//! see full matrix case. inline void decomr(double fac1,const MatrixReal& Jac) { E1.equal_minus(Jac); E1.addDiag(fac1); int nn=n,knsub=nsub,knsup=nsup,lldab=ldab,info; dgbtrf_(&nn,&nn,&knsub,&knsup,&E1,&lldab,&(ipivr[0]),&info); if(info!=0) throw OdesException("odes::Matrices::decomr dgbtrf,info=",info); }
/* Subroutine */ int dgbsv_(integer *n, integer *kl, integer *ku, integer * nrhs, doublereal *ab, integer *ldab, integer *ipiv, doublereal *b, integer *ldb, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, b_dim1, b_offset, i__1; /* Local variables */ extern /* Subroutine */ int dgbtrf_(integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, integer *), xerbla_(char *, integer *), dgbtrs_(char *, integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DGBSV computes the solution to a real 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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_("DGBSV ", &i__1); return 0; } /* Compute the LU factorization of the band matrix A. */ dgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ dgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[ 1], &b[b_offset], ldb, info); } return 0; /* End of DGBSV */ } /* dgbsv_ */
/* Subroutine */ int derrge_(char *path, integer *nunit) { /* Builtin functions */ integer s_wsle(cilist *), e_wsle(void); /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); /* Local variables */ doublereal a[16] /* was [4][4] */, b[4]; integer i__, j; doublereal w[12], x[4]; char c2[2]; doublereal r1[4], r2[4], af[16] /* was [4][4] */; integer ip[4], iw[4], info; doublereal anrm, ccond, rcond; extern /* Subroutine */ int dgbtf2_(integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, integer *), dgetf2_(integer *, integer *, doublereal *, integer *, integer *, integer *), dgbcon_(char *, integer *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dgecon_(char *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), alaesm_(char *, logical *, integer *), dgbequ_(integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *) , dgbrfs_(char *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dgbtrf_(integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, integer *), dgeequ_(integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *), dgerfs_(char *, integer * , integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, integer *, integer *), dgetrf_(integer *, integer *, doublereal *, integer *, integer *, integer *), dgetri_(integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); extern logical lsamen_(integer *, char *, char *); extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical *, logical *), dgbtrs_(char *, integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dgetrs_(char *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, 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 */ /* ======= */ /* DERRGE tests the error exits for the DOUBLE PRECISION 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__) { a[i__ + (j << 2) - 5] = 1. / (doublereal) (i__ + j); af[i__ + (j << 2) - 5] = 1. / (doublereal) (i__ + j); /* L10: */ } b[j - 1] = 0.; r1[j - 1] = 0.; r2[j - 1] = 0.; w[j - 1] = 0.; x[j - 1] = 0.; ip[j - 1] = j; iw[j - 1] = j; /* L20: */ } infoc_1.ok = TRUE_; if (lsamen_(&c__2, c2, "GE")) { /* Test error exits of the routines that use the LU decomposition */ /* of a general matrix. */ /* DGETRF */ s_copy(srnamc_1.srnamt, "DGETRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgetrf_(&c_n1, &c__0, a, &c__1, ip, &info); chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgetrf_(&c__0, &c_n1, a, &c__1, ip, &info); chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgetrf_(&c__2, &c__1, a, &c__1, ip, &info); chkxer_("DGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGETF2 */ s_copy(srnamc_1.srnamt, "DGETF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgetf2_(&c_n1, &c__0, a, &c__1, ip, &info); chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgetf2_(&c__0, &c_n1, a, &c__1, ip, &info); chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgetf2_(&c__2, &c__1, a, &c__1, ip, &info); chkxer_("DGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGETRI */ s_copy(srnamc_1.srnamt, "DGETRI", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgetri_(&c_n1, a, &c__1, ip, w, &c__12, &info); chkxer_("DGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgetri_(&c__2, a, &c__1, ip, w, &c__12, &info); chkxer_("DGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGETRS */ s_copy(srnamc_1.srnamt, "DGETRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 8; dgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info); chkxer_("DGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGERFS */ s_copy(srnamc_1.srnamt, "DGERFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, & c__1, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, & c__2, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, & c__2, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, & c__2, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; dgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, & c__1, r1, r2, w, iw, &info); chkxer_("DGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGECON */ s_copy(srnamc_1.srnamt, "DGECON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, iw, &info); chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, iw, &info); chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, iw, &info); chkxer_("DGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGEEQU */ s_copy(srnamc_1.srnamt, "DGEEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); } else if (lsamen_(&c__2, c2, "GB")) { /* Test error exits of the routines that use the LU decomposition */ /* of a general band matrix. */ /* DGBTRF */ s_copy(srnamc_1.srnamt, "DGBTRF", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info); chkxer_("DGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBTF2 */ s_copy(srnamc_1.srnamt, "DGBTF2", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info); chkxer_("DGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBTRS */ s_copy(srnamc_1.srnamt, "DGBTRS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; dgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 10; dgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, & info); chkxer_("DGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBRFS */ s_copy(srnamc_1.srnamt, "DGBRFS", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbrfs_("/", &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, & c__1, x, &c__1, r1, r2, w, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbrfs_("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, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbrfs_("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, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbrfs_("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, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 5; dgbrfs_("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, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 7; dgbrfs_("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, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 9; dgbrfs_("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, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 12; dgbrfs_("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, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 14; dgbrfs_("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, iw, &info); chkxer_("DGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBCON */ s_copy(srnamc_1.srnamt, "DGBCON", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, iw, &info); chkxer_("DGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); /* DGBEQU */ s_copy(srnamc_1.srnamt, "DGBEQU", (ftnlen)6, (ftnlen)6); infoc_1.infot = 1; dgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 2; dgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 3; dgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 4; dgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, & infoc_1.ok); infoc_1.infot = 6; dgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond, &anrm, &info); chkxer_("DGBEQU", &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 DERRGE */ } /* derrge_ */
