hbev - {hb,sb}ev: eig, QR iteration

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subroutinechbev(characterjobz,characteruplo,integern,integerkd,complex,dimension(ldab,*)ab,integerldab,real,dimension(*)w,complex,dimension(ldz,*)z,integerldz,complex,dimension(*)work,real,dimension(*)rwork,integerinfo)CHBEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatricesPurpose: CHBEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A. 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. KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB AB is 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 1. 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 (N) 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. subroutinedsbev(characterjobz,characteruplo,integern,integerkd,doubleprecision,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(*)w,doubleprecision,dimension(ldz,*)z,integerldz,doubleprecision,dimension(*)work,integerinfo)DSBEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatricesPurpose: DSBEV computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. 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. KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB AB is DOUBLE PRECISION array, dimension (LDAB, 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 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 1. 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 (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. subroutinessbev(characterjobz,characteruplo,integern,integerkd,real,dimension(ldab,*)ab,integerldab,real,dimension(*)w,real,dimension(ldz,*)z,integerldz,real,dimension(*)work,integerinfo)SSBEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatricesPurpose: SSBEV computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A. 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. KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB AB is REAL array, dimension (LDAB, 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 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 1. 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 (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. subroutinezhbev(characterjobz,characteruplo,integern,integerkd,complex*16,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(*)w,complex*16,dimension(ldz,*)z,integerldz,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork,integerinfo)ZHBEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatricesPurpose: ZHBEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A. 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. KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB AB is COMPLEX*16 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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 1. 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 (N) 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.

hbev - {hb,sb}ev: eig, QR iteration

Functions subroutine chbev (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info) CHBEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatrices subroutine dsbev (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info) DSBEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatrices subroutine ssbev (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info) SSBEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatrices subroutine zhbev (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info) ZHBEVcomputestheeigenvaluesand,optionally,theleftand/orrighteigenvectorsforOTHERmatrices