, &a[k1 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); scaloc = 1.; a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1]; da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = abs(vec[0]); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x[0] = vec[0] * scaloc / a11; if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L10: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; } else if (l1 == l2 && k1 != k2) { i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = ddot_(&i__2, &a[k1 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = ddot_(&i__2, &a[k2 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); d__1 = -sgn * b[l1 + l1 * b_dim1]; dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 * a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L20: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k2 + l1 * c_dim1] = x[1]; } else if (l1 != l2 && k1 == k2) { i__2 = *m - k1; /* Computing MIN */ i__3 = k1 + 1; /* Computing MIN */ i__4 = k1 + 1; suml = ddot_(&i__2, &a[k1 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn * sumr)); i__2 = *m - k1; /* Computing MIN */ i__3 = k1 + 1; /* Computing MIN */ i__4 = k1 + 1; suml = ddot_(&i__2, &a[k1 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l2 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn * sumr)); d__1 = -sgn * a[k1 + k1 * a_dim1]; dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 * b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L30: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[1]; } else if (l1 != l2 && k1 != k2) { i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = ddot_(&i__2, &a[k1 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = ddot_(&i__2, &a[k1 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l2 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k1 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr); i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = ddot_(&i__2, &a[k2 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l1 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = *m - k2; /* Computing MIN */ i__3 = k2 + 1; /* Computing MIN */ i__4 = k2 + 1; suml = ddot_(&i__2, &a[k2 + f2cmin(i__3,*m) * a_dim1], lda, & c__[f2cmin(i__4,*m) + l2 * c_dim1], &c__1); i__2 = l1 - 1; sumr = ddot_(&i__2, &c__[k2 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr); dlasy2_(&c_false, &c_false, isgn, &c__2, &c__2, &a[k1 + k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, &c__2, &scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L40: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[2]; c__[k2 + l1 * c_dim1] = x[1]; c__[k2 + l2 * c_dim1] = x[3]; } L50: ; } L60: ; } } 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 T 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 column loop (index = L) */ /* L1 (L2): column index of the first (last) row of X(K,L) */ lnext = 1; i__1 = *n; for (l = 1; l <= i__1; ++l) { if (l < lnext) { goto L120; } if (l == *n) { l1 = l; l2 = l; } else { if (b[l + 1 + l * b_dim1] != 0.) { l1 = l; l2 = l + 1; lnext = l + 2; } else { l1 = l; l2 = l; lnext = l + 1; } } /* Start row loop (index = K) */ /* K1 (K2): row index of the first (last) row of X(K,L) */ knext = 1; i__2 = *m; for (k = 1; k <= i__2; ++k) { if (k < knext) { goto L110; } if (k == *m) { k1 = k; k2 = k; } else { if (a[k + 1 + k * a_dim1] != 0.) { k1 = k; k2 = k + 1; knext = k + 2; } else { k1 = k; k2 = k; knext = k + 1; } } if (l1 == l2 && k1 == k2) { i__3 = k1 - 1; suml = ddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); scaloc = 1.; a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1]; da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = abs(vec[0]); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x[0] = vec[0] * scaloc / a11; if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L70: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; } else if (l1 == l2 && k1 != k2) { i__3 = k1 - 1; suml = ddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__3 = k1 - 1; suml = ddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); d__1 = -sgn * b[l1 + l1 * b_dim1]; dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 * a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L80: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k2 + l1 * c_dim1] = x[1]; } else if (l1 != l2 && k1 == k2) { i__3 = k1 - 1; suml = ddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn * sumr)); i__3 = k1 - 1; suml = ddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn * sumr)); d__1 = -sgn * a[k1 + k1 * a_dim1]; dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 * b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L90: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[1]; } else if (l1 != l2 && k1 != k2) { i__3 = k1 - 1; suml = ddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__3 = k1 - 1; suml = ddot_(&i__3, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k1 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr); i__3 = k1 - 1; suml = ddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l1 * b_dim1 + 1], &c__1); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); i__3 = k1 - 1; suml = ddot_(&i__3, &a[k2 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__3 = l1 - 1; sumr = ddot_(&i__3, &c__[k2 + c_dim1], ldc, &b[l2 * b_dim1 + 1], &c__1); vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr); dlasy2_(&c_true, &c_false, isgn, &c__2, &c__2, &a[k1 + k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, & c__2, &scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__3 = *n; for (j = 1; j <= i__3; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L100: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[2]; c__[k2 + l1 * c_dim1] = x[1]; c__[k2 + l2 * c_dim1] = x[3]; } L110: ; } L120: ; } } 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 column loop (index = L) */ /* L1 (L2): column index of the first (last) row of X(K,L) */ lnext = *n; for (l = *n; l >= 1; --l) { if (l > lnext) { goto L180; } if (l == 1) { l1 = l; l2 = l; } else { if (b[l + (l - 1) * b_dim1] != 0.) { l1 = l - 1; l2 = l; lnext = l - 2; } else { l1 = l; l2 = l; lnext = l - 1; } } /* Start row loop (index = K) */ /* K1 (K2): row index of the first (last) row of X(K,L) */ knext = 1; i__1 = *m; for (k = 1; k <= i__1; ++k) { if (k < knext) { goto L170; } if (k == *m) { k1 = k; k2 = k; } else { if (a[k + 1 + k * a_dim1] != 0.) { k1 = k; k2 = k + 1; knext = k + 2; } else { k1 = k; k2 = k; knext = k + 1; } } if (l1 == l2 && k1 == k2) { i__2 = k1 - 1; suml = ddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l1; /* Computing MIN */ i__3 = l1 + 1; /* Computing MIN */ i__4 = l1 + 1; sumr = ddot_(&i__2, &c__[k1 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__4,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); scaloc = 1.; a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1]; da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = abs(vec[0]); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x[0] = vec[0] * scaloc / a11; if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L130: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; } else if (l1 == l2 && k1 != k2) { i__2 = k1 - 1; suml = ddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = ddot_(&i__2, &c__[k1 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__4,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = k1 - 1; suml = ddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = ddot_(&i__2, &c__[k2 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__4,*n) * b_dim1], ldb); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); d__1 = -sgn * b[l1 + l1 * b_dim1]; dlaln2_(&c_true, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 * a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L140: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k2 + l1 * c_dim1] = x[1]; } else if (l1 != l2 && k1 == k2) { i__2 = k1 - 1; suml = ddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = ddot_(&i__2, &c__[k1 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__4,*n) * b_dim1], ldb); vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn * sumr)); i__2 = k1 - 1; suml = ddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = ddot_(&i__2, &c__[k1 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l2 + f2cmin(i__4,*n) * b_dim1], ldb); vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn * sumr)); d__1 = -sgn * a[k1 + k1 * a_dim1]; dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 * b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L150: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[1]; } else if (l1 != l2 && k1 != k2) { i__2 = k1 - 1; suml = ddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = ddot_(&i__2, &c__[k1 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__4,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = k1 - 1; suml = ddot_(&i__2, &a[k1 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = ddot_(&i__2, &c__[k1 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l2 + f2cmin(i__4,*n) * b_dim1], ldb); vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr); i__2 = k1 - 1; suml = ddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l1 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = ddot_(&i__2, &c__[k2 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__4,*n) * b_dim1], ldb); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); i__2 = k1 - 1; suml = ddot_(&i__2, &a[k2 * a_dim1 + 1], &c__1, &c__[l2 * c_dim1 + 1], &c__1); i__2 = *n - l2; /* Computing MIN */ i__3 = l2 + 1; /* Computing MIN */ i__4 = l2 + 1; sumr = ddot_(&i__2, &c__[k2 + f2cmin(i__3,*n) * c_dim1], ldc, &b[l2 + f2cmin(i__4,*n) * b_dim1], ldb); vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr); dlasy2_(&c_true, &c_true, isgn, &c__2, &c__2, &a[k1 + k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, & c__2, &scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__2 = *n; for (j = 1; j <= i__2; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L160: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[2]; c__[k2 + l1 * c_dim1] = x[1]; c__[k2 + l2 * c_dim1] = x[3]; } L170: ; } L180: ; } } 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 column loop (index = L) */ /* L1 (L2): column index of the