LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zhet22 ( integer ITYPE, character UPLO, integer N, integer M, integer KBAND, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) D, double precision, dimension( * ) E, complex*16, dimension( ldu, * ) U, integer LDU, complex*16, dimension( ldv, * ) V, integer LDV, complex*16, dimension( * ) TAU, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, double precision, dimension( 2 ) RESULT )

ZHET22

Purpose:
```      ZHET22  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' A U - S | / ( |A| m ulp ) *andC>              RESULT(2) = | I - U'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' | / ( |A| n ulp )   *andC>             RESULT(2) = | I - UU' | / ( 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, ZHET22 does nothing.
It must be at least zero.
Not modified.

M       INTEGER
The number of columns of U.  If it is zero, ZHET22 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*16 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       DOUBLE PRECISION array, dimension (N)
The diagonal of the (symmetric tri-) diagonal matrix.
Not modified.

E       DOUBLE PRECISION 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*16 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*16 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*16 array, dimension (N)
If ITYPE >= 2, then TAU(j) is the scalar factor of
v(j) v(j)' 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*16 array, dimension (2*N**2)
Workspace.
Modified.

RWORK   DOUBLE PRECISION array, dimension (N)
Workspace.
Modified.

RESULT  DOUBLE PRECISION 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.```
Date
November 2011

Definition at line 161 of file zhet22.f.

161 *
162 * -- LAPACK test routine (version 3.4.0) --
163 * -- LAPACK is a software package provided by Univ. of Tennessee, --
164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 * November 2011
166 *
167 * .. Scalar Arguments ..
168  CHARACTER uplo
169  INTEGER itype, kband, lda, ldu, ldv, m, n
170 * ..
171 * .. Array Arguments ..
172  DOUBLE PRECISION d( * ), e( * ), result( 2 ), rwork( * )
173  COMPLEX*16 a( lda, * ), tau( * ), u( ldu, * ),
174  \$ v( ldv, * ), work( * )
175 * ..
176 *
177 * =====================================================================
178 *
179 * .. Parameters ..
180  DOUBLE PRECISION zero, one
181  parameter ( zero = 0.0d0, one = 1.0d0 )
182  COMPLEX*16 czero, cone
183  parameter ( czero = ( 0.0d0, 0.0d0 ),
184  \$ cone = ( 1.0d0, 0.0d0 ) )
185 * ..
186 * .. Local Scalars ..
187  INTEGER j, jj, jj1, jj2, nn, nnp1
188  DOUBLE PRECISION anorm, ulp, unfl, wnorm
189 * ..
190 * .. External Functions ..
191  DOUBLE PRECISION dlamch, zlanhe
192  EXTERNAL dlamch, zlanhe
193 * ..
194 * .. External Subroutines ..
195  EXTERNAL zgemm, zhemm, zunt01
196 * ..
197 * .. Intrinsic Functions ..
198  INTRINSIC dble, max, min
199 * ..
200 * .. Executable Statements ..
201 *
202  result( 1 ) = zero
203  result( 2 ) = zero
204  IF( n.LE.0 .OR. m.LE.0 )
205  \$ RETURN
206 *
207  unfl = dlamch( 'Safe minimum' )
208  ulp = dlamch( 'Precision' )
209 *
210 * Do Test 1
211 *
212 * Norm of A:
213 *
214  anorm = max( zlanhe( '1', uplo, n, a, lda, rwork ), unfl )
215 *
216 * Compute error matrix:
217 *
218 * ITYPE=1: error = U' A U - S
219 *
220  CALL zhemm( 'L', uplo, n, m, cone, a, lda, u, ldu, czero, work,
221  \$ n )
222  nn = n*n
223  nnp1 = nn + 1
224  CALL zgemm( 'C', 'N', m, m, n, cone, u, ldu, work, n, czero,
225  \$ work( nnp1 ), n )
226  DO 10 j = 1, m
227  jj = nn + ( j-1 )*n + j
228  work( jj ) = work( jj ) - d( j )
229  10 CONTINUE
230  IF( kband.EQ.1 .AND. n.GT.1 ) THEN
231  DO 20 j = 2, m
232  jj1 = nn + ( j-1 )*n + j - 1
233  jj2 = nn + ( j-2 )*n + j
234  work( jj1 ) = work( jj1 ) - e( j-1 )
235  work( jj2 ) = work( jj2 ) - e( j-1 )
236  20 CONTINUE
237  END IF
238  wnorm = zlanhe( '1', uplo, m, work( nnp1 ), n, rwork )
239 *
240  IF( anorm.GT.wnorm ) THEN
241  result( 1 ) = ( wnorm / anorm ) / ( m*ulp )
242  ELSE
243  IF( anorm.LT.one ) THEN
244  result( 1 ) = ( min( wnorm, m*anorm ) / anorm ) / ( m*ulp )
245  ELSE
246  result( 1 ) = min( wnorm / anorm, dble( m ) ) / ( m*ulp )
247  END IF
248  END IF
249 *
250 * Do Test 2
251 *
252 * Compute U'U - I
253 *
254  IF( itype.EQ.1 )
255  \$ CALL zunt01( 'Columns', n, m, u, ldu, work, 2*n*n, rwork,
256  \$ result( 2 ) )
257 *
258  RETURN
259 *
260 * End of ZHET22
261 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
double precision function zlanhe(NORM, UPLO, N, A, LDA, WORK)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
Definition: zlanhe.f:126
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
subroutine zunt01(ROWCOL, M, N, U, LDU, WORK, LWORK, RWORK, RESID)
ZUNT01
Definition: zunt01.f:128
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:193

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