/* Subroutine */ int dgbsvx_(char *fact, char *trans, integer *n, integer *kl, integer *ku, integer *nrhs, doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb, integer *ipiv, char *equed, doublereal *r__, doublereal *c__, doublereal *b, integer *ldb, doublereal *x, integer *ldx, doublereal *rcond, doublereal *ferr, doublereal *berr, doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset, x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5; doublereal d__1, d__2, d__3; /* Local variables */ integer i__, j, j1, j2; doublereal amax; char norm[1]; doublereal rcmin, rcmax, anorm; logical equil; doublereal colcnd; logical nofact; doublereal bignum; integer infequ; logical colequ; doublereal rowcnd; logical notran; doublereal smlnum; logical rowequ; doublereal rpvgrw; /* -- LAPACK driver routine (version 3.2) -- */ /* November 2006 */ /* Purpose */ /* ======= */ /* DGBSVX uses the LU factorization to compute the solution to a real */ /* system of linear equations A * X = B, A**T * X = B, or A**H * 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. */ /* Error bounds on the solution and a condition estimate are also */ /* provided. */ /* Description */ /* =========== */ /* The following steps are performed by this subroutine: */ /* 1. If FACT = 'E', real 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 = 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. */ /* 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. If the */ /* reciprocal of the condition number is less than machine precision, */ /* INFO = N+1 is returned as a warning, but 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. Iterative refinement is applied to improve the computed solution */ /* matrix and calculate error bounds and backward error estimates */ /* for it. */ /* 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 */ /* ========= */ /* 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, AFB 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. */ /* AB, AFB, and IPIV are not modified. */ /* = 'N': The matrix A will be copied to AFB and factored. */ /* = 'E': The matrix A will be equilibrated if necessary, then */ /* copied to AFB 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 (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 A 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 DGBTRF. 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 AFB is an output argument and on exit */ /* returns details of the LU factorization of A. */ /* If FACT = 'E', then AFB is an output argument and on exit */ /* returns details of the LU factorization of the equilibrated */ /* matrix A (see the description of AB 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 = L*U */ /* as computed by DGBTRF; 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 = 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 = 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. */ /* 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. */ /* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) */ /* On entry, the 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 or INFO = N+1, 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 */ /* The estimate of the reciprocal condition number of the matrix */ /* A after equilibration (if done). If RCOND is less than the */ /* machine precision (in particular, if RCOND = 0), the matrix */ /* is singular to working precision. This condition is */ /* indicated by a return code of INFO > 0. */ /* FERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* The estimated forward error bound for each solution vector */ /* X(j) (the j-th column of the solution matrix X). */ /* If XTRUE is the true solution corresponding to X(j), FERR(j) */ /* is an estimated upper bound for the magnitude of the largest */ /* element in (X(j) - XTRUE) divided by the magnitude of the */ /* largest element in X(j). The estimate is as reliable as */ /* the estimate for RCOND, and is almost always a slight */ /* overestimate of the true error. */ /* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */ /* 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). */ /* WORK (workspace/output) DOUBLE PRECISION array, dimension (3*N) */ /* On exit, WORK(1) contains the reciprocal pivot growth */ /* factor norm(A)/norm(U). The "max absolute element" norm is */ /* used. If WORK(1) 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, condition */ /* estimator RCOND, and forward error bound FERR could be */ /* unreliable. If factorization fails with 0<INFO<=N, then */ /* WORK(1) contains the reciprocal pivot growth factor for the */ /* leading INFO columns of A. */ /* IWORK (workspace) INTEGER array, dimension (N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, and