void StrandBlockSolver::lspMap() { int mm,nn,jj,ii,j1,j2,jm,jmax,nmax,info,ldu,ldvt,rows,cols,lwork; double dsm,dx,dy,ds,w,r1,r2,rs,cond,rcond,xn,yn,ax,ay,xu,xl,bu,bl,xcn,ycn; double b[4]; double* sv; double* work1; double* uu; double* vt; double* dr; double** lspT; char u='U',jobu='n',jobvt='a'; cond = 0.; ldu = 1; ldvt = 2; cols = 2; for (int n=0; n<nNodes-nGnodes; n++){ mm = ncsp(n); rows = mm; ii = cols; if (rows < ii) ii = rows; jj = cols; if (rows > jj) jj = rows; lwork = 1; if (3*ii+jj > lwork) lwork = 3*ii+jj; if (5*ii > lwork) lwork = 5*ii; uu = new double[ldu*ldu]; sv = new double[cols]; vt = new double[ldvt*cols]; work1 = new double[lwork]; dr = new double[rows*2]; lspT = new double*[nPstr+1]; for (int j=0; j<nPstr+1; j++) lspT[j] = new double[rows]; rcond = 0.; info = 0; for (int m=0; m<ldu*ldu; m++) uu [m] = 0.; for (int m=0; m<cols; m++) sv [m] = 0.; for (int m=0; m<ldvt*cols; m++) vt [m] = 0.; for (int m=0; m<lwork; m++) work1[m] = 0.; double work [2] = {0.,0.}; double work2[4] = {0.,0.,0.,0.}; int iwork[2] = {0,0}; int ipiv [2] = {0,0}; for (int j=1; j<nPstr+1; j++){ //mid strand nodes // coordinates of the mid-strand location in question jm = j-1; xn = .5*(x(0,j,n)+x(0,jm,n)); yn = .5*(x(1,j,n)+x(1,jm,n)); // find data centroid xcn = 0.; ycn = 0.; for (int m=0; m<mm; m++){ nn = csp[n][m]; xcn = xcn+xc(0,j,nn); ycn = ycn+xc(1,j,nn); } xcn = xcn/double(mm); ycn = ycn/double(mm); // find plane which most closely fits surrounding cell centers for (int m=0; m<mm; m++){ nn = csp[n][m]; dr[m ] = xc(0,j,nn)-xcn; dr[m+mm] = xc(1,j,nn)-ycn; } sgesvd_(jobu,jobvt,rows,cols,dr,rows,sv,uu,ldu,vt,ldvt,work1,lwork,info); if (info != 0){ cout << "\n*** svd procedure failure in lspMap ***" << endl; exit(0); } ax = vt[0]; ay = vt[2]; ds = 1./sqrt(ax*ax+ay*ay); ax = ax*ds; ay = ay*ds; // compute 2d least squares problem with projected distances // largest distance in stencil dsm = 0.; for (int m=0; m<mm; m++){ nn = csp[n][m]; dx = xc(0,j,nn)-xn; dy = xc(1,j,nn)-yn; ds = dx*ax+dy*ay; ds = ds*ds; if (ds > dsm) dsm = ds; } dsm = 1./sqrt(dsm); // form least squares matrix jj = jm; for (int m=0; m<4; m++) b[m] = 0.; for (int m=0; m<mm; m++){ nn = csp[n][m]; dx = xc(0,j,nn)-xn; dy = xc(1,j,nn)-yn; ds =(dx*ax+dy*ay)*dsm; w = 1./(ds*ds); b[0] = b[0]+w; b[2] = b[2]+w*ds; b[3] = b[3]+w*ds*ds; } // find max abs row sum for condition number computation r1 = fabs(b[0])+fabs(b[2]); r2 = fabs(b[1])+fabs(b[3]); rs = r1; if (r2 > rs) rs = r2; // invert matrix and determine condition number ii = 2; ssytrf_(u,ii,b,ii,ipiv,work,ii,info); ssycon_(u,ii,b,ii,ipiv,rs,rcond,work2,iwork,info); ssytri_(u,ii,b,ii,ipiv,work,info); rcond = 1./rcond; if (rcond > cond){ nmax = n; jmax = j; cond = rcond; } // form and store least squares coefficient for (int m=0; m<mm; m++){ nn = csp[n][m]; dx = xc(0,j,nn)-xn; dy = xc(1,j,nn)-yn; ds =(dx*ax+dy*ay)*dsm; w = 1./(ds*ds); lspT[j][m] =(b[0]*w + b[2]*w*ds); } } // interpolate projected coefficients to the nodal positions along each strand for (int j=0; j<nPstr+1; j++){ if (j == 0 ){ j1 = 1; j2 = 2; } else if (j == nPstr){ j1 = nPstr-1; j2 = nPstr; } else{ j1 = j; j2 = j+1; } xn = xStr(j); jm = j1-1; xl = .5*(xStr(jm)+xStr(j1)); jm = j2-1; xu = .5*(xStr(jm)+xStr(j2)); bl =(xu-xn)/(xu-xl); bu =(xn-xl)/(xu-xl); indlsp(0,j,n,ii); for (int m=0; m<mm; m++){ lsp[ii ][m] = bl*lspT[j1][m]; lsp[ii+1][m] = bu*lspT[j2][m]; } } delete [] sv; delete [] uu; delete [] vt; delete [] work1; delete [] dr; for (int j=0; j<nPstr+1; j++) delete [] lspT[j]; delete [] lspT; } // output condition information xn = x(0,jmax,nmax); yn = x(1,jmax,nmax); cout << "\nMaximum condition number for LS procedure: " << cond << endl << "Index of maximum condition number: " << nmax << "\t" << jmax << endl << "Coordinates of maximum condition number: " << xn << "\t" << yn << "\n" << endl; /* // try using volume averaging on outer boundary nodes for (int n=0; n<nNodes-nGnodes; n++){ mm = ncsp(n); for (int j=nPstr; j<nPstr+1; j++){ if (j == 0 ) jj = 1; else if (j == nPstr) jj = nPstr-1; else jj = j; w = 0.; for (int k=0; k<2; k++){ indlsp(k,j,n,ii); for (int m=0; m<mm; m++){ nn = csp[n][m]; lsp[ii][m] = v(jj,nn); w += v(jj,nn); } jj++; } w = 1./w; for (int k=0; k<2; k++){ indlsp(k,j,n,ii); for (int m=0; m<mm; m++){ lsp[ii][m] = lsp[ii][m]*w; }}}} */ }
/* Subroutine */ int sdrvsy_(logical *dotype, integer *nn, integer *nval, integer *nrhs, real *thresh, logical *tsterr, integer *nmax, real *a, real *afac, real *ainv, real *b, real *x, real *xact, real *work, real *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char uplos[1*2] = "U" "L"; static char facts[1*2] = "F" "N"; /* Format strings */ static char fmt_9999[] = "(1x,a,\002, UPLO='\002,a1,\002', N =\002,i5" ",\002, type \002,i2,\002, test \002,i2,\002, ratio =\002,g12.5)"; static char fmt_9998[] = "(1x,a,\002, FACT='\002,a1,\002', UPLO='\002," "a1,\002', N =\002,i5,\002, type \002,i2,\002, test \002,i2,\002," " ratio =\002,g12.5)"; /* System generated locals */ address a__1[2]; integer i__1, i__2, i__3, i__4, i__5[2]; char ch__1[2]; /* Local variables */ integer i__, j, k, n, i1, i2, k1, nb, in, kl, ku, nt, lda; char fact[1]; integer ioff, mode, imat, info; char path[3], dist[1], uplo[1], type__[1]; integer nrun, ifact, nfail, iseed[4], nbmin; real rcond; integer nimat; real anorm; integer iuplo, izero, nerrs; integer lwork; logical zerot; char xtype[1]; real rcondc; real cndnum, ainvnm; real result[6]; /* Fortran I/O blocks */ static cilist io___42 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___45 = { 0, 0, 0, fmt_9998, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SDRVSY tests the driver routines SSYSV and -SVX. */ /* Arguments */ /* ========= */ /* DOTYPE (input) LOGICAL array, dimension (NTYPES) */ /* The matrix types to be used for testing. Matrices of type j */ /* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */ /* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */ /* NN (input) INTEGER */ /* The number of values of N contained in the vector NVAL. */ /* NVAL (input) INTEGER array, dimension (NN) */ /* The values of the matrix dimension N. */ /* NRHS (input) INTEGER */ /* The number of right hand side vectors to be generated for */ /* each linear system. */ /* THRESH (input) REAL */ /* The threshold value for the test ratios. A result is */ /* included in the output file if RESULT >= THRESH. To have */ /* every test ratio printed, use THRESH = 0. */ /* TSTERR (input) LOGICAL */ /* Flag that indicates whether error exits are to be tested. */ /* NMAX (input) INTEGER */ /* The maximum value permitted for N, used in dimensioning the */ /* work arrays. */ /* A (workspace) REAL array, dimension (NMAX*NMAX) */ /* AFAC (workspace) REAL array, dimension (NMAX*NMAX) */ /* AINV (workspace) REAL array, dimension (NMAX*NMAX) */ /* B (workspace) REAL array, dimension (NMAX*NRHS) */ /* X (workspace) REAL array, dimension (NMAX*NRHS) */ /* XACT (workspace) REAL array, dimension (NMAX*NRHS) */ /* WORK (workspace) REAL array, dimension */ /* (NMAX*max(2,NRHS)) */ /* RWORK (workspace) REAL array, dimension (NMAX+2*NRHS) */ /* IWORK (workspace) INTEGER array, dimension (2*NMAX) */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "SY", (ftnlen)2, (ftnlen)2); nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } /* Computing MAX */ i__1 = *nmax << 1, i__2 = *nmax * *nrhs; lwork = max(i__1,i__2); /* Test the error exits */ if (*tsterr) { serrvx_(path, nout); } infoc_1.infot = 0; /* Set the block size and minimum block size for testing. */ nb = 1; nbmin = 2; xlaenv_(&c__1, &nb); xlaenv_(&c__2, &nbmin); /* Do for each value of N in NVAL */ i__1 = *nn; for (in = 1; in <= i__1; ++in) { n = nval[in]; lda = max(n,1); *(unsigned char *)xtype = 'N'; nimat = 10; if (n <= 0) { nimat = 1; } i__2 = nimat; for (imat = 1; imat <= i__2; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L170; } /* Skip types 3, 4, 5, or 6 if the matrix size is too small. */ zerot = imat >= 3 && imat <= 6; if (zerot && n < imat - 2) { goto L170; } /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; /* Set up parameters with SLATB4 and generate a test matrix */ /* with SLATMS. */ slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen)6); slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1], &info); /* Check error code from SLATMS. */ if (info != 0) { alaerh_(path, "SLATMS", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L160; } /* For types 3-6, zero one or more rows and columns of the */ /* matrix to test that INFO is returned correctly. */ if (zerot) { if (imat == 3) { izero = 1; } else if (imat == 4) { izero = n; } else { izero = n / 2 + 1; } if (imat < 6) { /* Set row and column IZERO to zero. */ if (iuplo == 1) { ioff = (izero - 1) * lda; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { a[ioff + i__] = 0.f; /* L20: */ } ioff += izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { a[ioff] = 0.f; ioff += lda; /* L30: */ } } else { ioff = izero; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { a[ioff] = 0.f; ioff += lda; /* L40: */ } ioff -= izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { a[ioff + i__] = 0.f; /* L50: */ } } } else { ioff = 0; if (iuplo == 1) { /* Set the first IZERO rows and columns to zero. */ i__3 = n; for (j = 1; j <= i__3; ++j) { i2 = min(j,izero); i__4 = i2; for (i__ = 1; i__ <= i__4; ++i__) { a[ioff + i__] = 0.f; /* L60: */ } ioff += lda; /* L70: */ } } else { /* Set the last IZERO rows and columns to zero. */ i__3 = n; for (j = 1; j <= i__3; ++j) { i1 = max(j,izero); i__4 = n; for (i__ = i1; i__ <= i__4; ++i__) { a[ioff + i__] = 0.f; /* L80: */ } ioff += lda; /* L90: */ } } } } else { izero = 0; } for (ifact = 1; ifact <= 2; ++ifact) { /* Do first for FACT = 'F', then for other values. */ *(unsigned char *)fact = *(unsigned char *)&facts[ifact - 1]; /* Compute the condition number for comparison with */ /* the value returned by SSYSVX. */ if (zerot) { if (ifact == 1) { goto L150; } rcondc = 0.f; } else if (ifact == 1) { /* Compute the 1-norm of A. */ anorm = slansy_("1", uplo, &n, &a[1], &lda, &rwork[1]); /* Factor the matrix A. */ slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); ssytrf_(uplo, &n, &afac[1], &lda, &iwork[1], &work[1], &lwork, &info); /* Compute inv(A) and take its norm. */ slacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda); ssytri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1], &info); ainvnm = slansy_("1", uplo, &n, &ainv[1], &lda, & rwork[1]); /* Compute the 1-norm condition number of A. */ if (anorm <= 0.f || ainvnm <= 0.f) { rcondc = 1.f; } else { rcondc = 1.f / anorm / ainvnm; } } /* Form an exact solution and set the right hand side. */ s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)32, (ftnlen)6); slarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, nrhs, & a[1], &lda, &xact[1], &lda, &b[1], &lda, iseed, & info); *(unsigned char *)xtype = 'C'; /* --- Test SSYSV --- */ if (ifact == 2) { slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); slacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda); /* Factor the matrix and solve the system using SSYSV. */ s_copy(srnamc_1.srnamt, "SSYSV ", (ftnlen)32, (ftnlen) 6); ssysv_(uplo, &n, nrhs, &afac[1], &lda, &iwork[1], &x[ 1], &lda, &work[1], &lwork, &info); /* Adjust the expected value of INFO to account for */ /* pivoting. */ k = izero; if (k > 0) { L100: if (iwork[k] < 0) { if (iwork[k] != -k) { k = -iwork[k]; goto L100; } } else if (iwork[k] != k) { k = iwork[k]; goto L100; } } /* Check error code from SSYSV . */ if (info != k) { alaerh_(path, "SSYSV ", &info, &k, uplo, &n, &n, & c_n1, &c_n1, nrhs, &imat, &nfail, &nerrs, nout); goto L120; } else if (info != 0) { goto L120; } /* Reconstruct matrix from factors and compute */ /* residual. */ ssyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[ 1], &ainv[1], &lda, &rwork[1], result); /* Compute residual of the computed solution. */ slacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda); spot02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, & work[1], &lda, &rwork[1], &result[1]); /* Check solution from generated exact solution. */ sget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); nt = 3; /* Print information about the tests that did not pass */ /* the threshold. */ i__3 = nt; for (k = 1; k <= i__3; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } io___42.ciunit = *nout; s_wsfe(&io___42); do_fio(&c__1, "SSYSV ", (ftnlen)6); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(real)); e_wsfe(); ++nfail; } /* L110: */ } nrun += nt; L120: ; } /* --- Test SSYSVX --- */ if (ifact == 2) { slaset_(uplo, &n, &n, &c_b49, &c_b49, &afac[1], &lda); } slaset_("Full", &n, nrhs, &c_b49, &c_b49, &x[1], &lda); /* Solve the system and compute the condition number and */ /* error bounds using SSYSVX. */ s_copy(srnamc_1.srnamt, "SSYSVX", (ftnlen)32, (ftnlen)6); ssysvx_(fact, uplo, &n, nrhs, &a[1], &lda, &afac[1], &lda, &iwork[1], &b[1], &lda, &x[1], &lda, &rcond, & rwork[1], &rwork[*nrhs + 1], &work[1], &lwork, & iwork[n + 1], &info); /* Adjust the expected value of INFO to account for */ /* pivoting. */ k = izero; if (k > 0) { L130: if (iwork[k] < 0) { if (iwork[k] != -k) { k = -iwork[k]; goto L130; } } else if (iwork[k] != k) { k = iwork[k]; goto L130; } } /* Check the error code from SSYSVX. */ if (info != k) { /* Writing concatenation */ i__5[0] = 1, a__1[0] = fact; i__5[1] = 1, a__1[1] = uplo; s_cat(ch__1, a__1, i__5, &c__2, (ftnlen)2); alaerh_(path, "SSYSVX", &info, &k, ch__1, &n, &n, & c_n1, &c_n1, nrhs, &imat, &nfail, &nerrs, nout); goto L150; } if (info == 0) { if (ifact >= 2) { /* Reconstruct matrix from factors and compute */ /* residual. */ ssyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, & iwork[1], &ainv[1], &lda, &rwork[(*nrhs << 1) + 1], result); k1 = 1; } else { k1 = 2; } /* Compute residual of the computed solution. */ slacpy_("Full", &n, nrhs, &b[1], &lda, &work[1], &lda); spot02_(uplo, &n, nrhs, &a[1], &lda, &x[1], &lda, & work[1], &lda, &rwork[(*nrhs << 1) + 1], & result[1]); /* Check solution from generated exact solution. */ sget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); /* Check the error bounds from iterative refinement. */ spot05_(uplo, &n, nrhs, &a[1], &lda, &b[1], &lda, &x[ 1], &lda, &xact[1], &lda, &rwork[1], &rwork[* nrhs + 1], &result[3]); } else { k1 = 6; } /* Compare RCOND from SSYSVX with the computed value */ /* in RCONDC. */ result[5] = sget06_(&rcond, &rcondc); /* Print information about the tests that did not pass */ /* the threshold. */ for (k = k1; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } io___45.ciunit = *nout; s_wsfe(&io___45); do_fio(&c__1, "SSYSVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(real)); e_wsfe(); ++nfail; } /* L140: */ } nrun = nrun + 7 - k1; L150: ; } L160: ; } L170: ; } /* L180: */ } /* Print a summary of the results. */ alasvm_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of SDRVSY */ } /* sdrvsy_ */
/* Subroutine */ int schksy_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, real * thresh, logical *tsterr, integer *nmax, real *a, real *afac, real * ainv, real *b, real *x, real *xact, real *work, real *rwork, integer * iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char uplos[1*2] = "U" "L"; /* Format strings */ static char fmt_9999[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, " "NB =\002,i4,\002, type \002,i2,\002, test \002,i2,\002, ratio " "=\002,g12.5)"; static char fmt_9998[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002, " "NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i2,\002) =\002,g" "12.5)"; static char fmt_9997[] = "(\002 UPLO = '\002,a1,\002', N =\002,i5,\002" ",\002,10x,\002 type \002,i2,\002, test(\002,i2,\002) =\002,g12.5)" ; /* System generated locals */ integer i__1, i__2, i__3, i__4; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Local variables */ integer i__, j, k, n, i1, i2, nb, in, kl, ku, nt, lda, inb, ioff, mode, imat, info; char path[3], dist[1]; integer irhs, nrhs; char uplo[1], type__[1]; integer nrun; extern /* Subroutine */ int alahd_(integer *, char *); integer nfail, iseed[4]; real rcond; extern /* Subroutine */ int sget04_(integer *, integer *, real *, integer *, real *, integer *, real *, real *); integer nimat; extern doublereal sget06_(real *, real *); real anorm; extern /* Subroutine */ int spot02_(char *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *); integer iuplo, izero, nerrs; extern /* Subroutine */ int spot03_(char *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *), spot05_(char *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *); integer lwork; logical zerot; extern /* Subroutine */ int ssyt01_(char *, integer *, real *, integer *, real *, integer *, integer *, real *, integer *, real *, real *); char xtype[1]; extern /* Subroutine */ int slatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char * ), alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); real rcondc; extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); real cndnum; logical trfcon; extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer * , integer *, integer *), xlaenv_( integer *, integer *), slatms_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, integer *, integer *, char *, real *, integer *, real *, integer *); extern doublereal slansy_(char *, char *, integer *, real *, integer *, real *); real result[8]; extern /* Subroutine */ int ssycon_(char *, integer *, real *, integer *, integer *, real *, real *, real *, integer *, integer *), serrsy_(char *, integer *), ssyrfs_(char *, integer *, integer *, real *, integer *, real *, integer *, integer *, real * , integer *, real *, integer *, real *, real *, real *, integer *, integer *), ssytrf_(char *, integer *, real *, integer *, integer *, real *, integer *, integer *), ssytri_(char *, integer *, real *, integer *, integer *, real *, integer *), ssytrs_(char *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___39 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___42 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___44 = { 0, 0, 0, fmt_9997, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SCHKSY tests SSYTRF, -TRI, -TRS, -RFS, and -CON. */ /* Arguments */ /* ========= */ /* DOTYPE (input) LOGICAL array, dimension (NTYPES) */ /* The matrix types to be used for testing. Matrices of type j */ /* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */ /* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */ /* NN (input) INTEGER */ /* The number of values of N contained in the vector NVAL. */ /* NVAL (input) INTEGER array, dimension (NN) */ /* The values of the matrix dimension N. */ /* NNB (input) INTEGER */ /* The number of values of NB contained in the vector NBVAL. */ /* NBVAL (input) INTEGER array, dimension (NBVAL) */ /* The values of the blocksize NB. */ /* NNS (input) INTEGER */ /* The number of values of NRHS contained in the vector NSVAL. */ /* NSVAL (input) INTEGER array, dimension (NNS) */ /* The values of the number of right hand sides NRHS. */ /* THRESH (input) REAL */ /* The threshold value for the test ratios. A result is */ /* included in the output file if RESULT >= THRESH. To have */ /* every test ratio printed, use THRESH = 0. */ /* TSTERR (input) LOGICAL */ /* Flag that indicates whether error exits are to be tested. */ /* NMAX (input) INTEGER */ /* The maximum value permitted for N, used in dimensioning the */ /* work arrays. */ /* A (workspace) REAL array, dimension (NMAX*NMAX) */ /* AFAC (workspace) REAL array, dimension (NMAX*NMAX) */ /* AINV (workspace) REAL array, dimension (NMAX*NMAX) */ /* B (workspace) REAL array, dimension (NMAX*NSMAX) */ /* where NSMAX is the largest entry in NSVAL. */ /* X (workspace) REAL array, dimension (NMAX*NSMAX) */ /* XACT (workspace) REAL array, dimension (NMAX*NSMAX) */ /* WORK (workspace) REAL array, dimension */ /* (NMAX*max(3,NSMAX)) */ /* RWORK (workspace) REAL array, dimension */ /* (max(NMAX,2*NSMAX)) */ /* IWORK (workspace) INTEGER array, dimension (2*NMAX) */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --iwork; --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nbval; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "SY", (ftnlen)2, (ftnlen)2); nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } /* Test the error exits */ if (*tsterr) { serrsy_(path, nout); } infoc_1.infot = 0; xlaenv_(&c__2, &c__2); /* Do for each value of N in NVAL */ i__1 = *nn; for (in = 1; in <= i__1; ++in) { n = nval[in]; lda = max(n,1); *(unsigned char *)xtype = 'N'; nimat = 10; if (n <= 0) { nimat = 1; } izero = 0; i__2 = nimat; for (imat = 1; imat <= i__2; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L170; } /* Skip