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SUBROUTINE <a name="CLACN2.1"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>( N, V, X, EST, KASE, ISAVE )
<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> INTEGER ISAVE( 3 )
COMPLEX V( * ), X( * )
<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="CLACN2.19"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</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="CLACN2.36"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</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 ISAVE(1) = 3, EST should be
</span><span class="comment">*</span><span class="comment"> unchanged from the previous call to <a name="CLACN2.41"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</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="CLACN2.45"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</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="CLACN2.48"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>, KASE will again be 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ISAVE (input/output) INTEGER array, dimension (3)
</span><span class="comment">*</span><span class="comment"> ISAVE is used to save variables between calls to <a name="SLACN2.51"></a><a href="slacn2.f.html#SLACN2.1">SLACN2</a>
</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"> This is a thread safe version of <a name="CLACON.65"></a><a href="clacon.f.html#CLACON.1">CLACON</a>, which uses the array ISAVE
</span><span class="comment">*</span><span class="comment"> in place of a SAVE statement, as follows:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CLACON.68"></a><a href="clacon.f.html#CLACON.1">CLACON</a> <a name="CLACN2.68"></a><a href="clacn2.f.html#CLACN2.1">CLACN2</a>
</span><span class="comment">*</span><span class="comment"> JUMP ISAVE(1)
</span><span class="comment">*</span><span class="comment"> J ISAVE(2)
</span><span class="comment">*</span><span class="comment"> ITER ISAVE(3)
</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, JLAST
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="ICMAX1.89"></a><a href="icmax1.f.html#ICMAX1.1">ICMAX1</a>
REAL <a name="SCSUM1.90"></a><a href="scsum1.f.html#SCSUM1.1">SCSUM1</a>, <a name="SLAMCH.90"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
EXTERNAL <a name="ICMAX1.91"></a><a href="icmax1.f.html#ICMAX1.1">ICMAX1</a>, <a name="SCSUM1.91"></a><a href="scsum1.f.html#SCSUM1.1">SCSUM1</a>, <a name="SLAMCH.91"></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"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span> SAFMIN = <a name="SLAMCH.101"></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 ) )
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