/* Subroutine */ int chbev_(char *jobz, char *uplo, integer *n, integer *kd, complex *ab, integer *ldab, real *w, complex *z__, integer *ldz, complex *work, real *rwork, integer *info) { /* -- LAPACK driver routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CHBEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian 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) COMPLEX array, dimension (LDAB, N) On entry, the upper or lower triangle of the Hermitian 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) COMPLEX 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) COMPLEX array, dimension (N) RWORK (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. ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static real c_b11 = 1.f; static integer c__1 = 1; /* System generated locals */ integer ab_dim1, ab_offset, z_dim1, z_offset, i__1; real r__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer inde; static real anrm; static integer imax; static real rmin, rmax, sigma; extern logical lsame_(char *, char *); static integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); static logical lower, wantz; extern doublereal clanhb_(char *, char *, integer *, integer *, complex *, integer *, real *); static integer iscale; extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *), chbtrd_(char *, char *, integer *, integer *, complex *, integer *, real *, real *, complex *, integer *, complex *, integer *); extern doublereal slamch_(char *); static real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); static real bignum; static integer indrwk; extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, complex *, integer *, real *, integer *), ssterf_(integer *, real *, real *, integer *); static real smlnum, eps; #define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1 #define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)] #define ab_subscr(a_1,a_2) (a_2)*ab_dim1 + a_1 #define ab_ref(a_1,a_2) ab[ab_subscr(a_1,a_2)] ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --work; --rwork; /* 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_("CHBEV ", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { if (lower) { i__1 = ab_subscr(1, 1); w[1] = ab[i__1].r; } else { i__1 = ab_subscr(*kd + 1, 1); w[1] = ab[i__1].r; } if (wantz) { i__1 = z___subscr(1, 1); z__[i__1].r = 1.f, z__[i__1].i = 0.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 = clanhb_("M", uplo, n, kd, &ab[ab_offset], ldab, &rwork[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) { clascl_("B", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab, info); } else { clascl_("Q", kd, kd, &c_b11, &sigma, n, n, &ab[ab_offset], ldab, info); } } /* Call CHBTRD to reduce Hermitian band matrix to tridiagonal form. */ inde = 1; chbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &w[1], &rwork[inde], & z__[z_offset], ldz, &work[1], &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR. */ if (! wantz) { ssterf_(n, &w[1], &rwork[inde], info); } else { indrwk = inde + *n; csteqr_(jobz, n, &w[1], &rwork[inde], &z__[z_offset], ldz, &rwork[ indrwk], 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 CHBEV */ } /* chbev_ */
/* Subroutine */ int cdrvpb_(logical *dotype, integer *nn, integer *nval, integer *nrhs, real *thresh, logical *tsterr, integer *nmax, complex * a, complex *afac, complex *asav, complex *b, complex *bsav, complex * x, complex *xact, real *s, complex *work, real *rwork, 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,a6,\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,a6,\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,a6,\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; extern /* Subroutine */ int cget04_(integer *, integer *, complex *, integer *, complex *, integer *, real *, real *); integer nfail, iseed[4], nfact; extern /* Subroutine */ int cpbt01_(char *, integer *, integer *, complex *, integer *, complex *, integer *, real *, real *), cpbt02_(char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *), cpbt05_(char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, real *); integer kdval[4]; extern logical lsame_(char *, char *); char equed[1]; integer nbmin; real rcond, roldc, scond; integer nimat; extern doublereal sget06_(real *, real *); real anorm; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *), cpbsv_(char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, integer *); logical equil; extern /* Subroutine */ int cswap_(integer *, complex *, integer *, complex *, integer *); integer iuplo, izero, nerrs; logical zerot; char xtype[1]; extern /* Subroutine */ int clatb4_(char *, integer *, integer *, integer *, char *, integer *, integer *, real *, integer *, real *, char * ), aladhd_(integer *, char *); extern doublereal clanhb_(char *, char *, integer *, integer *, complex *, integer *, real *), clange_(char *, integer *, integer *, complex *, integer *, real *); extern /* Subroutine */ int claqhb_(char *, integer *, integer *, complex *, integer *, real *, real *, real *, char *), alaerh_(char *, char *, integer *, integer *, char *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *), claipd_(integer *, complex *, integer *, integer *); logical prefac; real rcondc; logical nofact; char packit[1]; integer iequed; extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), clarhs_(char *, char *, char *, char *, integer *, integer *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, integer *, integer *), claset_(char *, integer *, integer *, complex *, complex *, complex *, integer *), cpbequ_(char *, integer *, integer *, complex *, integer *, real *, real *, real *, integer *), alasvm_(char *, integer *, integer *, integer *, integer *); real cndnum; extern /* Subroutine */ int clatms_(integer *, integer *, char *, integer *, char *, real *, integer *, real *, real *, integer *, integer * , char *, complex *, integer *, complex *, integer *), cpbtrf_(char *, integer *, integer *, complex *, integer *, integer *); real ainvnm; extern /* Subroutine */ int cpbtrs_(char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, integer *), xlaenv_(integer *, integer *), cpbsvx_(char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, char *, real *, complex *, integer *, complex *, integer *, real *, real *, real *, complex *, real *, integer *), cerrvx_(char *, integer *); real result[6]; /* 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 */ /* ======= */ /* CDRVPB tests the driver routines CPBSV 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) COMPLEX array, dimension (NMAX*NMAX) */ /* AFAC (workspace) COMPLEX array, dimension (NMAX*NMAX) */ /* ASAV (workspace) COMPLEX array, dimension (NMAX*NMAX) */ /* B (workspace) COMPLEX array, dimension (NMAX*NRHS) */ /* BSAV (workspace) COMPLEX array, dimension (NMAX*NRHS) */ /* X (workspace) COMPLEX array, dimension (NMAX*NRHS) */ /* XACT (workspace) COMPLEX array, dimension (NMAX*NRHS) */ /* S (workspace) REAL array, dimension (NMAX) */ /* WORK (workspace) COMPLEX array, dimension */ /* (NMAX*max(3,NRHS)) */ /* RWORK (workspace) REAL array, dimension (NMAX+2*NRHS) */ /* 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 */ --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, "Complex precision", (ftnlen)1, (ftnlen)17); 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) { cerrvx_(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 CLATB4 and generate a test */ /* matrix with CLATMS. */ clatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "CLATMS", (ftnlen)6, (ftnlen) 6); clatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cndnum, &anorm, &kd, &kd, packit, &a[koff], &ldab, &work[1], &info); /* Check error code from CLATMS. */ if (info != 0) { alaerh_(path, "CLATMS", &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; ccopy_(&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); ccopy_(&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); ccopy_(&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; ccopy_(&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__) { i__5 = iw + i__; work[i__5].r = 0.f, work[i__5].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; cswap_(&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); cswap_(&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); cswap_(&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; cswap_(&i__4, &a[ioff], &c__1, &work[iw], &c__1); } } /* Set the imaginary part of the diagonals. */ if (iuplo == 1) { claipd_(&n, &a[kd + 1], &ldab, &c__0); } else { claipd_(&n, &a[1], &ldab, &c__0); } /* Save a copy of the matrix A in ASAV. */ i__4 = kd + 1; clacpy_("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 CPBSVX (FACT = */ /* 'N' reuses the condition number from the */ /* previous iteration with FACT = 'F'). */ i__5 = kd + 1; clacpy_("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. */ cpbequ_(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. */ claqhb_(uplo, &n, &kd, &afac[1], & ldab, &s[1], &scond, &amax, equed); } } /* Save the condition number of the */ /* non-equilibrated system for use in CGET04. */ if (equil) { roldc = rcondc; } /* Compute the 1-norm of A. */ anorm = clanhb_("1", uplo, &n, &kd, &afac[1], &ldab, &rwork[1]); /* Factor the matrix A. */ cpbtrf_(uplo, &n, &kd, &afac[1], &ldab, &info); /* Form the inverse of A. */ claset_("Full", &n, &n, &c_b47, &c_b48, &a[1], &lda); s_copy(srnamc_1.srnamt, "CPBTRS", (ftnlen)6, ( ftnlen)6); cpbtrs_(uplo, &n, &kd, &n, &afac[1], &ldab, & a[1], &lda, &info); /* Compute the 1-norm condition number of A. */ ainvnm = clange_("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; clacpy_("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, "CLARHS", (ftnlen)6, ( ftnlen)6); clarhs_(path, xtype, uplo, " ", &n, &n, &kd, &kd, nrhs, &a[1], &ldab, &xact[1], &lda, &b[1], &lda, iseed, &info); *(unsigned char *)xtype = 'C'; clacpy_("Full", &n, nrhs, &b[1], &lda, &bsav[1], & lda); if (nofact) { /* --- Test CPBSV --- */ /* Compute the L*L' or U'*U factorization of the */ /* matrix and solve the system. */ i__5 = kd + 1; clacpy_("Full", &i__5, &n, &a[1], &ldab, & afac[1], &ldab); clacpy_("Full", &n, nrhs, &b[1], &lda, &x[1], &lda); s_copy(srnamc_1.srnamt, "CPBSV ", (ftnlen)6, ( ftnlen)6); cpbsv_(uplo, &n, &kd, nrhs, &afac[1], &ldab, & x[1], &lda, &info); /* Check error code from CPBSV . */ if (info != izero) { alaerh_(path, "CPBSV ", &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. */ cpbt01_(uplo, &n, &kd, &a[1], &ldab, &afac[1], &ldab, &rwork[1], result); /* Compute residual of the computed solution. */ clacpy_("Full", &n, nrhs, &b[1], &lda, &work[ 1], &lda); cpbt02_(uplo, &n, &kd, nrhs, &a[1], &ldab, &x[ 1], &lda, &work[1], &lda, &rwork[1], & result[1]); /* Check solution from generated exact solution. */ cget04_(&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, "CPBSV ", (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 CPBSVX --- */ if (! prefac) { i__5 = kd + 1; claset_("Full", &i__5, &n, &c_b47, &c_b47, & afac[1], &ldab); } claset_("Full", &n, nrhs, &c_b47, &c_b47, &x[1], & lda); if (iequed > 1 && n > 0) { /* Equilibrate the matrix if FACT='F' and */ /* EQUED='Y' */ claqhb_(uplo, &n, &kd, &a[1], &ldab, &s[1], & scond, &amax, equed); } /* Solve the system and compute the condition */ /* number and error bounds using CPBSVX. */ s_copy(srnamc_1.srnamt, "CPBSVX", (ftnlen)6, ( ftnlen)6); cpbsvx_(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], &rwork[(*nrhs << 1) + 1], &info); /* Check the error code from CPBSVX. */ 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, "CPBSVX", &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. */ cpbt01_(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. */ clacpy_("Full", &n, nrhs, &bsav[1], &lda, & work[1], &lda); cpbt02_(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")) { cget04_(&n, nrhs, &x[1], &lda, &xact[1], & lda, &rcondc, &result[2]); } else { cget04_(&n, nrhs, &x[1], &lda, &xact[1], & lda, &roldc, &result[2]); } /* Check the error bounds from iterative */ /* refinement. */ cpbt05_(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 CPBSVX 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, "CPBSVX", (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, "CPBSVX", (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 CDRVPB */ } /* cdrvpb_ */