i is */ /* <= N: U(i,i) 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+1: U is nonsingular, but RCOND is less than machine */ /* precision, meaning that the matrix is singular */ /* to working precision. Nevertheless, the */ /* solution and error bounds are computed because */ /* there are a number of situations where the */ /* computed solution can be more accurate than the */ /* value of RCOND would suggest. */ /* ===================================================================== */ /* Parameter adjustments */ 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; --ferr; --berr; --work; --iwork; /* Function Body */ *info = 0; nofact = lsame_(fact, "N"); equil = lsame_(fact, "E"); notran = lsame_(trans, "N"); 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"); smlnum = dlamch_("Safe minimum"); bignum = 1. / smlnum; } /* Test the input parameters. */ 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); } 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); } 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 = -16; } else if (*ldx < max(1,*n)) { *info = -18; } } } if (*info != 0) { i__1 = -(*info); xerbla_("DGBSVX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ dgbequ_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], &rowcnd, &colcnd, &amax, &infequ); if (infequ == 0) { /* Equilibrate the matrix. */ dlaqgb_(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"); } } /* Scale the right hand side. */ if (notran) { if (rowequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = r__[i__] * b[i__ + j * b_dim1]; } } } } else if (colequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { b[i__ + j * b_dim1] = c__[i__] * b[i__ + j * b_dim1]; } } } if (nofact || equil) { /* Compute the LU factorization of the band matrix A. */ i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = j - *ku; j1 = max(i__2,1); /* Computing MIN */ i__2 = j + *kl; j2 = min(i__2,*n); i__2 = j2 - j1 + 1; dcopy_(&i__2, &ab[*ku + 1 - j + j1 + j * ab_dim1], &c__1, &afb[* kl + *ku + 1 - j + j1 + j * afb_dim1], &c__1); } dgbtrf_(n, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], info); /* Return if INFO is non-zero. */ if (*info > 0) { /* Compute the reciprocal pivot growth factor of the */ /* leading rank-deficient INFO columns of A. */ anorm = 0.; i__1 = *info; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = *ku + 2 - j; /* Computing MIN */ i__4 = *n + *ku + 1 - j, i__5 = *kl + *ku + 1; i__3 = min(i__4,i__5); for (i__ = max(i__2,1); i__ <= i__3; ++i__) { /* Computing MAX */ d__2 = anorm, d__3 = (d__1 = ab[i__ + j * ab_dim1], abs( d__1)); anorm = max(d__2,d__3); } } /* Computing MIN */ i__3 = *info - 1, i__2 = *kl + *ku; i__1 = min(i__3,i__2); /* Computing MAX */ i__4 = 1, i__5 = *kl + *ku + 2 - *info; rpvgrw = dlantb_("M", "U", "N", info, &i__1, &afb[max(i__4, i__5) + afb_dim1], ldafb, &work[1]); if (rpvgrw == 0.) { rpvgrw = 1.; } else { rpvgrw = anorm / rpvgrw; } work[1] = rpvgrw; *rcond = 0.; return 0; } } /* Compute the norm of the matrix A and the */ /* reciprocal pivot growth factor RPVGRW. */ if (notran) { *(unsigned char *)norm = '1'; } else { *(unsigned char *)norm = 'I'; } anorm = dlangb_(norm, n, kl, ku, &ab[ab_offset], ldab, &work[1]); i__1 = *kl + *ku; rpvgrw = dlantb_("M", "U", "N", n, &i__1, &afb[afb_offset], ldafb, &work[ 1]); if (rpvgrw == 0.) { rpvgrw = 1.; } else { rpvgrw = dlangb_("M", n, kl, ku, &ab[ab_offset], ldab, &work[1]) / rpvgrw; } /* Compute the reciprocal of the condition number of A. */ dgbcon_(norm, n, kl, ku, &afb[afb_offset], ldafb, &ipiv[1], &anorm, rcond, &work[1], &iwork[1], info); /* Compute the solution matrix X. */ dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); dgbtrs_(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. */ dgbrfs_(trans, n, kl, ku, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &ipiv[1], &b[b_offset], ldb, &x[x_offset], ldx, &ferr[1], & berr[1], &work[1], &iwork[1], info); /* Transform the solution matrix X to a solution of the original */ /* system. */ if (notran) { if (colequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { x[i__ + j * x_dim1] = c__[i__] * x[i__ + j * x_dim1]; } } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= colcnd; } } } else if (rowequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__3 = *n; for (i__ = 1; i__ <= i__3; ++i__) { x[i__ + j * x_dim1] = r__[i__] * x[i__ + j * x_dim1]; } } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= rowcnd; } } /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < dlamch_("Epsilon")) { *info = *n + 1; } work[1] = rpvgrw; return 0; /* End of DGBSVX */ } /* dgbsvx_ */
