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SUBROUTINE <a name="CLACON.1"></a><a href="clacon.f.html#CLACON.1">CLACON</a>( N, V, X, EST, KASE )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER KASE, N
REAL EST
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> COMPLEX V( N ), X( N )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CLACON.18"></a><a href="clacon.f.html#CLACON.1">CLACON</a> estimates the 1-norm of a square, complex matrix A.
</span><span class="comment">*</span><span class="comment"> Reverse communication is used for evaluating matrix-vector products.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix. N >= 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> V (workspace) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment"> On the final return, V = A*W, where EST = norm(V)/norm(W)
</span><span class="comment">*</span><span class="comment"> (W is not returned).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> X (input/output) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment"> On an intermediate return, X should be overwritten by
</span><span class="comment">*</span><span class="comment"> A * X, if KASE=1,
</span><span class="comment">*</span><span class="comment"> A' * X, if KASE=2,
</span><span class="comment">*</span><span class="comment"> where A' is the conjugate transpose of A, and <a name="CLACON.35"></a><a href="clacon.f.html#CLACON.1">CLACON</a> must be
</span><span class="comment">*</span><span class="comment"> re-called with all the other parameters unchanged.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> EST (input/output) REAL
</span><span class="comment">*</span><span class="comment"> On entry with KASE = 1 or 2 and JUMP = 3, EST should be
</span><span class="comment">*</span><span class="comment"> unchanged from the previous call to <a name="CLACON.40"></a><a href="clacon.f.html#CLACON.1">CLACON</a>.
</span><span class="comment">*</span><span class="comment"> On exit, EST is an estimate (a lower bound) for norm(A).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KASE (input/output) INTEGER
</span><span class="comment">*</span><span class="comment"> On the initial call to <a name="CLACON.44"></a><a href="clacon.f.html#CLACON.1">CLACON</a>, KASE should be 0.
</span><span class="comment">*</span><span class="comment"> On an intermediate return, KASE will be 1 or 2, indicating
</span><span class="comment">*</span><span class="comment"> whether X should be overwritten by A * X or A' * X.
</span><span class="comment">*</span><span class="comment"> On the final return from <a name="CLACON.47"></a><a href="clacon.f.html#CLACON.1">CLACON</a>, KASE will again be 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ======= =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Contributed by Nick Higham, University of Manchester.
</span><span class="comment">*</span><span class="comment"> Originally named CONEST, dated March 16, 1988.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
</span><span class="comment">*</span><span class="comment"> a real or complex matrix, with applications to condition estimation",
</span><span class="comment">*</span><span class="comment"> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Last modified: April, 1999
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> INTEGER ITMAX
PARAMETER ( ITMAX = 5 )
REAL ONE, TWO
PARAMETER ( ONE = 1.0E0, TWO = 2.0E0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ),
$ CONE = ( 1.0E0, 0.0E0 ) )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, ITER, J, JLAST, JUMP
REAL ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> INTEGER <a name="ICMAX1.77"></a><a href="icmax1.f.html#ICMAX1.1">ICMAX1</a>
REAL <a name="SCSUM1.78"></a><a href="scsum1.f.html#SCSUM1.1">SCSUM1</a>, <a name="SLAMCH.78"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
EXTERNAL <a name="ICMAX1.79"></a><a href="icmax1.f.html#ICMAX1.1">ICMAX1</a>, <a name="SCSUM1.79"></a><a href="scsum1.f.html#SCSUM1.1">SCSUM1</a>, <a name="SLAMCH.79"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL CCOPY
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, AIMAG, CMPLX, REAL
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Save statement ..