/* Subroutine */ int cpbt02_(char *uplo, integer *n, integer *kd, integer * nrhs, complex *a, integer *lda, complex *x, integer *ldx, complex *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; complex q__1; /* Local variables */ static integer j; extern /* Subroutine */ int chbmv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *); static real anorm, bnorm, xnorm; extern doublereal clanhb_(char *, char *, integer *, integer *, complex *, integer *, real *), slamch_(char *), scasum_(integer *, complex *, integer *); static real eps; #define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1 #define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)] #define x_subscr(a_1,a_2) (a_2)*x_dim1 + a_1 #define x_ref(a_1,a_2) x[x_subscr(a_1,a_2)] /* -- LAPACK test routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= CPBT02 computes the residual for a solution of a Hermitian 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 Hermitian 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) COMPLEX array, dimension (LDA,N) The original Hermitian 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 CPBTRF for further details. LDA (input) INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1). X (input) COMPLEX 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) COMPLEX 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 = clanhb_("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) { q__1.r = -1.f, q__1.i = 0.f; chbmv_(uplo, n, kd, &q__1, &a[a_offset], lda, &x_ref(1, j), &c__1, & c_b1, &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 = scasum_(n, &b_ref(1, j), &c__1); xnorm = scasum_(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 CPBT02 */ } /* cpbt02_ */
/* Subroutine */ int cpbsvx_(char *fact, char *uplo, integer *n, integer *kd, integer *nrhs, complex *ab, integer *ldab, complex *afb, integer * ldafb, char *equed, real *s, complex *b, integer *ldb, complex *x, integer *ldx, real *rcond, real *ferr, real *berr, complex *work, real *rwork, 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; real r__1, r__2; complex q__1; /* Local variables */ integer i__, j, j1, j2; real amax, smin, smax; extern logical lsame_(char *, char *); real scond, anorm; extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, complex *, integer *); logical equil, rcequ, upper; extern real clanhb_(char *, char *, integer *, integer *, complex *, integer *, real *); extern /* Subroutine */ int claqhb_(char *, integer *, integer *, complex *, integer *, real *, real *, real *, char *), cpbcon_(char *, integer *, integer *, complex *, integer *, real * , real *, complex *, real *, integer *); extern real slamch_(char *); logical nofact; extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *), xerbla_(char *, integer *), cpbequ_(char *, integer *, integer *, complex *, integer *, real *, real *, real *, integer *), cpbrfs_( char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, real *, real *, complex *, real *, integer *); real bignum; extern /* Subroutine */ int cpbtrf_(char *, integer *, integer *, complex *, integer *, integer *); integer infequ; extern /* Subroutine */ int cpbtrs_(char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, integer *); real smlnum; /* -- LAPACK driver routine (version 3.4.1) -- */ /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ /* April 2012 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* 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; --rwork; /* 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]; // , expr subst smin = min(r__1,r__2); /* Computing MAX */ r__1 = smax; r__2 = s[j]; // , expr subst smax = max(r__1,r__2); /* L10: */ } if (smin <= 0.f) { *info = -11; } else if (*n > 0) { scond = max(smin,smlnum) / min(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_("CPBSVX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ cpbequ_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, & infequ); if (infequ == 0) { /* Equilibrate the matrix. */ claqhb_(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__) { i__3 = i__ + j * b_dim1; i__4 = i__; i__5 = i__ + j * b_dim1; q__1.r = s[i__4] * b[i__5].r; q__1.i = s[i__4] * b[i__5].i; // , expr subst b[i__3].r = q__1.r; b[i__3].i = q__1.i; // , expr subst /* L20: */ } /* L30: */ } } if (nofact || equil) { /* Compute the Cholesky factorization A = U**H *U or A = L*L**H. */ 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; ccopy_(&i__2, &ab[*kd + 1 - j + j1 + j * ab_dim1], &c__1, & afb[*kd + 1 - j + j1 + j * afb_dim1], &c__1); /* L40: */ } } 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; ccopy_(&i__2, &ab[j * ab_dim1 + 1], &c__1, &afb[j * afb_dim1 + 1], &c__1); /* L50: */ } } cpbtrf_(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 = clanhb_("1", uplo, n, kd, &ab[ab_offset], ldab, &rwork[1]); /* Compute the reciprocal of the condition number of A. */ cpbcon_(uplo, n, kd, &afb[afb_offset], ldafb, &anorm, rcond, &work[1], & rwork[1], info); /* Compute the solution matrix X. */ clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); cpbtrs_(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. */ cpbrfs_(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] , &rwork[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__) { i__3 = i__ + j * x_dim1; i__4 = i__; i__5 = i__ + j * x_dim1; q__1.r = s[i__4] * x[i__5].r; q__1.i = s[i__4] * x[i__5].i; // , expr subst x[i__3].r = q__1.r; x[i__3].i = q__1.i; // , expr subst /* L60: */ } /* L70: */ } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= scond; /* L80: */ } } /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < slamch_("Epsilon")) { *info = *n + 1; } return 0; /* End of CPBSVX */ }
