//! see full matrix case. inline void decomc(double alpha,double beta,const MatrixReal& Jac) { for(int j=1;j<=n;j++) //#include "Ivdep.hpp" //gcc does not like ivdep here. for(int i=MAX(1,j-nsup);i<=MIN(n,j+nsub);i++) E2R.set(i,j,-Jac(i,j)); #include "Ivdep.hpp" for(int i=1;i<=n;i++) { E2R.Re(i,i)+=alpha; E2R.Im(i,i)=beta; } int nn=n,knsub=nsub,knsup=nsup,lldab=ldab,info; zgbtrf_(&nn,&nn,&knsub,&knsup,&E2R,&lldab,&(ipivc[0]),&info); if(info!=0) throw OdesException("odes::Matrices::decomc zgetrf,info=",info); }
int zgbsv_(int *n, int *kl, int *ku, int * nrhs, doublecomplex *ab, int *ldab, int *ipiv, doublecomplex * b, int *ldb, int *info) { /* System generated locals */ int ab_dim1, ab_offset, b_dim1, b_offset, i__1; /* Local variables */ extern int xerbla_(char *, int *), zgbtrf_( int *, int *, int *, int *, doublecomplex *, int *, int *, int *), zgbtrs_(char *, int *, int *, int *, int *, doublecomplex *, int *, int *, doublecomplex *, int *, int *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZGBSV computes the solution to a complex system of linear equations */ /* A * X = B, where A is a band matrix of order N with KL subdiagonals */ /* and KU superdiagonals, and X and B are N-by-NRHS matrices. */ /* The LU decomposition with partial pivoting and row interchanges is */ /* used to factor A as A = L * U, where L is a product of permutation */ /* and unit lower triangular matrices with KL subdiagonals, and U is */ /* upper triangular with KL+KU superdiagonals. The factored form of A */ /* is then used to solve the system of equations A * X = B. */ /* Arguments */ /* ========= */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* KL (input) INTEGER */ /* The number of subdiagonals within the band of A. KL >= 0. */ /* KU (input) INTEGER */ /* The number of superdiagonals within the band of A. KU >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrix B. NRHS >= 0. */ /* AB (input/output) COMPLEX*16 array, dimension (LDAB,N) */ /* On entry, the matrix A in band storage, in rows KL+1 to */ /* 2*KL+KU+1; rows 1 to KL of the array need not be set. */ /* The j-th column of A is stored in the j-th column of the */ /* array AB as follows: */ /* AB(KL+KU+1+i-j,j) = A(i,j) for MAX(1,j-KU)<=i<=MIN(N,j+KL) */ /* On exit, details of the factorization: U is stored as an */ /* upper triangular band matrix with KL+KU superdiagonals in */ /* rows 1 to KL+KU+1, and the multipliers used during the */ /* factorization are stored in rows KL+KU+2 to 2*KL+KU+1. */ /* See below for further details. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= 2*KL+KU+1. */ /* IPIV (output) INTEGER array, dimension (N) */ /* The pivot indices that define the permutation matrix P; */ /* row i of the matrix was interchanged with row IPIV(i). */ /* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */ /* On entry, the N-by-NRHS right hand side matrix B. */ /* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= MAX(1,N). */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, U(i,i) is exactly zero. The factorization */ /* has been completed, but the factor U is exactly */ /* singular, and the solution has not been computed. */ /* Further Details */ /* =============== */ /* The band storage scheme is illustrated by the following example, when */ /* M = N = 6, KL = 2, KU = 1: */ /* On entry: On exit: */ /* * * * + + + * * * u14 u25 u36 */ /* * * + + + + * * u13 u24 u35 u46 */ /* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 */ /* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 */ /* a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 * */ /* a31 a42 a53 a64 * * m31 m42 m53 m64 * * */ /* Array elements marked * are not used by the routine; elements marked */ /* + need not be set on entry, but are required by the routine to store */ /* elements of U because of fill-in resulting from the row interchanges. */ /* ===================================================================== */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; /* Function Body */ *info = 0; if (*n < 0) { *info = -1; } else if (*kl < 0) { *info = -2; } else if (*ku < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*ldab < (*kl << 1) + *ku + 1) { *info = -6; } else if (*ldb < MAX(*n,1)) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("ZGBSV ", &i__1); return 0; } /* Compute the LU factorization of the band matrix A. */ zgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ zgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[ 1], &b[b_offset], ldb, info); } return 0; /* End of ZGBSV */ } /* zgbsv_ */
/* Subroutine */ int zchkgb_(logical *dotype, integer *nm, integer *mval, integer *nn, integer *nval, integer *nnb, integer *nbval, integer * nns, integer *nsval, doublereal *thresh, logical *tsterr, doublecomplex *a, integer *la, doublecomplex *afac, integer *lafac, doublecomplex *b, doublecomplex *x, doublecomplex *xact, doublecomplex *work, doublereal *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char transs[1*3] = "N" "T" "C"; /* Format strings */ static char fmt_9999[] = "(\002 *** In ZCHKGB, LA=\002,i5,\002 is too sm" "all for M=\002,i5,\002, N=\002,i5,\002, KL=\002,i4,\002, KU=\002" ",i4,/\002 ==> Increase LA to at least \002,i5)"; static char fmt_9998[] = "(\002 *** In ZCHKGB, LAFAC=\002,i5,\002 is too" " small for M=\002,i5,\002, N=\002,i5,\002, KL=\002,i4,\002, KU" "=\002,i4,/\002 ==> Increase LAFAC to at least \002,i5)"; static char fmt_9997[] = "(\002 M =\002,i5,\002, N =\002,i5,\002, KL=" "\002,i5,\002, KU=\002,i5,\002, NB =\002,i4,\002, type \002,i1" ",\002, test(\002,i1,\002)=\002,g12.5)"; static char fmt_9996[] = "(\002 TRANS='\002,a1,\002', N=\002,i5,\002, " "KL=\002,i5,\002, KU=\002,i5,\002, NRHS=\002,i3,\002, type \002,i" "1,\002, test(\002,i1,\002)=\002,g12.5)"; static char fmt_9995[] = "(\002 NORM ='\002,a1,\002', N=\002,i5,\002, " "KL=\002,i5,\002, KU=\002,i5,\002,\002,10x,\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, i__8, i__9, i__10, i__11; /* 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, m, n, i1, i2, nb, im, in, kl, ku, lda, ldb, inb, ikl, nkl, iku, nku, ioff, mode, koff, imat, info; char path[3], dist[1]; integer irhs, nrhs; char norm[1], type__[1]; integer nrun; extern /* Subroutine */ int alahd_(integer *, char *); integer nfail, iseed[4]; extern doublereal dget06_(doublereal *, doublereal *); doublereal rcond; extern /* Subroutine */ int zgbt01_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, doublereal *); integer nimat, klval[4]; extern /* Subroutine */ int zgbt02_(char *, integer *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *), zgbt05_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer * , doublereal *, doublereal *, doublereal *); doublereal anorm; integer itran; extern /* Subroutine */ int zget04_(integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal * ); integer