</span> SAVE
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span> SAFMIN = <a name="SLAMCH.92"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'Safe minimum'</span> )
IF( KASE.EQ.0 ) THEN
DO 10 I = 1, N
X( I ) = CMPLX( ONE / REAL( N ) )
10 CONTINUE
KASE = 1
JUMP = 1
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span> GO TO ( 20, 40, 70, 90, 120 )JUMP
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ................ ENTRY (JUMP = 1)
</span><span class="comment">*</span><span class="comment"> FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
</span><span class="comment">*</span><span class="comment">
</span> 20 CONTINUE
IF( N.EQ.1 ) THEN
V( 1 ) = X( 1 )
EST = ABS( V( 1 ) )
<span class="comment">*</span><span class="comment"> ... QUIT
</span> GO TO 130
END IF
EST = <a name="SCSUM1.114"></a><a href="scsum1.f.html#SCSUM1.1">SCSUM1</a>( N, X, 1 )
<span class="comment">*</span><span class="comment">
</span> DO 30 I = 1, N
ABSXI = ABS( X( I ) )
IF( ABSXI.GT.SAFMIN ) THEN
X( I ) = CMPLX( REAL( X( I ) ) / ABSXI,
$ AIMAG( X( I ) ) / ABSXI )
ELSE
X( I ) = CONE
END IF
30 CONTINUE
KASE = 2
JUMP = 2
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ................ ENTRY (JUMP = 2)
</span><span class="comment">*</span><span class="comment"> FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
</span><span class="comment">*</span><span class="comment">
</span> 40 CONTINUE
J = <a name="ICMAX1.133"></a><a href="icmax1.f.html#ICMAX1.1">ICMAX1</a>( N, X, 1 )
ITER = 2
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
</span><span class="comment">*</span><span class="comment">
</span> 50 CONTINUE
DO 60 I = 1, N
X( I ) = CZERO
60 CONTINUE
X( J ) = CONE
KASE = 1
JUMP = 3
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ................ ENTRY (JUMP = 3)
</span><span class="comment">*</span><span class="comment"> X HAS BEEN OVERWRITTEN BY A*X.
</span><span class="comment">*</span><span class="comment">
</span> 70 CONTINUE
CALL CCOPY( N, X, 1, V, 1 )
ESTOLD = EST
EST = <a name="SCSUM1.153"></a><a href="scsum1.f.html#SCSUM1.1">SCSUM1</a>( N, V, 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TEST FOR CYCLING.
</span> IF( EST.LE.ESTOLD )
$ GO TO 100
<span class="comment">*</span><span class="comment">
</span> DO 80 I = 1, N
ABSXI = ABS( X( I ) )
IF( ABSXI.GT.SAFMIN ) THEN
X( I ) = CMPLX( REAL( X( I ) ) / ABSXI,
$ AIMAG( X( I ) ) / ABSXI )
ELSE
X( I ) = CONE
END IF
80 CONTINUE
KASE = 2
JUMP = 4
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ................ ENTRY (JUMP = 4)
</span><span class="comment">*</span><span class="comment"> X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
</span><span class="comment">*</span><span class="comment">
</span> 90 CONTINUE
JLAST = J
J = <a name="ICMAX1.177"></a><a href="icmax1.f.html#ICMAX1.1">ICMAX1</a>( N, X, 1 )
IF( ( ABS( X( JLAST ) ).NE.ABS( X( J ) ) ) .AND.
$ ( ITER.LT.ITMAX ) ) THEN
ITER = ITER + 1
GO TO 50
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ITERATION COMPLETE. FINAL STAGE.
</span><span class="comment">*</span><span class="comment">
</span> 100 CONTINUE
ALTSGN = ONE
DO 110 I = 1, N
X( I ) = CMPLX( ALTSGN*( ONE+REAL( I-1 ) / REAL( N-1 ) ) )
ALTSGN = -ALTSGN
110 CONTINUE
KASE = 1
JUMP = 5
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ................ ENTRY (JUMP = 5)
</span><span class="comment">*</span><span class="comment"> X HAS BEEN OVERWRITTEN BY A*X.
</span><span class="comment">*</span><span class="comment">
</span> 120 CONTINUE
TEMP = TWO*( <a name="SCSUM1.200"></a><a href="scsum1.f.html#SCSUM1.1">SCSUM1</a>( N, X, 1 ) / REAL( 3*N ) )
IF( TEMP.GT.EST ) THEN
CALL CCOPY( N, X, 1, V, 1 )
EST = TEMP
END IF
<span class="comment">*</span><span class="comment">
</span> 130 CONTINUE
KASE = 0
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="CLACON.210"></a><a href="clacon.f.html#CLACON.1">CLACON</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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