TESTING/EIG/ssyt22.f(3)    Library Functions Manual    TESTING/EIG/ssyt22.f(3)

NAME
       TESTING/EIG/ssyt22.f

SYNOPSIS
   Functions/Subroutines
       subroutine ssyt22 (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v,
           ldv, tau, work, result)
           SSYT22

Function/Subroutine Documentation
   subroutine ssyt22 (integer itype, character uplo, integer n, integer m,
       integer kband, real, dimension( lda, * ) a, integer lda, real,
       dimension( * ) d, real, dimension( * ) e, real, dimension( ldu, * ) u,
       integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension(
       * ) tau, real, dimension( * ) work, real, dimension( 2 ) result)
       SSYT22

       Purpose:


                 SSYT22  generally checks a decomposition of the form

                         A U = U S

                 where A is symmetric, the columns of U are orthonormal, and S
                 is diagonal (if KBAND=0) or symmetric tridiagonal (if
                 KBAND=1).  If ITYPE=1, then U is represented as a dense matrix,
                 otherwise the 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) = | U**T A U - S | / ( |A| m ulp ) and
                         RESULT(2) = | I - U**T U | / ( m ulp )

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

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

             N       INTEGER
                     The size of the matrix.  If it is zero, SSYT22 does nothing.
                     It must be at least zero.
                     Not modified.

             M       INTEGER
                     The number of columns of U.  If it is zero, SSYT22 does
                     nothing.  It must be at least zero.
                     Not modified.

             KBAND   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.
                     Not modified.

             A       REAL array, dimension (LDA , N)
                     The original (unfactored) matrix.  It is assumed to be
                     symmetric, and only the upper (UPLO='U') or only the lower
                     (UPLO='L') will be referenced.
                     Not modified.

             LDA     INTEGER
                     The leading dimension of A.  It must be at least 1
                     and at least N.
                     Not modified.

             D       REAL array, dimension (N)
                     The diagonal of the (symmetric tri-) diagonal matrix.
                     Not modified.

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

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

             LDU     INTEGER
                     The leading dimension of U.  LDU must be at least N and
                     at least 1.
                     Not modified.

             V       REAL array, dimension (LDV, N)
                     If ITYPE=2 or 3, the lower triangle of this array contains
                     the Householder vectors used to describe the orthogonal
                     matrix in the decomposition.  If ITYPE=1, then it is not
                     referenced.
                     Not modified.

             LDV     INTEGER
                     The leading dimension of V.  LDV must be at least N and
                     at least 1.
                     Not modified.

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

             WORK    REAL array, dimension (2*N**2)
                     Workspace.
                     Modified.

             RESULT  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 LDU is at least N.
                     Modified.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 155 of file ssyt22.f.

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

LAPACK                          Version 3.12.0         TESTING/EIG/ssyt22.f(3)