kuval[4]; char trans[1]; integer izero, nerrs; logical zerot; extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); char xtype[1]; extern /* Subroutine */ int zlatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, doublereal *, integer *, doublereal *, char *); integer ldafac; extern /* Subroutine */ int alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); doublereal rcondc; extern doublereal zlangb_(char *, integer *, integer *, integer *, doublecomplex *, integer *, doublereal *); doublereal rcondi; extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *); extern /* Subroutine */ int alasum_(char *, integer *, integer *, integer *, integer *); doublereal cndnum, anormi, rcondo; extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *); doublereal ainvnm; logical trfcon; doublereal anormo; extern /* Subroutine */ int xlaenv_(integer *, integer *), zerrge_(char *, integer *), zgbrfs_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zgbtrf_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *), zlarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer * , integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *), zlaset_(char *, integer *, integer *, doublecomplex *, doublecomplex *, doublecomplex *, integer *), zgbtrs_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zlatms_(integer *, integer *, char *, integer *, char *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, char *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal result[7]; /* Fortran I/O blocks */ static cilist io___25 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___26 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___45 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___59 = { 0, 0, 0, fmt_9996, 0 }; static cilist io___61 = { 0, 0, 0, fmt_9995, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZCHKGB tests ZGBTRF, -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. */ /* NM (input) INTEGER */ /* The number of values of M contained in the vector MVAL. */ /* MVAL (input) INTEGER array, dimension (NM) */ /* The values of the matrix row dimension M. */ /* 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 column 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) DOUBLE PRECISION */ /* 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. */ /* A (workspace) COMPLEX*16 array, dimension (LA) */ /* LA (input) INTEGER */ /* The length of the array A. LA >= (KLMAX+KUMAX+1)*NMAX */ /* where KLMAX is the largest entry in the local array KLVAL, */ /* KUMAX is the largest entry in the local array KUVAL and */ /* NMAX is the largest entry in the input array NVAL. */ /* AFAC (workspace) COMPLEX*16 array, dimension (LAFAC) */ /* LAFAC (input) INTEGER */ /* The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX */ /* where KLMAX is the largest entry in the local array KLVAL, */ /* KUMAX is the largest entry in the local array KUVAL and */ /* NMAX is the largest entry in the input array NVAL. */ /* B (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* X (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* XACT (workspace) COMPLEX*16 array, dimension (NMAX*NSMAX) */ /* WORK (workspace) COMPLEX*16 array, dimension */ /* (NMAX*max(3,NSMAX,NMAX)) */ /* RWORK (workspace) DOUBLE PRECISION array, dimension */ /* (max(NMAX,2*NSMAX)) */ /* IWORK (workspace) INTEGER array, dimension (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; --afac; --a; --nsval; --nbval; --nval; --mval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Zomplex precision", (ftnlen)1, (ftnlen)17); s_copy(path + 1, "GB", (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) { zerrge_(path, nout); } infoc_1.infot = 0; /* Initialize the first value for the lower and upper bandwidths. */ klval[0] = 0; kuval[0] = 0; /* Do for each value of M in MVAL */ i__1 = *nm; for (im = 1; im <= i__1; ++im) { m = mval[im]; /* Set values to use for the lower bandwidth. */ klval[1] = m + (m + 1) / 4; /* KLVAL( 2 ) = MAX( M-1, 0 ) */ klval[2] = (m * 3 - 1) / 4; klval[3] = (m + 1) / 4; /* Do for each value of N in NVAL */ i__2 = *nn; for (in = 1; in <= i__2; ++in) { n = nval[in]; *(unsigned char *)xtype = 'N'; /* Set values to use for the upper bandwidth. */ kuval[1] = n + (n + 1) / 4; /* KUVAL( 2 ) = MAX( N-1, 0 ) */ kuval[2] = (n * 3 - 1) / 4; kuval[3] = (n + 1) / 4; /* Set limits on the number of loop iterations. */ /* Computing MIN */ i__3 = m + 1; nkl = min(i__3,4); if (n == 0) { nkl = 2; } /* Computing MIN */ i__3 = n + 1; nku = min(i__3,4); if (m == 0) { nku = 2; } nimat = 8; if (m <= 0 || n <= 0) { nimat = 1; } i__3 = nkl; for (ikl = 1; ikl <= i__3; ++ikl) { /* Do for KL = 0, (5*M+1)/4, (3M-1)/4, and (M+1)/4. This */ /* order makes it easier to skip redundant values for small */ /* values of M. */ kl = klval[ikl - 1]; i__4 = nku; for (iku = 1; iku <= i__4; ++iku) { /* Do for KU = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This */ /* order makes it easier to skip redundant values for */ /* small values of N. */ ku = kuval[iku - 1]; /* Check that A and AFAC are big enough to generate this */ /* matrix. */ lda = kl + ku + 1; ldafac = (kl << 1) + ku + 1; if (lda * n > *la || ldafac * n > *lafac) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } if (n * (kl + ku + 1) > *la) { io___25.ciunit = *nout; s_wsfe(&io___25); do_fio(&c__1, (char *)&(*la), (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer) ); do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer) ); i__5 = n * (kl + ku + 1); do_fio(&c__1, (char *)&i__5, (ftnlen)sizeof( integer)); e_wsfe(); ++nerrs; } if (n * ((kl << 1) + ku + 1) > *lafac) { io___26.ciunit = *nout; s_wsfe(&io___26); do_fio(&c__1, (char *)&(*lafac), (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer)) ; do_fio(&c__1, (char *)&kl, (ftnlen)sizeof(integer) ); do_fio(&c__1, (char *)&ku, (ftnlen)sizeof(integer) ); i__5 = n * ((kl << 1) + ku + 1); do_fio(&c__1, (char *)&i__5, (ftnlen)sizeof( integer)); e_wsfe(); ++nerrs; } goto L130; } i__5 = nimat; for (imat = 1; imat <= i__5; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L120; } /* Skip types 2, 3, or 4 if the matrix size is too */ /* small. */ zerot = imat >= 2 && imat <= 4; if (zerot && n < imat - 1) { goto L120; } if (! zerot || ! dotype[1]) { /* Set up parameters with ZLATB4 and generate a */ /* test matrix with ZLATMS. */ zlatb4_(path, &imat, &m, &n, type__, &kl, &ku, & anorm, &mode, &cndnum, dist); /* Computing MAX */ i__6 = 1, i__7 = ku + 2 - n; koff = max(i__6,i__7); i__6 = koff - 1; for (i__ = 1; i__ <= i__6; ++i__) { i__7 = i__; a[i__7].r = 0., a[i__7].i = 0.; /* L20: */ } s_copy(srnamc_1.srnamt, "ZLATMS", (ftnlen)6, ( ftnlen)6); zlatms_(&m, &n, dist, iseed, type__, &rwork[1], & mode, &cndnum, &anorm, &kl, &ku, "Z", &a[ koff], &lda, &work[1], &info); /* Check the error code from ZLATMS. */ if (info != 