types 3, 4, 5, or 6 if the matrix size is too small. */ zerot = imat >= 3 && imat <= 6; if (zerot && n < imat - 2) { goto L170; } /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; /* Set up parameters with SLATB4 and generate a test matrix */ /* with SLATMS. */ slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen)6); slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, & cndnum, &anorm, &kl, &ku, uplo, &a[1], &lda, &work[1], &info); /* Check error code from SLATMS. */ if (info != 0) { alaerh_(path, "SLATMS", &info, &c__0, uplo, &n, &n, &c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); goto L160; } /* For types 3-6, zero one or more rows and columns of */ /* the matrix to test that INFO is returned correctly. */ if (zerot) { if (imat == 3) { izero = 1; } else if (imat == 4) { izero = n; } else { izero = n / 2 + 1; } if (imat < 6) { /* Set row and column IZERO to zero. */ if (iuplo == 1) { ioff = (izero - 1) * lda; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { a[ioff + i__] = 0.f; /* L20: */ } ioff += izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { a[ioff] = 0.f; ioff += lda; /* L30: */ } } else { ioff = izero; i__3 = izero - 1; for (i__ = 1; i__ <= i__3; ++i__) { a[ioff] = 0.f; ioff += lda; /* L40: */ } ioff -= izero; i__3 = n; for (i__ = izero; i__ <= i__3; ++i__) { a[ioff + i__] = 0.f; /* L50: */ } } } else { ioff = 0; if (iuplo == 1) { /* Set the first IZERO rows and columns to zero. */ i__3 = n; for (j = 1; j <= i__3; ++j) { i2 = min(j,izero); i__4 = i2; for (i__ = 1; i__ <= i__4; ++i__) { a[ioff + i__] = 0.f; /* L60: */ } ioff += lda; /* L70: */ } } else { /* Set the last IZERO rows and columns to zero. */ i__3 = n; for (j = 1; j <= i__3; ++j) { i1 = max(j,izero); i__4 = n; for (i__ = i1; i__ <= i__4; ++i__) { a[ioff + i__] = 0.f; /* L80: */ } ioff += lda; /* L90: */ } } } } else { izero = 0; } /* Do for each value of NB in NBVAL */ i__3 = *nnb; for (inb = 1; inb <= i__3; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the L*D*L' or U*D*U' factorization of the */ /* matrix. */ slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); lwork = max(2,nb) * lda; s_copy(srnamc_1.srnamt, "SSYTRF", (ftnlen)32, (ftnlen)6); ssytrf_(uplo, &n, &afac[1], &lda, &iwork[1], &ainv[1], & lwork, &info); /* Adjust the expected value of INFO to account for */ /* pivoting. */ k = izero; if (k > 0) { L100: if (iwork[k] < 0) { if (iwork[k] != -k) { k = -iwork[k]; goto L100; } } else if (iwork[k] != k) { k = iwork[k]; goto L100; } } /* Check error code from SSYTRF. */ if (info != k) { alaerh_(path, "SSYTRF", &info, &k, uplo, &n, &n, & c_n1, &c_n1, &nb, &imat, &nfail, &nerrs, nout); } if (info != 0) { trfcon = TRUE_; } else { trfcon = FALSE_; } /* + TEST 1 */ /* Reconstruct matrix from factors and compute residual. */ ssyt01_(uplo, &n, &a[1], &lda, &afac[1], &lda, &iwork[1], &ainv[1], &lda, &rwork[1], result); nt = 1; /* + TEST 2 */ /* Form the inverse and compute the residual. */ if (inb == 1 && ! trfcon) { slacpy_(uplo, &n, &n, &afac[1], &lda, &ainv[1], &lda); s_copy(srnamc_1.srnamt, "SSYTRI", (ftnlen)32, (ftnlen) 6); ssytri_(uplo, &n, &ainv[1], &lda, &iwork[1], &work[1], &info); /* Check error code from SSYTRI. */ if (info != 0) { alaerh_(path, "SSYTRI", &info, &c_n1, uplo, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); } spot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, &work[ 1], &lda, &rwork[1], &rcondc, &result[1]); nt = 2; } /* Print