/* Subroutine */ int ssbevx_(char *jobz, char *range, char *uplo, integer *n, integer *kd, real *ab, integer *ldab, real *q, integer *ldq, real *vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, real * w, real *z__, integer *ldz, real *work, integer *iwork, integer * ifail, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, q_dim1, q_offset, z_dim1, z_offset, i__1, i__2; real r__1, r__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer i__, j, jj; real eps, vll, vuu, tmp1; integer indd, inde; real anrm; integer imax; real rmin, rmax; logical test; integer itmp1, indee; real sigma; extern logical lsame_(char *, char *); integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); char order[1]; extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); logical lower; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), sswap_(integer *, real *, integer *, real *, integer * ); logical wantz, alleig, indeig; integer iscale, indibl; logical valeig; extern doublereal slamch_(char *); real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); real abstll, bignum; extern doublereal slansb_(char *, char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); integer indisp, indiwo; extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *); integer indwrk; extern /* Subroutine */ int ssbtrd_(char *, char *, integer *, integer *, real *, integer *, real *, real *, real *, integer *, real *, integer *), sstein_(integer *, real *, real *, integer *, real *, integer *, integer *, real *, integer *, real * , integer *, integer *, integer *), ssterf_(integer *, real *, real *, integer *); integer nsplit; real smlnum; extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, real *, integer *, integer *, real *, real *, real *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *), ssteqr_(char *, integer *, real *, real *, real *, integer *, real *, integer *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SSBEVX computes selected eigenvalues and, optionally, eigenvectors */ /* of a real symmetric band matrix A. Eigenvalues and eigenvectors can */ /* be selected by specifying either a range of values or a range of */ /* indices for the desired eigenvalues. */ /* Arguments */ /* ========= */ /* JOBZ (input) CHARACTER*1 */ /* = 'N': Compute eigenvalues only; */ /* = 'V': Compute eigenvalues and eigenvectors. */ /* RANGE (input) CHARACTER*1 */ /* = 'A': all eigenvalues will be found; */ /* = 'V': all eigenvalues in the half-open interval (VL,VU] */ /* will be found; */ /* = 'I': the IL-th through IU-th eigenvalues will be found. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* KD (input) INTEGER */ /* The number of superdiagonals of the matrix A if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */ /* AB (input/output) REAL array, dimension (LDAB, N) */ /* On entry, the upper or lower triangle of the symmetric band */ /* matrix A, stored in the first KD+1 rows of the array. The */ /* j-th column of A is stored in the j-th column of the array AB */ /* as follows: */ /* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */ /* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */ /* On exit, AB is overwritten by values generated during the */ /* reduction to tridiagonal form. If UPLO = 'U', the first */ /* superdiagonal and the diagonal of the tridiagonal matrix T */ /* are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */ /* the diagonal and first subdiagonal of T are returned in the */ /* first two rows of AB. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KD + 1. */ /* Q (output) REAL array, dimension (LDQ, N) */ /* If JOBZ = 'V', the N-by-N orthogonal matrix used in the */ /* reduction to tridiagonal form. */ /* If JOBZ = 'N', the array Q is not referenced. */ /* LDQ (input) INTEGER */ /* The leading dimension of the array Q. If JOBZ = 'V', then */ /* LDQ >= max(1,N). */ /* VL (input) REAL */ /* VU (input) REAL */ /* If RANGE='V', the lower and upper bounds of the interval to */ /* be searched for eigenvalues. VL < VU. */ /* Not referenced if RANGE = 'A' or 'I'. */ /* IL (input) INTEGER */ /* IU (input) INTEGER */ /* If RANGE='I', the indices (in ascending order) of the */ /* smallest and largest eigenvalues to be returned. */ /* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */ /* Not referenced if RANGE = 'A' or 'V'. */ /* ABSTOL (input) REAL */ /* The absolute error tolerance for the eigenvalues. */ /* An approximate eigenvalue is accepted as converged */ /* when it is determined to lie in an interval [a,b] */ /* of width less than or equal to */ /* ABSTOL + EPS * max( |a|,|b| ) , */ /* where EPS is the machine precision. If ABSTOL is less than */ /* or equal to zero, then EPS*|T| will be used in its place, */ /* where |T| is the 1-norm of the tridiagonal matrix obtained */ /* by reducing AB to tridiagonal form. */ /* Eigenvalues will be computed most accurately when ABSTOL is */ /* set to twice the underflow threshold 2*SLAMCH('S'), not zero. */ /* If this routine returns with INFO>0, indicating that some */ /* eigenvectors did not converge, try setting ABSTOL to */ /* 2*SLAMCH('S'). */ /* See "Computing Small Singular Values of Bidiagonal Matrices */ /* with Guaranteed High Relative Accuracy," by Demmel and */ /* Kahan, LAPACK Working Note #3. */ /* M (output) INTEGER */ /* The total number of eigenvalues found. 0 <= M <= N. */ /* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. */ /* W (output) REAL array, dimension (N) */ /* The first M elements contain the selected eigenvalues in */ /* ascending order. */ /* Z (output) REAL array, dimension (LDZ, max(1,M)) */ /* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */ /* contain the orthonormal eigenvectors of the matrix A */ /* corresponding to the selected eigenvalues, with the i-th */ /* column of Z holding the eigenvector associated with W(i). */ /* If an eigenvector fails to converge, then that column of Z */ /* contains the latest approximation to the eigenvector, and the */ /* index of the eigenvector is returned in IFAIL. */ /* If JOBZ = 'N', then Z is not referenced. */ /* Note: the user must ensure that at least max(1,M) columns are */ /* supplied in the array Z; if RANGE = 'V', the exact value of M */ /* is not known in advance and an upper bound must be used. */ /* LDZ (input) INTEGER */ /* The leading dimension of the array Z. LDZ >= 1, and if */ /* JOBZ = 'V', LDZ >= max(1,N). */ /* WORK (workspace) REAL array, dimension (7*N) */ /* IWORK (workspace) INTEGER array, dimension (5*N) */ /* IFAIL (output) INTEGER array, dimension (N) */ /* If JOBZ = 'V', then if INFO = 0, the first M elements of */ /* IFAIL are zero. If INFO > 0, then IFAIL contains the */ /* indices of the eigenvectors that failed to converge. */ /* If JOBZ = 'N', then IFAIL is not referenced. */ /* INFO (output) INTEGER */ /* = 0: successful exit. */ /* < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > 0: if INFO = i, then i eigenvectors failed to converge. */ /* Their indices are stored in array IFAIL. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; q_dim1 = *ldq; q_offset = 1 + q_dim1; q -= q_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --iwork; --ifail; /* Function Body */ wantz = lsame_(jobz, "V"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); lower = lsame_(uplo, "L"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (! (lower || lsame_(uplo, "U"))) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*kd < 0) { *info = -5; } else if (*ldab < *kd + 1) { *info = -7; } else if (wantz && *ldq < max(1,*n)) { *info = -9; } else { if (valeig) { if (*n > 0 && *vu <= *vl) { *info = -11; } } else if (indeig) { if (*il < 1 || *il > max(1,*n)) { *info = -12; } else if (*iu < min(*n,*il) || *iu > *n) { *info = -13; } } } if (*info == 0) { if (*ldz < 1 || wantz && *ldz < *n) { *info = -18; } } if (*info != 0) { i__1 = -(*info); xerbla_("SSBEVX", &i__1); return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } if (*n == 1) { *m = 1; if (lower) { tmp1 = ab[ab_dim1 + 1]; } else { tmp1 = ab[*kd + 1 + ab_dim1]; } if (valeig) { if (! (*vl < tmp1 && *vu >= tmp1)) { *m = 0; } } if (*m == 1) { w[1] = tmp1; if (wantz) { z__[z_dim1 + 1] = 1.f; } } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin)); rmax = dmin(r__1,r__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } else { vll = 0.f; vuu = 0.f; } anrm = slansb_("M", uplo, n, kd, &ab[ab_offset], ldab, &work[1]); if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { if (lower) { slascl_("B", kd, kd, &c_b14, &sigma, n, n, &ab[ab_offset], ldab, info); } else { slascl_("Q", kd, kd, &c_b14, &sigma, n, n, &ab[ab_offset], ldab, info); } if (*abstol > 0.f) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call SSBTRD to reduce symmetric band matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indwrk = inde + *n; ssbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &work[indd], &work[inde], &q[q_offset], ldq, &work[indwrk], &iinfo); /* If all eigenvalues are desired and ABSTOL is less than or equal */ /* to zero, then call SSTERF or SSTEQR. If this fails for some */ /* eigenvalue, then try SSTEBZ. */ test = FALSE_; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE_; } } if ((alleig || test) && *abstol <= 0.f) { scopy_(n, &work[indd], &c__1, &w[1], &c__1); indee = indwrk + (*n << 1); if (! wantz) { i__1 = *n - 1; scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1); ssterf_(n, &w[1], &work[indee], info); } else { slacpy_("A", n, n, &q[q_offset], ldq, &z__[z_offset], ldz); i__1 = *n - 1; scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1); ssteqr_(jobz, n, &w[1], &work[indee], &z__[z_offset], ldz, &work[ indwrk], info); if (*info == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { ifail[i__] = 0; /* L10: */ } } } if (*info == 0) { *m = *n; goto L30; } *info = 0; } /* Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwo = indisp + *n; sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &work[indd], &work[ inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[ indwrk], &iwork[indiwo], info); if (wantz) { sstein_(n, &work[indd], &work[inde], m, &w[1], &iwork[indibl], &iwork[ indisp], &z__[z_offset], ldz, &work[indwrk], &iwork[indiwo], & ifail[1], info); /* Apply orthogonal matrix used in reduction to tridiagonal */ /* form to eigenvectors returned by SSTEIN. */ i__1 = *m; for (j = 1; j <= i__1; ++j) { scopy_(n, &z__[j * z_dim1 + 1], &c__1, &work[1], &c__1); sgemv_("N", n, n, &c_b14, &q[q_offset], ldq, &work[1], &c__1, & c_b34, &z__[j * z_dim1 + 1], &c__1); /* L20: */ } } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L30: if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } r__1 = 1.f / sigma; sscal_(&imax, &r__1, &w[1], &c__1); } /* If eigenvalues are not in order, then sort them, along with */ /* eigenvectors. */ if (wantz) { i__1 = *m - 1; for (j = 1; j <= i__1; ++j) { i__ = 0; tmp1 = w[j]; i__2 = *m; for (jj = j + 1; jj <= i__2; ++jj) { if (w[jj] < tmp1) { i__ = jj; tmp1 = w[jj]; } /* L40: */ } if (i__ != 0) { itmp1 = iwork[indibl + i__ - 1]; w[i__] = w[j]; iwork[indibl + i__ - 1] = iwork[indibl + j - 1]; w[j] = tmp1; iwork[indibl + j - 1] = itmp1; sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); if (*info != 0) { itmp1 = ifail[i__]; ifail[i__] = ifail[j]; ifail[j] = itmp1; } } /* L50: */ } } return 0; /* End of SSBEVX */ } /* ssbevx_ */
/* Subroutine */ int spbsvx_(char *fact, char *uplo, integer *n, integer *kd, integer *nrhs, real *ab, integer *ldab, real *afb, integer *ldafb, char *equed, real *s, real *b, integer *ldb, real *x, integer *ldx, real *rcond, real *ferr, real *berr, real *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; real r__1, r__2; /* Local variables */ integer i__, j, j1, j2; real amax, smin, smax; real scond, anorm; logical equil, rcequ, upper; logical nofact; real bignum; integer infequ; real smlnum; /* -- LAPACK driver routine (version 3.2) -- */ /* November 2006 */ /* Purpose */ /* ======= */ /* SPBSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to */ /* compute the solution to a real system of linear equations */ /* A * X = B, */ /* where A is an N-by-N symmetric positive definite band matrix 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: */ /* 1. If FACT = 'E', real scaling factors are computed to equilibrate */ /* the system: */ /* diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * 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(S)*A*diag(S) and B by diag(S)*B. */ /* 2. If FACT = 'N' or 'E', the Cholesky decomposition is used to */ /* factor the matrix A (after equilibration if FACT = 'E') as */ /* A = U**T * U, if UPLO = 'U', or */ /* A = L * L**T, if UPLO = 'L', */ /* where U is an upper triangular band matrix, and L is a lower */ /* triangular band matrix. */ /* 3. If the leading i-by-i principal minor is not positive definite, */ /* 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(S) 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 contains the factored form of A. */ /* If EQUED = 'Y', the matrix A has been equilibrated */ /* with scaling factors given by S. AB and AFB will not */ /* be 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. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The number of linear equations, i.e., the order of the */ /* matrix A. N >= 0. */ /* KD (input) INTEGER */ /* The number of superdiagonals of the matrix A if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KD >= 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) REAL array, dimension (LDAB,N) */ /* On entry, the upper or lower triangle of the symmetric band */ /* matrix A, stored in the first KD+1 rows of the array, except */ /* if FACT = 'F' and EQUED = 'Y', then A must contain the */ /* equilibrated matrix diag(S)*A*diag(S). The j-th column of A */ /* is stored in the j-th column of the array AB as follows: */ /* if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; */ /* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). */ /* See below for further details. */ /* On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by */ /* diag(S)*A*diag(S). */ /* LDAB (input) INTEGER */ /* The leading dimension of the array A. LDAB >= KD+1. */ /* AFB (input or output) REAL array, dimension (LDAFB,N) */ /* If FACT = 'F', then AFB is an input argument and on entry */ /* contains the triangular factor U or L from the Cholesky */ /* factorization A = U**T*U or A = L*L**T of the band matrix */ /* A, in the same storage format as A (see AB). If EQUED = 'Y', */ /* then AFB is the factored form of the equilibrated matrix A. */ /* If FACT = 'N', then AFB is an output argument and on exit */ /* returns the triangular factor U or L from the Cholesky */ /* factorization A = U**T*U or A = L*L**T. */ /* If FACT = 'E', then AFB is an output argument and on exit */ /* returns the triangular factor U or L from the Cholesky */ /* factorization A = U**T*U or A = L*L**T 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 >= KD+1. */ /* EQUED (input or output) CHARACTER*1 */ /* Specifies the form of equilibration that was done. */ /* = 'N': No equilibration (always true if FACT = 'N'). */ /* = 'Y': Equilibration was done, i.e., A has been replaced by */ /* diag(S) * A * diag(S). */ /* EQUED is an input argument if FACT = 'F'; otherwise, it is an */ /* output argument. */ /* S (input or output) REAL array, dimension (N) */ /* The scale factors for A; not accessed if EQUED = 'N'. S is */ /* an input argument if FACT = 'F'; otherwise, S is an output */ /* argument. If FACT = 'F' and EQUED = 'Y', each element of S */ /* must be positive. */ /* B (input/output) REAL 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 EQUED = 'Y', */ /* B is overwritten by diag(S) * B. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* X (output) REAL 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 if EQUED = 'Y', */ /* A and B are modified on exit, and the solution to the */ /* equilibrated system is inv(diag(S))*X. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* RCOND (output) REAL */ /* 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) REAL 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) REAL 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) REAL array, dimension (3*N) */ /* 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: the leading minor of order i of A is */ /* not positive definite, so the factorization */ /* could not be completed, and the solution has not */ /* been 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. */ /* Further Details */ /* =============== */ /* The band storage scheme is illustrated by the following example, when */ /* N = 6, KD = 2, and UPLO = 'U': */ /* Two-dimensional storage of the symmetric matrix A: */ /* a11 a12 a13 */ /* a22 a23 a24 */ /* a33 a34 a35 */ /* a44 a45 a46 */ /* a55 a56 */ /* (aij=conjg(aji)) a66 */ /* Band storage of the upper triangle of A: */ /* * * a13 a24 a35 a46 */ /* * a12 a23 a34 a45 a56 */ /* a11 a22 a33 a44 a55 a66 */ /* Similarly, if UPLO = 'L' the format of A is as follows: */ /* a11 a22 a33 a44 a55 a66 */ /* a21 a32 a43 a54 a65 * */ /* a31 a42 a53 a64 * * */ /* Array elements marked * are not used by the routine. */ /* ===================================================================== */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; afb_dim1 = *ldafb; afb_offset = 1 + afb_dim1; afb -= afb_offset; --s; 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"); upper = lsame_(uplo, "U"); if (nofact || equil) { *(unsigned char *)equed = 'N'; rcequ = FALSE_; } else { rcequ = lsame_(equed, "Y"); smlnum = slamch_("Safe minimum"); bignum = 1.f / smlnum; } /* Test the input parameters. */ if (! nofact && ! equil && ! lsame_(fact, "F")) { *info = -1; } else if (! upper && ! lsame_(uplo, "L")) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*kd < 0) { *info = -4; } else if (*nrhs < 0) { *info = -5; } else if (*ldab < *kd + 1) { *info = -7; } else if (*ldafb < *kd + 1) { *info = -9; } else if (lsame_(fact, "F") && ! (rcequ || lsame_( equed, "N"))) { *info = -10; } else { if (rcequ) { smin = bignum; smax = 0.f; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ r__1 = smin, r__2 = s[j]; smin = dmin(r__1,r__2); /* Computing MAX */ r__1 = smax, r__2 = s[j]; smax = dmax(r__1,r__2); } if (smin <= 0.f) { *info = -11; } else if (*n > 0) { scond = dmax(smin,smlnum) / dmin(smax,bignum); } else { scond = 1.f; } } if (*info == 0) { if (*ldb < max(1,*n)) { *info = -13; } else if (*ldx < max(1,*n)) { *info = -15; } } } if (*info != 0) { i__1 = -(*info); xerbla_("SPBSVX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ spbequ_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, & infequ); if (infequ == 0) { /* Equilibrate the matrix. */ slaqsb_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, equed); rcequ = lsame_(equed, "Y"); } } /* Scale the right-hand side. */ if (rcequ) { 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] = s[i__] * b[i__ + j * b_dim1]; } } } if (nofact || equil) { /* Compute the Cholesky factorization A = U'*U or A = L*L'. */ if (upper) { i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = j - *kd; j1 = max(i__2,1); i__2 = j - j1 + 1; scopy_(&i__2, &ab[*kd + 1 - j + j1 + j * ab_dim1], &c__1, & afb[*kd + 1 - j + j1 + j * afb_dim1], &c__1); } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ i__2 = j + *kd; j2 = min(i__2,*n); i__2 = j2 - j + 1; scopy_(&i__2, &ab[j * ab_dim1 + 1], &c__1, &afb[j * afb_dim1 + 1], &c__1); } } spbtrf_(uplo, n, kd, &afb[afb_offset], ldafb, info); /* Return if INFO is non-zero. */ if (*info > 0) { *rcond = 0.f; return 0; } } /* Compute the norm of the matrix A. */ anorm = slansb_("1", uplo, n, kd, &ab[ab_offset], ldab, &work[1]); /* Compute the reciprocal of the condition number of A. */ spbcon_(uplo, n, kd, &afb[afb_offset], ldafb, &anorm, rcond, &work[1], & iwork[1], info); /* Compute the solution matrix X. */ slacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); spbtrs_(uplo, n, kd, nrhs, &afb[afb_offset], ldafb, &x[x_offset], ldx, info); /* Use iterative refinement to improve the computed solution and */ /* compute error bounds and backward error estimates for it. */ spbrfs_(uplo, n, kd, nrhs, &ab[ab_offset], ldab, &afb[afb_offset], ldafb, &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 (rcequ) { i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { i__2 = *n; for (i__ = 1; i__ <= i__2; ++i__) { x[i__ + j * x_dim1] = s[i__] * x[i__ + j * x_dim1]; } } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= scond; } } /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < slamch_("Epsilon")) { *info = *n + 1; } return 0; /* End of SPBSVX */ } /* spbsvx_ */
/* Subroutine */ int spbt02_(char *uplo, integer *n, integer *kd, integer * nrhs, real *a, integer *lda, real *x, integer *ldx, real *b, integer * ldb, real *rwork, real *resid) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1; real r__1, r__2; /* Local variables */ static integer j; static real anorm, bnorm; extern doublereal sasum_(integer *, real *, integer *); extern /* Subroutine */ int ssbmv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static real xnorm; extern doublereal slamch_(char *), slansb_(char *, char *, integer *, integer *, real *, integer *, real *); static real eps; #define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1] #define x_ref(a_1,a_2) x[(a_2)*x_dim1 + a_1] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University February 29, 1992 Purpose ======= SPBT02 computes the residual for a solution of a symmetric banded system of equations A*x = b: RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS) where EPS is the machine precision. Arguments ========= UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The number of rows and columns of the matrix A. N >= 0. KD (input) INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0. A (input) REAL array, dimension (LDA,N) The original symmetric band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See SPBTRF for further details. LDA (input) INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1). X (input) REAL array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations. LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). B (input/output) REAL array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). RWORK (workspace) REAL array, dimension (N) RESID (output) REAL The maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ). ===================================================================== Quick exit if N = 0 or NRHS = 0. Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1 * 1; x -= x_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; --rwork; /* Function Body */ if (*n <= 0 || *nrhs <= 0) { *resid = 0.f; return 0; } /* Exit with RESID = 1/EPS if ANORM = 0. */ eps = slamch_("Epsilon"); anorm = slansb_("1", uplo, n, kd, &a[a_offset], lda, &rwork[1]); if (anorm <= 0.f) { *resid = 1.f / eps; return 0; } /* Compute B - A*X */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ssbmv_(uplo, n, kd, &c_b5, &a[a_offset], lda, &x_ref(1, j), &c__1, & c_b7, &b_ref(1, j), &c__1); /* L10: */ } /* Compute the maximum over the number of right hand sides of norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) */ *resid = 0.f; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { bnorm = sasum_(n, &b_ref(1, j), &c__1); xnorm = sasum_(n, &x_ref(1, j), &c__1); if (xnorm <= 0.f) { *resid = 1.f / eps; } else { /* Computing MAX */ r__1 = *resid, r__2 = bnorm / anorm / xnorm / eps; *resid = dmax(r__1,r__2); } /* L20: */ } return 0; /* End of SPBT02 */ } /* spbt02_ */
int ssbev_(char *jobz, char *uplo, int *n, int *kd, float *ab, int *ldab, float *w, float *z__, int *ldz, float *work, int *info) { /* System generated locals */ int ab_dim1, ab_offset, z_dim1, z_offset, i__1; float r__1; /* Builtin functions */ double sqrt(double); /* Local variables */ float eps; int inde; float anrm; int imax; float rmin, rmax, sigma; extern int lsame_(char *, char *); int iinfo; extern int sscal_(int *, float *, float *, int *); int lower, wantz; int iscale; extern double slamch_(char *); float safmin; extern int xerbla_(char *, int *); float bignum; extern double slansb_(char *, char *, int *, int *, float *, int *, float *); extern int slascl_(char *, int *, int *, float *, float *, int *, int *, float *, int *, int *); int indwrk; extern int ssbtrd_(char *, char *, int *, int *, float *, int *, float *, float *, float *, int *, float *, int *), ssterf_(int *, float *, float *, int *); float smlnum; extern int ssteqr_(char *, int *, float *, float *, float *, int *, float *, int *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SSBEV computes all the eigenvalues and, optionally, eigenvectors of */ /* a float symmetric band matrix A. */ /* Arguments */ /* ========= */ /* JOBZ (input) CHARACTER*1 */ /* = 'N': Compute eigenvalues only; */ /* = 'V': Compute eigenvalues and eigenvectors. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangle of A is stored; */ /* = 'L': Lower triangle of A is stored. */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* KD (input) INTEGER */ /* The number of superdiagonals of the matrix A if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */ /* AB (input/output) REAL array, dimension (LDAB, N) */ /* On entry, the upper or lower triangle of the symmetric band */ /* matrix A, stored in the first KD+1 rows of the array. The */ /* j-th column of A is stored in the j-th column of the array AB */ /* as follows: */ /* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for MAX(1,j-kd)<=i<=j; */ /* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=MIN(n,j+kd). */ /* On exit, AB is overwritten by values generated during the */ /* reduction to tridiagonal form. If UPLO = 'U', the first */ /* superdiagonal and the diagonal of the tridiagonal matrix T */ /* are returned in rows KD and KD+1 of AB, and if UPLO = 'L', */ /* the diagonal and first subdiagonal of T are returned in the */ /* first two rows of AB. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KD + 1. */ /* W (output) REAL array, dimension (N) */ /* If INFO = 0, the eigenvalues in ascending order. */ /* Z (output) REAL array, dimension (LDZ, N) */ /* If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal */ /* eigenvectors of the matrix A, with the i-th column of Z */ /* holding the eigenvector associated with W(i). */ /* If JOBZ = 'N', then Z is not referenced. */ /* LDZ (input) INTEGER */ /* The leading dimension of the array Z. LDZ >= 1, and if */ /* JOBZ = 'V', LDZ >= MAX(1,N). */ /* WORK (workspace) REAL array, dimension (MAX(1,3*N-2)) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, the algorithm failed to converge; i */ /* off-diagonal elements of an intermediate tridiagonal */ /* form did not converge to zero. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; /* Function Body */ wantz = lsame_(jobz, "V"); lower = lsame_(uplo, "L"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (lower || lsame_(uplo, "U"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*kd < 0) { *info = -4; } else if (*ldab < *kd + 1) { *info = -6; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("SSBEV ", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { if (lower) { w[1] = ab[ab_dim1 + 1]; } else { w[1] = ab[*kd + 1 + ab_dim1]; } if (wantz) { z__[z_dim1 + 1] = 1.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = slansb_("M", uplo, n, kd, &ab[ab_offset], ldab, &work[1]); iscale = 0; if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { if (lower) { slascl_("B", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab, info); } else { slascl_("Q", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab, info); } } /* Call SSBTRD to reduce symmetric band matrix to tridiagonal form. */ inde = 1; indwrk = inde + *n; ssbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &w[1], &work[inde], &z__[ z_offset], ldz, &work[indwrk], &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEQR. */ if (! wantz) { ssterf_(n, &w[1], &work[inde], info); } else { ssteqr_(jobz, n, &w[1], &work[inde], &z__[z_offset], ldz, &work[ indwrk], info); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { if (*info == 0) { imax = *n; } else { imax = *info - 1; } r__1 = 1.f / sigma; sscal_(&imax, &r__1, &w[1], &c__1); } return 0; /* End of SSBEV */ } /* ssbev_ */
/* Subroutine */ int ssbt21_(char *uplo, integer *n, integer *ka, integer *ks, real *a, integer *lda, real *d__, real *e, real *u, integer *ldu, real *work, real *result) { /* System generated locals */ integer a_dim1, a_offset, u_dim1, u_offset, i__1, i__2, i__3, i__4; real r__1, r__2; /* Local variables */ integer j, jc, jr, lw, ika; real ulp, unfl; extern /* Subroutine */ int sspr_(char *, integer *, real *, real *, integer *, real *), sspr2_(char *, integer *, real *, real *, integer *, real *, integer *, real *); extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); real anorm; char cuplo[1]; logical lower; real wnorm; extern doublereal slamch_(char *), slange_(char *, integer *, integer *, real *, integer *, real *), slansb_(char *, char *, integer *, integer *, real *, integer *, real *), slansp_(char *, char *, integer *, real *, real *); /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SSBT21 generally checks a decomposition of the form */ /* A = U S U' */ /* where ' means transpose, A is symmetric banded, U is */ /* orthogonal, and S is diagonal (if KS=0) or symmetric */ /* tridiagonal (if KS=1). */ /* Specifically: */ /* RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and* */ /* RESULT(2) = | I - UU' | / ( n ulp ) */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER */ /* If UPLO='U', the upper triangle of A and V will be used and */ /* the (strictly) lower triangle will not be referenced. */ /* If UPLO='L', the lower triangle of A and V will be used and */ /* the (strictly) upper triangle will not be referenced. */ /* N (input) INTEGER */ /* The size of the matrix. If it is zero, SSBT21 does nothing. */ /* It must be at least zero. */ /* KA (input) INTEGER */ /* The bandwidth of the matrix A. It must be at least zero. If */ /* it is larger than N-1, then max( 0, N-1 ) will be used. */ /* KS (input) INTEGER */ /* The bandwidth of the matrix S. It may only be zero or one. */ /* If zero, then S is diagonal, and E is not referenced. If */ /* one, then S is symmetric tri-diagonal. */ /* A (input) REAL array, dimension (LDA, N) */ /* The original (unfactored) matrix. It is assumed to be */ /* symmetric, and only the upper (UPLO='U') or only the lower */ /* (UPLO='L') will be referenced. */ /* LDA (input) INTEGER */ /* The leading dimension of A. It must be at least 1 */ /* and at least min( KA, N-1 ). */ /* D (input) REAL array, dimension (N) */ /* The diagonal of the (symmetric tri-) diagonal matrix S. */ /* E (input) REAL array, dimension (N-1) */ /* The off-diagonal of the (symmetric tri-) diagonal matrix S. */ /* E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and */ /* (3,2) element, etc. */ /* Not referenced if KS=0. */ /* U (input) REAL array, dimension (LDU, N) */ /* The orthogonal matrix in the decomposition, expressed as a */ /* dense matrix (i.e., not as a product of Householder */ /* transformations, Givens transformations, etc.) */ /* LDU (input) INTEGER */ /* The leading dimension of U. LDU must be at least N and */ /* at least 1. */ /* WORK (workspace) REAL array, dimension (N**2+N) */ /* RESULT (output) REAL array, dimension (2) */ /* The values computed by the two tests described above. The */ /* values are currently limited to 1/ulp, to avoid overflow. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Constants */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --d__; --e; u_dim1 = *ldu; u_offset = 1 + u_dim1; u -= u_offset; --work; --result; /* Function Body */ result[1] = 0.f; result[2] = 0.f; if (*n <= 0) { return 0; } /* Computing MAX */ /* Computing MIN */ i__3 = *n - 1; i__1 = 0, i__2 = min(i__3,*ka); ika = max(i__1,i__2); lw = *n * (*n + 1) / 2; if (lsame_(uplo, "U")) { lower = FALSE_; *(unsigned char *)cuplo = 'U'; } else { lower = TRUE_; *(unsigned char *)cuplo = 'L'; } unfl = slamch_("Safe minimum"); ulp = slamch_("Epsilon") * slamch_("Base"); /* Some Error Checks */ /* Do Test 1 */ /* Norm of A: */ /* Computing MAX */ r__1 = slansb_("1", cuplo, n, &ika, &a[a_offset], lda, &work[1]); anorm = dmax(r__1,unfl); /* Compute error matrix: Error = A - U S U' */ /* Copy A from SB to SP storage format. */ j = 0; i__1 = *n; for (jc = 1; jc <= i__1; ++jc) { if (lower) { /* Computing MIN */ i__3 = ika + 1, i__4 = *n + 1 - jc; i__2 = min(i__3,i__4); for (jr = 1; jr <= i__2; ++jr) { ++j; work[j] = a[jr + jc * a_dim1]; /* L10: */ } i__2 = *n + 1 - jc; for (jr = ika + 2; jr <= i__2; ++jr) { ++j; work[j] = 0.f; /* L20: */ } } else { i__2 = jc; for (jr = ika + 2; jr <= i__2; ++jr) { ++j; work[j] = 0.f; /* L30: */ } /* Computing MIN */ i__2 = ika, i__3 = jc - 1; for (jr = min(i__2,i__3); jr >= 0; --jr) { ++j; work[j] = a[ika + 1 - jr + jc * a_dim1]; /* L40: */ } } /* L50: */ } i__1 = *n; for (j = 1; j <= i__1; ++j) { r__1 = -d__[j]; sspr_(cuplo, n, &r__1, &u[j * u_dim1 + 1], &c__1, &work[1]) ; /* L60: */ } if (*n > 1 && *ks == 1) { i__1 = *n - 1; for (j = 1; j <= i__1; ++j) { r__1 = -e[j]; sspr2_(cuplo, n, &r__1, &u[j * u_dim1 + 1], &c__1, &u[(j + 1) * u_dim1 + 1], &c__1, &work[1]); /* L70: */ } } wnorm = slansp_("1", cuplo, n, &work[1], &work[lw + 1]); if (anorm > wnorm) { result[1] = wnorm / anorm / (*n * ulp); } else { if (anorm < 1.f) { /* Computing MIN */ r__1 = wnorm, r__2 = *n * anorm; result[1] = dmin(r__1,r__2) / anorm / (*n * ulp); } else { /* Computing MIN */ r__1 = wnorm / anorm, r__2 = (real) (*n); result[1] = dmin(r__1,r__2) / (*n * ulp); } } /* Do Test 2 */ /* Compute UU' - I */ sgemm_("N", "C", n, n, n, &c_b22, &u[u_offset], ldu, &u[u_offset], ldu, & c_b23, &work[1], n); i__1 = *n; for (j = 1; j <= i__1; ++j) { work[(*n + 1) * (j - 1) + 1] += -1.f; /* L80: */ } /* Computing MIN */ /* Computing 2nd power */ i__1 = *n; r__1 = slange_("1", n, n, &work[1], n, &work[i__1 * i__1 + 1]), r__2 = (real) (*n); result[2] = dmin(r__1,r__2) / (*n * ulp); return 0; /* End of SSBT21 */ } /* ssbt21_ */
