#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 DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format). */ /* =========== DOCUMENTATION =========== */ /* Online html documentation available at */ /* http://www.netlib.org/lapack/explore-html/ */ /* > \htmlonly */ /* > Download DTFSM + dependencies */ /* > */ /* > [TGZ] */ /* > */ /* > [ZIP] */ /* > */ /* > [TXT] */ /* > \endhtmlonly */ /* Definition: */ /* =========== */ /* SUBROUTINE DTFSM( TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, */ /* B, LDB ) */ /* CHARACTER TRANSR, DIAG, SIDE, TRANS, UPLO */ /* INTEGER LDB, M, N */ /* DOUBLE PRECISION ALPHA */ /* DOUBLE PRECISION A( 0: * ), B( 0: LDB-1, 0: * ) */ /* > \par Purpose: */ /* ============= */ /* > */ /* > \verbatim */ /* > */ /* > Level 3 BLAS like routine for A in RFP Format. */ /* > */ /* > DTFSM solves the matrix equation */ /* > */ /* > op( A )*X = alpha*B or X*op( A ) = alpha*B */ /* > */ /* > where alpha is a scalar, X and B are m by n matrices, A is a unit, or */ /* > non-unit, upper or lower triangular matrix and op( A ) is one of */ /* > */ /* > op( A ) = A or op( A ) = A**T. */ /* > */ /* > A is in Rectangular Full Packed (RFP) Format. */ /* > */ /* > The matrix X is overwritten on B. */ /* > \endverbatim */ /* Arguments: */ /* ========== */ /* > \param[in] TRANSR */ /* > \verbatim */ /* > TRANSR is CHARACTER*1 */ /* > = 'N': The Normal Form of RFP A is stored; */ /* > = 'T': The Transpose Form of RFP A is stored. */ /* > \endverbatim */ /* > */ /* > \param[in] SIDE */ /* > \verbatim */ /* > SIDE is CHARACTER*1 */ /* > On entry, SIDE specifies whether op( A ) appears on the left */ /* > or right of X as follows: */ /* > */ /* > SIDE = 'L' or 'l' op( A )*X = alpha*B. */ /* > */ /* > SIDE = 'R' or 'r' X*op( A ) = alpha*B. */ /* > */ /* > Unchanged on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] UPLO */ /* > \verbatim */ /* > UPLO is CHARACTER*1 */ /* > On entry, UPLO specifies whether the RFP matrix A came from */ /* > an upper or lower triangular matrix as follows: */ /* > UPLO = 'U' or 'u' RFP A came from an upper triangular matrix */ /* > UPLO = 'L' or 'l' RFP A came from a lower triangular matrix */ /* > */ /* > Unchanged on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] TRANS */ /* > \verbatim */ /* > TRANS is CHARACTER*1 */ /* > On entry, TRANS specifies the form of op( A ) to be used */ /* > in the matrix multiplication as follows: */ /* > */ /* > TRANS = 'N' or 'n' op( A ) = A. */ /* > */ /* > TRANS = 'T' or 't' op( A ) = A'. */ /* > */ /* > Unchanged on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] DIAG */ /* > \verbatim */ /* > DIAG is CHARACTER*1 */ /* > On entry, DIAG specifies whether or not RFP A is unit */ /* > triangular as follows: */ /* > */ /* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */ /* > */ /* > DIAG = 'N' or 'n' A is not assumed to be unit */ /* > triangular. */ /* > */ /* > Unchanged on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] M */ /* > \verbatim */ /* > M is INTEGER */ /* > On entry, M specifies the number of rows of B. M must be at */ /* > least zero. */ /* > Unchanged on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] N */ /* > \verbatim */ /* > N is INTEGER */ /* > On entry, N specifies the number of columns of B. N must be */ /* > at least zero. */ /* > Unchanged on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] ALPHA */ /* > \verbatim */ /* > ALPHA is DOUBLE PRECISION */ /* > On entry, ALPHA specifies the scalar alpha. When alpha is */ /* > zero then A is not referenced and B need not be set before */ /* > entry. */ /* > Unchanged on exit. */ /* > \endverbatim */ /* > */ /* > \param[in] A */ /* > \verbatim */ /* > A is DOUBLE PRECISION array, dimension (NT) */ /* > NT = N*(N+1)/2. On entry, the matrix A in RFP Format. */ /* > RFP Format is described by TRANSR, UPLO and N as follows: */ /* > If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; */ /* > K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If */ /* > TRANSR = 'T' then RFP is the transpose of RFP A as */ /* > defined when TRANSR = 'N'. The contents of RFP A are defined */ /* > by UPLO as follows: If UPLO = 'U' the RFP A contains the NT */ /* > elements of upper packed A either in normal or */ /* > transpose Format. If UPLO = 'L' the RFP A contains */ /* > the NT elements of lower packed A either in normal or */ /* > transpose Format. The LDA of RFP A is (N+1)/2 when */ /* > TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is */ /* > even and is N when is odd. */ /* > See the Note below for more details. Unchanged on exit. */ /* > \endverbatim */ /* > */ /* > \param[in,out] B */ /* > \verbatim */ /* > B is DOUBLE PRECISION array, dimension (LDB,N) */ /* > Before entry, the leading m by n part of the array B must */ /* > contain the right-hand side matrix B, and on exit is */ /* > overwritten by the solution matrix X. */ /* > \endverbatim */ /* > */ /* > \param[in] LDB */ /* > \verbatim */ /* > LDB is INTEGER */ /* > On entry, LDB specifies the first dimension of B as declared */ /* > in the calling (sub) program. LDB must be at least */ /* > f2cmax( 1, m ). */ /* > Unchanged on exit. */ /* > \endverbatim */ /* Authors: */ /* ======== */ /* > \author Univ. of Tennessee */ /* > \author Univ. of California Berkeley */ /* > \author Univ. of Colorado Denver */ /* > \author NAG Ltd. */ /* > \date December 2016 */ /* > \ingroup doubleOTHERcomputational */ /* > \par Further Details: */ /* ===================== */ /* > */ /* > \verbatim */ /* > */ /* > We first consider Rectangular Full Packed (RFP) Format when N is */ /* > even. We give an example where N = 6. */ /* > */ /* > AP is Upper AP is Lower */ /* > */ /* > 00 01 02 03 04 05 00 */ /* > 11 12 13 14 15 10 11 */ /* > 22 23 24 25 20 21 22 */ /* > 33 34 35 30 31 32 33 */ /* > 44 45 40 41 42 43 44 */ /* > 55 50 51 52 53 54 55 */ /* > */ /* > */ /* > Let TRANSR = 'N'. RFP holds AP as follows: */ /* > For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */ /* > three columns of AP upper. The lower triangle A(4:6,0:2) consists of */ /* > the transpose of the first three columns of AP upper. */ /* > For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */ /* > three columns of AP lower. The upper triangle A(0:2,0:2) consists of */ /* > the transpose of the last three columns of AP lower. */ /* > This covers the case N even and TRANSR = 'N'. */ /* > */ /* > RFP A RFP A */ /* > */ /* > 03 04 05 33 43 53 */ /* > 13 14 15 00 44 54 */ /* > 23 24 25 10 11 55 */ /* > 33 34 35 20 21 22 */ /* > 00 44 45 30 31 32 */ /* > 01 11 55 40 41 42 */ /* > 02 12 22 50 51 52 */ /* > */ /* > Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */ /* > transpose of RFP A above. One therefore gets: */ /* > */ /* > */ /* > RFP A RFP A */ /* > */ /* > 03 13 23 33 00 01 02 33 00 10 20 30 40 50 */ /* > 04 14 24 34 44 11 12 43 44 11 21 31 41 51 */ /* > 05 15 25 35 45 55 22 53 54 55 22 32 42 52 */ /* > */ /* > */ /* > We then consider Rectangular Full Packed (RFP) Format when N is */ /* > odd. We give an example where N = 5. */ /* > */ /* > AP is Upper AP is Lower */ /* > */ /* > 00 01 02 03 04 00 */ /* > 11 12 13 14 10 11 */ /* > 22 23 24 20 21 22 */ /* > 33 34 30 31 32 33 */ /* > 44 40 41 42 43 44 */ /* > */ /* > */ /* > Let TRANSR = 'N'. RFP holds AP as follows: */ /* > For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */ /* > three columns of AP upper. The lower triangle A(3:4,0:1) consists of */ /* > the transpose of the first two columns of AP upper. */ /* > For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */ /* > three columns of AP lower. The upper triangle A(0:1,1:2) consists of */ /* > the transpose of the last two columns of AP lower. */ /* > This covers the case N odd and TRANSR = 'N'. */ /* > */ /* > RFP A RFP A */ /* > */ /* > 02 03 04 00 33 43 */ /* > 12 13 14 10 11 44 */ /* > 22 23 24 20 21 22 */ /* > 00 33 34 30 31 32 */ /* > 01 11 44 40 41 42 */ /* > */ /* > Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */ /* > transpose of RFP A above. One therefore gets: */ /* > */ /* > RFP A RFP A */ /* > */ /* > 02 12 22 00 01 00 10 20 30 40 50 */ /* > 03 13 23 33 11 33 11 21 31 41 51 */ /* > 04 14 24 34 44 43 44 22 32 42 52 */ /* > \endverbatim */ /* ===================================================================== */ /* Subroutine */ int dtfsm_(char *transr, char *side, char *uplo, char *trans, char *diag, integer *m, integer *n, doublereal *alpha, doublereal *a, doublereal *b, integer *ldb) { /* System generated locals */ integer b_dim1, b_offset, i__1, i__2; /* Local variables */ integer info, i__, j, k; logical normaltransr; extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); logical lside; extern logical lsame_(char *, char *); logical lower; extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *); integer m1, m2, n1, n2; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); logical misodd, nisodd, notrans; /* -- 