0) { alaerh_(path, "ZLATMS", &info, &c__0, " ", &m, &n, &kl, &ku, &c_n1, &imat, &nfail, & nerrs, nout); goto L120; } } else if (izero > 0) { /* Use the same matrix for types 3 and 4 as for */ /* type 2 by copying back the zeroed out column. */ i__6 = i2 - i1 + 1; zcopy_(&i__6, &b[1], &c__1, &a[ioff + i1], &c__1); } /* For types 2, 3, and 4, zero one or more columns of */ /* the matrix to test that INFO is returned correctly. */ izero = 0; if (zerot) { if (imat == 2) { izero = 1; } else if (imat == 3) { izero = min(m,n); } else { izero = min(m,n) / 2 + 1; } ioff = (izero - 1) * lda; if (imat < 4) { /* Store the column to be zeroed out in B. */ /* Computing MAX */ i__6 = 1, i__7 = ku + 2 - izero; i1 = max(i__6,i__7); /* Computing MIN */ i__6 = kl + ku + 1, i__7 = ku + 1 + (m - izero); i2 = min(i__6,i__7); i__6 = i2 - i1 + 1; zcopy_(&i__6, &a[ioff + i1], &c__1, &b[1], & c__1); i__6 = i2; for (i__ = i1; i__ <= i__6; ++i__) { i__7 = ioff + i__; a[i__7].r = 0., a[i__7].i = 0.; /* L30: */ } } else { i__6 = n; for (j = izero; j <= i__6; ++j) { /* Computing MAX */ i__7 = 1, i__8 = ku + 2 - j; /* Computing MIN */ i__10 = kl + ku + 1, i__11 = ku + 1 + (m - j); i__9 = min(i__10,i__11); for (i__ = max(i__7,i__8); i__ <= i__9; ++i__) { i__7 = ioff + i__; a[i__7].r = 0., a[i__7].i = 0.; /* L40: */ } ioff += lda; /* L50: */ } } } /* These lines, if used in place of the calls in the */ /* loop over INB, cause the code to bomb on a Sun */ /* SPARCstation. */ /* ANORMO = ZLANGB( 'O', N, KL, KU, A, LDA, RWORK ) */ /* ANORMI = ZLANGB( 'I', N, KL, KU, A, LDA, RWORK ) */ /* Do for each blocksize in NBVAL */ i__6 = *nnb; for (inb = 1; inb <= i__6; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the LU factorization of the band matrix. */ if (m > 0 && n > 0) { i__9 = kl + ku + 1; zlacpy_("Full", &i__9, &n, &a[1], &lda, &afac[ kl + 1], &ldafac); } s_copy(srnamc_1.srnamt, "ZGBTRF", (ftnlen)6, ( ftnlen)6); zgbtrf_(&m, &n, &kl, &ku, &afac[1], &ldafac, & iwork[1], &info); /* Check error code from ZGBTRF. */ if (info != izero) { alaerh_(path, "ZGBTRF", &info, &izero, " ", & m, &n, &kl, &ku, &nb, &imat, &nfail, & nerrs, nout); } trfcon = FALSE_; /* + TEST 1 */ /* Reconstruct matrix from factors and compute */ /* residual. */ zgbt01_(&m, &n, &kl, &ku, &a[1], &lda, &afac[1], & ldafac, &iwork[1], &work[1], result); /* Print information about the tests so far that */ /* did not pass the threshold. */ if (result[0] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___45.ciunit = *nout; s_wsfe(&io___45); do_fio(&c__1, (char *)&m, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&kl, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&ku, (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 *)&c__1, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[0], (ftnlen) sizeof(doublereal)); e_wsfe(); ++nfail; } ++nrun; /* Skip the remaining tests if this is not the */ /* first block size or if M .ne. N. */ if (inb > 1 || m != n) { goto L110; } anormo = zlangb_("O", &n, &kl, &ku, &a[1], &lda, & rwork[1]); anormi = zlangb_("I", &n, &kl, &ku, &a[1], &lda, & rwork[1]); if (info == 0) { /* Form the inverse of A so we can get a good */ /* estimate of CNDNUM = norm(A) * norm(inv(A)). */ ldb = max(1,n); zlaset_("Full", &n, &n, &c_b61, &c_b62, &work[ 1], &ldb); s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)6, ( ftnlen)6); zgbtrs_("No transpose", &n, &kl, &ku, &n, & afac[1], &ldafac, &iwork[1], &work[1], &ldb, &info); /* Compute the 1-norm condition number of A. */ ainvnm = zlange_("O", &n, &n, &work[1], &ldb, &rwork[1]); if (anormo <= 0. || ainvnm <= 0.) { rcondo = 1.; } else { rcondo = 1. / anormo / ainvnm; } /* Compute the infinity-norm condition number of */ /* A. */ ainvnm = zlange_("I", &n, &n, &work[1], &ldb, &rwork[1]); if (anormi <= 0. || ainvnm <= 0.) { rcondi = 1.; } else { rcondi = 1. / anormi / ainvnm; } } else { /* Do only the condition estimate if INFO.NE.0. */ trfcon = TRUE_; rcondo = 0.; rcondi = 0.; } /* Skip the solve tests if the matrix is singular. */ if (trfcon) { goto L90; } i__9 = *nns; for (irhs = 1; irhs <= i__9; ++irhs) { nrhs = nsval[irhs]; *(unsigned char *)xtype = 'N'; for (itran = 1; itran <= 3; ++itran) { *(unsigned char *)trans = *(unsigned char *)&transs[itran - 1]; if (itran == 1) { rcondc = rcondo; *(unsigned char *)norm = 'O'; } else { rcondc = rcondi; *(unsigned char *)norm = 'I'; } /* + TEST 2: */ /* Solve and compute residual for A * X = B. */ s_copy(srnamc_1.srnamt, "ZLARHS", (ftnlen) 6, (ftnlen)6); zlarhs_(path, xtype, " ", trans, &n, &n, & kl, &ku, &nrhs, &a[1], &lda, & xact[1], &ldb, &b[1], &ldb, iseed, &info); *(unsigned char *)xtype = 'C'; zlacpy_("Full", &n, &nrhs, &b[1], &ldb, & x[1], &ldb); s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen) 6, (ftnlen)6); zgbtrs_(trans, &n, &kl, &ku, &nrhs, &afac[ 1], &ldafac, &iwork[1], &x[1], & ldb, &info); /* Check error code from ZGBTRS. */ if (info != 0) { alaerh_(path, "ZGBTRS", &info, &c__0, trans, &n, &n, &kl, &ku, & c_n1, &imat, &nfail, &nerrs, nout); } zlacpy_("Full", &n, &nrhs, &b[1], &ldb, & work[1], &ldb); zgbt02_(trans, &m, &n, &kl, &ku, &nrhs, & a[1], &lda, &x[1], &ldb, &work[1], &ldb, &result[1]); /* + TEST 3: */ /* Check solution from generated exact */ /* solution. */ zget04_(&n, &nrhs, &x[1], &ldb, &xact[1], &ldb, &rcondc, &result[2]); /* + TESTS 4, 5, 6: */ /* Use iterative refinement to improve the */ /* solution. */ s_copy(srnamc_1.srnamt, "ZGBRFS", (ftnlen) 6, (ftnlen)6); zgbrfs_(trans, &n, &kl, &ku, &nrhs, &a[1], &lda, &afac[1], &ldafac, &iwork[ 1], &b[1], &ldb, &x[1], &ldb, & rwork[1], &rwork[nrhs + 1], &work[ 1], &rwork[(nrhs << 1) + 1], & info); /* Check error code from ZGBRFS. */ if (info != 0) { alaerh_(path, "ZGBRFS", &info, &c__0, trans, &n, &n, &kl, &ku, & nrhs, &imat, &nfail, &nerrs, nout); } zget04_(&n, &nrhs, &x[1], &ldb, &xact[1], &ldb, &rcondc, &result[3]); zgbt05_(trans, &n, &kl, &ku, &nrhs, &a[1], &lda, &b[1], &ldb, &x[1], &ldb, & xact[1], &ldb, &rwork[1], &rwork[ nrhs + 1], &result[4]); /* Print information about the tests that did */ /* not pass the threshold. */ for (k = 2; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___59.ciunit = *nout; s_wsfe(&io___59); do_fio(&c__1, trans, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&kl, ( ftnlen)sizeof(integer)); do_fio(&c__1, (char *)&ku, ( 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( doublereal)); e_wsfe(); ++nfail; } /* L60: */ } nrun += 5; /* L70: */ } /* L80: */ } /* + TEST 7: */ /* Get an estimate of RCOND = 1/CNDNUM. */ L90: for (itran = 1; itran <= 2; ++itran) { if (itran == 1) { anorm = anormo; rcondc = rcondo; *(unsigned char *)norm = 'O'; } else { anorm = anormi; rcondc = rcondi; *(unsigned char *)norm = 'I'; } s_copy(srnamc_1.srnamt, "ZGBCON", (ftnlen)6, ( ftnlen)6); zgbcon_(norm, &n, &kl, &ku, &afac[1], &ldafac, &iwork[1], &anorm, &rcond, &work[1], &rwork[1], &info); /* Check error code from ZGBCON. */ if (info != 0) { alaerh_(path, "ZGBCON", &info, &c__0, norm, &n, &n, &kl, &ku, &c_n1, & imat, &nfail, &nerrs, nout); } result[6] = dget06_(&rcond, &rcondc); /* Print information about the tests that did */ /* not pass the threshold. */ if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___61.ciunit = *nout; s_wsfe(&io___61); do_fio(&c__1, norm, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&kl, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&ku, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&imat, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&c__7, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[6], (ftnlen) sizeof(doublereal)); e_wsfe(); ++nfail; } ++nrun; /* L100: */ } L110: ; } L120: ; } L130: ; } /* L140: */ } /* L150: */ } /* L160: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of ZCHKGB */ } /* zchkgb_ */