/* Subroutine */ int sdrvpb_(logical *dotype, integer *nn, integer *nval, integer *nrhs, real *thresh, logical *tsterr, integer *nmax, real *a, real *afac, real *asav, real *b, real *bsav, real *x, real *xact, real *s, real *work, real *rwork, integer *iwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; static char facts[1*3] = "F" "N" "E"; static char equeds[1*2] = "N" "Y"; /* Format strings */ static char fmt_9999[] = "(1x,a,\002, UPLO='\002,a1,\002', N =\002,i5" ",\002, KD =\002,i5,\002, type \002,i1,\002, test(\002,i1,\002)" "=\002,g12.5)"; static char fmt_9997[] = "(1x,a,\002( '\002,a1,\002', '\002,a1,\002'," " \002,i5,\002, \002,i5,\002, ... ), EQUED='\002,a1,\002', type" " \002,i1,\002, test(\002,i1,\002)=\002,g12.5)"; static char fmt_9998[] = "(1x,a,\002( '\002,a1,\002', '\002,a1,\002'," " \002,i5,\002, \002,i5,\002, ... ), type \002,i1,\002, test(\002" ",i1,\002)=\002,g12.5)"; /* System generated locals */ address a__1[2]; integer i__1, i__2, i__3, i__4, i__5, i__6, i__7[2]; char ch__1[2]; /* Builtin functions */ /* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen); integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void); /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen); /* Local variables */ integer i__, k, n, i1, i2, k1, kd, nb, in, kl, iw, ku, nt, lda, ikd, nkd, ldab; char fact[1]; integer ioff, mode, koff; real amax; char path[3]; integer imat, info; char dist[1], uplo[1], type__[1]; integer nrun, ifact, nfail, iseed[4], nfact, kdval[4]; extern logical lsame_(char *, char *); char equed[1]; integer nbmin; real rcond, roldc, scond; integer nimat; extern doublereal sget06_(real *, real *); extern /* Subroutine */ int sget04_(integer *, integer *, real *, integer *, real *, integer *, real *, real *), spbt01_(char *, integer *, integer *, real *, integer *, real *, integer *, real *, real *); real anorm; extern /* Subroutine */ int spbt02_(char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real * , real *), spbt05_(char *, integer *, integer *, integer * , real *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, real *, real *); logical equil; integer iuplo, izero, nerrs; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), spbsv_(char *, integer *, integer *, integer *, real * , integer *, real *, integer *, integer *), sswap_( integer *, real *, integer *, real *, integer *); logical zerot; char xtype[1]; extern /* Subroutine */ int slatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char * ), aladhd_(integer *, char *), alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *); logical prefac; real rcondc; extern doublereal slange_(char *, integer *, integer *, real *, integer *, real *); logical nofact; char packit[1]; integer iequed; extern doublereal slansb_(char *, char *, integer *, integer *, real *, integer *, real *); real cndnum; extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer *, integer *), slaqsb_(char *, integer *, integer *, real *, integer *, real *, real *, real *, char *); real ainvnm; extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *), slarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer * , integer *, integer *), slaset_( char *, integer *, integer *, real *, real *, real *, integer *), spbequ_(char *, integer *, integer *, real *, integer *, real *, real *, real *, integer *), spbtrf_(char *, integer *, integer *, real *, integer *, integer *), xlaenv_(integer *, integer *), slatms_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, integer * , integer *, char *, real *, integer *, real *, integer *), spbtrs_(char *, integer *, integer *, integer *, real *, integer *, real *, integer *, integer *); real result[6]; extern /* Subroutine */ int spbsvx_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, char *, real *, real *, integer *, real *, integer *, real *, real *, real *, real *, integer *, integer *), serrvx_( char *, integer *); /* Fortran I/O blocks */ static cilist io___57 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___60 = { 0, 0, 0, fmt_9997, 0 }; static cilist io___61 = { 0, 0, 0, fmt_9998, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SDRVPB tests the driver routines SPBSV and -SVX. */ /* Arguments */ /* ========= */ /* DOTYPE (input) LOGICAL array, dimension (NTYPES) */ /* The matrix types to be used for testing. Matrices of type j */ /* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */ /* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */ /* NN (input) INTEGER */ /* The number of values of N contained in the vector NVAL. */ /* NVAL (input) INTEGER array, dimension (NN) */ /* The values of the matrix dimension N. */ /* NRHS (input) INTEGER */ /* The number of right hand side vectors to be generated for */ /* each linear system. */ /* THRESH (input) REAL */ /* The threshold value for the test ratios. A result is */ /* included in the output file if RESULT >= THRESH. To have */ /* every test ratio printed, use THRESH = 0. */ /* TSTERR (input) LOGICAL */ /* Flag that indicates whether error exits are to be tested. */ /* NMAX (input) INTEGER */ /* The maximum value permitted for N, used in dimensioning the */ /* work arrays. */ /* A (workspace) REAL array, dimension (NMAX*NMAX) */ /* AFAC (workspace) REAL array, dimension (NMAX*NMAX) */ /* ASAV (workspace) REAL array, dimension (NMAX*NMAX) */ /* B (workspace) REAL array, dimension (NMAX*NRHS) */ /* BSAV (workspace) REAL array, dimension (NMAX*NRHS) */ /* X (workspace) REAL array, dimension (NMAX*NRHS) */ /* XACT (workspace) REAL array, dimension (NMAX*NRHS) */ /* S (workspace) REAL array, dimension (NMAX) */ /* WORK (workspace) REAL array, dimension */ /* (NMAX*max(3,NRHS)) */ /* RWORK (workspace) REAL array, dimension (NMAX+2*NRHS) */ /* 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; --s; --xact; --x; --bsav; --b; --asav; --afac; --a; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Single precision", (ftnlen)1, (ftnlen)16); s_copy(path + 1, "PB", (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) { serrvx_(path, nout); } infoc_1.infot = 0; kdval[0] = 0; /* Set the block size and minimum block size for testing. */ nb = 1; nbmin = 2; xlaenv_(&c__1, &nb); xlaenv_(&c__2, &nbmin); /* Do for each value of N in NVAL */ i__1 = *nn; for (in = 1; in <= i__1; ++in) { n = nval[in]; lda = max(n,1); *(unsigned char *)xtype = 'N'; /* Set limits on the number of loop iterations. */ /* Computing MAX */ i__2 = 1, i__3 = min(n,4); nkd = max(i__2,i__3); nimat = 8; if (n == 0) { nimat = 1; } kdval[1] = n + (n + 1) / 4; kdval[2] = (n * 3 - 1) / 4; kdval[3] = (n + 1) / 4; i__2 = nkd; for (ikd = 1; ikd <= i__2; ++ikd) { /* Do for KD = 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. */ kd = kdval[ikd - 1]; ldab = kd + 1; /* Do first for UPLO = 'U', then for UPLO = 'L' */ for (iuplo = 1; iuplo <= 2; ++iuplo) { koff = 1; if (iuplo == 1) { *(unsigned char *)uplo = 'U'; *(unsigned char *)packit = 'Q'; /* Computing MAX */ i__3 = 1, i__4 = kd + 2 - n; koff = max(i__3,i__4); } else { *(unsigned char *)uplo = 'L'; *(unsigned char *)packit = 'B'; } i__3 = nimat; for (imat = 1; imat <= i__3; ++imat) { /* Do the tests only if DOTYPE( IMAT ) is true. */ if (! dotype[imat]) { goto L80; } /* Skip types 2, 3, or 4 if the matrix size is too small. */ zerot = imat >= 2 && imat <= 4; if (zerot && n < imat - 1) { goto L80; } if (! zerot || ! dotype[1]) { /* Set up parameters with SLATB4 and generate a test */ /* matrix with SLATMS. */ slatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "SLATMS", (ftnlen)32, (ftnlen) 6); slatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cndnum, &anorm, &kd, &kd, packit, &a[koff], &ldab, &work[1], &info); /* Check error code from SLATMS. */ if (info != 0) { alaerh_(path, "SLATMS", &info, &c__0, uplo, &n, & n, &c_n1, &c_n1, &c_n1, &imat, &nfail, & nerrs, nout); goto L80; } } else if (izero > 0) { /* Use the same matrix for types 3 and 4 as for type */ /* 2 by copying back the zeroed out column, */ iw = (lda << 1) + 1; if (iuplo == 1) { ioff = (izero - 1) * ldab + kd + 1; i__4 = izero - i1; scopy_(&i__4, &work[iw], &c__1, &a[ioff - izero + i1], &c__1); iw = iw + izero - i1; i__4 = i2 - izero + 1; /* Computing MAX */ i__6 = ldab - 1; i__5 = max(i__6,1); scopy_(&i__4, &work[iw], &c__1, &a[ioff], &i__5); } else { ioff = (i1 - 1) * ldab + 1; i__4 = izero - i1; /* Computing MAX */ i__6 = ldab - 1; i__5 = max(i__6,1); scopy_(&i__4, &work[iw], &c__1, &a[ioff + izero - i1], &i__5); ioff = (izero - 1) * ldab + 1; iw = iw + izero - i1; i__4 = i2 - izero + 1; scopy_(&i__4, &work[iw], &c__1, &a[ioff], &c__1); } } /* For types 2-4, zero one row and column of the matrix */ /* to test that INFO is returned correctly. */ izero = 0; if (zerot) { if (imat == 2) { izero = 1; } else if (imat == 3) { izero = n; } else { izero = n / 2 + 1; } /* Save the zeroed out row and column in WORK(*,3) */ iw = lda << 1; /* Computing MIN */ i__5 = (kd << 1) + 1; i__4 = min(i__5,n); for (i__ = 1; i__ <= i__4; ++i__) { work[iw + i__] = 0.f; /* L20: */ } ++iw; /* Computing MAX */ i__4 = izero - kd; i1 = max(i__4,1); /* Computing MIN */ i__4 = izero + kd; i2 = min(i__4,n); if (iuplo == 1) { ioff = (izero - 1) * ldab + kd + 1; i__4 = izero - i1; sswap_(&i__4, &a[ioff - izero + i1], &c__1, &work[ iw], &c__1); iw = iw + izero - i1; i__4 = i2 - izero + 1; /* Computing MAX */ i__6 = ldab - 1; i__5 = max(i__6,1); sswap_(&i__4, &a[ioff], &i__5, &work[iw], &c__1); } else { ioff = (i1 - 1) * ldab + 1; i__4 = izero - i1; /* Computing MAX */ i__6 = ldab - 1; i__5 = max(i__6,1); sswap_(&i__4, &a[ioff + izero - i1], &i__5, &work[ iw], &c__1); ioff = (izero - 1) * ldab + 1; iw = iw + izero - i1; i__4 = i2 - izero + 1; sswap_(&i__4, &a[ioff], &c__1, &work[iw], &c__1); } } /* Save a copy of the matrix A in ASAV. */ i__4 = kd + 1; slacpy_("Full", &i__4, &n, &a[1], &ldab, &asav[1], &ldab); for (iequed = 1; iequed <= 2; ++iequed) { *(unsigned char *)equed = *(unsigned char *)&equeds[ iequed - 1]; if (iequed == 1) { nfact = 3; } else { nfact = 1; } i__4 = nfact; for (ifact = 1; ifact <= i__4; ++ifact) { *(unsigned char *)fact = *(unsigned char *)&facts[ ifact - 1]; prefac = lsame_(fact, "F"); nofact = lsame_(fact, "N"); equil = lsame_(fact, "E"); if (zerot) { if (prefac) { goto L60; } rcondc = 0.f; } else if (! lsame_(fact, "N")) { /* Compute the condition number for comparison */ /* with the value returned by SPBSVX (FACT = */ /* 'N' reuses the condition number from the */ /* previous iteration with FACT = 'F'). */ i__5 = kd + 1; slacpy_("Full", &i__5, &n, &asav[1], &ldab, & afac[1], &ldab); if (equil || iequed > 1) { /* Compute row and column scale factors to */ /* equilibrate the matrix A. */ spbequ_(uplo, &n, &kd, &afac[1], &ldab, & s[1], &scond, &amax, &info); if (info == 0 && n > 0) { if (iequed > 1) { scond = 0.f; } /* Equilibrate the matrix. */ slaqsb_(uplo, &n, &kd, &afac[1], & ldab, &s[1], &scond, &amax, equed); } } /* Save the condition number of the */ /* non-equilibrated system for use in SGET04. */ if (equil) { roldc = rcondc; } /* Compute the 1-norm of A. */ anorm = slansb_("1", uplo, &n, &kd, &afac[1], &ldab, &rwork[1]); /* Factor the matrix A. */ spbtrf_(uplo, &n, &kd, &afac[1], &ldab, &info); /* Form the inverse of A. */ slaset_("Full", &n, &n, &c_b45, &c_b46, &a[1], &lda); s_copy(srnamc_1.srnamt, "SPBTRS", (ftnlen)32, (ftnlen)6); spbtrs_(uplo, &n, &kd, &n, &afac[1], &ldab, & a[1], &lda, &info); /* Compute the 1-norm condition number of A. */ ainvnm = slange_("1", &n, &n, &a[1], &lda, & rwork[1]); if (anorm <= 0.f || ainvnm <= 0.f) { rcondc = 1.f; } else { rcondc = 1.f / anorm / ainvnm; } } /* Restore the matrix A. */ i__5 = kd + 1; slacpy_("Full", &i__5, &n, &asav[1], &ldab, &a[1], &ldab); /* Form an exact solution and set the right hand */ /* side. */ s_copy(srnamc_1.srnamt, "SLARHS", (ftnlen)32, ( ftnlen)6); slarhs_(path, xtype, uplo, " ", &n, &n, &kd, &kd, nrhs, &a[1], &ldab, &xact[1], &lda, &b[1], &lda, iseed, &info); *(unsigned char *)xtype = 'C'; slacpy_("Full", &n, nrhs, &b[1], &lda, &bsav[1], & lda); if (nofact) { /* --- Test SPBSV --- */ /* Compute the L*L' or U'*U factorization of the */ /* matrix and solve the system. */ i__5 = kd + 1; slacpy_("Full", &i__5, &n, &a[1], &ldab, & afac[1], &ldab); slacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "SPBSV ", (ftnlen)32, (ftnlen)6); spbsv_(uplo, &n, &kd, nrhs, &afac[1], &ldab, & x[1], &lda, &info); /* Check error code from SPBSV . */ if (info != izero) { alaerh_(path, "SPBSV ", &info, &izero, uplo, &n, &n, &kd, &kd, nrhs, & imat, &nfail, &nerrs, nout); goto L40; } else if (info != 0) { goto L40; } /* Reconstruct matrix from factors and compute */ /* residual. */ spbt01_(uplo, &n, &kd, &a[1], &ldab, &afac[1], &ldab, &rwork[1], result); /* Compute residual of the computed solution. */ slacpy_("Full", &n, nrhs, &b[1], &lda, &work[ 1], &lda); spbt02_(uplo, &n, &kd, nrhs, &a[1], &ldab, &x[ 1], &lda, &work[1], &lda, &rwork[1], & result[1]); /* Check solution from generated exact solution. */ sget04_(&n, nrhs, &x[1], &lda, &xact[1], &lda, &rcondc, &result[2]); nt = 3; /* Print information about the tests that did */ /* not pass the threshold. */ i__5 = nt; for (k = 1; k <= i__5; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } io___57.ciunit = *nout; s_wsfe(&io___57); do_fio(&c__1, "SPBSV ", (ftnlen)6); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&kd, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&k, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof(real)); e_wsfe(); ++nfail; } /* L30: */ } nrun += nt; L40: ; } /* --- Test SPBSVX --- */ if (! prefac) { i__5 = kd + 1; slaset_("Full", &i__5, &n, &c_b45, &c_b45, & afac[1], &ldab); } slaset_("Full", &n, nrhs, &c_b45, &c_b45, &x[1], & lda); if (iequed > 1 && n > 0) { /* Equilibrate the matrix if FACT='F' and */ /* EQUED='Y' */ slaqsb_(uplo, &n, &kd, &a[1], &ldab, &s[1], & scond, &amax, equed); } /* Solve the system and compute the condition */ /* number and error bounds using SPBSVX. */ s_copy(srnamc_1.srnamt, "SPBSVX", (ftnlen)32, ( ftnlen)6); spbsvx_(fact, uplo, &n, &kd, nrhs, &a[1], &ldab, & afac[1], &ldab, equed, &s[1], &b[1], &lda, &x[1], &lda, &rcond, &rwork[1], &rwork[* nrhs + 1], &work[1], &iwork[1], &info); /* Check the error code from SPBSVX. */ if (info != izero) { /* Writing concatenation */ i__7[0] = 1, a__1[0] = fact; i__7[1] = 1, a__1[1] = uplo; s_cat(ch__1, a__1, i__7, &c__2, (ftnlen)2); alaerh_(path, "SPBSVX", &info, &izero, ch__1, &n, &n, &kd, &kd, nrhs, &imat, &nfail, &nerrs, nout); goto L60; } if (info == 0) { if (! prefac) { /* Reconstruct matrix from factors and */ /* compute residual. */ spbt01_(uplo, &n, &kd, &a[1], &ldab, & afac[1], &ldab, &rwork[(*nrhs << 1) + 1], result); k1 = 1; } else { k1 = 2; } /* Compute residual of the computed solution. */ slacpy_("Full", &n, nrhs, &bsav[1], &lda, & work[1], &lda); spbt02_(uplo, &n, &kd, nrhs, &asav[1], &ldab, &x[1], &lda, &work[1], &lda, &rwork[(* nrhs << 1) + 1], &result[1]); /* Check solution from generated exact solution. */ if (nofact || prefac && lsame_(equed, "N")) { sget04_(&n, nrhs, &x[1], &lda, &xact[1], & lda, &rcondc, &result[2]); } else { sget04_(&n, nrhs, &x[1], &lda, &xact[1], & lda, &roldc, &result[2]); } /* Check the error bounds from iterative */ /* refinement. */ spbt05_(uplo, &n, &kd, nrhs, &asav[1], &ldab, &b[1], &lda, &x[1], &lda, &xact[1], & lda, &rwork[1], &rwork[*nrhs + 1], & result[3]); } else { k1 = 6; } /* Compare RCOND from SPBSVX with the computed */ /* value in RCONDC. */ result[5] = sget06_(&rcond, &rcondc); /* Print information about the tests that did not */ /* pass the threshold. */ for (k = k1; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { aladhd_(nout, path); } if (prefac) { io___60.ciunit = *nout; s_wsfe(&io___60); do_fio(&c__1, "SPBSVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&kd, (ftnlen) sizeof(integer)); do_fio(&c__1, equed, (ftnlen)1); do_fio(&c__1, (char *)&imat, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&k, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof(real)); e_wsfe(); } else { io___61.ciunit = *nout; s_wsfe(&io___61); do_fio(&c__1, "SPBSVX", (ftnlen)6); do_fio(&c__1, fact, (ftnlen)1); do_fio(&c__1, uplo, (ftnlen)1); do_fio(&c__1, (char *)&n, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&kd, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&k, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&result[k - 1], (ftnlen)sizeof(real)); e_wsfe(); } ++nfail; } /* L50: */ } nrun = nrun + 7 - k1; L60: ; } /* L70: */ } L80: ; } /* L90: */ } /* L100: */ } /* L110: */ } /* Print a summary of the results. */ alasvm_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of SDRVPB */ } /* sdrvpb_ */
