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Notice revision #20110804
- (global) TheBLACScontext handle.
- (global) Must be'A'or'V'or'I'.If, therange='A'functioncomputes all eigenvalues.If, therange='V'functioncomputes eigenvalues in the interval[.vl,vu]If, therange='I'functioncomputes eigenvaluesilthroughiu.
- (global) Must be'B'or'E'.If, the eigenvalues are to be ordered from smallest to largest within each split-off block.order='B'If, the eigenvalues for the entire matrix are to be ordered from smallest to largest.order='E'
- (global) The order of the tridiagonal matrixT(.n≥0)
- (global)If, therange='V'functioncomputes the lower and the upper bounds for the eigenvalues on the interval[.1,vu]Iforrange='A''I',vlandvuare not referenced.
- (global)Constraint:1≤.il≤iu≤nIf, the index of the smallest eigenvalue is returned forrange='I'iland of the largest eigenvalue foriu(assuming that the eigenvalues are in ascending order) must be returned.Iforrange='A''V',ilandiuare not referenced.
- (global)The absolute tolerance to which each eigenvalue is required. An eigenvalue (or cluster) is considered to have converged if it lies in an interval of widthabstol. If, then the tolerance is taken asabstol≤0ulp||T||, whereulpis the machine precision, and ||T|| means the 1-norm ofTEigenvalues will be computed most accurately whenabstolis set to the underflow thresholdslamch('U'), not 0. Note that if eigenvectors are desired later by inverse iteration (p?stein),abstolshould be set to2*.p?lamch('S')
- (global)Array of sizen.Containsndiagonal elements of the tridiagonal matrixT. To avoid overflow, the matrix must be scaled so that its largest entry is no greater than thein absolute value, and for greatest accuracy, it should not be much smaller than that.overflow(1/2)*underflow(1/4)
- (global)Array of size.n- 1Contains(off-diagonal elements of the tridiagonal matrixn-1)T. To avoid overflow, the matrix must be scaled so that its largest entry is no greater thanoverflowin absolute value, and for greatest accuracy, it should not be much smaller than that.(1/2)* underflow(1/4)
- (local)Array of sizemax(5. This is a workspace array.n, 7)
- (local) The size of theworkarray must be≥.max(5n, 7)If, thenlwork= -1lworkis global input and a workspace query is assumed; thefunctiononly calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued bypxerbla.
- (local) Array of sizemax(4. This is a workspace array.n, 14)
- (local) The size of theiworkarray must ≥.max(4n, 14,NPROCS)If, thenliwork= -1liworkis global input and a workspace query is assumed; thefunctiononly calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued bypxerbla.
- (global) The actual number of eigenvalues found.0≤m≤n
- (global) The number of diagonal blocks detected inT.1≤nsplit≤n
- (global)Array of sizen. On exit, the firstmelements ofwcontain the eigenvalues on all processes.
- (global)Array of sizen. At each row/columnjwheree[is zero or small, the matrixj-1]Tis considered to split into a block diagonal matrix. On exitiblock[specifies which block (from 1 to the number of blocks) the eigenvaluei]w[belongs to.i]In the (theoretically impossible) event that bisection does not converge for some or all eigenvalues,infois set to 1 and the ones for which it did not are identified by a negative block number.
- (global)Array of sizen.Contains the splitting points, at whichTbreaks up into submatrices. The first submatrix consists of rows/columns 1 toisplit, the second of rows/columnsthroughisplit+1, and so on, and theisplitnsplit-th submatrix consists of rows/columnsthroughisplit[+1nsplit-2]. (Only the firstisplit[=nsplit-1]nnsplitelements are used, but since thensplitvalues are not known,nwords must be reserved forisplit.)
- (global)If, the execution is successful.info= 0If, ifinfo< 0= -infoi, thei-th argument has an illegal value.If, some or all of the eigenvalues fail to converge or are not computed.info>0If, bisection fails to converge for some eigenvalues; these eigenvalues are flagged by a negative block number. The effect is that the eigenvalues may not be as accurate as the absolute and relative tolerances.info= 1If, mismatch between the number of eigenvalues output and the number desired.info= 2If:info= 3, and the Gershgorin interval initially used is incorrect. No eigenvalues are computed. Probable cause: the machine has a sloppy floating-point arithmetic. Increase therange='I'fudgeparameter, recompile, and try again.