/* Subroutine */ int dgbsvxx_(char *fact, char *trans, integer *n, integer * kl, integer *ku, integer *nrhs, doublereal *ab, integer *ldab, doublereal *afb, integer *ldafb, integer *ipiv, char *equed, doublereal *r__, doublereal *c__, doublereal *b, integer *ldb, doublereal *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, doublereal *work, integer *iwork, 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; doublereal d__1, d__2; /* Local variables */ integer i__, j; doublereal amax; extern doublereal dla_gbrpvgrw__(integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *); extern logical lsame_(char *, char *); doublereal rcmin, rcmax; logical equil; extern doublereal dlamch_(char *); extern /* Subroutine */ int dlaqgb_(integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, char *); doublereal colcnd; extern /* Subroutine */ int dgbtrf_(integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, integer *); logical nofact; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *); doublereal bignum; extern /* Subroutine */ int dgbtrs_(char *, integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); integer infequ; logical colequ; doublereal rowcnd; logical notran; doublereal smlnum; logical rowequ; extern /* Subroutine */ int dlascl2_(integer *, integer *, doublereal *, doublereal *, integer *), dgbequb_(integer *, integer *, integer * , integer *, doublereal *, integer *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, integer *), dgbrfsx_( char *, char *, integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *, doublereal *, integer *, 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 */ /* ======= */ /* DGBSVXX uses the LU factorization to compute the solution to a */ /* double precision 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. DGBSVXX 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. */ /* DGBSVXX 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 */ /* DGBSVXX 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 DGBSVXX 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 DGBTRF. 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; --iwork; /* 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 DGBRFSX. */ *rpvgrw = 0.; /* Test the input parameters. PARAMS is not tested until DGBRFSX. */ 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_("DGBSVXX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ dgbequb_(n, n, kl, ku, &ab[ab_offset], ldab, &r__[1], &c__[1], & rowcnd, &colcnd, &amax, &infequ); if (infequ == 0) { /* Equilibrate the matrix. */ dlaqgb_(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) { dlascl2_(n, nrhs, &r__[1], &b[b_offset], ldb); } } else { if (colequ) { dlascl2_(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__) { afb[i__ + j * afb_dim1] = ab[i__ - *kl + j * ab_dim1]; /* L30: */ } /* L40: */ } dgbtrf_(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 = dla_gbrpvgrw__(n, kl, ku, info, &ab[ab_offset], ldab, & afb[afb_offset], ldafb); return 0; } } /* Compute the reciprocal pivot growth factor RPVGRW. */ *rpvgrw = dla_gbrpvgrw__(n, kl, ku, n, &ab[ab_offset], ldab, &afb[ afb_offset], ldafb); /* Compute the solution matrix X. */ dlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); dgbtrs_(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. */ dgbrfsx_(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], &iwork[1], info); /* Scale solutions. */ if (colequ && notran) { dlascl2_(n, nrhs, &c__[1], &x[x_offset], ldx); } else if (rowequ && ! notran) { dlascl2_(n, nrhs, &r__[1], &x[x_offset], ldx); } return 0; /* End of DGBSVXX */ } /* dgbsvxx_ */