/* Subroutine */ int zerrge_(char *path, integer *nunit) { /* System generated locals */ integer i__1; doublereal d__1, d__2; doublecomplex z__1; /* Builtin functions */ integer s_wsle(cilist *), e_wsle(void); /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ doublecomplex a[16] /* was [4][4] */, b[4]; integer i__, j; doublereal r__[4]; doublecomplex w[8], x[4]; char c2[2]; doublereal r1[4], r2[4]; doublecomplex af[16] /* was [4][4] */; integer ip[4], info; doublereal anrm, ccond, rcond; extern /* Subroutine */ int zgbtf2_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, integer *), zgetf2_(integer *, integer *, doublecomplex *, integer *, integer *, integer *), alaesm_(char *, logical *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), chkxer_(char *, integer *, integer *, logical *, logical *), zgecon_(char *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zgbequ_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *), zgbrfs_( char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zgbtrf_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, integer *), zgeequ_(integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *), zgerfs_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublecomplex *, doublereal *, integer *), zgetrf_(integer *, integer *, doublecomplex *, integer *, integer *, integer *), zgetri_(integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zgbtrs_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *), zgetrs_(char *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *); /* Fortran I/O blocks */ static cilist io___1 = { 0, 0, 0, 0, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZERRGE tests the error exits for the COMPLEX*16 routines */ /* for general matrices. */ /* Arguments */ /* ========= */ /* PATH (input) CHARACTER*3 */ /* The LAPACK path name for the routines to be tested. */ /* NUNIT (input) INTEGER */ /* The unit number for output. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. Local Arrays .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Scalars in Common .. */ /* .. */ /* .. Common blocks .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ infoc_1.nout = *nunit; io___1.ciunit = infoc_1.nout; s_wsle(&io___1); e_wsle(); s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2); /* Set the variables to innocuous values. */ for (j = 1; j <= 4; ++j) { for (i__ = 1; i__ <= 4; ++i__) { i__1 = i__ + (j << 2) - 5; d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; a[i__1].r = z__1.r, a[i__1].i = z__1.i; i__1 = i__ + (j << 2) - 5; d__1 = 1. / (doublereal) (i__ + j); d__2 = -1. / (doublereal) (i__ + j); z__1.r = d__1, z__1.i = d__2; af[i__1].r = z__1.r, af[i__1].i = z__1.i; /* L10: */ } i__1 = j - 1; b[i__1].r = 0., b[i__1].i = 0.; r1[j - 1] = 0.; r2[j - 1] = 0.; i__1 = j - 1; w[i__1].r = 0., w[i__1].i = 0.; i__1 = j - 1; x[i__1].r = 0., x[i__1].i = 0.; ip[j - 1] = j; /* L20: */ } infoc_1.ok = TRUE_; /* Test error exits of the routines that use the LU decomposition */ /* of a general matrix. */ if (lsamen_(&c__2, c2, "GE")) { /* ZGETRF */ s_copy(srnamc_1.srnamt, "ZGETRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgetrf_(&c_n1, &c__0, a, &c__1, ip, &info); chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgetrf_(&c__0, &c_n1, a, &c__1, ip, &info); chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgetrf_(&c__2, &c__1, a, &c__1, ip, &info); chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGETF2 */ s_copy(srnamc_1.srnamt, "ZGETF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgetf2_(&c_n1, &c__0, a, &c__1, ip, &info); chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgetf2_(&c__0, &c_n1, a, &c__1, ip, &info); chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgetf2_(&c__2, &c__1, a, &c__1, ip, &info); chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGETRI */ s_copy(srnamc_1.srnamt, "ZGETRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgetri_(&c_n1, a, &c__1, ip, w, &c__1, &info); chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgetri_(&c__2, a, &c__1, ip, w, &c__2, &info); chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zgetri_(&c__2, a, &c__2, ip, w, &c__1, &info); chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGETRS */ s_copy(srnamc_1.srnamt, "ZGETRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info); chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info); chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info); chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info); chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; zgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info); chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGERFS */ s_copy(srnamc_1.srnamt, "ZGERFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, & c__2, r1, r2, w, r__, &info); chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, & c__1, r1, r2, w, r__, &info); chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGECON */ s_copy(srnamc_1.srnamt, "ZGECON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info) ; chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGEEQU */ s_copy(srnamc_1.srnamt, "ZGEEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* Test error exits of the routines that use the LU decomposition */ /* of a general band matrix. */ } else if (lsamen_(&c__2, c2, "GB")) { /* ZGBTRF */ s_copy(srnamc_1.srnamt, "ZGBTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info); chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info); chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info); chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGBTF2 */ s_copy(srnamc_1.srnamt, "ZGBTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info); chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info); chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info); chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGBTRS */ s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, & info); chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, & info); chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; zgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGBRFS */ s_copy(srnamc_1.srnamt, "ZGBRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgbrfs_("/", &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgbrfs_("N", &c_n1, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgbrfs_("N", &c__1, &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgbrfs_("N", &c__1, &c__0, &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; zgbrfs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; zgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__2, af, &c__4, ip, b, & c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; zgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__3, ip, b, & c__2, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; zgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__2, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 14; zgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, & c__2, x, &c__1, r1, r2, w, r__, &info); chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGBCON */ s_copy(srnamc_1.srnamt, "ZGBCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__, &info); chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__, &info); chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__, &info); chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, r__, &info); chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, r__, &info); chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* ZGBEQU */ s_copy(srnamc_1.srnamt, "ZGBEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; zgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; zgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; zgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; zgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; zgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } /* Print a summary line. */ alaesm_(path, &infoc_1.ok, &infoc_1.nout); return 0; /* End of ZERRGE */ } /* zerrge_ */
/* Subroutine */ int zgbsvxx_(char *fact, char *trans, integer *n, integer * kl, integer *ku, integer *nrhs, doublecomplex *ab, integer *ldab, doublecomplex *afb, integer *ldafb, integer *ipiv, char *equed, doublereal *r__, doublereal *c__, doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx, doublereal *rcond, doublereal *rpvgrw, doublereal *berr, integer *n_err_bnds__, doublereal *err_bnds_norm__, doublereal *err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex *work, doublereal *rwork, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, x_dim1, x_offset, err_bnds_norm_dim1, err_bnds_norm_offset, err_bnds_comp_dim1, err_bnds_comp_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2; /* Local variables */ integer i__, j; doublereal amax; extern doublereal zla_gbrpvgrw__(integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); extern logical lsame_(char *, char *); doublereal rcmin, rcmax; logical equil; extern doublereal dlamch_(char *); doublereal colcnd; logical nofact; extern /* Subroutine */ int xerbla_(char *, integer *), zlaqgb_( integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, char *); doublereal bignum; integer infequ; logical colequ; doublereal rowcnd; extern /* Subroutine */ int zgbtrf_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, integer *); logical notran; extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal smlnum; extern /* Subroutine */ int zgbtrs_(char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, integer *, doublecomplex *, integer *, integer *); logical rowequ; extern /* Subroutine */ int zlascl2_(integer *, integer *, doublereal *, doublecomplex *, integer *), zgbequb_(integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *) , zgbrfsx_(char *, char *, integer *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, doublereal *, doublereal *, doublecomplex *, integer * , doublecomplex *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublecomplex *, doublereal *, integer *); /* -- LAPACK driver routine (version 3.2) -- */ /* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */ /* -- Jason Riedy of Univ. of California Berkeley. -- */ /* -- November 2008 -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley and NAG Ltd. -- */ /* .. */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZGBSVXX uses the LU factorization to compute the solution to a */ /* complex*16 system of linear equations A * X = B, where A is an */ /* N-by-N matrix and X and B are N-by-NRHS matrices. */ /* If requested, both normwise and maximum componentwise error bounds */ /* are returned. ZGBSVXX will return a solution with a tiny */ /* guaranteed error (O(eps) where eps is the working machine */ /* precision) unless the matrix is very ill-conditioned, in which */ /* case a warning is returned. Relevant condition numbers also are */ /* calculated and returned. */ /* ZGBSVXX accepts user-provided factorizations and equilibration */ /* factors; see the definitions of the FACT and EQUED options. */ /* Solving with refinement and using a factorization from a previous */ /* ZGBSVXX call will also produce a solution with either O(eps) */ /* errors or warnings, but we cannot make that claim for general */ /* user-provided factorizations and equilibration factors if they */ /* differ from what ZGBSVXX would itself produce. */ /* Description */ /* =========== */ /* The following steps are performed: */ /* 1. If FACT = 'E', double precision scaling factors are computed to equilibrate */ /* the system: */ /* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */ /* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */ /* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */ /* Whether or not the system will be equilibrated depends on the */ /* scaling of the matrix A, but if equilibration is used, A is */ /* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */ /* or diag(C)*B (if TRANS = 'T' or 'C'). */ /* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor */ /* the matrix A (after equilibration if FACT = 'E') as */ /* A = P * L * U, */ /* where P is a permutation matrix, L is a unit lower triangular */ /* matrix, and U is upper triangular. */ /* 3. If some U(i,i)=0, so that U is exactly singular, then the */ /* routine returns with INFO = i. Otherwise, the factored form of A */ /* is used to estimate the condition number of the matrix A (see */ /* argument RCOND). If the reciprocal of the condition number is less */ /* than machine precision, the routine still goes on to solve for X */ /* and compute error bounds as described below. */ /* 4. The system of equations is solved for X using the factored form */ /* of A. */ /* 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */ /* the routine will use iterative refinement to try to get a small */ /* error and error bounds. Refinement calculates the residual to at */ /* least twice the working precision. */ /* 6. If equilibration was used, the matrix X is premultiplied by */ /* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */ /* that it solves the original system before equilibration. */ /* Arguments */ /* ========= */ /* Some optional parameters are bundled in the PARAMS array. These */ /* settings determine how refinement is performed, but often the */ /* defaults are acceptable. If the defaults are acceptable, users */ /* can pass NPARAMS = 0 which prevents the source code from accessing */ /* the PARAMS argument. */ /* FACT (input) CHARACTER*1 */ /* Specifies whether or not the factored form of the matrix A is */ /* supplied on entry, and if not, whether the matrix A should be */ /* equilibrated before it is factored. */ /* = 'F': On entry, AF and IPIV contain the factored form of A. */ /* If EQUED is not 'N', the matrix A has been */ /* equilibrated with scaling factors given by R and C. */ /* A, AF, and IPIV are not modified. */ /* = 'N': The matrix A will be copied to AF and factored. */ /* = 'E': The matrix A will be equilibrated if necessary, then */ /* copied to AF and factored. */ /* TRANS (input) CHARACTER*1 */ /* Specifies the form of the system of equations: */ /* = 'N': A * X = B (No transpose) */ /* = 'T': A**T * X = B (Transpose) */ /* = 'C': A**H * X = B (Conjugate Transpose = Transpose) */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* KL (input) INTEGER */ /* The number of subdiagonals within the band of A. KL >= 0. */ /* KU (input) INTEGER */ /* The number of superdiagonals within the band of A. KU >= 0. */ /* NRHS (input) INTEGER */ /* The number of right hand sides, i.e., the number of columns */ /* of the matrices B and X. NRHS >= 0. */ /* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */ /* On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */ /* The j-th column of A is stored in the j-th column of the */ /* array AB as follows: */ /* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) */ /* If FACT = 'F' and EQUED is not 'N', then AB must have been */ /* equilibrated by the scaling factors in R and/or C. AB is not */ /* modified if FACT = 'F' or 'N', or if FACT = 'E' and */ /* EQUED = 'N' on exit. */ /* On exit, if EQUED .ne. 'N', A is scaled as follows: */ /* EQUED = 'R': A := diag(R) * A */ /* EQUED = 'C': A := A * diag(C) */ /* EQUED = 'B': A := diag(R) * A * diag(C). */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KL+KU+1. */ /* AFB (input or output) DOUBLE PRECISION array, dimension (LDAFB,N) */ /* If FACT = 'F', then AFB is an input argument and on entry */ /* contains details of the LU factorization of the band matrix */ /* A, as computed by ZGBTRF. U is stored as an upper triangular */ /* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */ /* and the multipliers used during the factorization are stored */ /* in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is */ /* the factored form of the equilibrated matrix A. */ /* If FACT = 'N', then AF is an output argument and on exit */ /* returns the factors L and U from the factorization A = P*L*U */ /* of the original matrix A. */ /* If FACT = 'E', then AF is an output argument and on exit */ /* returns the factors L and U from the factorization A = P*L*U */ /* of the equilibrated matrix A (see the description of A for */ /* the form of the equilibrated matrix). */ /* LDAFB (input) INTEGER */ /* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */ /* IPIV (input or output) INTEGER array, dimension (N) */ /* If FACT = 'F', then IPIV is an input argument and on entry */ /* contains the pivot indices from the factorization A = P*L*U */ /* as computed by DGETRF; row i of the matrix was interchanged */ /* with row IPIV(i). */ /* If FACT = 'N', then IPIV is an output argument and on exit */ /* contains the pivot indices from the factorization A = P*L*U */ /* of the original matrix A. */ /* If FACT = 'E', then IPIV is an output argument and on exit */ /* contains the pivot indices from the factorization A = P*L*U */ /* of the equilibrated matrix A. */ /* EQUED (input or output) CHARACTER*1 */ /* Specifies the form of equilibration that was done. */ /* = 'N': No equilibration (always true if FACT = 'N'). */ /* = 'R': Row equilibration, i.e., A has been premultiplied by */ /* diag(R). */ /* = 'C': Column equilibration, i.e., A has been postmultiplied */ /* by diag(C). */ /* = 'B': Both row and column equilibration, i.e., A has been */ /* replaced by diag(R) * A * diag(C). */ /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ /* output argument. */ /* R (input or output) DOUBLE PRECISION array, dimension (N) */ /* The row scale factors for A. If EQUED = 'R' or 'B', A is */ /* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */ /* is not accessed. R is an input argument if FACT = 'F'; */ /* otherwise, R is an output argument. If FACT = 'F' and */ /* EQUED = 'R' or 'B', each element of R must be positive. */ /* If R is output, each element of R is a power of the radix. */ /* If R is input, each element of R should be a power of the radix */ /* to ensure a reliable solution and error estimates. Scaling by */ /* powers of the radix does not cause rounding errors unless the */ /* result underflows or overflows. Rounding errors during scaling */ /* lead to refining with a matrix that is not equivalent to the */ /* input matrix, producing error estimates that may not be */ /* reliable. */ /* C (input or output) DOUBLE PRECISION array, dimension (N) */ /* The column scale factors for A. If EQUED = 'C' or 'B', A is */ /* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */ /* is not accessed. C is an input argument if FACT = 'F'; */ /* otherwise, C is an output argument. If FACT = 'F' and */ /* EQUED = 'C' or 'B', each element of C must be positive. */ /* If C is output, each element of C is a power of the radix. */ /* If C is input, each element of C should be a power of the radix */ /* to ensure a reliable solution and error estimates. Scaling by */ /* powers of the radix does not cause rounding errors unless the */ /* result underflows or overflows. Rounding errors during scaling */ /* lead to refining with a matrix that is not equivalent to the */ /* input matrix, producing error estimates that may not be */ /* reliable. */ /* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */ /* On entry, the N-by-NRHS right hand side matrix B. */ /* On exit, */ /* if EQUED = 'N', B is not modified; */ /* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */ /* diag(R)*B; */ /* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */ /* overwritten by diag(C)*B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS) */ /* If INFO = 0, the N-by-NRHS solution matrix X to the original */ /* system of equations. Note that A and B are modified on exit */ /* if EQUED .ne. 