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 */ /* ===================================================================== */ /* Test the input parameters. */ /* Parameter adjustments */ b_dim1 = *ldb - 1 - 0 + 1; b_offset = 0 + b_dim1 * 0; b -= b_offset; /* Function Body */ info = 0; normaltransr = lsame_(transr, "N"); lside = lsame_(side, "L"); lower = lsame_(uplo, "L"); notrans = lsame_(trans, "N"); if (! normaltransr && ! lsame_(transr, "T")) { info = -1; } else if (! lside && ! lsame_(side, "R")) { info = -2; } else if (! lower && ! lsame_(uplo, "U")) { info = -3; } else if (! notrans && ! lsame_(trans, "T")) { info = -4; } else if (! lsame_(diag, "N") && ! lsame_(diag, "U")) { info = -5; } else if (*m < 0) { info = -6; } else if (*n < 0) { info = -7; } else if (*ldb < f2cmax(1,*m)) { info = -11; } if (info != 0) { i__1 = -info; xerbla_("DTFSM ", &i__1, (ftnlen)6); return 0; } /* Quick return when ( (N.EQ.0).OR.(M.EQ.0) ) */ if (*m == 0 || *n == 0) { return 0; } /* Quick return when ALPHA.EQ.(0D+0) */ if (*alpha == 0.) { i__1 = *n - 1; for (j = 0; j <= i__1; ++j) { i__2 = *m - 1; for (i__ = 0; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = 0.; /* L10: */ } /* L20: */ } return 0; } if (lside) { /* SIDE = 'L' */ /* A is M-by-M. */ /* If M is odd, set NISODD = .TRUE., and M1 and M2. */ /* If M is even, NISODD = .FALSE., and M. */ if (*m % 2 == 0) { misodd = FALSE_; k = *m / 2; } else { misodd = TRUE_; if (lower) { m2 = *m / 2; m1 = *m - m2; } else { m1 = *m / 2; m2 = *m - m1; } } if (misodd) { /* SIDE = 'L' and N is odd */ if (normaltransr) { /* SIDE = 'L', N is odd, and TRANSR = 'N' */ if (lower) { /* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'L' */ if (notrans) { /* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and */ /* TRANS = 'N' */ if (*m == 1) { dtrsm_("L", "L", "N", diag, &m1, n, alpha, a, m, & b[b_offset], ldb); } else { dtrsm_("L", "L", "N", diag, &m1, n, alpha, a, m, & b[b_offset], ldb); dgemm_("N", "N", &m2, n, &m1, &c_b23, &a[m1], m, & b[b_offset], ldb, alpha, &b[m1], ldb); dtrsm_("L", "U", "T", diag, &m2, n, &c_b27, &a[*m] , m, &b[m1], ldb); } } else { /* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'L', and */ /* TRANS = 'T' */ if (*m == 1) { dtrsm_("L", "L", "T", diag, &m1, n, alpha, a, m, & b[b_offset], ldb); } else { dtrsm_("L", "U", "N", diag, &m2, n, alpha, &a[*m], m, &b[m1], ldb); dgemm_("T", "N", &m1, n, &m2, &c_b23, &a[m1], m, & b[m1], ldb, alpha, &b[b_offset], ldb); dtrsm_("L", "L", "T", diag, &m1, n, &c_b27, a, m, &b[b_offset], ldb); } } } else { /* SIDE ='L', N is odd, TRANSR = 'N', and UPLO = 'U' */ if (! notrans) { /* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and */ /* TRANS = 'N' */ dtrsm_("L", "L", "N", diag, &m1, n, alpha, &a[m2], m, &b[b_offset], ldb); dgemm_("T", "N", &m2, n, &m1, &c_b23, a, m, &b[ b_offset], ldb, alpha, &b[m1], ldb); dtrsm_("L", "U", "T", diag, &m2, n, &c_b27, &a[m1], m, &b[m1], ldb); } else { /* SIDE ='L', N is odd, TRANSR = 'N', UPLO = 'U', and */ /* TRANS = 'T' */ dtrsm_("L", "U", "N", diag, &m2, n, alpha, &a[m1], m, &b[m1], ldb); dgemm_("N", "N", &m1, n, &m2, &c_b23, a, m, &b[m1], ldb, alpha, &b[b_offset], ldb); dtrsm_("L", "L", "T", diag, &m1, n, &c_b27, &a[m2], m, &b[b_offset], ldb); } } } else { /* SIDE = 'L', N is odd, and TRANSR = 'T' */ if (lower) { /* SIDE ='L', N is odd, TRANSR = 'T', and UPLO = 'L' */ if (notrans) { /* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'L', and */ /* TRANS = 'N' */ if (*m == 1) { dtrsm_("L", "U", "T", diag, &m1, n, alpha, a, &m1, &b[b_offset], ldb); } else { dtrsm_("L", "U", "T", diag, &m1, n, alpha, a, &m1, &b[b_offset], ldb); dgemm_("T", "N", &m2, n, &m1, &c_b23, &a[m1 * m1], &m1, &b[b_offset], ldb, alpha, &b[m1], ldb); dtrsm_("L", "L", "N", diag, &m2, n, &c_b27, &a[1], &m1, &b[m1], ldb); } } else { /* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'L', and */ /* TRANS = 'T' */ if (*m == 1) { dtrsm_("L", "U", "N", diag, &m1, n, alpha, a, &m1, &b[b_offset], ldb); } else { dtrsm_("L", "L", "T", diag, &m2, n, alpha, &a[1], &m1, &b[m1], ldb); dgemm_("N", "N", &m1, n, &m2, &c_b23, &a[m1 * m1], &m1, &b[m1], ldb, alpha, &b[b_offset], ldb); dtrsm_("L", "U", "N", diag, &m1, n, &c_b27, a, & m1, &b[b_offset], ldb); } } } else { /* SIDE ='L', N is odd, TRANSR = 'T', and UPLO = 'U' */ if (! notrans) { /* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'U', and */ /* TRANS = 'N' */ dtrsm_("L", "U", "T", diag, &m1, n, alpha, &a[m2 * m2] , &m2, &b[b_offset], ldb); dgemm_("N", "N", &m2, n, &m1, &c_b23, a, &m2, &b[ b_offset], ldb, alpha, &b[m1], ldb); dtrsm_("L", "L", "N", diag, &m2, n, &c_b27, &a[m1 * m2], &m2, &b[m1], ldb); } else { /* SIDE ='L', N is odd, TRANSR = 'T', UPLO = 'U', and */ /* TRANS = 'T' */ dtrsm_("L", "L", "T", diag, &m2, n, alpha, &a[m1 * m2] , &m2, &b[m1], ldb); dgemm_("T", "N", &m1, n, &m2, &c_b23, a, &m2, &b[m1], ldb, alpha, &b[b_offset], ldb); dtrsm_("L", "U", "N", diag, &m1, n, &c_b27, &a[m2 * m2], &m2, &b[b_offset], ldb); } } } } else { /* SIDE = 'L' and N is even */ if (normaltransr) { /* SIDE = 'L', N is even, and TRANSR = 'N' */ if (lower) { /* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'L' */ if (notrans) { /* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L', */ /* and TRANS = 'N' */ i__1 = *m + 1; dtrsm_("L", "L", "N", diag, &k, n, alpha, &a[1], & i__1, &b[b_offset], ldb); i__1 = *m + 1; dgemm_("N", "N", &k, n, &k, &c_b23, &a[k + 1], &i__1, &b[b_offset], ldb, alpha, &b[k], ldb); i__1 = *m + 1; dtrsm_("L", "U", "T", diag, &k, n, &c_b27, a, &i__1, & b[k], ldb); } else { /* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'L', */ /* and TRANS = 'T' */ i__1 = *m + 1; dtrsm_("L", "U", "N", diag, &k, n, alpha, a, &i__1, & b[k], ldb); i__1 = *m + 1; dgemm_("T", "N", &k, n, &k, &c_b23, &a[k + 1], &i__1, &b[k], ldb, alpha, &b[b_offset], ldb); i__1 = *m + 1; dtrsm_("L", "L", "T", diag, &k, n, &c_b27, &a[1], & i__1, &b[b_offset], ldb); } } else { /* SIDE ='L', N is