int sspevx_(char *jobz, char *range, char *uplo, int *n, float *ap, float *vl, float *vu, int *il, int *iu, float *abstol, int *m, float *w, float *z__, int *ldz, float *work, int * iwork, int *ifail, int *info) { /* System generated locals */ int z_dim1, z_offset, i__1, i__2; float r__1, r__2; /* Builtin functions */ double sqrt(double); /* Local variables */ int i__, j, jj; float eps, vll, vuu, tmp1; int indd, inde; float anrm; int imax; float rmin, rmax; int test; int itmp1, indee; float sigma; extern int lsame_(char *, char *); int iinfo; extern int sscal_(int *, float *, float *, int *); char order[1]; extern int scopy_(int *, float *, int *, float *, int *), sswap_(int *, float *, int *, float *, int * ); int wantz, alleig, indeig; int iscale, indibl; int valeig; extern double slamch_(char *); float safmin; extern int xerbla_(char *, int *); float abstll, bignum; int indtau, indisp, indiwo, indwrk; extern double slansp_(char *, char *, int *, float *, float *); extern int sstein_(int *, float *, float *, int *, float *, int *, int *, float *, int *, float *, int * , int *, int *), ssterf_(int *, float *, float *, int *); int nsplit; extern int sstebz_(char *, char *, int *, float *, float *, int *, int *, float *, float *, float *, int *, int *, float *, int *, int *, float *, int *, int *); float smlnum; extern int sopgtr_(char *, int *, float *, float *, float *, int *, float *, int *), ssptrd_(char *, int *, float *, float *, float *, float *, int *), ssteqr_(char *, int *, float *, float *, float *, int *, float *, int *), sopmtr_(char *, char *, char *, int *, int *, float *, float *, float *, int *, float *, int *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SSPEVX computes selected eigenvalues and, optionally, eigenvectors */ /* of a float symmetric matrix A in packed storage. Eigenvalues/vectors */ /* 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. */ /* AP (input/output) REAL array, dimension (N*(N+1)/2) */ /* On entry, the upper or lower triangle of the symmetric matrix */ /* A, packed columnwise in a linear array. The j-th column of A */ /* is stored in the array AP as follows: */ /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */ /* On exit, AP is overwritten by values generated during the */ /* reduction to tridiagonal form. If UPLO = 'U', the diagonal */ /* and first superdiagonal of the tridiagonal matrix T overwrite */ /* the corresponding elements of A, and if UPLO = 'L', the */ /* diagonal and first subdiagonal of T overwrite the */ /* corresponding elements of A. */ /* 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 AP 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) */ /* If INFO = 0, the selected eigenvalues in ascending order. */ /* Z (output) REAL array, dimension (LDZ, MAX(1,M)) */ /* If JOBZ = 'V', then if INFO = 0, the first M columns of Z */ /* contain the orthonormal eigenvectors of the matrix A */ /* corresponding to the selected eigenvalues, with the i-th */ /* column of Z holding the eigenvector associated with W(i). */ /* If an eigenvector fails to converge, then that column of Z */ /* contains the latest approximation to the eigenvector, and the */ /* index of the eigenvector is returned in IFAIL. */ /* If JOBZ = 'N', then Z is not referenced. */ /* Note: the user must ensure that at least MAX(1,M) columns are */ /* supplied in the array Z; if RANGE = 'V', the exact value of M */ /* is not known in advance and an upper bound must be used. */ /* LDZ (input) INTEGER */ /* The leading dimension of the array Z. LDZ >= 1, and if */ /* JOBZ = 'V', LDZ >= MAX(1,N). */ /* WORK (workspace) REAL array, dimension (8*N) */ /* IWORK (workspace) INTEGER array, dimension (5*N) */ /* IFAIL (output) INTEGER array, dimension (N) */ /* If JOBZ = 'V', then if INFO = 0, the first M elements of */ /* IFAIL are zero. If INFO > 0, then IFAIL contains the */ /* indices of the eigenvectors that failed to converge. */ /* If JOBZ = 'N', then IFAIL is not referenced. */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, then i eigenvectors failed to converge. */ /* Their indices are stored in array IFAIL. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ --ap; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --iwork; --ifail; /* Function Body */ wantz = lsame_(jobz, "V"); alleig = lsame_(range, "A"); valeig = lsame_(range, "V"); indeig = lsame_(range, "I"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (alleig || valeig || indeig)) { *info = -2; } else if (! (lsame_(uplo, "L") || lsame_(uplo, "U"))) { *info = -3; } else if (*n < 0) { *info = -4; } else { if (valeig) { if (*n > 0 && *vu <= *vl) { *info = -7; } } else if (indeig) { if (*il < 1 || *il > MAX(1,*n)) { *info = -8; } else if (*iu < MIN(*n,*il) || *iu > *n) { *info = -9; } } } if (*info == 0) { if (*ldz < 1 || wantz && *ldz < *n) { *info = -14; } } if (*info != 0) { i__1 = -(*info); xerbla_("SSPEVX", &i__1); return 0; } /* Quick return if possible */ *m = 0; if (*n == 0) { return 0; } if (*n == 1) { if (alleig || indeig) { *m = 1; w[1] = ap[1]; } else { if (*vl < ap[1] && *vu >= ap[1]) { *m = 1; w[1] = ap[1]; } } if (wantz) { z__[z_dim1 + 1] = 1.