Visible to Intel only — GUID: GUID-EDCE0EF0-7E02-4287-9A2A-53668140F604
Visible to Intel only — GUID: GUID-EDCE0EF0-7E02-4287-9A2A-53668140F604
?upgtr
Generates the complex unitary matrix Q determined by ?hptrd.
Syntax
call cupgtr(uplo, n, ap, tau, q, ldq, work, info)
call zupgtr(uplo, n, ap, tau, q, ldq, work, info)
call upgtr(ap, tau, q [,uplo] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine explicitly generates the n-by-n unitary matrix Q formed by hptrd when reducing a packed complex Hermitian matrix A to tridiagonal form: A = Q*T*QH. Use this routine after a call to ?hptrd.
Input Parameters
- uplo
-
CHARACTER*1. Must be 'U' or 'L'. Use the same uplo as supplied to ?hptrd.
- n
-
INTEGER. The order of the matrix Q (n≥ 0).
- ap, tau
-
COMPLEX for cupgtr
DOUBLE COMPLEX for zupgtr.
Arrays ap and tau, as returned by ?hptrd.
The dimension of ap must be at least max(1, n(n+1)/2).
The dimension of tau must be at least max(1, n-1).
- ldq
-
INTEGER. The leading dimension of the output array q;
at least max(1, n).
- work
-
COMPLEX for cupgtr
DOUBLE COMPLEX for zupgtr.
Workspace array, size at least max(1, n-1).
Output Parameters
- q
-
COMPLEX for cupgtr
DOUBLE COMPLEX for zupgtr.
Array, size (ldq,*) .
Contains the computed matrix Q.
The second dimension of q must be at least max(1, n).
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine upgtr interface are the following:
- ap
-
Holds the array A of size (n*(n+1)/2).
- tau
-
Holds the vector with the number of elements n - 1.
- q
-
Holds the matrix Q of size (n,n).
- uplo
-
Must be 'U' or 'L'. The default value is 'U'.
Application Notes
The computed matrix Q differs from an exactly orthogonal matrix by a matrix E such that ||E||2 = O(ε), where ε is the machine precision.
The approximate number of floating-point operations is (16/3)n3.
The real counterpart of this routine is opgtr.