int BandArpackSolver::solve(int numModes, bool generalized, bool findSmallest) { if (generalized == false) { opserr << "BandArpackSolver::solve(int numMode, bool generalized) - only solves generalized problem\n"; return -1; } if (theSOE == 0) { opserr << "WARNING BandGenLinLapackSolver::solve(void)- "; opserr << " No LinearSOE object has been set\n"; return -1; } int n = theSOE->size; // check iPiv is large enough if (iPivSize < n) { opserr << "WARNING BandGenLinLapackSolver::solve(void)- "; opserr << " iPiv not large enough - has setSize() been called?\n"; return -1; } // set some variables int kl = theSOE->numSubD; int ku = theSOE->numSuperD; int ldA = 2*kl + ku +1; int nrhs = 1; int ldB = n; int info; double *Aptr = theSOE->A; int *iPIV = iPiv; int nev = numModes;; int ncv = getNCV(n, nev); // set up the space for ARPACK functions. // this is done each time method is called!! .. this needs to be cleaned up int ldv = n; int lworkl = ncv*ncv + 8*ncv; double *v = new double[ldv * ncv]; double *workl = new double[lworkl + 1]; double *workd = new double[3 * n + 1]; double *d = new double[nev]; double *z= new double[n * nev]; double *resid = new double[n]; int *iparam = new int[11]; int *ipntr = new int[11]; logical *select = new logical[ncv]; static char which[3]; if (findSmallest == true) { strcpy(which, "LM"); } else { strcpy(which, "SM"); } char bmat = 'G'; char howmy = 'A'; // some more variables int maxitr, mode; double tol = 0.0; info = 0; maxitr = 1000; mode = 3; iparam[0] = 1; iparam[2] = maxitr; iparam[6] = mode; bool rvec = true; int ido = 0; int ierr = 0; // Do the factorization of Matrix (A-dM) here. #ifdef _WIN32 DGBTRF(&n, &n, &kl, &ku, Aptr, &ldA, iPiv, &ierr); #else dgbtrf_(&n, &n, &kl, &ku, Aptr, &ldA, iPiv, &ierr); #endif if ( ierr != 0 ) { opserr << " BandArpackSolver::Error in dgbtrf_ " << endln; return -1; } while (1) { #ifdef _WIN32 unsigned int sizeWhich =2; unsigned int sizeBmat =1; unsigned int sizeHowmany =1; unsigned int sizeOne = 1; /* DSAUPD(&ido, &bmat, &sizeBmat, &n, which, &sizeWhich, &nev, &tol, resid, &ncv, v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info); */ DSAUPD(&ido, &bmat, &n, which, &nev, &tol, resid, &ncv, v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info); #else dsaupd_(&ido, &bmat, &n, which, &nev, &tol, resid, &ncv, v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info); #endif if (ido == -1) { myMv(n, &workd[ipntr[0]-1], &workd[ipntr[1]-1]); #ifdef _WIN32 /* DGBTRS("N", &sizeOne, &n, &kl, &ku, &nrhs, Aptr, &ldA, iPIV, &workd[ipntr[1] - 1], &ldB, &ierr); */ DGBTRS("N", &n, &kl, &ku, &nrhs, Aptr, &ldA, iPIV, &workd[ipntr[1] - 1], &ldB, &ierr); #else dgbtrs_("N", &n, &kl, &ku, &nrhs, Aptr, &ldA, iPIV, &workd[ipntr[1] - 1], &ldB, &ierr); #endif if (ierr != 0) { opserr << "BandArpackSolver::Error with dgbtrs_ 1" <<endln; exit(0); } continue; } else if (ido == 1) { // double ratio = 1.0; myCopy(n, &workd[ipntr[2]-1], &workd[ipntr[1]-1]); #ifdef _WIN32 /* DGBTRS("N", &sizeOne, &n, &kl, &ku, &nrhs, Aptr, &ldA, iPIV, &workd[ipntr[1] - 1], &ldB, &ierr); */ DGBTRS("N", &n, &kl, &ku, &nrhs, Aptr, &ldA, iPIV, &workd[ipntr[1] - 1], &ldB, &ierr); #else dgbtrs_("N", &n, &kl, &ku, &nrhs, Aptr, &ldA, iPIV, &workd[ipntr[1] - 1], &ldB, &ierr); #endif if (ierr != 0) { opserr << "BandArpackSolver::Error with dgbtrs_ 2" <<endln; exit(0); } continue; } else if (ido == 2) { myMv(n, &workd[ipntr[0]-1], &workd[ipntr[1]-1]); continue; } break; } if (info < 0) { opserr << "BandArpackSolver::Error with _saupd info = " << info << endln; switch(info) { case -1: opserr << "N must be positive.\n"; break; case -2: opserr << "NEV must be positive.\n"; break; case -3: opserr << "NCV must be greater than NEV and less than or equal to N.\n"; break; case -4: opserr << "The maximum number of Arnoldi update iterations allowed"; break; case -5: opserr << "WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'.\n"; break; case -6: opserr << "BMAT must be one of 'I' or 'G'.\n"; break; case -7: opserr << "Length of private work array WORKL is not sufficient.\n"; break; case -8: opserr << "Error return from trid. eigenvalue calculation"; opserr << "Informatinal error from LAPACK routine dsteqr.\n"; break; case -9: opserr << "Starting vector is zero.\n"; break; case -10: opserr << "IPARAM(7) must be 1,2,3,4,5.\n"; break; case -11: opserr << "IPARAM(7) = 1 and BMAT = 'G' are incompatable.\n"; break; case -12: opserr << "IPARAM(1) must be equal to 0 or 1.\n"; break; case -13: opserr << "NEV and WHICH = 'BE' are incompatable.\n"; break; case -9999: opserr << "Could not build an Arnoldi factorization."; opserr << "IPARAM(5) returns the size of the current Arnoldi\n"; opserr << "factorization. The user is advised to check that"; opserr << "enough workspace and array storage has been allocated.