LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ chet22()

subroutine chet22 ( integer  ITYPE,
character  UPLO,
integer  N,
integer  M,
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 
)

CHET22

Purpose:
      CHET22  generally checks a decomposition of the form

              A U = U S

      where A is complex Hermitian, 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**H A U - S | / ( |A| m ulp ) and
              RESULT(2) = | I - U**H 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**H | / ( |A| n ulp )  and
             RESULT(2) = | I - U U**H | / ( 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, CHET22 does nothing.
          It must be at least zero.
          Not modified.

  M       INTEGER
          The number of columns of U.  If it is zero, CHET22 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       COMPLEX 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       COMPLEX array, dimension (LDU, N)
          If ITYPE=1, this contains the orthogonal matrix in
          the decomposition, expressed as a dense matrix.
          Not modified.

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

  V       COMPLEX 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     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.
          Not modified.

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

  RWORK   REAL array, dimension (N)
          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 159 of file chet22.f.

161 *
162 * -- LAPACK test routine --
163 * -- LAPACK is a software package provided by Univ. of Tennessee, --
164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 *
166 * .. Scalar Arguments ..
167  CHARACTER UPLO
168  INTEGER ITYPE, KBAND, LDA, LDU, LDV, M, N
169 * ..
170 * .. Array Arguments ..
171  REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
172  COMPLEX A( LDA, * ), TAU( * ), U( LDU, * ),
173  $ V( LDV, * ), WORK( * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Parameters ..
179  REAL ZERO, ONE
180  parameter( zero = 0.0e0, one = 1.0e0 )
181  COMPLEX CZERO, CONE
182  parameter( czero = ( 0.0e0, 0.0e0 ),
183  $ cone = ( 1.0e0, 0.0e0 ) )
184 * ..
185 * .. Local Scalars ..
186  INTEGER J, JJ, JJ1, JJ2, NN, NNP1
187  REAL ANORM, ULP, UNFL, WNORM
188 * ..
189 * .. External Functions ..
190  REAL CLANHE, SLAMCH
191  EXTERNAL clanhe, slamch
192 * ..
193 * .. External Subroutines ..
194  EXTERNAL cgemm, chemm
195 * ..
196 * .. Intrinsic Functions ..
197  INTRINSIC max, min, real
198 * ..
199 * .. Executable Statements ..
200 *
201  result( 1 ) = zero
202  result( 2 ) = zero
203  IF( n.LE.0 .OR. m.LE.0 )
204  $ RETURN
205 *
206  unfl = slamch( 'Safe minimum' )
207  ulp = slamch( 'Precision' )
208 *
209 * Do Test 1
210 *
211 * Norm of A:
212 *
213  anorm = max( clanhe( '1', uplo, n, a, lda, rwork ), unfl )
214 *
215 * Compute error matrix:
216 *
217 * ITYPE=1: error = U**H A U - S
218 *
219  CALL chemm( 'L', uplo, n, m, cone, a, lda, u, ldu, czero, work,
220  $ n )
221  nn = n*n
222  nnp1 = nn + 1
223  CALL cgemm( 'C', 'N', m, m, n, cone, u, ldu, work, n, czero,
224  $ work( nnp1 ), n )
225  DO 10 j = 1, m
226  jj = nn + ( j-1 )*n + j
227  work( jj ) = work( jj ) - d( j )
228  10 CONTINUE
229  IF( kband.EQ.1 .AND. n.GT.1 ) THEN
230  DO 20 j = 2, m
231  jj1 = nn + ( j-1 )*n + j - 1
232  jj2 = nn + ( j-2 )*n + j
233  work( jj1 ) = work( jj1 ) - e( j-1 )
234  work( jj2 ) = work( jj2 ) - e( j-1 )
235  20 CONTINUE
236  END IF
237  wnorm = clanhe( '1', uplo, m, work( nnp1 ), n, rwork )
238 *
239  IF( anorm.GT.wnorm ) THEN
240  result( 1 ) = ( wnorm / anorm ) / ( m*ulp )
241  ELSE
242  IF( anorm.LT.one ) THEN
243  result( 1 ) = ( min( wnorm, m*anorm ) / anorm ) / ( m*ulp )
244  ELSE
245  result( 1 ) = min( wnorm / anorm, real( m ) ) / ( m*ulp )
246  END IF
247  END IF
248 *
249 * Do Test 2
250 *
251 * Compute U**H U - I
252 *
253  IF( itype.EQ.1 )
254  $ CALL cunt01( 'Columns', n, m, u, ldu, work, 2*n*n, rwork,
255  $ result( 2 ) )
256 *
257  RETURN
258 *
259 * End of CHET22
260 *
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine chemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CHEMM
Definition: chemm.f:191
subroutine cunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
CUNT01
Definition: cunt01.f:126
real function clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhe.f:124
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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