even, TRANSR = 'N', and UPLO = 'U' */ if (! notrans) { /* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U', */ /* and TRANS = 'N' */ i__1 = *m + 1; dtrsm_("L", "L", "N", diag, &k, n, alpha, &a[k + 1], & i__1, &b[b_offset], ldb); i__1 = *m + 1; dgemm_("T", "N", &k, n, &k, &c_b23, a, &i__1, &b[ b_offset], ldb, alpha, &b[k], ldb); i__1 = *m + 1; dtrsm_("L", "U", "T", diag, &k, n, &c_b27, &a[k], & i__1, &b[k], ldb); } else { /* SIDE ='L', N is even, TRANSR = 'N', UPLO = 'U', */ /* and TRANS = 'T' */ i__1 = *m + 1; dtrsm_("L", "U", "N", diag, &k, n, alpha, &a[k], & i__1, &b[k], ldb); i__1 = *m + 1; dgemm_("N", "N", &k, n, &k, &c_b23, a, &i__1, &b[k], ldb, alpha, &b[b_offset], ldb); i__1 = *m + 1; dtrsm_("L", "L", "T", diag, &k, n, &c_b27, &a[k + 1], &i__1, &b[b_offset], ldb); } } } else { /* SIDE = 'L', N is even, and TRANSR = 'T' */ if (lower) { /* SIDE ='L', N is even, TRANSR = 'T', and UPLO = 'L' */ if (notrans) { /* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'L', */ /* and TRANS = 'N' */ dtrsm_("L", "U", "T", diag, &k, n, alpha, &a[k], &k, & b[b_offset], ldb); dgemm_("T", "N", &k, n, &k, &c_b23, &a[k * (k + 1)], & k, &b[b_offset], ldb, alpha, &b[k], ldb); dtrsm_("L", "L", "N", diag, &k, n, &c_b27, a, &k, &b[ k], ldb); } else { /* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'L', */ /* and TRANS = 'T' */ dtrsm_("L", "L", "T", diag, &k, n, alpha, a, &k, &b[k] , ldb); dgemm_("N", "N", &k, n, &k, &c_b23, &a[k * (k + 1)], & k, &b[k], ldb, alpha, &b[b_offset], ldb); dtrsm_("L", "U", "N", diag, &k, n, &c_b27, &a[k], &k, &b[b_offset], ldb); } } else { /* SIDE ='L', N is even, TRANSR = 'T', and UPLO = 'U' */ if (! notrans) { /* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'U', */ /* and TRANS = 'N' */ dtrsm_("L", "U", "T", diag, &k, n, alpha, &a[k * (k + 1)], &k, &b[b_offset], ldb); dgemm_("N", "N", &k, n, &k, &c_b23, a, &k, &b[ b_offset], ldb, alpha, &b[k], ldb); dtrsm_("L", "L", "N", diag, &k, n, &c_b27, &a[k * k], &k, &b[k], ldb); } else { /* SIDE ='L', N is even, TRANSR = 'T', UPLO = 'U', */ /* and TRANS = 'T' */ dtrsm_("L", "L", "T", diag, &k, n, alpha, &a[k * k], & k, &b[k], ldb); dgemm_("T", "N", &k, n, &k, &c_b23, a, &k, &b[k], ldb, alpha, &b[b_offset], ldb); dtrsm_("L", "U", "N", diag, &k, n, &c_b27, &a[k * (k + 1)], &k, &b[b_offset], ldb); } } } } } else { /* SIDE = 'R' */ /* A is N-by-N. */ /* If N is odd, set NISODD = .TRUE., and N1 and N2. */ /* If N is even, NISODD = .FALSE., and K. */ if (*n % 2 == 0) { nisodd = FALSE_; k = *n / 2; } else { nisodd = TRUE_; if (lower) { n2 = *n / 2; n1 = *n - n2; } else { n1 = *n / 2; n2 = *n - n1; } } if (nisodd) { /* SIDE = 'R' and N is odd */ if (normaltransr) { /* SIDE = 'R', N is odd, and TRANSR = 'N' */ if (lower) { /* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'L' */ if (notrans) { /* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and */ /* TRANS = 'N' */ dtrsm_("R", "U", "T", diag, m, &n2, alpha, &a[*n], n, &b[n1 * b_dim1], ldb); dgemm_("N", "N", m, &n1, &n2, &c_b23, &b[n1 * b_dim1], ldb, &a[n1], n, alpha, b, ldb); dtrsm_("R", "L", "N", diag, m, &n1, &c_b27, a, n, b, ldb); } else { /* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'L', and */ /* TRANS = 'T' */ dtrsm_("R", "L", "T", diag, m, &n1, alpha, a, n, b, ldb); dgemm_("N", "T", m, &n2, &n1, &c_b23, b, ldb, &a[n1], n, alpha, &b[n1 * b_dim1], ldb); dtrsm_("R", "U", "N", diag, m, &n2, &c_b27, &a[*n], n, &b[n1 * b_dim1], ldb); } } else { /* SIDE ='R', N is odd, TRANSR = 'N', and UPLO = 'U' */ if (notrans) { /* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and */ /* TRANS = 'N' */ dtrsm_("R", "L", "T", diag, m, &n1, alpha, &a[n2], n, b, ldb); dgemm_("N", "N", m, &n2, &n1, &c_b23, b, ldb, a, n, alpha, &b[n1 * b_dim1], ldb); dtrsm_("R", "U", "N", diag, m, &n2, &c_b27, &a[n1], n, &b[n1 * b_dim1], ldb); } else { /* SIDE ='R', N is odd, TRANSR = 'N', UPLO = 'U', and */ /* TRANS = 'T' */ dtrsm_("R", "U", "T", diag, m, &n2, alpha, &a[n1], n, &b[n1 * b_dim1], ldb); dgemm_("N", "T", m, &n1, &n2, &c_b23, &b[n1 * b_dim1], ldb, a, n, alpha, b, ldb); dtrsm_("R", "L", "N", diag, m, &n1, &c_b27, &a[n2], n, b, ldb); } } } else { /* SIDE = 'R', N is odd, and TRANSR = 'T' */ if (lower) { /* SIDE ='R', N is odd, TRANSR = 'T', and UPLO = 'L' */ if (notrans) { /* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'L', and */ /* TRANS = 'N' */ dtrsm_("R", "L", "N", diag, m, &n2, alpha, &a[1], &n1, &b[n1 * b_dim1], ldb); dgemm_("N", "T", m, &n1, &n2, &c_b23, &b[n1 * b_dim1], ldb, &a[n1 * n1], &n1, alpha, b, ldb); dtrsm_("R", "U", "T", diag, m, &n1, &c_b27, a, &n1, b, ldb); } else { /* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'L', and */ /* TRANS = 'T' */ dtrsm_("R", "U", "N", diag, m, &n1, alpha, a, &n1, b, ldb); dgemm_("N", "N", m, &n2, &n1, &c_b23, b, ldb, &a[n1 * n1], &n1, alpha, &b[n1 * b_dim1], ldb); dtrsm_("R", "L", "T", diag, m, &n2, &c_b27, &a[1], & n1, &b[n1 * b_dim1], ldb); } } else { /* SIDE ='R', N is odd, TRANSR = 'T', and UPLO = 'U' */ if (notrans) { /* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'U', and */ /* TRANS = 'N' */ dtrsm_("R", "U", "N", diag, m, &n1, alpha, &a[n2 * n2] , &n2, b, ldb); dgemm_("N", "T", m, &n2, &n1, &c_b23, b, ldb, a, &n2, alpha, &b[n1 * b_dim1], ldb); dtrsm_("R", "L", "T", diag, m, &n2, &c_b27, &a[n1 * n2], &n2, &b[n1 * b_dim1], ldb); } else { /* SIDE ='R', N is odd, TRANSR = 'T', UPLO = 'U', and */ /* TRANS = 'T' */ dtrsm_("R", "L", "N", diag, m, &n2, alpha, &a[n1 * n2] , &n2, &b[n1 * b_dim1], ldb); dgemm_("N", "N", m, &n1, &n2, &c_b23, &b[n1 * b_dim1], ldb, a, &n2, alpha, b, ldb); dtrsm_("R", "U", "T", diag, m, &n1, &c_b27, &a[n2 * n2], &n2, b, ldb); } } } } else { /* SIDE = 'R' and N is even */ if (normaltransr) { /* SIDE = 'R', N is even, and TRANSR = 'N' */ if (lower) { /* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'L' */ if (notrans) { /* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L', */ /* and TRANS = 'N' */ i__1 = *n + 