zhpevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
SUBROUTINE ZHPEVX(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO DOUBLE COMPLEX A(*), Z(LDZ,*), WORK(*) INTEGER N, IL, IU, NFOUND, LDZ, INFO INTEGER IWORK3(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION W(*), WORK2(*) SUBROUTINE ZHPEVX_64(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO DOUBLE COMPLEX A(*), Z(LDZ,*), WORK(*) INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO INTEGER*8 IWORK3(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION W(*), WORK2(*) F95 INTERFACE SUBROUTINE HPEVX(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX(8), DIMENSION(:) :: A, WORK COMPLEX(8), DIMENSION(:,:) :: Z INTEGER :: N, IL, IU, NFOUND, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK3, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: W, WORK2 SUBROUTINE HPEVX_64(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX(8), DIMENSION(:) :: A, WORK COMPLEX(8), DIMENSION(:,:) :: Z INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK3, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: W, WORK2 C INTERFACE #include <sunperf.h> void zhpevx(char jobz, char range, char uplo, int n, doublecomplex *a, double vl, double vu, int il, int iu, double abtol, int *nfound, double *w, doublecomplex *z, int ldz, int *ifail, int *info); void zhpevx_64(char jobz, char range, char uplo, long n, doublecomplex *a, double vl, double vu, long il, long iu, double abtol, long *nfound, double *w, doublecomplex *z, long ldz, long *ifail, long *info);
Oracle Solaris Studio Performance Library zhpevx(3P) NAME zhpevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage SYNOPSIS SUBROUTINE ZHPEVX(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO DOUBLE COMPLEX A(*), Z(LDZ,*), WORK(*) INTEGER N, IL, IU, NFOUND, LDZ, INFO INTEGER IWORK3(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION W(*), WORK2(*) SUBROUTINE ZHPEVX_64(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO DOUBLE COMPLEX A(*), Z(LDZ,*), WORK(*) INTEGER*8 N, IL, IU, NFOUND, LDZ, INFO INTEGER*8 IWORK3(*), IFAIL(*) DOUBLE PRECISION VL, VU, ABTOL DOUBLE PRECISION W(*), WORK2(*) F95 INTERFACE SUBROUTINE HPEVX(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX(8), DIMENSION(:) :: A, WORK COMPLEX(8), DIMENSION(:,:) :: Z INTEGER :: N, IL, IU, NFOUND, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK3, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: W, WORK2 SUBROUTINE HPEVX_64(JOBZ, RANGE, UPLO, N, A, VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, WORK2, IWORK3, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX(8), DIMENSION(:) :: A, WORK COMPLEX(8), DIMENSION(:,:) :: Z INTEGER(8) :: N, IL, IU, NFOUND, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK3, IFAIL REAL(8) :: VL, VU, ABTOL REAL(8), DIMENSION(:) :: W, WORK2 C INTERFACE #include <sunperf.h> void zhpevx(char jobz, char range, char uplo, int n, doublecomplex *a, double vl, double vu, int il, int iu, double abtol, int *nfound, double *w, doublecomplex *z, int ldz, int *ifail, int *info); void zhpevx_64(char jobz, char range, char uplo, long n, doublecomplex *a, double vl, double vu, long il, long iu, double abtol, long *nfound, double *w, doublecomplex *z, long ldz, long *ifail, long *info); PURPOSE zhpevx computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian 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) = '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. A (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, A 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 diag- onal and first subdiagonal of T overwrite the corresponding elements of A. 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) 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) 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) 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'. 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) If INFO = 0, the selected eigenvalues in ascending order. Z (output) COMPLEX*16 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) COMPLEX*16 array, dimension(2*N) WORK2 (workspace) DOUBLE PRECISION array, dimension(7*N) IWORK3 (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 zhpevx(3P)