/* Subroutine */ int chbevx_(char *jobz, char *range, char *uplo, integer *n, integer *kd, complex *ab, integer *ldab, complex *q, integer *ldq, real *vl, real *vu, integer *il, integer *iu, real *abstol, integer * m, real *w, complex *z__, integer *ldz, complex *work, real *rwork, 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; /* Local variables */ integer i__, j, jj; real eps, vll, vuu, tmp1; integer indd, inde; real anrm; integer imax; real rmin, rmax; logical test; complex ctmp1; integer itmp1, indee; real sigma; integer iinfo; char order[1]; logical lower; logical wantz; logical alleig, indeig; integer iscale, indibl; logical valeig; real safmin; real abstll, bignum; integer indiwk, indisp; integer indrwk, indwrk; integer nsplit; real smlnum; /* -- LAPACK driver routine (version 3.2) -- */ /* November 2006 */ /* Purpose */ /* ======= */ /* CHBEVX computes selected eigenvalues and, optionally, eigenvectors */ /* of a complex Hermitian 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) COMPLEX array, dimension (LDAB, N) */ /* On entry, the upper or lower triangle of the Hermitian 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. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KD + 1. */ /* Q (output) COMPLEX array, dimension (LDQ, N) */ /* If JOBZ = 'V', the N-by-N unitary 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) COMPLEX 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) COMPLEX array, dimension (N) */ /* RWORK (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 */ 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; --rwork; --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_("CHBEVX", &i__1); return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } if (*n == 1) { *m = 1; if (lower) { i__1 = ab_dim1 + 1; ctmp1.r = ab[i__1].r, ctmp1.i = ab[i__1].i; } else { i__1 = *kd + 1 + ab_dim1; ctmp1.r = ab[i__1].r, ctmp1.i = ab[i__1].i; } tmp1 = ctmp1.r; if (valeig) { if (! (*vl < tmp1 && *vu >= tmp1)) { *m = 0; } } if (*m == 1) { w[1] = ctmp1.r; if (wantz) { i__1 = z_dim1 + 1; z__[i__1].r = 1.f, z__[i__1].i = 0.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 = clanhb_("M", uplo, n, kd, &ab[ab_offset], ldab, &rwork[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) { clascl_("B", kd, kd, &c_b16, &sigma, n, n, &ab[ab_offset], ldab, info); } else { clascl_("Q", kd, kd, &c_b16, &sigma, n, n, &ab[ab_offset], ldab, info); } if (*abstol > 0.f) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call CHBTRD to reduce Hermitian band matrix to tridiagonal form. */ indd = 1; inde = indd + *n; indrwk = inde + *n; indwrk = 1; chbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &rwork[indd], &rwork[ 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 CSTEQR. 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, &rwork[indd], &c__1, &w[1], &c__1); indee = indrwk + (*n << 1); if (! wantz) { i__1 = *n - 1; scopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); ssterf_(n, &w[1], &rwork[indee], info); } else { clacpy_("A", n, n, &q[q_offset], ldq, &z__[z_offset], ldz); i__1 = *n - 1; scopy_(&i__1, &rwork[inde], &c__1, &rwork[indee], &c__1); csteqr_(jobz, n, &w[1], &rwork[indee], &z__[z_offset], ldz, & rwork[indrwk], info); if (*info == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { ifail[i__] = 0; } } } if (*info == 0) { *m = *n; goto L30; } *info = 0; } /* Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwk = indisp + *n; sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &rwork[indd], & rwork[inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], & rwork[indrwk], &iwork[indiwk], info); if (wantz) { cstein_(n, &rwork[indd], &rwork[inde], m, &w[1], &iwork[indibl], & iwork[indisp], &z__[z_offset], ldz, &rwork[indrwk], &iwork[ indiwk], &ifail[1], info); /* Apply unitary matrix used in reduction to tridiagonal */ /* form to eigenvectors returned by CSTEIN. */ i__1 = *m; for (j = 1; j <= i__1; ++j) { ccopy_(n, &z__[j * z_dim1 + 1], &c__1, &work[1], &c__1); cgemv_("N", n, n, &c_b2, &q[q_offset], ldq, &work[1], &c__1, & c_b1, &z__[j * z_dim1 + 1], &c__1); } } /* 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]; } } 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; cswap_(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; } } } } return 0; /* End of CHBEVX */ } /* chbevx_ */
/* Subroutine */ int cchkpb_(logical *dotype, integer *nn, integer *nval, integer *nnb, integer *nbval, integer *nns, integer *nsval, real * thresh, logical *tsterr, integer *nmax, complex *a, complex *afac, complex *ainv, complex *b, complex *x, complex *xact, complex *work, real *rwork, integer *nout) { /* Initialized data */ static integer iseedy[4] = { 1988,1989,1990,1991 }; /* Format strings */ static char fmt_9999[] = "(\002 UPLO='\002,a1,\002', N=\002,i5,\002, KD" "=\002,i5,\002, NB=\002,i4,\002, type \002,i2,\002, test \002,i2" ",\002, ratio= \002,g12.5)"; static char fmt_9998[] = "(\002 UPLO='\002,a1,\002', N=\002,i5,\002, KD" "=\002,i5,\002, NRHS=\002,i3,\002, type \002,i2,\002, test(\002,i" "2,\002) = \002,g12.5)"; static char fmt_9997[] = "(\002 UPLO='\002,a1,\002', N=\002,i5,\002, KD" "=\002,i5,\002,\002,10x,\002 type \002,i2,\002, test(\002,i2,\002" ") = \002,g12.5)"; /* System generated locals */ integer i__1, i__2, i__3, i__4, i__5, i__6; /* Local variables */ integer i__, k, n, i1, i2, kd, nb, in, kl, iw, ku, lda, ikd, inb, nkd, ldab, ioff, mode, koff, imat, info; char path[3], dist[1]; integer irhs, nrhs; char uplo[1], type__[1]; integer nrun; integer nfail, iseed[4]; integer kdval[4]; real rcond; integer nimat; real anorm; integer iuplo, izero, nerrs; logical zerot; char xtype[1]; real rcondc; char packit[1]; real cndnum; real ainvnm; real result[7]; /* Fortran I/O blocks */ static cilist io___40 = { 0, 0, 0, fmt_9999, 0 }; static cilist io___46 = { 0, 0, 0, fmt_9998, 0 }; static cilist io___48 = { 0, 0, 0, fmt_9997, 0 }; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CCHKPB tests CPBTRF, -TRS, -RFS, and -CON. */ /* Arguments */ /* ========= */ /* DOTYPE (input) LOGICAL array, dimension (NTYPES) */ /* The matrix types to be used for testing. Matrices of type j */ /* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */ /* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */ /* NN (input) INTEGER */ /* The number of values of N contained in the vector NVAL. */ /* NVAL (input) INTEGER array, dimension (NN) */ /* The values of the matrix dimension N. */ /* NNB (input) INTEGER */ /* The number of values of NB contained in the vector NBVAL. */ /* NBVAL (input) INTEGER array, dimension (NBVAL) */ /* The values of the blocksize NB. */ /* NNS (input) INTEGER */ /* The number of values of NRHS contained in the vector NSVAL. */ /* NSVAL (input) INTEGER array, dimension (NNS) */ /* The values of the number of right hand sides NRHS. */ /* THRESH (input) REAL */ /* The threshold value for the test ratios. A result is */ /* included in the output file if RESULT >= THRESH. To have */ /* every test ratio printed, use THRESH = 0. */ /* TSTERR (input) LOGICAL */ /* Flag that indicates whether error exits are to be tested. */ /* NMAX (input) INTEGER */ /* The maximum value permitted for N, used in dimensioning the */ /* work arrays. */ /* A (workspace) REAL array, dimension (NMAX*NMAX) */ /* AFAC (workspace) REAL array, dimension (NMAX*NMAX) */ /* AINV (workspace) REAL array, dimension (NMAX*NMAX) */ /* B (workspace) REAL array, dimension (NMAX*NSMAX) */ /* where NSMAX is the largest entry in NSVAL. */ /* X (workspace) REAL array, dimension (NMAX*NSMAX) */ /* XACT (workspace) REAL array, dimension (NMAX*NSMAX) */ /* WORK (workspace) REAL array, dimension */ /* (NMAX*max(3,NSMAX)) */ /* RWORK (workspace) REAL array, dimension */ /* (max(NMAX,2*NSMAX)) */ /* 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 */ --rwork; --work; --xact; --x; --b; --ainv; --afac; --a; --nsval; --nbval; --nval; --dotype; /* Function Body */ /* .. */ /* .. Executable Statements .. */ /* Initialize constants and the random number seed. */ s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17); 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) { cerrpo_(path, nout); } infoc_1.infot = 0; kdval[0] = 0; /* 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'; /* Computing MAX */ i__3 = 1, i__4 = kd + 2 - n; koff = max(i__3,i__4); *(unsigned char *)packit = 'Q'; } 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 L60; } /* Skip types 2, 3, or 4 if the matrix size is too small. */ zerot = imat >= 2 && imat <= 4; if (zerot && n < imat - 1) { goto L60; } if (! zerot || ! dotype[1]) { /* Set up parameters with CLATB4 and generate a test */ /* matrix with CLATMS. */ clatb4_(path, &imat, &n, &n, type__, &kl, &ku, &anorm, &mode, &cndnum, dist); s_copy(srnamc_1.srnamt, "CLATMS", (ftnlen)32, (ftnlen) 6); clatms_(&n, &n, dist, iseed, type__, &rwork[1], &mode, &cndnum, &anorm, &kd, &kd, packit, &a[koff], &ldab, &work[1], &info); /* Check error code from CLATMS. */ if (info != 0) { alaerh_(path, "CLATMS", &info, &c__0, uplo, &n, & n, &kd, &kd, &c_n1, &imat, &nfail, &nerrs, nout); goto L60; } } 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; ccopy_(&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); ccopy_(&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); ccopy_(&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; ccopy_(&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__) { i__5 = iw + i__; work[i__5].r = 0.f, work[i__5].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; cswap_(&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); cswap_(&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); cswap_(&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; cswap_(&i__4, &a[ioff], &c__1, &work[iw], &c__1); } } /* Set the imaginary part of the diagonals. */ if (iuplo == 1) { claipd_(&n, &a[kd + 1], &ldab, &c__0); } else { claipd_(&n, &a[1], &ldab, &c__0); } /* Do for each value of NB in NBVAL */ i__4 = *nnb; for (inb = 1; inb <= i__4; ++inb) { nb = nbval[inb]; xlaenv_(&c__1, &nb); /* Compute the L*L' or U'*U factorization of the band */ /* matrix. */ i__5 = kd + 1; clacpy_("Full", &i__5, &n, &a[1], &ldab, &afac[1], & ldab); s_copy(srnamc_1.srnamt, "CPBTRF", (ftnlen)32, (ftnlen) 6); cpbtrf_(uplo, &n, &kd, &afac[1], &ldab, &info); /* Check error code from CPBTRF. */ if (info != izero) { alaerh_(path, "CPBTRF", &info, &izero, uplo, &n, & n, &kd, &kd, &nb, &imat, &nfail, &nerrs, nout); goto L50; } /* Skip the tests if INFO is not 0. */ if (info != 0) { goto L50; } /* + TEST 1 */ /* Reconstruct matrix from factors and compute */ /* residual. */ i__5 = kd + 1; clacpy_("Full", &i__5, &n, &afac[1], &ldab, &ainv[1], &ldab); cpbt01_(uplo, &n, &kd, &a[1], &ldab, &ainv[1], &ldab, &rwork[1], result); /* Print the test ratio if it is .GE. THRESH. */ if (result[0] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___40.ciunit = *nout; s_wsfe(&io___40); 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 *)&nb, (ftnlen)sizeof(integer) ); do_fio(&c__1, (char *)&imat, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&c__1, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[0], (ftnlen)sizeof( real)); e_wsfe(); ++nfail; } ++nrun; /* Only do other tests if this is the first blocksize. */ if (inb > 1) { goto L50; } /* Form the inverse of A so we can get a good estimate */ /* of RCONDC = 1/(norm(A) * norm(inv(A))). */ claset_("Full", &n, &n, &c_b50, &c_b51, &ainv[1], & lda); s_copy(srnamc_1.srnamt, "CPBTRS", (ftnlen)32, (ftnlen) 6); cpbtrs_(uplo, &n, &kd, &n, &afac[1], &ldab, &ainv[1], &lda, &info); /* Compute RCONDC = 1/(norm(A) * norm(inv(A))). */ anorm = clanhb_("1", uplo, &n, &kd, &a[1], &ldab, & rwork[1]); ainvnm = clange_("1", &n, &n, &ainv[1], &lda, &rwork[ 1]); if (anorm <= 0.f || ainvnm <= 0.f) { rcondc = 1.f; } else { rcondc = 1.f / anorm / ainvnm; } i__5 = *nns; for (irhs = 1; irhs <= i__5; ++irhs) { nrhs = nsval[irhs]; /* + TEST 2 */ /* Solve and compute residual for A * X = B. */ s_copy(srnamc_1.srnamt, "CLARHS", (ftnlen)32, ( ftnlen)6); clarhs_(path, xtype, uplo, " ", &n, &n, &kd, &kd, &nrhs, &a[1], &ldab, &xact[1], &lda, &b[1] , &lda, iseed, &info); clacpy_("Full", &n, &nrhs, &b[1], &lda, &x[1], & lda); s_copy(srnamc_1.srnamt, "CPBTRS", (ftnlen)32, ( ftnlen)6); cpbtrs_(uplo, &n, &kd, &nrhs, &afac[1], &ldab, &x[ 1], &lda, &info); /* Check error code from CPBTRS. */ if (info != 0) { alaerh_(path, "CPBTRS", &info, &c__0, uplo, & n, &n, &kd, &kd, &nrhs, &imat, &nfail, &nerrs, nout); } clacpy_("Full", &n, &nrhs, &b[1], &lda, &work[1], &lda); cpbt02_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &x[1], &lda, &work[1], &lda, &rwork[1], &result[ 1]); /* + TEST 3 */ /* Check solution from generated exact solution. */ cget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[2]); /* + TESTS 4, 5, and 6 */ /* Use iterative refinement to improve the solution. */ s_copy(srnamc_1.srnamt, "CPBRFS", (ftnlen)32, ( ftnlen)6); cpbrfs_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &afac[ 1], &ldab, &b[1], &lda, &x[1], &lda, & rwork[1], &rwork[nrhs + 1], &work[1], & rwork[(nrhs << 1) + 1], &info); /* Check error code from CPBRFS. */ if (info != 0) { alaerh_(path, "CPBRFS", &info, &c__0, uplo, & n, &n, &kd, &kd, &nrhs, &imat, &nfail, &nerrs, nout); } cget04_(&n, &nrhs, &x[1], &lda, &xact[1], &lda, & rcondc, &result[3]); cpbt05_(uplo, &n, &kd, &nrhs, &a[1], &ldab, &b[1], &lda, &x[1], &lda, &xact[1], &lda, & rwork[1], &rwork[nrhs + 1], &result[4]); /* Print information about the tests that did not */ /* pass the threshold. */ for (k = 2; k <= 6; ++k) { if (result[k - 1] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___46.ciunit = *nout; s_wsfe(&io___46); 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 *)&nrhs, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&imat, (ftnlen) sizeof(integer)); do_fio(&c__1, (char *)&k, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[k - 1], ( ftnlen)sizeof(real)); e_wsfe(); ++nfail; } /* L30: */ } nrun += 5; /* L40: */ } /* + TEST 7 */ /* Get an estimate of RCOND = 1/CNDNUM. */ s_copy(srnamc_1.srnamt, "CPBCON", (ftnlen)32, (ftnlen) 6); cpbcon_(uplo, &n, &kd, &afac[1], &ldab, &anorm, & rcond, &work[1], &rwork[1], &info); /* Check error code from CPBCON. */ if (info != 0) { alaerh_(path, "CPBCON", &info, &c__0, uplo, &n, & n, &kd, &kd, &c_n1, &imat, &nfail, &nerrs, nout); } result[6] = sget06_(&rcond, &rcondc); /* Print the test ratio if it is .GE. THRESH. */ if (result[6] >= *thresh) { if (nfail == 0 && nerrs == 0) { alahd_(nout, path); } io___48.ciunit = *nout; s_wsfe(&io___48); 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 *)&c__7, (ftnlen)sizeof( integer)); do_fio(&c__1, (char *)&result[6], (ftnlen)sizeof( real)); e_wsfe(); ++nfail; } ++nrun; L50: ; } L60: ; } /* L70: */ } /* L80: */ } /* L90: */ } /* Print a summary of the results. */ alasum_(path, nout, &nfail, &nrun, &nerrs); return 0; /* End of CCHKPB */ } /* cchkpb_ */
int cpbsvx_(char *fact, char *uplo, int *n, int *kd, int *nrhs, complex *ab, int *ldab, complex *afb, int * ldafb, char *equed, float *s, complex *b, int *ldb, complex *x, int *ldx, float *rcond, float *ferr, float *berr, complex *work, float *rwork, int *info) { /* System generated locals */ int 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; float r__1, r__2; complex q__1; /* Local variables */ int i__, j, j1, j2; float amax, smin, smax; extern int lsame_(char *, char *); float scond, anorm; extern int ccopy_(int *, complex *, int *, complex *, int *); int equil, rcequ, upper; extern double clanhb_(char *, char *, int *, int *, complex *, int *, float *); extern int claqhb_(char *, int *, int *, complex *, int *, float *, float *, float *, char *), cpbcon_(char *, int *, int *, complex *, int *, float * , float *, complex *, float *, int *); extern double slamch_(char *); int nofact; extern int clacpy_(char *, int *, int *, complex *, int *, complex *, int *), xerbla_(char *, int *), cpbequ_(char *, int *, int *, complex *, int *, float *, float *, float *, int *), cpbrfs_( char *, int *, int *, int *, complex *, int *, complex *, int *, complex *, int *, complex *, int *, float *, float *, complex *, float *, int *); float bignum; extern int cpbtrf_(char *, int *, int *, complex *, int *, int *); int infequ; extern int cpbtrs_(char *, int *, int *, int *, complex *, int *, complex *, int *, int *); float smlnum; /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CPBSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to */ /* compute the solution to a complex system of linear equations */ /* A * X = B, */ /* where A is an N-by-N Hermitian 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', float 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**H * U, if UPLO = 'U', or */ /* A = L * L**H, 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) COMPLEX array, dimension (LDAB,N) */ /* On entry, the upper or lower triangle of the Hermitian 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) COMPLEX 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**H*U or A = L*L**H 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**H*U or A = L*L**H. */ /* 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**H*U or A = L*L**H 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) COMPLEX 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) COMPLEX 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) COMPLEX array, dimension (2*N) */ /* RWORK (workspace) REAL 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 Hermitian 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. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* 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; --rwork; /* 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 = MIN(r__1,r__2); /* Computing MAX */ r__1 = smax, r__2 = s[j]; smax = MAX(r__1,r__2); /* L10: */ } if (smin <= 0.f) { *info = -11; } else if (*n > 0) { scond = MAX(smin,smlnum) / MIN(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_("CPBSVX", &i__1); return 0; } if (equil) { /* Compute row and column scalings to equilibrate the matrix A. */ cpbequ_(uplo, n, kd, &ab[ab_offset], ldab, &s[1], &scond, &amax, & infequ); if (infequ == 0) { /* Equilibrate the matrix. */ claqhb_(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__) { i__3 = i__ + j * b_dim1; i__4 = i__; i__5 = i__ + j * b_dim1; q__1.r = s[i__4] * b[i__5].r, q__1.i = s[i__4] * b[i__5].i; b[i__3].r = q__1.r, b[i__3].i = q__1.i; /* L20: */ } /* L30: */ } } 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; ccopy_(&i__2, &ab[*kd + 1 - j + j1 + j * ab_dim1], &c__1, & afb[*kd + 1 - j + j1 + j * afb_dim1], &c__1); /* L40: */ } } 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; ccopy_(&i__2, &ab[j * ab_dim1 + 1], &c__1, &afb[j * afb_dim1 + 1], &c__1); /* L50: */ } } cpbtrf_(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 = clanhb_("1", uplo, n, kd, &ab[ab_offset], ldab, &rwork[1]); /* Compute the reciprocal of the condition number of A. */ cpbcon_(uplo, n, kd, &afb[afb_offset], ldafb, &anorm, rcond, &work[1], & rwork[1], info); /* Compute the solution matrix X. */ clacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx); cpbtrs_(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. */ cpbrfs_(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] , &rwork[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__) { i__3 = i__ + j * x_dim1; i__4 = i__; i__5 = i__ + j * x_dim1; q__1.r = s[i__4] * x[i__5].r, q__1.i = s[i__4] * x[i__5].i; x[i__3].r = q__1.r, x[i__3].i = q__1.i; /* L60: */ } /* L70: */ } i__1 = *nrhs; for (j = 1; j <= i__1; ++j) { ferr[j] /= scond; /* L80: */ } } /* Set INFO = N+1 if the matrix is singular to working precision. */ if (*rcond < slamch_("Epsilon")) { *info = *n + 1; } return 0; /* End of CPBSVX */ } /* cpbsvx_ */
/* Subroutine */ int cpbt01_(char *uplo, integer *n, integer *kd, complex *a, integer *lda, complex *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, i__4, i__5; complex q__1; /* Builtin functions */ double r_imag(complex *); /* Local variables */ integer i__, j, k, kc, ml, mu; real akk, eps; extern /* Subroutine */ int cher_(char *, integer *, real *, complex *, integer *, complex *, integer *); integer klen; extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer *, complex *, integer *); extern logical lsame_(char *, char *); real anorm; extern /* Subroutine */ int ctrmv_(char *, char *, char *, integer *, complex *, integer *, complex *, integer *); extern doublereal clanhb_(char *, char *, integer *, integer *, complex *, integer *, real *), slamch_(char *); extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer *); /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CPBT01 reconstructs a Hermitian 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 */ /* Hermitian 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) COMPLEX array, dimension (LDA,N) */ /* The original Hermitian 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 CPBTRF for further details. */ /* LDA (input) INTEGER. */ /* The leading dimension of the array A. LDA >= max(1,KD+1). */ /* AFAC (input) COMPLEX 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 CPBTRF. */ /* 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 = clanhb_("1", uplo, n, kd, &a[a_offset], lda, &rwork[1]); if (anorm <= 0.f) { *resid = 1.f / eps; return 0; } /* Check the imaginary parts of the diagonal elements and return with */ /* an error code if any are nonzero. */ if (lsame_(uplo, "U")) { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (r_imag(&afac[*kd + 1 + j * afac_dim1]) != 0.f) { *resid = 1.f / eps; return 0; } /* L10: */ } } else { i__1 = *n; for (j = 1; j <= i__1; ++j) { if (r_imag(&afac[j * afac_dim1 + 1]) != 0.f) { *resid = 1.f / eps; return 0; } /* L20: */ } } /* 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; cdotc_(&q__1, &i__1, &afac[kc + k * afac_dim1], &c__1, &afac[kc + k * afac_dim1], &c__1); akk = q__1.r; i__1 = *kd + 1 + k * afac_dim1; afac[i__1].r = akk, afac[i__1].i = 0.f; /* Compute the rest of column K. */ if (klen > 0) { i__1 = *ldafac - 1; ctrmv_("Upper", "Conjugate", "Non-unit", &klen, &afac[*kd + 1 + (k - klen) * afac_dim1], &i__1, &afac[kc + k * afac_dim1], &c__1); } /* L30: */ } /* 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; cher_("Lower", &klen, &c_b17, &afac[k * afac_dim1 + 2], &c__1, &afac[(k + 1) * afac_dim1 + 1], &i__1); } /* Scale column K by the diagonal element. */ i__1 = k * afac_dim1 + 1; akk = afac[i__1].r; i__1 = klen + 1; csscal_(&i__1, &akk, &afac[k * afac_dim1 + 1], &c__1); /* L40: */ } } /* 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__) { i__3 = i__ + j * afac_dim1; i__4 = i__ + j * afac_dim1; i__5 = i__ + j * a_dim1; q__1.r = afac[i__4].r - a[i__5].r, q__1.i = afac[i__4].i - a[ i__5].i; afac[i__3].r = q__1.r, afac[i__3].i = q__1.i; /* L50: */ } /* L60: */ } } 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__) { i__3 = i__ + j * afac_dim1; i__4 = i__ + j * afac_dim1; i__5 = i__ + j * a_dim1; q__1.r = afac[i__4].r - a[i__5].r, q__1.i = afac[i__4].i - a[ i__5].i; afac[i__3].r = q__1.r, afac[i__3].i = q__1.i; /* L70: */ } /* L80: */ } } /* Compute norm( L*L' - A ) / ( N * norm(A) * EPS ) */ *resid = clanhb_("1", uplo, n, kd, &afac[afac_offset], ldafac, &rwork[1]); *resid = *resid / (real) (*n) / anorm / eps; return 0; /* End of CPBT01 */ } /* cpbt01_ */
/* Subroutine */ int cpbt02_(char *uplo, integer *n, integer *kd, integer * nrhs, complex *a, integer *lda, complex *x, integer *ldx, complex *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; complex q__1; /* Local variables */ integer j; real eps; real anorm, bnorm, xnorm; /* -- LAPACK test routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CPBT02 computes the residual for a solution of a Hermitian 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 */ /* Hermitian 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) COMPLEX array, dimension (LDA,N) */ /* The original Hermitian 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 CPBTRF for further details. */ /* LDA (input) INTEGER. */ /* The leading dimension of the array A. LDA >= max(1,KD+1). */ /* X (input) COMPLEX 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) COMPLEX 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 = clanhb_("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) { q__1.r = -1.f, q__1.i = -0.f; chbmv_(uplo, n, kd, &q__1, &a[a_offset], lda, &x[j * x_dim1 + 1], & c__1, &c_b1, &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 = scasum_(n, &b[j * b_dim1 + 1], &c__1); xnorm = scasum_(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 CPBT02 */ } /* cpbt02_ */