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum"); eps = slamch_("Precision"); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); /* Computing MIN */ r__1 = sqrt(bignum), r__2 = 1.f / sqrt(sqrt(safmin)); rmax = MIN(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 = slansp_("M", uplo, n, &ap[1], &work[1]); if (anrm > 0.f && anrm < rmin) { iscale = 1; sigma = rmin / anrm; } else if (anrm > rmax) { iscale = 1; sigma = rmax / anrm; } if (iscale == 1) { i__1 = *n * (*n + 1) / 2; sscal_(&i__1, &sigma, &ap[1], &c__1); if (*abstol > 0.f) { abstll = *abstol * sigma; } if (valeig) { vll = *vl * sigma; vuu = *vu * sigma; } } /* Call SSPTRD to reduce symmetric packed matrix to tridiagonal form. */ indtau = 1; inde = indtau + *n; indd = inde + *n; indwrk = indd + *n; ssptrd_(uplo, n, &ap[1], &work[indd], &work[inde], &work[indtau], &iinfo); /* If all eigenvalues are desired and ABSTOL is less than or equal */ /* to zero, then call SSTERF or SOPGTR and SSTEQR. If this fails */ /* for some eigenvalue, then try SSTEBZ. */ test = FALSE; if (indeig) { if (*il == 1 && *iu == *n) { test = TRUE; } } if ((alleig || test) && *abstol <= 0.f) { scopy_(n, &work[indd], &c__1, &w[1], &c__1); indee = indwrk + (*n << 1); if (! wantz) { i__1 = *n - 1; scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1); ssterf_(n, &w[1], &work[indee], info); } else { sopgtr_(uplo, n, &ap[1], &work[indtau], &z__[z_offset], ldz, & work[indwrk], &iinfo); i__1 = *n - 1; scopy_(&i__1, &work[inde], &c__1, &work[indee], &c__1); ssteqr_(jobz, n, &w[1], &work[indee], &z__[z_offset], ldz, &work[ indwrk], info); if (*info == 0) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { ifail[i__] = 0; /* L10: */ } } } if (*info == 0) { *m = *n; goto L20; } *info = 0; } /* Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN. */ if (wantz) { *(unsigned char *)order = 'B'; } else { *(unsigned char *)order = 'E'; } indibl = 1; indisp = indibl + *n; indiwo = indisp + *n; sstebz_(range, order, n, &vll, &vuu, il, iu, &abstll, &work[indd], &work[ inde], m, &nsplit, &w[1], &iwork[indibl], &iwork[indisp], &work[ indwrk], &iwork[indiwo], info); if (wantz) { sstein_(n, &work[indd], &work[inde], m, &w[1], &iwork[indibl], &iwork[ indisp], &z__[z_offset], ldz, &work[indwrk], &iwork[indiwo], & ifail[1], info); /* Apply orthogonal matrix used in reduction to tridiagonal */ /* form to eigenvectors returned by SSTEIN. */ sopmtr_("L", uplo, "N", n, m, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[indwrk], &iinfo); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ L20: 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]; } /* L30: */ } if (i__ != 0) { itmp1 = iwork[indibl + i__ - 1]; w[i__] = w[j]; iwork[indibl + i__ - 1] = iwork[indibl + j - 1]; w[j] = tmp1; iwork[indibl + j - 1] = itmp1; sswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[j * z_dim1 + 1], &c__1); if (*info != 0) { itmp1 = ifail[i__]; ifail[i__] = ifail[j]; ifail[j] = itmp1; } } /* L40: */ } } return 0; /* End of SSPEVX */ } /* sspevx_ */
/* Subroutine */ int sspevd_(char *jobz, char *uplo, integer *n, real *ap, real *w, real *z__, integer *ldz, real *work, integer *lwork, integer *iwork, integer *liwork, integer *info, ftnlen jobz_len, ftnlen uplo_len) { /* System generated locals */ integer z_dim1, z_offset, i__1; real r__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static real eps; static integer inde; static real anrm, rmin, rmax, sigma; extern logical lsame_(char *, char *, ftnlen, ftnlen); static integer iinfo; extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); static integer lwmin; static logical wantz; static integer iscale; extern doublereal slamch_(char *, ftnlen); static real safmin; extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen); static real bignum; static integer indtau; extern /* Subroutine */ int sstedc_(char *, integer *, real *, real *, real *, integer *, real *, integer *, integer *, integer *, integer *, ftnlen); static integer indwrk, liwmin; extern doublereal slansp_(char *, char *, integer *, real *, real *, ftnlen, ftnlen); extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *); static integer llwork; static real smlnum; extern /* Subroutine */ int ssptrd_(char *, integer *, real *, real *, real *, real *, integer *, ftnlen); static logical lquery; extern /* Subroutine */ int sopmtr_(char *, char *, char *, integer *, integer *, real *, real *, real *, integer *, real *, integer *, ftnlen, ftnlen, ftnlen); /* -- 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 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SSPEVD computes all the eigenvalues and, optionally, eigenvectors */ /* of a real symmetric matrix A in packed storage. 