/* sdrvrfp.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" #include "blaswrap.h" /* Common Block Declarations */ struct { char srnamt[32]; } srnamc_; #define srnamc_1 srnamc_ /* Table of constant values */ static integer c__0 = 0; static integer c_n1 = -1; static integer c__1 = 1; /* Subroutine */ int sdrvrfp_(integer *nout, integer *nn, integer *nval, integer *nns, integer *nsval, integer *nnt, integer *ntval, real * thresh, real *a, real *asav, real *afac, real *ainv, real *b, real * bsav, real *xact, real *x, real *arf, real *arfinv, real * s_work_slatms__, real *s_work_spot01__, real *s_temp_spot02__, real * s_temp_spot03__, real *s_work_slansy__, real *s_work_spot02__, real * s_work_spot03__) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char uplos[1*2] = "U" "L"; static char forms[1*2] = "N" "T"; /* Format strings */ static char fmt_9999[] = "(1x,a6,\002, UPLO='\002,a1,\002', N =\002,i5" ",\002, type \002,i1,\002, test(\002,i1,\002)=\002,g12.5)"; /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5, i__6, i__7; /* 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__, k, n, kl, ku, nt, lda, ldb, iin, iis, iit, ioff, mode, info, imat; char dist[1]; integer nrhs; char uplo[1]; integer nrun, nfail, iseed[4]; char cform[1]; extern /* Subroutine */ int sget04_(integer *, integer *, real *, integer *, real *, integer *, real *, real *); integer iform; real anorm; char ctype[1]; extern /* Subroutine */ int spot01_(char *, integer *, real *, integer *, real *, integer *, real *, real *); integer iuplo, nerrs, izero; extern /* Subroutine */ int spot02_(char *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *), spot03_(char *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *); logical zerot; extern /* Subroutine */ int slatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char * ), aladhd_(integer *, char *), alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); real rcondc; extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer *, integer *); real cndnum, ainvnm; 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 *), slatms_( integer *, integer *, char *, integer *, char *, real *, integer * , real *, real *, integer *, integer *, char *, real *, integer *, real *, integer *), spftrf_(char *, char *, integer *, real *, integer *), spftri_(char *, char *, integer *, real *, integer *); extern doublereal slansy_(char *, char *, integer *, real *, integer *, real *); extern /* Subroutine */ int spotrf_(char *, integer *, real *, integer *, integer *); real result[4]; extern /* Subroutine */ int spftrs_(char *, char *, integer *, integer *, real *, real *, integer *, integer *), spotri_( char *, integer *, real *, integer *, integer *), stfttr_( char *, char *, integer *, real *, real *, integer *, integer *), strttf_(char *, char *, integer *, real *, integer *, real *, integer *); /* Fortran I/O blocks */ static cilist io___37 = { 0, 0, 0, fmt_9999, 0 }; /* -- LAPACK test routine (version 3.2.0) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2008 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SDRVRFP tests the LAPACK RFP routines: */ /* SPFTRF, SPFTRS, and SPFTRI. */ /* This testing routine follow the same tests as DDRVPO (test for the full */ /* format Symmetric Positive Definite solver). */ /* The tests are performed in Full Format, convertion back and forth from */ /* full format to RFP format are performed using the routines STRTTF and */ /* STFTTR. */ /* First, a specific matrix A of size N is created. There is nine types of */ /* different matrixes possible. */ /* 1. Diagonal 6. Random, CNDNUM = sqrt(0.1/EPS) */ /* 2. Random, CNDNUM = 2 7. Random, CNDNUM = 0.1/EPS */ /* *3. First row and column zero 8. Scaled near underflow */ /* *4. Last row and column zero 9. Scaled near overflow */ /* *5. Middle row and column zero */ /* (* - tests error exits from SPFTRF, no test ratios are computed) */ /* A solution XACT of size N-by-NRHS is created and the associated right */ /* hand side B as well. Then SPFTRF is called to compute L (or U), the */ /* Cholesky factor of A. Then L (or U) is used to solve the linear system */ /* of equations AX = B. This gives X. Then L (or U) is used to