SUBROUTINE CLAGGE( M, N, KL, KU, D, 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, KL, KU, LDA, M, N
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
REAL D( * )
COMPLEX A( LDA, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CLAGGE generates a complex general m by n matrix A, by pre- and post-
* multiplying a real diagonal matrix D with random unitary matrices:
* A = U*D*V. The lower and upper bandwidths may then be reduced to
* kl and ku by additional unitary transformations.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= 0.
*
* KL (input) INTEGER
* The number of nonzero subdiagonals within the band of A.
* 0 <= KL <= M-1.
*
* KU (input) INTEGER
* The number of nonzero superdiagonals within the band of A.
* 0 <= KU <= N-1.
*
* D (input) REAL array, dimension (min(M,N))
* The diagonal elements of the diagonal matrix D.
*
* A (output) COMPLEX array, dimension (LDA,N)
* The generated m by n matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= M.
*
* 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) COMPLEX array, dimension (M+N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO, ONE
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
$ ONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, J
REAL WN
COMPLEX TAU, WA, WB
* ..
* .. External Subroutines ..
EXTERNAL CGEMV, CGERC, CLACGV, CLARNV, CSCAL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, REAL
* ..
* .. External Functions ..
REAL SCNRM2
EXTERNAL SCNRM2
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
INFO = -3
ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -7
END IF
IF( INFO.LT.0 ) THEN
CALL XERBLA( 'CLAGGE', -INFO )
RETURN
END IF
*
* initialize A to diagonal matrix
*
DO 20 J = 1, N
DO 10 I = 1, M
A( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
DO 30 I = 1, MIN( M, N )
A( I, I ) = D( I )
30 CONTINUE
*
* pre- and post-multiply A by random unitary matrices
*
DO 40 I = MIN( M, N ), 1, -1
IF( I.LT.M ) THEN
*
* generate random reflection
*
CALL CLARNV( 3, ISEED, M-I+1, WORK )
WN = SCNRM2( M-I+1, WORK, 1 )
WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
IF( WN.EQ.ZERO ) THEN
TAU = ZERO
ELSE
WB = WORK( 1 ) + WA
CALL CSCAL( M-I, ONE / WB, WORK( 2 ), 1 )
WORK( 1 ) = ONE
TAU = REAL( WB / WA )
END IF
*
* multiply A(i:m,i:n) by random reflection from the left
*
CALL CGEMV( 'Conjugate transpose', M-I+1, N-I+1, ONE,
$ A( I, I ), LDA, WORK, 1, ZERO, WORK( M+1 ), 1 )
CALL CGERC( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1,
$ A( I, I ), LDA )
END IF
IF( I.LT.N ) THEN
*
* generate random reflection
*
CALL CLARNV( 3, ISEED, N-I+1, WORK )
WN = SCNRM2( N-I+1, WORK, 1 )
WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
IF( WN.EQ.ZERO ) THEN
TAU = ZERO
ELSE
WB = WORK( 1 ) + WA
CALL CSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
WORK( 1 ) = ONE
TAU = REAL( WB / WA )
END IF
*
* multiply A(i:m,i:n) by random reflection from the right
*
CALL CGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ),
$ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 )
CALL CGERC( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1,
$ A( I, I ), LDA )
END IF
40 CONTINUE
*
* Reduce number of subdiagonals to KL and number of superdiagonals
* to KU
*
DO 70 I = 1, MAX( M-1-KL, N-1-KU )
IF( KL.LE.KU ) THEN
*
* annihilate subdiagonal elements first (necessary if KL = 0)
*
IF( I.LE.MIN( M-1-KL, N ) ) THEN
*
* generate reflection to annihilate A(kl+i+1:m,i)
*
WN = SCNRM2( M-KL-I+1, A( KL+I, I ), 1 )
WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I )
IF( WN.EQ.ZERO ) THEN
TAU = ZERO
ELSE
WB = A( KL+I, I ) + WA
CALL CSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
A( KL+I, I ) = ONE
TAU = REAL( WB / WA )
END IF
*
* apply reflection to A(kl+i:m,i+1:n) from the left
*
CALL CGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE,
$ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
$ WORK, 1 )
CALL CGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK,
$ 1, A( KL+I, I+1 ), LDA )
A( KL+I, I ) = -WA
END IF
*
IF( I.LE.MIN( N-1-KU, M ) ) THEN
*
* generate reflection to annihilate A(i,ku+i+1:n)
*
WN = SCNRM2( N-KU-I+1, A( I, KU+I ), LDA )
WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I )
IF( WN.EQ.ZERO ) THEN
TAU = ZERO
ELSE
WB = A( I, KU+I ) + WA
CALL CSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
A( I, KU+I ) = ONE
TAU = REAL( WB / WA )
END IF
*
* apply reflection to A(i+1:m,ku+i:n) from the right
*
CALL CLACGV( N-KU-I+1, A( I, KU+I ), LDA )
CALL CGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
$ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
$ WORK, 1 )
CALL CGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
$ LDA, A( I+1, KU+I ), LDA )
A( I, KU+I ) = -WA
END IF
ELSE
*
* annihilate superdiagonal elements first (necessary if
* KU = 0)
*
IF( I.LE.MIN( N-1-KU, M ) ) THEN
*
* generate reflection to annihilate A(i,ku+i+1:n)
*
WN = SCNRM2( N-KU-I+1, A( I, KU+I ), LDA )
WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I )
IF( WN.EQ.ZERO ) THEN
TAU = ZERO
ELSE
WB = A( I, KU+I ) + WA
CALL CSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
A( I, KU+I ) = ONE
TAU = REAL( WB / WA )
END IF
*
* apply reflection to A(i+1:m,ku+i:n) from the right
*
CALL CLACGV( N-KU-I+1, A( I, KU+I ), LDA )
CALL CGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
$ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
$ WORK, 1 )
CALL CGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
$ LDA, A( I+1, KU+I ), LDA )
A( I, KU+I ) = -WA
END IF
*
IF( I.LE.MIN( M-1-KL, N ) ) THEN
*
* generate reflection to annihilate A(kl+i+1:m,i)
*
WN = SCNRM2( M-KL-I+1, A( KL+I, I ), 1 )
WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I )
IF( WN.EQ.ZERO ) THEN
TAU = ZERO
ELSE
WB = A( KL+I, I ) + WA
CALL CSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
A( KL+I, I ) = ONE
TAU = REAL( WB / WA )
END IF
*
* apply reflection to A(kl+i:m,i+1:n) from the left
*
CALL CGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE,
$ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
$ WORK, 1 )
CALL CGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK,
$ 1, A( KL+I, I+1 ), LDA )
A( KL+I, I ) = -WA
END IF
END IF
*
DO 50 J = KL + I + 1, M
A( J, I ) = ZERO
50 CONTINUE
*
DO 60 J = KU + I + 1, N
A( I, J ) = ZERO
60 CONTINUE
70 CONTINUE
RETURN
*
* End of CLAGGE
*
END