\n"; break; default: opserr << "unrecognised return value\n"; } // clean up the memory delete [] workl; delete [] workd; delete [] resid; delete [] iparam; delete [] v; delete [] select; delete [] ipntr; delete [] d; delete [] z; value = 0; eigenvector = 0; return info; } else { if (info == 1) { opserr << "BandArpackSolver::Maximum number of iteration reached." << endln; } else if (info == 3) { opserr << "BandArpackSolver::No Shifts could be applied during implicit,"; opserr << "Arnoldi update, try increasing NCV." << endln; } double sigma = theSOE->shift; if (iparam[4] > 0) { rvec = true; n = theSOE->size; ldv = n; #ifdef _WIN32 unsigned int sizeWhich =2; unsigned int sizeBmat =1; unsigned int sizeHowmany =1; /* DSEUPD(&rvec, &howmy, &sizeHowmany, select, d, z, &ldv, &sigma, &bmat, &sizeBmat, &n, which, &sizeWhich, &nev, &tol, resid, &ncv, v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info); */ DSEUPD(&rvec, &howmy, select, d, z, &ldv, &sigma, &bmat, &n, which, &nev, &tol, resid, &ncv, v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info); #else dseupd_(&rvec, &howmy, select, d, z, &ldv, &sigma, &bmat, &n, which, &nev, &tol, resid, &ncv, v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info); #endif if (info != 0) { opserr << "BandArpackSolver::Error with dseupd_" << info; switch(info) { case -1: opserr << " N must be positive.\n"; break; case -2: opserr << " NEV must be positive.\n"; break; case -3: opserr << " NCV must be greater than NEV and less than or equal to N.\n"; break; case -5: opserr << " WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'.\n"; break; case -6: opserr << " BMAT must be one of 'I' or 'G'.\n"; break; case -7: opserr << " Length of private work WORKL array is not sufficient.\n"; break; case -8: opserr << " Error return from trid. eigenvalue calculation"; opserr << "Information error from LAPACK routine dsteqr.\n"; break; case -9: opserr << " Starting vector is zero.\n"; break; case -10: opserr << " IPARAM(7) must be 1,2,3,4,5.\n"; break; case -11: opserr << " IPARAM(7) = 1 and BMAT = 'G' are incompatibl\n"; break; case -12: opserr << " NEV and WHICH = 'BE' are incompatible.\n"; break; case -14: opserr << " DSAUPD did not find any eigenvalues to sufficient accuracy.\n"; break; case -15: opserr << " HOWMNY must be one of 'A' or 'S' if RVEC = .true.\n"; break; case -16: opserr << " HOWMNY = 'S' not yet implemented\n"; break; default: ; } // clean up the memory delete [] workl; delete [] workd; delete [] resid; delete [] iparam; delete [] v; delete [] select; delete [] ipntr; delete [] d; delete [] z; value = 0; eigenvector = 0; return info; } } } value = d; eigenvector = z; theSOE->factored = true; // clean up the memory delete [] workl; delete [] workd; delete [] resid; delete [] iparam; delete [] v; delete [] select; delete [] ipntr; return 0; }
/* Subroutine */ int dgbsv_(integer *n, integer *kl, integer *ku, integer * nrhs, doublereal *ab, integer *ldab, integer *ipiv, doublereal *b, integer *ldb, integer *info) { /* -- LAPACK driver routine (version 2.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= DGBSV computes the solution to a real 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 * * VISArray 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. ===================================================================== Test the input parameters. Parameter adjustments Function Body */ /* System generated locals */ integer ab_dim1, ab_offset, b_dim1, b_offset, i__1; /* Local variables */ extern /* Subroutine */ int dgbtrf_(integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, integer *), xerbla_(char *, integer *), dgbtrs_(char *, integer *, integer *, integer *, integer *, doublereal *, integer *, integer *, doublereal *, integer *, integer *); #define IPIV(I) ipiv[(I)-1] #define AB(I,J) ab[(I)-1 + ((J)-1)* ( *ldab)] #define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)] *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_("DGBSV ", &i__1); return 0; } /* Compute the LU factorization of the band matrix A. */ dgbtrf_(n, n, kl, ku, &AB(1,1), ldab, &IPIV(1), info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ dgbtrs_("No transpose", n, kl, ku, nrhs, &AB(1,1), ldab, &IPIV( 1), &B(1,1), ldb, info); } return 0; /* End of DGBSV */ } /* dgbsv_ */