'N', and the solution to the equilibrated system is */ /* inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */ /* inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* RCOND (output) DOUBLE PRECISION */ /* Reciprocal scaled condition number. This is an estimate of the */ /* reciprocal Skeel condition number of the matrix A after */ /* equilibration (if done). If this is less than the machine */ /* precision (in particular, if it is zero), the matrix is singular */ /* to working precision. Note that the error may still be small even */ /* if this number is very small and the matrix appears ill- */ /* conditioned. */ /* RPVGRW (output) DOUBLE PRECISION */ /* Reciprocal pivot growth. On exit, this contains the reciprocal */ /* pivot growth factor norm(A)/norm(U). The "max absolute element" */ /* norm is used. If this is much less than 1, then the stability of */ /* the LU factorization of the (equilibrated) matrix A could be poor. */ /* This also means that the solution X, estimated condition numbers, */ /* and error bounds could be unreliable. If factorization fails with */ /* 0<INFO<=N, then this contains the reciprocal pivot growth factor */ /* for the leading INFO columns of A. In DGESVX, this quantity is */ /* returned in WORK(1). */ /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* Componentwise relative backward error. This is the */ /* componentwise relative backward error of each solution vector X(j) */ /* (i.e., the smallest relative change in any element of A or B that */ /* makes X(j) an exact solution). */ /* N_ERR_BNDS (input) INTEGER */ /* Number of error bounds to return for each right hand side */ /* and each type (normwise or componentwise). See ERR_BNDS_NORM and */ /* ERR_BNDS_COMP below. */ /* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ /* For each right-hand side, this array contains information about */ /* various error bounds and condition numbers corresponding to the */ /* normwise relative error, which is defined as follows: */ /* Normwise relative error in the ith solution vector: */ /* max_j (abs(XTRUE(j,i) - X(j,i))) */ /* ------------------------------ */ /* max_j abs(X(j,i)) */ /* The array is indexed by the type of error information as described */ /* below. There currently are up to three pieces of information */ /* returned. */ /* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */ /* right-hand side. */ /* The second index in ERR_BNDS_NORM(:,err) contains the following */ /* three fields: */ /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* reciprocal condition number is less than the threshold */ /* sqrt(n) * dlamch('Epsilon'). */ /* err = 2 "Guaranteed" error bound: The estimated forward error, */ /* almost certainly within a factor of 10 of the true error */ /* so long as the next entry is greater than the threshold */ /* sqrt(n) * dlamch('Epsilon'). This error bound should only */ /* be trusted if the previous boolean is true. */ /* err = 3 Reciprocal condition number: Estimated normwise */ /* reciprocal condition number. Compared with the threshold */ /* sqrt(n) * dlamch('Epsilon') to determine if the error */ /* estimate is "guaranteed". These reciprocal condition */ /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* appropriately scaled matrix Z. */ /* Let Z = S*A, where S scales each row by a power of the */ /* radix so all absolute row sums of Z are approximately 1. */ /* See Lapack Working Note 165 for further details and extra */ /* cautions. */ /* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */ /* For each right-hand side, this array contains information about */ /* various error bounds and condition numbers corresponding to the */ /* componentwise relative error, which is defined as follows: */ /* Componentwise relative error in the ith solution vector: */ /* abs(XTRUE(j,i) - X(j,i)) */ /* max_j ---------------------- */ /* abs(X(j,i)) */ /* The array is indexed by the right-hand side i (on which the */ /* componentwise relative error depends), and the type of error */ /* information as described below. There currently are up to three */ /* pieces of information returned for each right-hand side. If */ /* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */ /* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */ /* the first (:,N_ERR_BNDS) entries are returned. */ /* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */ /* right-hand side. */ /* The second index in ERR_BNDS_COMP(:,err) contains the following */ /* three fields: */ /* err = 1 "Trust/don't trust" boolean. Trust the answer if the */ /* reciprocal condition number is less than the threshold */ /* sqrt(n) * dlamch('Epsilon'). */ /* err = 2 "Guaranteed" error bound: The estimated forward error, */ /* almost certainly within a factor of 10 of the true error */ /* so long as the next entry is greater than the threshold */ /* sqrt(n) * dlamch('Epsilon'). This error bound should only */ /* be trusted if the previous boolean is true. */ /* err = 3 Reciprocal condition number: Estimated componentwise */ /* reciprocal condition number. Compared with the threshold */ /* sqrt(n) * dlamch('Epsilon') to determine if the error */ /* estimate is "guaranteed". These reciprocal condition */ /* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */ /* appropriately scaled matrix Z. */ /* Let Z = S*(A*diag(x)), where x is the solution for the */ /* current right-hand side and S scales each row of */ /* A*diag(x) by a power of the radix so all absolute row */ /* sums of Z are approximately 1. */ /* See Lapack Working Note 165 for further details and extra */ /* cautions. */ /* NPARAMS (input) INTEGER */ /* Specifies the number of parameters set in PARAMS. If .LE. 0, the */ /* PARAMS array is never referenced and default values are used. */ /* PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS */ /* Specifies algorithm parameters. If an entry is .LT. 0.0, then */ /* that entry will be filled with default value used for that */ /* parameter. Only positions up to NPARAMS are accessed; defaults */ /* are used for higher-numbered parameters. */ /* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */ /* refinement or not. */ /* Default: 1.0D+0 */ /* = 0.0 : No refinement is performed, and no error bounds are */ /* computed. */ /* = 1.0 : Use the extra-precise refinement algorithm. */ /* (other values are reserved for future use) */ /* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */ /* computations allowed for refinement. */ /* Default: 10 */ /* Aggressive: Set to 100 to permit convergence using approximate */ /* factorizations or factorizations other than LU. If */ /* the factorization uses a technique other than */ /* Gaussian elimination, the guarantees in */ /* err_bnds_norm and err_bnds_comp may no longer be */ /* trustworthy. */ /* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */ /* will attempt to find a solution with small componentwise */ /* relative error in the double-precision algorithm. Positive */ /* is true, 0.0 is false. */ /* Default: 1.0 (attempt componentwise convergence) */ /* WORK (workspace) DOUBLE PRECISION array, dimension (4*N) */ /* IWORK (workspace) INTEGER array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: Successful exit. The solution to every right-hand side is */ /* guaranteed. */ /* < 0: If INFO = -i, the i-th argument had an illegal value */ /* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */ /* has been completed, but the factor U is exactly singular, so */ /* the solution and error bounds could not be computed. RCOND = 0 */ /* is returned. */ /* = N+J: The solution corresponding to the Jth right-hand side is */ /* not guaranteed. The solutions corresponding to other right- */ /* hand sides K with K > J may not be guaranteed as well, but */ /* only the first such right-hand side is reported. If a small */ /* componentwise error is not requested (PARAMS(3) = 0.0) then */ /* the Jth right-hand side is the first with a normwise error */ /* bound that is not guaranteed (the smallest J such */ /* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */ /* the Jth right-hand side is the first with either a normwise or */ /* componentwise error bound that is not guaranteed (the smallest */ /* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */ /* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */ /* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */ /* about all of the right-hand sides check ERR_BNDS_NORM or */ /* ERR_BNDS_COMP. */ /* ================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Parameter adjustments */ err_bnds_comp_dim1 = *nrhs; err_bnds_comp_offset = 1 + err_bnds_comp_dim1; err_bnds_comp__ -= err_bnds_comp_offset; err_bnds_norm_dim1 = *nrhs; err_bnds_norm_offset = 1 + err_bnds_norm_dim1; err_bnds_norm__ -= err_bnds_norm_offset; ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; afb_dim1 = *ldafb; afb_offset = 1 + afb_dim1; afb -= afb_offset; --ipiv; --r__; --c__; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; --berr; --params; --work; --rwork; /* Function Body */ *info = 0; nofact = lsame_(fact, "N"); equil = lsame_(fact, "E"); notran = lsame_(trans, "N"); smlnum = dlamch_("Safe minimum"); bignum = 1. / smlnum; if (nofact || equil) { *(unsigned char *)equed = 'N'; rowequ = FALSE_; colequ = FALSE_; } else { rowequ = lsame_(equed, "R") || lsame_(equed, "B"); colequ = lsame_(equed, "C") || lsame_(equed, "B"); } /* Default is failure. If an input parameter is wrong or */ /* factorization fails, make everything look horrible. Only the */ /* pivot growth is set here, the rest is initialized in ZGBRFSX. */ *rpvgrw = 0.; /* Test the input parameters. PARAMS is not tested until DGERFSX. */ if (! nofact && ! equil && ! lsame_(fact, "F")) { *info = -1; } else if (! notran && ! lsame_(trans, "T") && ! lsame_(trans, "C")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*kl < 0) { *info = -4; } else if (*ku < 0) { *info = -5; } else if (*nrhs < 0) { *info = -6; } else if (*ldab < *kl + *ku + 1) { *info = -8; } else if (*ldafb < (*kl << 1) + *ku + 1) { *info = -10; } else if (lsame_(fact, "F") && ! (rowequ || colequ || lsame_(equed, "N"))) { *info = -12; } else { if (rowequ) { rcmin = bignum; rcmax = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ d__1 = rcmin, d__2 = r__[j]; rcmin = min(d__1,d__2); /* Computing MAX */ d__1 = rcmax, d__2 = r__[j]; rcmax = max(d__1,d__2); /* L10: */ } if (rcmin <= 0.) { *info = -13; } else if (*n > 0) { rowcnd = max(rcmin,smlnum) / min(rcmax,bignum); } else { rowcnd = 1.; } } if (colequ && *info == 0) { rcmin = bignum; rcmax = 0.; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ d__1 = rcmin, d__2 = c__[j]; rcmin = min(d__1,d__2); /* Computing MAX */ d__1 = rcmax, d__2 = c__[j]; rcmax = max(d__1,d__2); /* L20: */ } if (rcmin <= 0.) { *info = -14; } else if (*n > 0) { colcnd = max(rcmin,smlnum) / min(rcmax,bignum); } else { colcnd = 1.; } } if (*info == 0) { if (*ldb < max(1,*n)) { *info = -15; } else if (*ldx < max(1,*n)) { *info = -16; } } } if (*info != 0) { i__1 = -(*info); xerbla_("ZGBSVXX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ zgbequb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], & rowcnd, &colcnd, &amax, &infequ); if (infequ == 0) { /* Equilibrate the matrix. */ zlaqgb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], & rowcnd, &colcnd, &amax, equed); rowequ = lsame_(equed, "R") || lsame_(equed, "B"); colequ = lsame_(equed, "C") || lsame_(equed, "B"); } /* If the scaling factors are not applied, set them to 1.0. */ if (! rowequ) { i__1 = *n; for (j = 1; j <= i__1; ++j) { r__[j] = 1.; } } if (! colequ) { i__1 = *n; for (j = 1; j <= i__1; ++j) { c__[j] = 1.; } } } /* Scale the right-hand side. */ if (notran) { if (rowequ) { zlascl2_(n, nrhs, &r__[1], &b[b_offset], ldb); } } else { if (colequ) { zlascl2_(n, nrhs, &c__[1], &b[b_offset], ldb); } } if (nofact || equil) { /* Compute the LU factorization of A. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { i__2 = (*kl << 1) + *ku + 1; for (i__ = *kl + 1; i__ <= i__2; ++i__) { i__3 = i__ + j * afb_dim1; i__4 = i__ - *kl + j * ab_dim1; afb[i__3].r = ab[i__4].r, afb[i__3].i = ab[i__4].i; /* L30: */ } /* L40: */ } zgbtrf_(n, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], info); /* Return if INFO is non-zero. */ if (*info > 0) { /* Pivot in column INFO is exactly 0 */ /* Compute the reciprocal pivot growth factor of the */ /* leading rank-deficient INFO columns of A. */ *rpvgrw = zla_gbrpvgrw__(n, kl, ku, info, &ab[ab_offset], ldab, & afb[afb_offset], ldafb); return 0; } } /* Compute the reciprocal pivot growth factor RPVGRW. */ *rpvgrw = zla_gbrpvgrw__(n, kl, ku, n, &ab[ab_offset], ldab, &afb[ afb_offset], ldafb); /* Compute the solution matrix X. */ zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); zgbtrs_(trans, n, kl, ku, nrhs, &afb[afb_offset], ldafb, &ipiv[1], &x[ x_offset], ldx, info); /* Use iterative refinement to improve the computed solution and */ /* compute error bounds and backward error estimates for it. */ zgbrfsx_(trans, equed, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[ afb_offset], ldafb, &ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb, &x[x_offset], ldx, rcond, &berr[1], n_err_bnds__, & err_bnds_norm__[err_bnds_norm_offset], &err_bnds_comp__[ err_bnds_comp_offset], nparams, ¶ms[1], &work[1], &rwork[1], info); /* Scale solutions. */ if (colequ && notran) { zlascl2_(n, nrhs, &c__[1], &x[x_offset], ldx); } else if (rowequ && ! notran) { zlascl2_(n, nrhs, &r__[1], &x[x_offset], ldx); } return 0; /* End of ZGBSVXX */ } /* zgbsvxx_ */