compute the */ /* inverse of A, AINV. The following four tests are then performed: */ /* (1) norm( L*L' - A ) / ( N * norm(A) * EPS ) or */ /* norm( U'*U - A ) / ( N * norm(A) * EPS ), */ /* (2) norm(B - A*X) / ( norm(A) * norm(X) * EPS ), */ /* (3) norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ), */ /* (4) ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ), */ /* where EPS is the machine precision, RCOND the condition number of A, and */ /* norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4). */ /* Errors occur when INFO parameter is not as expected. Failures occur when */ /* a test ratios is greater than THRES. */ /* Arguments */ /* ========= */ /* NOUT (input) INTEGER */ /* The unit number for output. */ /* 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. */ /* 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. */ /* NNT (input) INTEGER */ /* The number of values of MATRIX TYPE contained in the vector NTVAL. */ /* NTVAL (input) INTEGER array, dimension (NNT) */ /* The values of matrix type (between 0 and 9 for PO/PP/PF matrices). */ /* 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. */ /* A (workspace) REAL array, dimension (NMAX*NMAX) */ /* ASAV (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*MAXRHS) */ /* BSAV (workspace) REAL array, dimension (NMAX*MAXRHS) */ /* XACT (workspace) REAL array, dimension (NMAX*MAXRHS) */ /* X (workspace) REAL array, dimension (NMAX*MAXRHS) */ /* ARF (workspace) REAL array, dimension ((NMAX*(NMAX+1))/2) */ /* ARFINV (workspace) REAL array, dimension ((NMAX*(NMAX+1))/2) */ /* S_WORK_SLATMS (workspace) REAL array, dimension ( 3*NMAX ) */ /* S_WORK_SPOT01 (workspace) REAL array, dimension ( NMAX ) */ /* S_TEMP_SPOT02 (workspace) REAL array, dimension ( NMAX*MAXRHS ) */ /* S_TEMP_SPOT03 (workspace) REAL array, dimension ( NMAX*NMAX ) */ /* S_WORK_SLATMS (workspace) REAL array, dimension ( NMAX ) */ /* S_WORK_SLANSY (workspace) REAL array, dimension ( NMAX ) */ /* S_WORK_SPOT02 (workspace) REAL array, dimension ( NMAX ) */ /* S_WORK_SPOT03 (workspace) REAL array, dimension ( NMAX ) */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Data statements .. */ /* Parameter adjustments */ --nval; --nsval; --ntval; --a; --asav; --afac; --ainv; --b; --bsav; --xact; --x; --arf; --arfinv; --s_work_slatms__; --s_work_spot01__; --s_temp_spot02__; --s_temp_spot03__; --s_work_slansy__; --s_work_spot02__; --s_work_spot03__; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ nrun = 0; nfail = 0; nerrs = 0; for (i__ = 1; i__ <= 4; ++i__) { iseed[i__ - 1] = iseedy[i__ - 1]; /* L10: */ } i__1 = *nn; for (iin = 1; iin <= i__1; ++iin) { n = nval[iin]; lda = max(n,1); ldb = max(n,1); i__2 = *nns; for (iis = 1; iis <= i__2; ++iis) { nrhs = nsval[iis]; i__3 = *nnt; for (iit = 1; iit <= i__3; ++iit) { imat = ntval[iit]; /* If N.EQ.0, only consider the first type */ if (n == 0 && iit > 1) { goto L120; } /* Skip types 3, 4, or 5 if the matrix size is too small. */ if (imat == 4 && n <= 1) { goto L120; } if (imat == 5 && n <= 2) { goto L120; } /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { *(unsigned char *)uplo = *(unsigned char *)&uplos[iuplo - 1]; /* Do first for CFORM = 'N', then for CFORM = 'C' */ for (iform = 1; iform <= 2; ++iform) { *(unsigned char *)cform = *(unsigned char *)&forms[ iform - 1]; /* Set up parameters with SLATB4 and generate a test */ /* matrix with SLATMS. */ slatb4_("SPO", &imat, &n, &n, ctype, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen) 6); slatms_(&n, &n, dist, iseed, ctype, &s_work_slatms__[ 1], &mode, &cndnum, &anorm, &kl, &ku, uplo, & a[1], &lda, &s_work_slatms__[1], &info); /* Check error code from SLATMS. */ if (info != 0) { alaerh_("SPF", "SLATMS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &c_n1, &iit, &nfail, & nerrs, nout); goto L100; } /* For types 3-5, zero one row and column of the matrix to */ /* test that INFO is returned correctly. */ zerot = imat >= 3 && imat <= 5; if (zerot) { if (iit == 3) { izero = 1; } else if (iit == 4) { izero = n; } else { izero = n / 2 + 1; } ioff = (izero - 1) * lda; /* Set row and column IZERO of A to 0. */ if (iuplo == 1) { i__4 = izero - 1; for (i__ = 1; i__ <= i__4; ++i__) { a[ioff + i__] = 0.f; /* L20: */ } ioff += izero; i__4 = n; for (i__ = izero; i__ <= i__4; ++i__) { a[ioff] = 0.f; ioff += lda; /* L30: */ } } else { ioff = izero; i__4 = izero - 1; for (i__ = 1; i__ <= i__4; ++i__) { a[ioff] = 0.f; ioff += lda; /* L40: */ } ioff -= izero; i__4 = n; for (i__ = izero; i__ <= i__4; ++i__) { a[ioff + i__] = 0.f; /* L50: */ } } } else { izero = 0; } /* Save a copy of the matrix A in ASAV. */ slacpy_(uplo, &n, &n, &a[1], &lda, &asav[1], &lda); /* Compute the condition number of A (RCONDC). */ if (zerot) { rcondc = 0.f; } else { /* Compute the 1-norm of A. */ anorm = slansy_("1", uplo, &n, &a[1], &lda, & s_work_slansy__[1]); /* Factor the matrix A. */ spotrf_(uplo, &n, &a[1], &lda, &info); /* Form the inverse of A. */ spotri_(uplo, &n, &a[1], &lda, &info); /* Compute the 1-norm condition number of A. */ ainvnm = slansy_("1", uplo, &n, &a[1], &lda, & s_work_slansy__[1]); rcondc = 1.f / anorm / ainvnm; /* Restore the matrix A. */ slacpy_(uplo, &n, &n, &asav[1], &lda, &a[1], &lda); } /* Form an exact solution and set the right hand side. */ s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)32, (ftnlen) 6); slarhs_("SPO", "N", uplo, " ", &n, &n, &kl, &ku, & nrhs, &a[1], &lda, &xact[1], &lda, &b[1], & lda, iseed, &info); slacpy_("Full", &n, &nrhs, &b[1], &lda, &bsav[1], & lda); /* Compute the L*L' or U'*U factorization of the */ /* matrix and solve the system. */ slacpy_(uplo, &n, &n, &a[1], &lda, &afac[1], &lda); slacpy_("Full", &n, &nrhs, &b[1], &ldb, &x[1], &ldb); s_copy(srnamc_1.srnamt, "STRTTF", (ftnlen)32, (ftnlen) 6); strttf_(cform, uplo, &n, &afac[1], &lda, &arf[1], & info); s_copy(srnamc_1.srnamt, "SPFTRF", (ftnlen)32, (ftnlen) 6); spftrf_(cform, uplo, &n, &arf[1], &info); /* Check error code from SPFTRF. */ if (info != izero) { /* LANGOU: there is a small hick here: IZERO should */ /* always be INFO however if INFO is ZERO, ALAERH does not */ /* complain. */ alaerh_("SPF", "SPFSV ", &info, &izero, uplo, &n, &n, &c_n1, &c_n1, &nrhs, &iit, &nfail, & nerrs, nout); goto L100; } /* Skip the tests if INFO is not 0. */ if (info != 0) { goto L100; } s_copy(srnamc_1.srnamt, "SPFTRS", (ftnlen)32, (ftnlen) 6); spftrs_(cform, uplo, &n, &nrhs, &arf[1], &x[1], &ldb, &info); s_copy(srnamc_1.srnamt, "STFTTR", (ftnlen)32, (ftnlen) 6); stfttr_(cform, uplo, &n, &arf[1], &afac[1], &lda, & info); /* Reconstruct matrix from factors and compute */ /* residual. */ slacpy_(uplo, &n, &n, &afac[1], &lda, &asav[1], &lda); spot01_(uplo, &n, &a[1], &lda, &afac[1], &lda, & s_work_spot01__[1], result); slacpy_(uplo, &n, &n, &asav[1], &lda, &afac[1], &lda); /* Form the inverse and compute the residual. */ if (n % 2 == 0) { i__4 = n + 1; i__5 = n / 2; i__6 = n + 1; i__7 = n + 1; slacpy_("A", &i__4, &i__5, &arf[1], &i__6, & arfinv[1], &i__7); } else { i__4 = (n + 1) / 2; slacpy_("A", &n, &i__4, &arf[1], &n, &arfinv[1], & n); } s_copy(srnamc_1.srnamt, "SPFTRI", (ftnlen)32, (ftnlen) 6); spftri_(cform, uplo, &n, &arfinv[1], &info); s_copy(srnamc_1.srnamt, "STFTTR", (ftnlen)32, (ftnlen) 6); stfttr_(cform, uplo, &n, &arfinv[1], &ainv[1], &lda, & info); /* Check error code from SPFTRI. */ if (info != 0) { alaerh_("SPO", "SPFTRI", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); } spot03_(uplo, &n, &a[1], &lda, &ainv[1], &lda, & s_temp_spot03__[1], &lda, &s_work_spot03__[1], &rcondc, &result[1]); /* Compute residual of the computed solution. */ slacpy_("Full", &n, &nrhs, &b[1], &lda, & s_temp_spot02__[1], &lda); spot02_(uplo, &n, &nrhs, &a[1], &lda, &x[1], &lda, & s_temp_spot02__[1], &lda, &s_work_spot02__[1], &result[2]); /* Check solution from generated exact solution. */ sget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); nt = 4; /* 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) { aladhd_(nout, "SPF"); } io___37.ciunit = *nout; s_wsfe(&io___37); do_fio(&c__1, "SPFSV ", (ftnlen)6); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&iit, (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; } /* L60: */ } nrun += nt; L100: ; } /* L110: */ } L120: ; } /* L980: */ } /* L130: */ } /* Print a summary of the results. */ alasvm_("SPF", nout, &nfail, &nrun, &nerrs); return 0; /* End of SDRVRFP */ } /* sdrvrfp_ */