first (last) row of X(K,L) */ lnext = *n; for (l = *n; l >= 1; --l) { if (l > lnext) { goto L240; } if (l == 1) { l1 = l; l2 = l; } else { if (b[l + (l - 1) * b_dim1] != 0.) { l1 = l - 1; l2 = l; lnext = l - 2; } else { l1 = l; l2 = l; lnext = l - 1; } } /* Start row loop (index = K) */ /* K1 (K2): row index of the first (last) row of X(K,L) */ knext = *m; for (k = *m; k >= 1; --k) { if (k > knext) { goto L230; } if (k == 1) { k1 = k; k2 = k; } else { if (a[k + (k - 1) * a_dim1] != 0.) { k1 = k - 1; k2 = k; knext = k - 2; } else { k1 = k; k2 = k; knext = k - 1; } } if (l1 == l2 && k1 == k2) { i__1 = *m - k1; /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; suml = ddot_(&i__1, &a[k1 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l1; /* Computing MIN */ i__2 = l1 + 1; /* Computing MIN */ i__3 = l1 + 1; sumr = ddot_(&i__1, &c__[k1 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__3,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); scaloc = 1.; a11 = a[k1 + k1 * a_dim1] + sgn * b[l1 + l1 * b_dim1]; da11 = abs(a11); if (da11 <= smin) { a11 = smin; da11 = smin; *info = 1; } db = abs(vec[0]); if (da11 < 1. && db > 1.) { if (db > bignum * da11) { scaloc = 1. / db; } } x[0] = vec[0] * scaloc / a11; if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L190: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; } else if (l1 == l2 && k1 != k2) { i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = ddot_(&i__1, &a[k1 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = ddot_(&i__1, &c__[k1 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__3,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = ddot_(&i__1, &a[k2 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = ddot_(&i__1, &c__[k2 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__3,*n) * b_dim1], ldb); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); d__1 = -sgn * b[l1 + l1 * b_dim1]; dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &a[k1 + k1 * a_dim1], lda, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L200: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k2 + l1 * c_dim1] = x[1]; } else if (l1 != l2 && k1 == k2) { i__1 = *m - k1; /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; suml = ddot_(&i__1, &a[k1 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = ddot_(&i__1, &c__[k1 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__3,*n) * b_dim1], ldb); vec[0] = sgn * (c__[k1 + l1 * c_dim1] - (suml + sgn * sumr)); i__1 = *m - k1; /* Computing MIN */ i__2 = k1 + 1; /* Computing MIN */ i__3 = k1 + 1; suml = ddot_(&i__1, &a[k1 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l2 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = ddot_(&i__1, &c__[k1 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l2 + f2cmin(i__3,*n) * b_dim1], ldb); vec[1] = sgn * (c__[k1 + l2 * c_dim1] - (suml + sgn * sumr)); d__1 = -sgn * a[k1 + k1 * a_dim1]; dlaln2_(&c_false, &c__2, &c__1, &smin, &c_b26, &b[l1 + l1 * b_dim1], ldb, &c_b26, &c_b26, vec, &c__2, &d__1, &c_b30, x, &c__2, &scaloc, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L210: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[1]; } else if (l1 != l2 && k1 != k2) { i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = ddot_(&i__1, &a[k1 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = ddot_(&i__1, &c__[k1 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__3,*n) * b_dim1], ldb); vec[0] = c__[k1 + l1 * c_dim1] - (suml + sgn * sumr); i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = ddot_(&i__1, &a[k1 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l2 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = ddot_(&i__1, &c__[k1 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l2 + f2cmin(i__3,*n) * b_dim1], ldb); vec[2] = c__[k1 + l2 * c_dim1] - (suml + sgn * sumr); i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = ddot_(&i__1, &a[k2 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l1 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = ddot_(&i__1, &c__[k2 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l1 + f2cmin(i__3,*n) * b_dim1], ldb); vec[1] = c__[k2 + l1 * c_dim1] - (suml + sgn * sumr); i__1 = *m - k2; /* Computing MIN */ i__2 = k2 + 1; /* Computing MIN */ i__3 = k2 + 1; suml = ddot_(&i__1, &a[k2 + f2cmin(i__2,*m) * a_dim1], lda, & c__[f2cmin(i__3,*m) + l2 * c_dim1], &c__1); i__1 = *n - l2; /* Computing MIN */ i__2 = l2 + 1; /* Computing MIN */ i__3 = l2 + 1; sumr = ddot_(&i__1, &c__[k2 + f2cmin(i__2,*n) * c_dim1], ldc, &b[l2 + f2cmin(i__3,*n) * b_dim1], ldb); vec[3] = c__[k2 + l2 * c_dim1] - (suml + sgn * sumr); dlasy2_(&c_false, &c_true, isgn, &c__2, &c__2, &a[k1 + k1 * a_dim1], lda, &b[l1 + l1 * b_dim1], ldb, vec, & c__2, &scaloc, x, &c__2, &xnorm, &ierr); if (ierr != 0) { *info = 1; } if (scaloc != 1.) { i__1 = *n; for (j = 1; j <= i__1; ++j) { dscal_(m, &scaloc, &c__[j * c_dim1 + 1], &c__1); /* L220: */ } *scale *= scaloc; } c__[k1 + l1 * c_dim1] = x[0]; c__[k1 + l2 * c_dim1] = x[2]; c__[k2 + l1 * c_dim1] = x[1]; c__[k2 + l2 * c_dim1] = x[3]; } L230: ; } L240: ; } } return 0; /* End of DTRSYL */ } /* dtrsyl_ */