LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ 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
Here is the call graph for this function:
Here is the caller graph for this function: