hpev - {hp,sp}ev: eig, QR iteration

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subroutinechpev(characterjobz,characteruplo,integern,complex,dimension(*)ap,real,dimension(*)w,complex,dimension(ldz,*)z,integerldz,complex,dimension(*)work,real,dimension(*)rwork,integerinfo)CHPEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatricesPurpose: CHPEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. ParametersJOBZ JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. AP AP is COMPLEX 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 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 W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z Z is 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 LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK WORK is COMPLEX array, dimension (max(1, 2*N-1)) RWORK RWORK is REAL array, dimension (max(1, 3*N-2)) INFO INFO is 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. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedspev(characterjobz,characteruplo,integern,doubleprecision,dimension(*)ap,doubleprecision,dimension(*)w,doubleprecision,dimension(ldz,*)z,integerldz,doubleprecision,dimension(*)work,integerinfo)DSPEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatricesPurpose: DSPEV computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. ParametersJOBZ JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. AP AP is DOUBLE PRECISION 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 W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z Z is DOUBLE PRECISION 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 LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK WORK is DOUBLE PRECISION array, dimension (3*N) INFO INFO is 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. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinesspev(characterjobz,characteruplo,integern,real,dimension(*)ap,real,dimension(*)w,real,dimension(ldz,*)z,integerldz,real,dimension(*)work,integerinfo)SSPEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatricesPurpose: SSPEV computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage. ParametersJOBZ JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. AP AP is 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 W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z Z is 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 LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK WORK is REAL array, dimension (3*N) INFO INFO is 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. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezhpev(characterjobz,characteruplo,integern,complex*16,dimension(*)ap,doubleprecision,dimension(*)w,complex*16,dimension(ldz,*)z,integerldz,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork,integerinfo)ZHPEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatricesPurpose: ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. ParametersJOBZ JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. AP AP is 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 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 W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z Z is COMPLEX*16 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 LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). WORK WORK is COMPLEX*16 array, dimension (max(1, 2*N-1)) RWORK RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) INFO INFO is 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. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

hpev - {hp,sp}ev: eig, QR iteration

Functions subroutine chpev (jobz, uplo, n, ap, w, z, ldz, work, rwork, info) CHPEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatrices subroutine dspev (jobz, uplo, n, ap, w, z, ldz, work, info) DSPEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatrices subroutine sspev (jobz, uplo, n, ap, w, z, ldz, work, info) SSPEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatrices subroutine zhpev (jobz, uplo, n, ap, w, z, ldz, work, rwork, info) ZHPEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatrices