TESTING/EIG/chet21.f(3)    Library Functions Manual    TESTING/EIG/chet21.f(3)

NAME
       TESTING/EIG/chet21.f

SYNOPSIS
   Functions/Subroutines
       subroutine chet21 (itype, uplo, n, kband, a, lda, d, e, u, ldu, v, ldv,
           tau, work, rwork, result)
           CHET21

Function/Subroutine Documentation
   subroutine chet21 (integer itype, character uplo, integer n, integer kband,
       complex, dimension( lda, * ) a, integer lda, real, dimension( * ) d,
       real, dimension( * ) e, complex, dimension( ldu, * ) u, integer ldu,
       complex, dimension( ldv, * ) v, integer ldv, complex, dimension( * )
       tau, complex, dimension( * ) work, real, dimension( * ) rwork, real,
       dimension( 2 ) result)
       CHET21

       Purpose:


            CHET21 generally checks a decomposition of the form

               A = U S U**H

            where **H means conjugate transpose, A is hermitian, U is unitary, and
            S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if
            KBAND=1).

            If ITYPE=1, then U is represented as a dense matrix; otherwise U is
            expressed as a product of Householder transformations, whose vectors
            are stored in the array 'V' and whose scaling constants are in 'TAU'.
            We shall use the letter 'V' to refer to the product of Householder
            transformations (which should be equal to U).

            Specifically, if ITYPE=1, then:

               RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
               RESULT(2) = | I - U U**H | / ( n ulp )

            If ITYPE=2, then:

               RESULT(1) = | A - V S V**H | / ( |A| n ulp )

            If ITYPE=3, then:

               RESULT(1) = | I - U V**H | / ( n ulp )

            For ITYPE > 1, the transformation U is expressed as a product
            V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)**H and each
            vector v(j) has its first j elements 0 and the remaining n-j elements
            stored in V(j+1:n,j).

       Parameters
           ITYPE

                     ITYPE is INTEGER
                     Specifies the type of tests to be performed.
                     1: U expressed as a dense unitary matrix:
                        RESULT(1) = | A - U S U**H | / ( |A| n ulp ) and
                        RESULT(2) = | I - U U**H | / ( n ulp )

                     2: U expressed as a product V of Housholder transformations:
                        RESULT(1) = | A - V S V**H | / ( |A| n ulp )

                     3: U expressed both as a dense unitary matrix and
                        as a product of Housholder transformations:
                        RESULT(1) = | I - U V**H | / ( n ulp )

           UPLO

                     UPLO is CHARACTER
                     If UPLO='U', the upper triangle of A and V will be used and
                     the (strictly) lower triangle will not be referenced.
                     If UPLO='L', the lower triangle of A and V will be used and
                     the (strictly) upper triangle will not be referenced.

           N

                     N is INTEGER
                     The size of the matrix.  If it is zero, CHET21 does nothing.
                     It must be at least zero.

           KBAND

                     KBAND is INTEGER
                     The bandwidth of the matrix.  It may only be zero or one.
                     If zero, then S is diagonal, and E is not referenced.  If
                     one, then S is symmetric tri-diagonal.

           A

                     A is COMPLEX array, dimension (LDA, N)
                     The original (unfactored) matrix.  It is assumed to be
                     hermitian, and only the upper (UPLO='U') or only the lower
                     (UPLO='L') will be referenced.

           LDA

                     LDA is INTEGER
                     The leading dimension of A.  It must be at least 1
                     and at least N.

           D

                     D is REAL array, dimension (N)
                     The diagonal of the (symmetric tri-) diagonal matrix.

           E

                     E is REAL array, dimension (N-1)
                     The off-diagonal of the (symmetric tri-) diagonal matrix.
                     E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and
                     (3,2) element, etc.
                     Not referenced if KBAND=0.

           U

                     U is COMPLEX array, dimension (LDU, N)
                     If ITYPE=1 or 3, this contains the unitary matrix in
                     the decomposition, expressed as a dense matrix.  If ITYPE=2,
                     then it is not referenced.

           LDU

                     LDU is INTEGER
                     The leading dimension of U.  LDU must be at least N and
                     at least 1.

           V

                     V is COMPLEX array, dimension (LDV, N)
                     If ITYPE=2 or 3, the columns of this array contain the
                     Householder vectors used to describe the unitary matrix
                     in the decomposition.  If UPLO='L', then the vectors are in
                     the lower triangle, if UPLO='U', then in the upper
                     triangle.
                     *NOTE* If ITYPE=2 or 3, V is modified and restored.  The
                     subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')
                     is set to one, and later reset to its original value, during
                     the course of the calculation.
                     If ITYPE=1, then it is neither referenced nor modified.

           LDV

                     LDV is INTEGER
                     The leading dimension of V.  LDV must be at least N and
                     at least 1.

           TAU

                     TAU is COMPLEX array, dimension (N)
                     If ITYPE >= 2, then TAU(j) is the scalar factor of
                     v(j) v(j)**H in the Householder transformation H(j) of
                     the product  U = H(1)...H(n-2)
                     If ITYPE < 2, then TAU is not referenced.

           WORK

                     WORK is COMPLEX array, dimension (2*N**2)

           RWORK

                     RWORK is REAL array, dimension (N)

           RESULT

                     RESULT is REAL array, dimension (2)
                     The values computed by the two tests described above.  The
                     values are currently limited to 1/ulp, to avoid overflow.
                     RESULT(1) is always modified.  RESULT(2) is modified only
                     if ITYPE=1.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 212 of file chet21.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/EIG/chet21.f(3)