LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ shst01()

subroutine shst01 ( integer  N,
integer  ILO,
integer  IHI,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldh, * )  H,
integer  LDH,
real, dimension( ldq, * )  Q,
integer  LDQ,
real, dimension( lwork )  WORK,
integer  LWORK,
real, dimension( 2 )  RESULT 
)

SHST01

Purpose:
 SHST01 tests the reduction of a general matrix A to upper Hessenberg
 form:  A = Q*H*Q'.  Two test ratios are computed;

 RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
 RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )

 The matrix Q is assumed to be given explicitly as it would be
 following SGEHRD + SORGHR.

 In this version, ILO and IHI are not used and are assumed to be 1 and
 N, respectively.
Parameters
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]ILO
          ILO is INTEGER
[in]IHI
          IHI is INTEGER

          A is assumed to be upper triangular in rows and columns
          1:ILO-1 and IHI+1:N, so Q differs from the identity only in
          rows and columns ILO+1:IHI.
[in]A
          A is REAL array, dimension (LDA,N)
          The original n by n matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]H
          H is REAL array, dimension (LDH,N)
          The upper Hessenberg matrix H from the reduction A = Q*H*Q'
          as computed by SGEHRD.  H is assumed to be zero below the
          first subdiagonal.
[in]LDH
          LDH is INTEGER
          The leading dimension of the array H.  LDH >= max(1,N).
[in]Q
          Q is REAL array, dimension (LDQ,N)
          The orthogonal matrix Q from the reduction A = Q*H*Q' as
          computed by SGEHRD + SORGHR.
[in]LDQ
          LDQ is INTEGER
          The leading dimension of the array Q.  LDQ >= max(1,N).
[out]WORK
          WORK is REAL array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= 2*N*N.
[out]RESULT
          RESULT is REAL array, dimension (2)
          RESULT(1) = norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( N * EPS )
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 132 of file shst01.f.

134 *
135 * -- LAPACK test routine --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 *
139 * .. Scalar Arguments ..
140  INTEGER IHI, ILO, LDA, LDH, LDQ, LWORK, N
141 * ..
142 * .. Array Arguments ..
143  REAL A( LDA, * ), H( LDH, * ), Q( LDQ, * ),
144  $ RESULT( 2 ), WORK( LWORK )
145 * ..
146 *
147 * =====================================================================
148 *
149 * .. Parameters ..
150  REAL ONE, ZERO
151  parameter( one = 1.0e+0, zero = 0.0e+0 )
152 * ..
153 * .. Local Scalars ..
154  INTEGER LDWORK
155  REAL ANORM, EPS, OVFL, SMLNUM, UNFL, WNORM
156 * ..
157 * .. External Functions ..
158  REAL SLAMCH, SLANGE
159  EXTERNAL slamch, slange
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL sgemm, slabad, slacpy, sort01
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC max, min
166 * ..
167 * .. Executable Statements ..
168 *
169 * Quick return if possible
170 *
171  IF( n.LE.0 ) THEN
172  result( 1 ) = zero
173  result( 2 ) = zero
174  RETURN
175  END IF
176 *
177  unfl = slamch( 'Safe minimum' )
178  eps = slamch( 'Precision' )
179  ovfl = one / unfl
180  CALL slabad( unfl, ovfl )
181  smlnum = unfl*n / eps
182 *
183 * Test 1: Compute norm( A - Q*H*Q' ) / ( norm(A) * N * EPS )
184 *
185 * Copy A to WORK
186 *
187  ldwork = max( 1, n )
188  CALL slacpy( ' ', n, n, a, lda, work, ldwork )
189 *
190 * Compute Q*H
191 *
192  CALL sgemm( 'No transpose', 'No transpose', n, n, n, one, q, ldq,
193  $ h, ldh, zero, work( ldwork*n+1 ), ldwork )
194 *
195 * Compute A - Q*H*Q'
196 *
197  CALL sgemm( 'No transpose', 'Transpose', n, n, n, -one,
198  $ work( ldwork*n+1 ), ldwork, q, ldq, one, work,
199  $ ldwork )
200 *
201  anorm = max( slange( '1', n, n, a, lda, work( ldwork*n+1 ) ),
202  $ unfl )
203  wnorm = slange( '1', n, n, work, ldwork, work( ldwork*n+1 ) )
204 *
205 * Note that RESULT(1) cannot overflow and is bounded by 1/(N*EPS)
206 *
207  result( 1 ) = min( wnorm, anorm ) / max( smlnum, anorm*eps ) / n
208 *
209 * Test 2: Compute norm( I - Q'*Q ) / ( N * EPS )
210 *
211  CALL sort01( 'Columns', n, n, q, ldq, work, lwork, result( 2 ) )
212 *
213  RETURN
214 *
215 * End of SHST01
216 *
subroutine slabad(SMALL, LARGE)
SLABAD
Definition: slabad.f:74
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
subroutine sort01(ROWCOL, M, N, U, LDU, WORK, LWORK, RESID)
SORT01
Definition: sort01.f:116
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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