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. */ /* AP (input/output) REAL array, dimension (N*(N+1)/2) */ /* On entry, the upper or lower triangle of the symmetric matrix */ /* A, packed columnwise in a linear array. The j-th column of A */ /* is stored in the array AP as follows: */ /* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; */ /* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. */ /* On exit, AP is overwritten by values generated during the */ /* reduction to tridiagonal form. If UPLO = 'U', the diagonal */ /* and first superdiagonal of the tridiagonal matrix T overwrite */ /* the corresponding elements of A, and if UPLO = 'L', the */ /* diagonal and first subdiagonal of T overwrite the */ /* corresponding elements of A. */ /* W (output) REAL array, dimension (N) */ /* If INFO = 0, the eigenvalues in ascending order. */ /* Z (output) REAL array, dimension (LDZ, N) */ /* If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal */ /* eigenvectors of the matrix A, with the i-th column of Z */ /* holding the eigenvector associated with W(i). */ /* If JOBZ = 'N', then Z is not referenced. */ /* LDZ (input) INTEGER */ /* The leading dimension of the array Z. LDZ >= 1, and if */ /* JOBZ = 'V', LDZ >= max(1,N). */ /* WORK (workspace/output) REAL array, */ /* dimension (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 2*N. */ /* If JOBZ = 'V' and N > 1, LWORK must be at least */ /* 1 + 6*N + N**2. */ /* If LWORK = -1, then a workspace query is assumed; the routine */ /* only calculates the optimal size of the WORK array, returns */ /* this value as the first entry of the WORK array, and no error */ /* message related to LWORK is issued by XERBLA. */ /* IWORK (workspace/output) INTEGER array, dimension (LIWORK) */ /* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */ /* LIWORK (input) INTEGER */ /* The dimension of the 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 size of the IWORK array, */ /* returns this value as the first entry of the IWORK array, and */ /* no error message related to 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 */ --ap; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --iwork; /* Function Body */ wantz = lsame_(jobz, "V", (ftnlen)1, (ftnlen)1); lquery = *lwork == -1 || *liwork == -1; *info = 0; if (*n <= 1) { liwmin = 1; lwmin = 1; } else { if (wantz) { liwmin = *n * 5 + 3; /* Computing 2nd power */ i__1 = *n; lwmin = *n * 6 + 1 + i__1 * i__1; } else { liwmin = 1; lwmin = *n << 1; } } if (! (wantz || lsame_(jobz, "N", (ftnlen)1, (ftnlen)1))) { *info = -1; } else if (! (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) || lsame_(uplo, "L", (ftnlen)1, (ftnlen)1))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -7; } else if (*lwork < lwmin && ! lquery) { *info = -9; } else if (*liwork < liwmin && ! lquery) { *info = -11; } if (*info == 0) { work[1] = (real) lwmin; iwork[1] = liwmin; } if (*info != 0) { i__1 = -(*info); xerbla_("SSPEVD", &i__1, (ftnlen)6); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (*n == 1) { w[1] = ap[1]; if (wantz) { z__[z_dim1 + 1] = 1.f; } return 0; } /* Get machine constants. */ safmin = slamch_("Safe minimum", (ftnlen)12); eps = slamch_("Precision", (ftnlen)9); smlnum = safmin / eps; bignum = 1.f / smlnum; rmin = sqrt(smlnum); rmax = sqrt(bignum); /* Scale matrix to allowable range, if necessary. */ anrm = slansp_("M", uplo, n, &ap[1], &work[1], (ftnlen)1, (ftnlen)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) { i__1 = *n * (*n + 1) / 2; sscal_(&i__1, &sigma, &ap[1], &c__1); } /* Call SSPTRD to reduce symmetric packed matrix to tridiagonal form. */ inde = 1; indtau = inde + *n; ssptrd_(uplo, n, &ap[1], &w[1], &work[inde], &work[indtau], &iinfo, ( ftnlen)1); /* For eigenvalues only, call SSTERF. For eigenvectors, first call */ /* SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the */ /* tridiagonal matrix, then call SOPMTR to multiply it by the */ /* Householder transformations represented in AP. */ if (! wantz) { ssterf_(n, &w[1], &work[inde], info); } else { indwrk = indtau + *n; llwork = *lwork - indwrk + 1; sstedc_("I", n, &w[1], &work[inde], &z__[z_offset], ldz, &work[indwrk] , &llwork, &iwork[1], liwork, info, (ftnlen)1); sopmtr_("L", uplo, "N", n, n, &ap[1], &work[indtau], &z__[z_offset], ldz, &work[indwrk], &iinfo, (ftnlen)1, (ftnlen)1, (ftnlen)1); } /* If matrix was scaled, then rescale eigenvalues appropriately. */ if (iscale == 1) { r__1 = 1.f / sigma; sscal_(n, &r__1, &w[1], &c__1); } work[1] = (real) lwmin; iwork[1] = liwmin; return 0; /* End of SSPEVD */ } /* sspevd_ */