119 lines
3.3 KiB
FortranFixed
119 lines
3.3 KiB
FortranFixed
SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO )
|
|
*
|
|
* -- LAPACK auxiliary test routine (version 3.1)
|
|
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
|
|
* November 2006
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, LDA, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER ISEED( 4 )
|
|
DOUBLE PRECISION A( LDA, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* DLARGE pre- and post-multiplies a real general n by n matrix A
|
|
* with a random orthogonal matrix: A = U*D*U'.
|
|
*
|
|
* Arguments
|
|
* =========
|
|
*
|
|
* N (input) INTEGER
|
|
* The order of the matrix A. N >= 0.
|
|
*
|
|
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
|
|
* On entry, the original n by n matrix A.
|
|
* On exit, A is overwritten by U*A*U' for some random
|
|
* orthogonal matrix U.
|
|
*
|
|
* LDA (input) INTEGER
|
|
* The leading dimension of the array A. LDA >= N.
|
|
*
|
|
* ISEED (input/output) INTEGER array, dimension (4)
|
|
* On entry, the seed of the random number generator; the array
|
|
* elements must be between 0 and 4095, and ISEED(4) must be
|
|
* odd.
|
|
* On exit, the seed is updated.
|
|
*
|
|
* WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
|
|
*
|
|
* INFO (output) INTEGER
|
|
* = 0: successful exit
|
|
* < 0: if INFO = -i, the i-th argument had an illegal value
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I
|
|
DOUBLE PRECISION TAU, WA, WB, WN
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DGEMV, DGER, DLARNV, DSCAL, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX, SIGN
|
|
* ..
|
|
* .. External Functions ..
|
|
DOUBLE PRECISION DNRM2
|
|
EXTERNAL DNRM2
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input arguments
|
|
*
|
|
INFO = 0
|
|
IF( N.LT.0 ) THEN
|
|
INFO = -1
|
|
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
|
|
INFO = -3
|
|
END IF
|
|
IF( INFO.LT.0 ) THEN
|
|
CALL XERBLA( 'DLARGE', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* pre- and post-multiply A by random orthogonal matrix
|
|
*
|
|
DO 10 I = N, 1, -1
|
|
*
|
|
* generate random reflection
|
|
*
|
|
CALL DLARNV( 3, ISEED, N-I+1, WORK )
|
|
WN = DNRM2( N-I+1, WORK, 1 )
|
|
WA = SIGN( WN, WORK( 1 ) )
|
|
IF( WN.EQ.ZERO ) THEN
|
|
TAU = ZERO
|
|
ELSE
|
|
WB = WORK( 1 ) + WA
|
|
CALL DSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
|
|
WORK( 1 ) = ONE
|
|
TAU = WB / WA
|
|
END IF
|
|
*
|
|
* multiply A(i:n,1:n) by random reflection from the left
|
|
*
|
|
CALL DGEMV( 'Transpose', N-I+1, N, ONE, A( I, 1 ), LDA, WORK,
|
|
$ 1, ZERO, WORK( N+1 ), 1 )
|
|
CALL DGER( N-I+1, N, -TAU, WORK, 1, WORK( N+1 ), 1, A( I, 1 ),
|
|
$ LDA )
|
|
*
|
|
* multiply A(1:n,i:n) by random reflection from the right
|
|
*
|
|
CALL DGEMV( 'No transpose', N, N-I+1, ONE, A( 1, I ), LDA,
|
|
$ WORK, 1, ZERO, WORK( N+1 ), 1 )
|
|
CALL DGER( N, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, A( 1, I ),
|
|
$ LDA )
|
|
10 CONTINUE
|
|
RETURN
|
|
*
|
|
* End of DLARGE
|
|
*
|
|
END
|