LAPACK  3.9.0
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.
Date
December 2016

Definition at line 163 of file chet22.f.

163 *
164 * -- LAPACK test routine (version 3.7.0) --
165 * -- LAPACK is a software package provided by Univ. of Tennessee, --
166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
167 * December 2016
168 *
169 * .. Scalar Arguments ..
170  CHARACTER UPLO
171  INTEGER ITYPE, KBAND, LDA, LDU, LDV, M, N
172 * ..
173 * .. Array Arguments ..
174  REAL D( * ), E( * ), RESULT( 2 ), RWORK( * )
175  COMPLEX A( LDA, * ), TAU( * ), U( LDU, * ),
176  $ V( LDV, * ), WORK( * )
177 * ..
178 *
179 * =====================================================================
180 *
181 * .. Parameters ..
182  REAL ZERO, ONE
183  parameter( zero = 0.0e0, one = 1.0e0 )
184  COMPLEX CZERO, CONE
185  parameter( czero = ( 0.0e0, 0.0e0 ),
186  $ cone = ( 1.0e0, 0.0e0 ) )
187 * ..
188 * .. Local Scalars ..
189  INTEGER J, JJ, JJ1, JJ2, NN, NNP1
190  REAL ANORM, ULP, UNFL, WNORM
191 * ..
192 * .. External Functions ..
193  REAL CLANHE, SLAMCH
194  EXTERNAL clanhe, slamch
195 * ..
196 * .. External Subroutines ..
197  EXTERNAL cgemm, chemm
198 * ..
199 * .. Intrinsic Functions ..
200  INTRINSIC max, min, real
201 * ..
202 * .. Executable Statements ..
203 *
204  result( 1 ) = zero
205  result( 2 ) = zero
206  IF( n.LE.0 .OR. m.LE.0 )
207  $ RETURN
208 *
209  unfl = slamch( 'Safe minimum' )
210  ulp = slamch( 'Precision' )
211 *
212 * Do Test 1
213 *
214 * Norm of A:
215 *
216  anorm = max( clanhe( '1', uplo, n, a, lda, rwork ), unfl )
217 *
218 * Compute error matrix:
219 *
220 * ITYPE=1: error = U**H A U - S
221 *
222  CALL chemm( 'L', uplo, n, m, cone, a, lda, u, ldu, czero, work,
223  $ n )
224  nn = n*n
225  nnp1 = nn + 1
226  CALL cgemm( 'C', 'N', m, m, n, cone, u, ldu, work, n, czero,
227  $ work( nnp1 ), n )
228  DO 10 j = 1, m
229  jj = nn + ( j-1 )*n + j
230  work( jj ) = work( jj ) - d( j )
231  10 CONTINUE
232  IF( kband.EQ.1 .AND. n.GT.1 ) THEN
233  DO 20 j = 2, m
234  jj1 = nn + ( j-1 )*n + j - 1
235  jj2 = nn + ( j-2 )*n + j
236  work( jj1 ) = work( jj1 ) - e( j-1 )
237  work( jj2 ) = work( jj2 ) - e( j-1 )
238  20 CONTINUE
239  END IF
240  wnorm = clanhe( '1', uplo, m, work( nnp1 ), n, rwork )
241 *
242  IF( anorm.GT.wnorm ) THEN
243  result( 1 ) = ( wnorm / anorm ) / ( m*ulp )
244  ELSE
245  IF( anorm.LT.one ) THEN
246  result( 1 ) = ( min( wnorm, m*anorm ) / anorm ) / ( m*ulp )
247  ELSE
248  result( 1 ) = min( wnorm / anorm, real( m ) ) / ( m*ulp )
249  END IF
250  END IF
251 *
252 * Do Test 2
253 *
254 * Compute U**H U - I
255 *
256  IF( itype.EQ.1 )
257  $ CALL cunt01( 'Columns', n, m, u, ldu, work, 2*n*n, rwork,
258  $ result( 2 ) )
259 *
260  RETURN
261 *
262 * End of CHET22
263 *
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cgemm
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:189
chemm
subroutine chemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CHEMM
Definition: chemm.f:193
clanhe
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:126
cunt01
subroutine cunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
CUNT01
Definition: cunt01.f:128
slamch
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:70