/* Subroutine */ int spbt01_(char *uplo, integer *n, integer *kd, real *a, integer *lda, real *afac, integer *ldafac, real *rwork, real *resid) { /* System generated locals */ integer a_dim1, a_offset, afac_dim1, afac_offset, i__1, i__2, i__3; /* Local variables */ integer i__, j, k; real t; integer kc, ml, mu; real eps; integer klen; extern doublereal sdot_(integer *, real *, integer *, real *, integer *); extern /* Subroutine */ int ssyr_(char *, integer *, real *, real *, integer *, real *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); real anorm; extern /* Subroutine */ int strmv_(char *, char *, char *, integer *, real *, integer *, real *, integer *); extern doublereal slamch_(char *), slansb_(char *, char *, integer *, integer *, real *, integer *, real *); /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SPBT01 reconstructs a symmetric positive definite band matrix A from */ /* its L*L' or U'*U factorization and computes the residual */ /* norm( L*L' - A ) / ( N * norm(A) * EPS ) or */ /* norm( U'*U - A ) / ( N * norm(A) * EPS ), */ /* where EPS is the machine epsilon, L' is the conjugate transpose of */ /* L, and U' is the conjugate transpose of U. */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* Specifies whether the upper or lower triangular part of the */ /* symmetric matrix A is stored: */ /* = 'U': Upper triangular */ /* = 'L': Lower triangular */ /* N (input) INTEGER */ /* The number of rows and columns of the matrix A. N >= 0. */ /* KD (input) INTEGER */ /* The number of super-diagonals of the matrix A if UPLO = 'U', */ /* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. */ /* A (input) REAL array, dimension (LDA,N) */ /* The original symmetric band matrix A. If UPLO = 'U', the */ /* upper triangular part of A is stored as a band matrix; if */ /* UPLO = 'L', the lower triangular part of A is stored. The */ /* columns of the appropriate triangle are stored in the columns */ /* of A and the diagonals of the triangle are stored in the rows */ /* of A. See SPBTRF for further details. */ /* LDA (input) INTEGER. */ /* The leading dimension of the array A. LDA >= max(1,KD+1). */ /* AFAC (input) REAL array, dimension (LDAFAC,N) */ /* The factored form of the matrix A. AFAC contains the factor */ /* L or U from the L*L' or U'*U factorization in band storage */ /* format, as computed by SPBTRF. */ /* LDAFAC (input) INTEGER */ /* The leading dimension of the array AFAC. */ /* LDAFAC >= max(1,KD+1). */ /* RWORK (workspace) REAL array, dimension (N) */ /* RESID (output) REAL */ /* If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) */ /* If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Quick exit if N = 0. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; afac_dim1 = *ldafac; afac_offset = 1 + afac_dim1; afac -= afac_offset; --rwork; /* Function Body */ if (*n <= 0) { *resid = 0.f; return 0; } /* Exit with RESID = 1/EPS if ANORM = 0. */ eps = slamch_("Epsilon"); anorm = slansb_("1", uplo, n, kd, &a[a_offset], lda, &rwork[1]); if (anorm <= 0.f) { *resid = 1.f / eps; return 0; } /* Compute the product U'*U, overwriting U. */ if (lsame_(uplo, "U")) { for (k = *n; k >= 1; --k) { /* Computing MAX */ i__1 = 1, i__2 = *kd + 2 - k; kc = max(i__1,i__2); klen = *kd + 1 - kc; /* Compute the (K,K) element of the result. */ i__1 = klen + 1; t = sdot_(&i__1, &afac[kc + k * afac_dim1], &c__1, &afac[kc + k * afac_dim1], &c__1); afac[*kd + 1 + k * afac_dim1] = t; /* Compute the rest of column K. */ if (klen > 0) { i__1 = *ldafac - 1; strmv_("Upper", "Transpose", "Non-unit", &klen, &afac[*kd + 1 + (k - klen) * afac_dim1], &i__1, &afac[kc + k * afac_dim1], &c__1); } /* L10: */ } /* UPLO = 'L': Compute the product L*L', overwriting L. */ } else { for (k = *n; k >= 1; --k) { /* Computing MIN */ i__1 = *kd, i__2 = *n - k; klen = min(i__1,i__2); /* Add a multiple of column K of the factor L to each of */ /* columns K+1 through N. */ if (klen > 0) { i__1 = *ldafac - 1; ssyr_("Lower", &klen, &c_b14, &afac[k * afac_dim1 + 2], &c__1, &afac[(k + 1) * afac_dim1 + 1], &i__1); } /* Scale column K by the diagonal element. */ t = afac[k * afac_dim1 + 1]; i__1 = klen + 1; sscal_(&i__1, &t, &afac[k * afac_dim1 + 1], &c__1); /* L20: */ } } /* Compute the difference L*L' - A or U'*U - A. */ if (lsame_(uplo, "U")) { i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MAX */ i__2 = 1, i__3 = *kd + 2 - j; mu = max(i__2,i__3); i__2 = *kd + 1; for (i__ = mu; i__ <= i__2; ++i__) { afac[i__ + j * afac_dim1] -= a[i__ + j * a_dim1]; /* L30: */ } /* L40: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Computing MIN */ i__2 = *kd + 1, i__3 = *n - j + 1; ml = min(i__2,i__3); i__2 = ml; for (i__ = 1; i__ <= i__2; ++i__) { afac[i__ + j * afac_dim1] -= a[i__ + j * a_dim1]; /* L50: */ } /* L60: */ } } /* Compute norm( L*L' - A ) / ( N * norm(A) * EPS ) */ *resid = slansb_("I", uplo, n, kd, &afac[afac_offset], ldafac, &rwork[1]); *resid = *resid / (real) (*n) / anorm / eps; return 0; /* End of SPBT01 */ } /* spbt01_ */
/* Subroutine */ int ssbevx_(char *jobz, char *range, char *uplo, integer *n, integer *kd, real *ab, integer *ldab, real *q, integer *ldq, real *vl, real *vu, integer *il, integer *iu, real *abstol, integer *m, real * w, real *z, integer *ldz, real *work, integer *iwork, integer *ifail, 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 September 30, 1994 Purpose ======= SSBEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. Arguments ========= JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. RANGE (input) CHARACTER*1 = 'A': all eigenvalues will be found; = 'V': all eigenvalues in the half-open interval (VL,VU] will be found; = 'I': the IL-th through IU-th eigenvalues will be found. UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB (input/output) REAL array, dimension (LDAB, N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, AB is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD + 1. Q (output) REAL array, dimension (LDQ, N) If JOBZ = 'V', the N-by-N orthogonal matrix used in the reduction to tridiagonal form. If JOBZ = 'N', the array Q is not referenced. LDQ (input) INTEGER The leading dimension of the array Q. If JOBZ = 'V', then LDQ >= max(1,N). VL (input) REAL VU (input) REAL If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. IL (input) INTEGER IU (input) INTEGER If RANGE='I', the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. ABSTOL (input) REAL The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing AB to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. M (output) INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. W (output) REAL array, dimension (N) The first M elements contain the selected eigenvalues in ascending order. Z (output) REAL array, dimension (LDZ, max(1,M)) If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = 'N', then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK (workspace) REAL array, dimension (7*N) IWORK (workspace) INTEGER array, dimension (5*N) IFAIL (output) INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced. INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in array IFAIL. ===================================================================== Test the input parameters. Parameter adjustments Function Body */ /* Table of constant values */ static real c_b14 = 1.f; static integer c__1 = 1; static real c_b34 = 0.f; /* System generated locals */ integer ab_dim1, ab_offset, q_dim1, q_offset, z_dim1, z_offset, i__1, i__2; real r__1, r__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer indd, inde; static real anrm; static integer imax; static real rmin, rmax; static integer itmp1, i, j, indee; static real sigma; extern logical lsame_(char *, char *); static integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); static char order[1]; extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static logical lower; extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, integer *), sswap_(integer *, real *, integer *, real *, integer * ); static logical wantz; static integer jj; static logical alleig, indeig; static integer iscale, indibl; static logical valeig; extern doublereal slamch_(char *); static real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); static real abstll, bignum; extern doublereal slansb_(char *, char *, integer *, integer *, real *, integer *, real *); extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, real *, integer *, integer *, real *, integer *, integer *); static integer indisp, indiwo; extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, integer *, real *, integer *); static integer indwrk; extern /* Subroutine */ int ssbtrd_(char *, char *, integer *, integer *, real *, integer *, real *, real *, real *, integer *, real *, integer *), sstein_(integer *, real *, real *, integer *, real *, integer *, integer *, real *, integer *, real * , integer *, integer *, integer *), ssterf_(integer *, real *, real *, integer *); static integer nsplit; static real smlnum; extern /* Subroutine */ int sstebz_(char *, char *, integer *, real *, real *, integer *, integer *, real *, real *, real *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *), ssteqr_(char *, integer *, real *, real *, real *, integer *, real *, integer *); static real eps, vll, vuu, tmp1; #define W(I) w[(I)-1] #define WORK(I) work[(I)-1] #define IWORK(I) iwork[(I)-1] #define IFAIL(I) ifail[(I)-1] #define AB(I,J) ab[(I)-1 + ((J)-1)* ( *ldab)] #define Q(I,J) q[(I)-1 + ((J)-1)* ( *ldq)] #define Z(I,J) z[(I)-1 + ((J)-1)* ( *ldz)] wantz = lsame_(jobz, "V"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); lower = lsame_(uplo, "L"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (! (lower || lsame_(uplo, "U"))) { *info = -3; } else if (*n < 0) { *info = -4; } else if (*kd < 0) { *info = -5; } else if (*ldab < *kd + 1) { *info = -7; } else if (*ldq < *n) { *info = -9; } else if (valeig && *n > 0 && *vu <= *vl) { *info = -11; } else if (indeig && *il < 1) { *info = -12; } else if (indeig && (*iu < min(*n,*il) || *iu > *n)) { *info = -13; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -18; } if (*info != 0) { i__1 = -(*info); xerbla_("SSBEVX", &i__1); return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } if (*n == 1) { if (alleig || indeig) { *m = 1; W(1) = AB(1,1); } else { if (*vl < AB(1,1) && *vu >= AB(1,1)) { *m = 1; W(1) = AB(1,1); } } if (wantz) { Z(1,1) = 1.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin)); rmax = dmin(r__1,r__2); /* Scale matrix to allowable range, if necessary. */ iscale = 0; abstll = *abstol; if (valeig) { vll = *vl; vuu = *vu; } anrm = slansb_("M", uplo, n, kd, &AB(1,1), ldab, &WORK(1)); if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { if (lower) { slascl_("B", kd, kd, &c_b14, &sigma, n, n, &AB(1,1), ldab, info); } else { slascl_("Q", kd, kd, &c_b14, &sigma, n, n, &AB(1,1), ldab, info); } if (*abstol > 0.f) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call SSBTRD to reduce symmetric band matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indwrk = inde + *n; ssbtrd_(jobz, uplo, n, kd, &AB(1,1), ldab, &WORK(indd), &WORK(inde), &Q(1,1), ldq, &WORK(indwrk), &iinfo); /* If all eigenvalues are desired and ABSTOL is less than or equal to zero, then call SSTERF or SSTEQR. If this fails for some eigenvalue, then try SSTEBZ. */ if ((alleig || indeig && *il == 1 && *iu == *n) && *abstol <= 0.f) { scopy_(n, &WORK(indd), &c__1, &W(1), &c__1); indee = indwrk + (*n << 1); if (! wantz) { i__1 = *n - 1; scopy_(&i__1, &WORK(inde), &c__1, &WORK(indee), &c__1); ssterf_(n, &W(1), &WORK(indee), info); } else { slacpy_("A", n, n, &Q(1,1), ldq, &Z(1,1), ldz); i__1 = *n - 1; scopy_(&i__1, &WORK(inde), &c__1, &WORK(indee), &c__1); ssteqr_(jobz, n, &W(1), &WORK(indee), &Z(1,1), ldz, &WORK( indwrk), info); if (*info == 0) { i__1 = *n; for (i = 1; i <= *n; ++i) { IFAIL(i) = 0; /* L10: */ } } } if (*info == 0) { *m = *n; goto L30; } *info = 0; } /* Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwo = indisp + *n; sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &WORK(indd), &WORK( inde), m, &nsplit, &W(1), &IWORK(indibl), &IWORK(indisp), &WORK( indwrk), &IWORK(indiwo), info); if (wantz) { sstein_(n, &WORK(indd), &WORK(inde), m, &W(1), &IWORK(indibl), &IWORK( indisp), &Z(1,1), ldz, &WORK(indwrk), &IWORK(indiwo), & IFAIL(1), info); /* Apply orthogonal matrix used in reduction to tridiagonal form to eigenvectors returned by SSTEIN. */ i__1 = *m; for (j = 1; j <= *m; ++j) { scopy_(n, &Z(1,j), &c__1, &WORK(1), &c__1); sgemv_("N", n, n, &c_b14, &Q(1,1), ldq, &WORK(1), &c__1, & c_b34, &Z(1,j), &c__1); /* L20: */ } } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L30: if (iscale == 1) { if (*info == 0) { imax = *m; } else { imax = *info - 1; } r__1 = 1.f / sigma; sscal_(&imax, &r__1, &W(1), &c__1); } /* If eigenvalues are not in order, then sort them, along with eigenvectors. */ if (wantz) { i__1 = *m - 1; for (j = 1; j <= *m-1; ++j) { i = 0; tmp1 = W(j); i__2 = *m; for (jj = j + 1; jj <= *m; ++jj) { if (W(jj) < tmp1) { i = jj; tmp1 = W(jj); } /* L40: */ } if (i != 0) { itmp1 = IWORK(indibl + i - 1); W(i) = W(j); IWORK(indibl + i - 1) = IWORK(indibl + j - 1); W(j) = tmp1; IWORK(indibl + j - 1) = itmp1; sswap_(n, &Z(1,i), &c__1, &Z(1,j), & c__1); if (*info != 0) { itmp1 = IFAIL(i); IFAIL(i) = IFAIL(j); IFAIL(j) = itmp1; } } /* L50: */ } } return 0; /* End of SSBEVX */ } /* ssbevx_ */
/* Subroutine */ int spbt02_(char *uplo, integer *n, integer *kd, integer * nrhs, real *a, integer *lda, real *x, integer *ldx, real *b, integer * ldb, real *rwork, real *resid) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, x_dim1, x_offset, i__1; real r__1, r__2; /* Local variables */ integer j; real eps, anorm, bnorm; real xnorm; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SPBT02 computes the residual for a solution of a symmetric banded */ /* system of equations A*x = b: */ /* RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS) */ /* where EPS is the machine precision. */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* Specifies whether the upper or lower triangular part of the */ /* symmetric matrix A is stored: */ /* = 'U': Upper triangular */ /* = 'L': Lower triangular */ /* N (input) INTEGER */ /* The number of rows and columns of the matrix A. N >= 0. */ /* KD (input) INTEGER */ /* The number of super-diagonals of the matrix A if UPLO = 'U', */ /* or the number of sub-diagonals if UPLO = 'L'. KD >= 0. */ /* A (input) REAL array, dimension (LDA,N) */ /* The original symmetric band matrix A. If UPLO = 'U', the */ /* upper triangular part of A is stored as a band matrix; if */ /* UPLO = 'L', the lower triangular part of A is stored. The */ /* columns of the appropriate triangle are stored in the columns */ /* of A and the diagonals of the triangle are stored in the rows */ /* of A. See SPBTRF for further details. */ /* LDA (input) INTEGER. */ /* The leading dimension of the array A. LDA >= max(1,KD+1). */ /* X (input) REAL array, dimension (LDX,NRHS) */ /* The computed solution vectors for the system of linear */ /* equations. */ /* LDX (input) INTEGER */ /* The leading dimension of the array X. LDX >= max(1,N). */ /* B (input/output) REAL array, dimension (LDB,NRHS) */ /* On entry, the right hand side vectors for the system of */ /* linear equations. */ /* On exit, B is overwritten with the difference B - A*X. */ /* LDB (input) INTEGER */ /* The leading dimension of the array B. LDB >= max(1,N). */ /* RWORK (workspace) REAL array, dimension (N) */ /* RESID (output) REAL */ /* The maximum over the number of right hand sides of */ /* norm(B - A*X) / ( norm(A) * norm(X) * EPS ). */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Quick exit if N = 0 or NRHS = 0. */ /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; x_dim1 = *ldx; x_offset = 1 + x_dim1; x -= x_offset; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; --rwork; /* Function Body */ if (*n <= 0 || *nrhs <= 0) { *resid = 0.f; return 0; } /* Exit with RESID = 1/EPS if ANORM = 0. */ eps = slamch_("Epsilon"); anorm = slansb_("1", uplo, n, kd, &a[a_offset], lda, &rwork[1]); if (anorm <= 0.f) { *resid = 1.f / eps; return 0; } /* Compute B - A*X */ i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ssbmv_(uplo, n, kd, &c_b5, &a[a_offset], lda, &x[j * x_dim1 + 1], & c__1, &c_b7, &b[j * b_dim1 + 1], &c__1); /* L10: */ } /* Compute the maximum over the number of right hand sides of */ /* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) */ *resid = 0.f; i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { bnorm = sasum_(n, &b[j * b_dim1 + 1], &c__1); xnorm = sasum_(n, &x[j * x_dim1 + 1], &c__1); if (xnorm <= 0.f) { *resid = 1.f / eps; } else { /* Computing MAX */ r__1 = *resid, r__2 = bnorm / anorm / xnorm / eps; *resid = dmax(r__1,r__2); } /* L20: */ } return 0; /* End of SPBT02 */ } /* spbt02_ */