information about the tests that did not pass */ /* the threshold. */ i__4 = nt; for (k = 1; k <= i__4; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___39.ciunit = *nout; s_wsfe(&io___39); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(integer) ); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(real)); e_wsfe(); ++nfail; } /* L110: */ } nrun += nt; /* Skip the other tests if this is not the first block */ /* size. */ if (inb > 1) { goto L150; } /* Do only the condition estimate if INFO is not 0. */ if (trfcon) { rcondc = 0.f; goto L140; } i__4 = *nns; for (irhs = 1; irhs <= i__4; ++irhs) { nrhs = nsval[irhs]; /* + TEST 3 */ /* Solve and compute residual for A * X = B. */ s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)32, (ftnlen) 6); slarhs_(path, xtype, uplo, " ", &n, &n, &kl, &ku, & nrhs, &a[1], &lda, &xact[1], &lda, &b[1], & lda, iseed, &info); slacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "SSYTRS", (ftnlen)32, (ftnlen) 6); ssytrs_(uplo, &n, &nrhs, &afac[1], &lda, &iwork[1], & x[1], &lda, &info); /* Check error code from SSYTRS. */ if (info != 0) { alaerh_(path, "SSYTRS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } slacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], & lda); spot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, & work[1], &lda, &rwork[1], &result[2]); /* + TEST 4 */ /* Check solution from generated exact solution. */ sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); /* + TESTS 5, 6, and 7 */ /* Use iterative refinement to improve the solution. */ s_copy(srnamc_1.srnamt, "SSYRFS", (ftnlen)32, (ftnlen) 6); ssyrfs_(uplo, &n, &nrhs, &a[1], &lda, &afac[1], &lda, &iwork[1], &b[1], &lda, &x[1], &lda, &rwork[1] , &rwork[nrhs + 1], &work[1], &iwork[n + 1], & info); /* Check error code from SSYRFS. */ if (info != 0) { alaerh_(path, "SSYRFS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &nrhs, &imat, &nfail, & nerrs, nout); } sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[4]); spot05_(uplo, &n, &nrhs, &a[1], &lda, &b[1], &lda, &x[ 1], &lda, &xact[1], &lda, &rwork[1], &rwork[ nrhs + 1], &result[5]); /* Print information about the tests that did not pass */ /* the threshold. */ for (k = 3; k <= 7; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___42.ciunit = *nout; s_wsfe(&io___42); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&nrhs, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen) sizeof(real)); e_wsfe(); ++nfail; } /* L120: */ } nrun += 5; /* L130: */ } /* + TEST 8 */ /* Get an estimate of RCOND = 1/CNDNUM. */ L140: anorm = slansy_("1", uplo, &n, &a[1], &lda, &rwork[1]); s_copy(srnamc_1.srnamt, "SSYCON", (ftnlen)32, (ftnlen)6); ssycon_(uplo, &n, &afac[1], &lda, &iwork[1], &anorm, & rcond, &work[1], &iwork[n + 1], &info); /* Check error code from SSYCON. */ if (info != 0) { alaerh_(path, "SSYCON", &info, &c__0, uplo, &n, &n, & c_n1, &c_n1, &c_n1, &imat, &nfail, &nerrs, nout); } result[7] = sget06_(&rcond, &rcondc); /* Print information about the tests that did not pass */ /* the threshold. */ if (result[7] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___44.ciunit = *nout; s_wsfe(&io___44); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&c__8, (ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&result[7], (ftnlen)sizeof(real) ); e_wsfe(); ++nfail; } ++nrun; L150: ; } L160: ; } L170: ; } /* L180: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of SCHKSY */ } /* schksy_ */