dsbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
SUBROUTINE DSBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO INTEGER N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO INTEGER IWORK2(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*) SUBROUTINE DSBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO INTEGER*8 N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO INTEGER*8 IWORK2(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE SBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO INTEGER :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK2, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: W, WORK REAL(8), DIMENSION(:,:) :: A, Q, Z SUBROUTINE SBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO INTEGER(8) :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: W, WORK REAL(8), DIMENSION(:,:) :: A, Q, Z C INTERFACE #include <sunperf.h> void dsbevx(char jobz, char range, char uplo, int n, int kd, double *a, int lda, double *q, int ldq, double vl, double vu, int il, int iu, double abtol, int *nfound, double *w, double *z, int ldz, int *ifail, int *info); void dsbevx_64(char jobz, char range, char uplo, long n, long kd, dou- ble *a, long lda, double *q, long ldq, double vl, double vu, long il, long iu, double abtol, long *nfound, double *w, dou- ble *z, long ldz, long *ifail, long *info);
Oracle Solaris Studio Performance Library dsbevx(3P) NAME dsbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A SYNOPSIS SUBROUTINE DSBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO INTEGER N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO INTEGER IWORK2(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*) SUBROUTINE DSBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO INTEGER*8 N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO INTEGER*8 IWORK2(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE SBEVX(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO INTEGER :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK2, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: W, WORK REAL(8), DIMENSION(:,:) :: A, Q, Z SUBROUTINE SBEVX_64(JOBZ, RANGE, UPLO, N, KD, A, LDA, Q, LDQ, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO INTEGER(8) :: N, KD, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: W, WORK REAL(8), DIMENSION(:,:) :: A, Q, Z C INTERFACE #include <sunperf.h> void dsbevx(char jobz, char range, char uplo, int n, int kd, double *a, int lda, double *q, int ldq, double vl, double vu, int il, int iu, double abtol, int *nfound, double *w, double *z, int ldz, int *ifail, int *info); void dsbevx_64(char jobz, char range, char uplo, long n, long kd, dou- ble *a, long lda, double *q, long ldq, double vl, double vu, long il, long iu, double abtol, long *nfound, double *w, dou- ble *z, long ldz, long *ifail, long *info); PURPOSE dsbevx computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. ARGUMENTS JOBZ (input) = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. RANGE (input) = '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) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) The order of the matrix A. N >= 0. KD (input) The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. A (input/output) DOUBLE PRECISION array, dimension (LDA, N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array. The j- th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j- kd)<=i<=j; if UPLO = 'L', A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, A 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 A, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of A. LDA (input) The leading dimension of the array A. LDA >= KD + 1. Q (output) DOUBLE PRECISION array, dimension (LDQ, N) If JOBZ = 'V', the N-by-N orthogonal matrix used in the reduction to tridiagonal form. If JOBZ = 'N', the array Q is not referenced. LDQ (input) The leading dimension of the array Q. If JOBZ = 'V', then LDQ >= max(1,N). VL (input) 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'. VU (input) See the description of VL. IL (input) If RANGE='I', the indices (in ascending order) of the small- est 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'. IU (input) See the description of IL. ABTOL (input) The absolute error tolerance for the eigenvalues. An approx- imate eigenvalue is accepted as converged when it is deter- mined to lie in an interval [a,b] of width less than or equal to ABTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision. If ABTOL 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 A to tridiagonal form. Eigenvalues will be computed most accurately when ABTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABTOL to 2*DLAMCH('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3. NFOUND (output) The total number of eigenvalues found. 0 <= NFOUND <= N. If RANGE = 'A', NFOUND = N, and if RANGE = 'I', NFOUND = IU- IL+1. W (output) DOUBLE PRECISION array, dimension (N) The first NFOUND elements contain the selected eigenvalues in ascending order. Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M)) If JOBZ = 'V', then if INFO = 0, the first NFOUND columns of Z contain the orthonormal eigenvectors of the matrix A corre- sponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigen- vector 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,NFOUND) columns are supplied in the array Z; if RANGE = 'V', the exact value of NFOUND is not known in advance and an upper bound must be used. LDZ (input) The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK (workspace) DOUBLE PRECISION array, dimension (7*N) IWORK2 (workspace) INTEGER array, dimension (5*N) IFAIL (output) INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first NFOUND 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) = 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. 7 Nov 2015 dsbevx(3P)