/* Subroutine */ int chbevd_(char *jobz, char *uplo, integer *n, integer *kd, complex *ab, integer *ldab, real *w, complex *z__, integer *ldz, complex *work, integer *lwork, real *rwork, integer *lrwork, integer * iwork, integer *liwork, integer *info) { /* System generated locals */ integer ab_dim1, ab_offset, z_dim1, z_offset, i__1; real r__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ real eps; integer inde; real anrm; integer imax; real rmin, rmax; integer llwk2; extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, integer *, complex *, complex *, integer *, complex *, integer *, complex *, complex *, integer *); real sigma; extern logical lsame_(char *, char *); integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); integer lwmin; logical lower; integer llrwk; logical wantz; integer indwk2; extern doublereal clanhb_(char *, char *, integer *, integer *, complex *, integer *, real *); integer iscale; extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *, real *, integer *, integer *, complex *, integer *, integer *), cstedc_(char *, integer *, real *, real *, complex *, integer *, complex *, integer *, real *, integer *, integer *, integer *, integer *), chbtrd_(char *, char *, integer *, integer *, complex *, integer *, real *, real *, complex *, integer *, complex *, integer *); extern doublereal slamch_(char *); extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex *, integer *, complex *, integer *); real safmin; extern /* Subroutine */ int xerbla_(char *, integer *); real bignum; integer indwrk, liwmin; extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *); integer lrwmin; real smlnum; logical lquery; /* -- LAPACK driver routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CHBEVD computes all the eigenvalues and, optionally, eigenvectors of */ /* a complex Hermitian band matrix A. If eigenvectors are desired, it */ /* uses a divide and conquer algorithm. */ /* The divide and conquer algorithm makes very mild assumptions about */ /* floating point arithmetic. It will work on machines with a guard */ /* digit in add/subtract, or on those binary machines without guard */ /* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ /* Cray-2. It could conceivably fail on hexadecimal or decimal machines */ /* without guard digits, but we know of none. */ /* 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) COMPLEX array, dimension (LDAB, N) */ /* On entry, the upper or lower triangle of the Hermitian 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) COMPLEX 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/output) COMPLEX array, dimension (MAX(1,LWORK)) */ /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* LWORK (input) INTEGER */ /* The dimension of the array WORK. */ /* If N <= 1, LWORK must be at least 1. */ /* If JOBZ = 'N' and N > 1, LWORK must be at least N. */ /* If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2. */ /* If LWORK = -1, then a workspace query is assumed; the routine */ /* only calculates the optimal sizes of the WORK, RWORK and */ /* IWORK arrays, returns these values as the first entries of */ /* the WORK, RWORK and IWORK arrays, and no error message */ /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ /* RWORK (workspace/output) REAL array, */ /* dimension (LRWORK) */ /* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */ /* LRWORK (input) INTEGER */ /* The dimension of array RWORK. */ /* If N <= 1, LRWORK must be at least 1. */ /* If JOBZ = 'N' and N > 1, LRWORK must be at least N. */ /* If JOBZ = 'V' and N > 1, LRWORK must be at least */ /* 1 + 5*N + 2*N**2. */ /* If LRWORK = -1, then a workspace query is assumed; the */ /* routine only calculates the optimal sizes of the WORK, RWORK */ /* and IWORK arrays, returns these values as the first entries */ /* of the WORK, RWORK and IWORK arrays, and no error message */ /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ /* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */ /* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ /* LIWORK (input) INTEGER */ /* The dimension of array IWORK. */ /* If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. */ /* If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N . */ /* If LIWORK = -1, then a workspace query is assumed; the */ /* routine only calculates the optimal sizes of the WORK, RWORK */ /* and IWORK arrays, returns these values as the first entries */ /* of the WORK, RWORK and IWORK arrays, and no error message */ /* related to LWORK or LRWORK or LIWORK is issued by XERBLA. */ /* 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; --rwork; --iwork; /* Function Body */ wantz = lsame_(jobz, "V"); lower = lsame_(uplo, "L"); lquery = *lwork == -1 || *liwork == -1 || *lrwork == -1; *info = 0; if (*n <= 1) { lwmin = 1; lrwmin = 1; liwmin = 1; } else { if (wantz) { /* Computing 2nd power */ i__1 = *n; lwmin = i__1 * i__1 << 1; /* Computing 2nd power */ i__1 = *n; lrwmin = *n * 5 + 1 + (i__1 * i__1 << 1); liwmin = *n * 5 + 3; } else { lwmin = *n; lrwmin = *n; liwmin = 1; } } 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) { work[1].r = (real) lwmin, work[1].i = 0.f; rwork[1] = (real) lrwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -11; } else if (*lrwork < lrwmin && ! lquery) { *info = -13; } else if (*liwork < liwmin && ! lquery) { *info = -15; } } if (*info != 0) { i__1 = -(*info); xerbla_("CHBEVD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { i__1 = ab_dim1 + 1; w[1] = ab[i__1].r; if (wantz) { i__1 = z_dim1 + 1; z__[i__1].r = 1.f, z__[i__1].i = 0.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 = clanhb_("M", uplo, n, kd, &ab[ab_offset], ldab, &rwork[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) { clascl_("B", kd, kd, &c_b13, &sigma, n, n, &ab[ab_offset], ldab, info); } else { clascl_("Q", kd, kd, &c_b13, &sigma, n, n, &ab[ab_offset], ldab, info); } } /* Call CHBTRD to reduce Hermitian band matrix to tridiagonal form. */ inde = 1; indwrk = inde + *n; indwk2 = *n * *n + 1; llwk2 = *lwork - indwk2 + 1; llrwk = *lrwork - indwrk + 1; chbtrd_(jobz, uplo, n, kd, &ab[ab_offset], ldab, &w[1], &rwork[inde], & z__[z_offset], ldz, &work[1], &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEDC. */ if (! wantz) { ssterf_(n, &w[1], &rwork[inde], info); } else { cstedc_("I", n, &w[1], &rwork[inde], &work[1], n, &work[indwk2], & llwk2, &rwork[indwrk], &llrwk, &iwork[1], liwork, info); cgemm_("N", "N", n, n, n, &c_b2, &z__[z_offset], ldz, &work[1], n, & c_b1, &work[indwk2], n); clacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz); } /* 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); } work[1].r = (real) lwmin, work[1].i = 0.f; rwork[1] = (real) lrwmin; iwork[1] = liwmin; return 0; /* End of CHBEVD */ } /* chbevd_ */