1; dtrsm_("R", "U", "T", diag, m, &k, alpha, a, &i__1, & b[k * b_dim1], ldb); i__1 = *n + 1; dgemm_("N", "N", m, &k, &k, &c_b23, &b[k * b_dim1], ldb, &a[k + 1], &i__1, alpha, b, ldb); i__1 = *n + 1; dtrsm_("R", "L", "N", diag, m, &k, &c_b27, &a[1], & i__1, b, ldb); } else { /* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'L', */ /* and TRANS = 'T' */ i__1 = *n + 1; dtrsm_("R", "L", "T", diag, m, &k, alpha, &a[1], & i__1, b, ldb); i__1 = *n + 1; dgemm_("N", "T", m, &k, &k, &c_b23, b, ldb, &a[k + 1], &i__1, alpha, &b[k * b_dim1], ldb); i__1 = *n + 1; dtrsm_("R", "U", "N", diag, m, &k, &c_b27, a, &i__1, & b[k * b_dim1], ldb); } } else { /* SIDE ='R', N is even, TRANSR = 'N', and UPLO = 'U' */ if (notrans) { /* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U', */ /* and TRANS = 'N' */ i__1 = *n + 1; dtrsm_("R", "L", "T", diag, m, &k, alpha, &a[k + 1], & i__1, b, ldb); i__1 = *n + 1; dgemm_("N", "N", m, &k, &k, &c_b23, b, ldb, a, &i__1, alpha, &b[k * b_dim1], ldb); i__1 = *n + 1; dtrsm_("R", "U", "N", diag, m, &k, &c_b27, &a[k], & i__1, &b[k * b_dim1], ldb); } else { /* SIDE ='R', N is even, TRANSR = 'N', UPLO = 'U', */ /* and TRANS = 'T' */ i__1 = *n + 1; dtrsm_("R", "U", "T", diag, m, &k, alpha, &a[k], & i__1, &b[k * b_dim1], ldb); i__1 = *n + 1; dgemm_("N", "T", m, &k, &k, &c_b23, &b[k * b_dim1], ldb, a, &i__1, alpha, b, ldb); i__1 = *n + 1; dtrsm_("R", "L", "N", diag, m, &k, &c_b27, &a[k + 1], &i__1, b, ldb); } } } else { /* SIDE = 'R', N is even, and TRANSR = 'T' */ if (lower) { /* SIDE ='R', N is even, TRANSR = 'T', and UPLO = 'L' */ if (notrans) { /* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'L', */ /* and TRANS = 'N' */ dtrsm_("R", "L", "N", diag, m, &k, alpha, a, &k, &b[k * b_dim1], ldb); dgemm_("N", "T", m, &k, &k, &c_b23, &b[k * b_dim1], ldb, &a[(k + 1) * k], &k, alpha, b, ldb); dtrsm_("R", "U", "T", diag, m, &k, &c_b27, &a[k], &k, b, ldb); } else { /* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'L', */ /* and TRANS = 'T' */ dtrsm_("R", "U", "N", diag, m, &k, alpha, &a[k], &k, b, ldb); dgemm_("N", "N", m, &k, &k, &c_b23, b, ldb, &a[(k + 1) * k], &k, alpha, &b[k * b_dim1], ldb); dtrsm_("R", "L", "T", diag, m, &k, &c_b27, a, &k, &b[ k * b_dim1], ldb); } } else { /* SIDE ='R', N is even, TRANSR = 'T', and UPLO = 'U' */ if (notrans) { /* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'U', */ /* and TRANS = 'N' */ dtrsm_("R", "U", "N", diag, m, &k, alpha, &a[(k + 1) * k], &k, b, ldb); dgemm_("N", "T", m, &k, &k, &c_b23, b, ldb, a, &k, alpha, &b[k * b_dim1], ldb); dtrsm_("R", "L", "T", diag, m, &k, &c_b27, &a[k * k], &k, &b[k * b_dim1], ldb); } else { /* SIDE ='R', N is even, TRANSR = 'T', UPLO = 'U', */ /* and TRANS = 'T' */ dtrsm_("R", "L", "N", diag, m, &k, alpha, &a[k * k], & k, &b[k * b_dim1], ldb); dgemm_("N", "N", m, &k, &k, &c_b23, &b[k * b_dim1], ldb, a, &k, alpha, b, ldb); dtrsm_("R", "U", "T", diag, m, &k, &c_b27, &a[(k + 1) * k], &k, b, ldb); } } } } } return 0; /* End of DTFSM */ } /* dtfsm_ */