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REAL FUNCTION <a name="CLANTR.1"></a><a href="clantr.f.html#CLANTR.1">CLANTR</a>( NORM, UPLO, DIAG, M, N, A, LDA,
$ WORK )
<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> CHARACTER DIAG, NORM, UPLO
INTEGER LDA, M, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL WORK( * )
COMPLEX A( LDA, * )
<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="CLANTR.20"></a><a href="clantr.f.html#CLANTR.1">CLANTR</a> returns the value of the one norm, or the Frobenius norm, or
</span><span class="comment">*</span><span class="comment"> the infinity norm, or the element of largest absolute value of a
</span><span class="comment">*</span><span class="comment"> trapezoidal or triangular matrix A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Description
</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="CLANTR.27"></a><a href="clantr.f.html#CLANTR.1">CLANTR</a> returns the value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CLANTR.29"></a><a href="clantr.f.html#CLANTR.1">CLANTR</a> = ( max(abs(A(i,j))), NORM = 'M' or 'm'
</span><span class="comment">*</span><span class="comment"> (
</span><span class="comment">*</span><span class="comment"> ( norm1(A), NORM = '1', 'O' or 'o'
</span><span class="comment">*</span><span class="comment"> (
</span><span class="comment">*</span><span class="comment"> ( normI(A), NORM = 'I' or 'i'
</span><span class="comment">*</span><span class="comment"> (
</span><span class="comment">*</span><span class="comment"> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where norm1 denotes the one norm of a matrix (maximum column sum),
</span><span class="comment">*</span><span class="comment"> normI denotes the infinity norm of a matrix (maximum row sum) and
</span><span class="comment">*</span><span class="comment"> normF denotes the Frobenius norm of a matrix (square root of sum of
</span><span class="comment">*</span><span class="comment"> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
</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"> NORM (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies the value to be returned in <a name="CLANTR.46"></a><a href="clantr.f.html#CLANTR.1">CLANTR</a> as described
</span><span class="comment">*</span><span class="comment"> above.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether the matrix A is upper or lower trapezoidal.
</span><span class="comment">*</span><span class="comment"> = 'U': Upper trapezoidal
</span><span class="comment">*</span><span class="comment"> = 'L': Lower trapezoidal
</span><span class="comment">*</span><span class="comment"> Note that A is triangular instead of trapezoidal if M = N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DIAG (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether or not the matrix A has unit diagonal.
</span><span class="comment">*</span><span class="comment"> = 'N': Non-unit diagonal
</span><span class="comment">*</span><span class="comment"> = 'U': Unit diagonal
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of rows of the matrix A. M >= 0, and if
</span><span class="comment">*</span><span class="comment"> UPLO = 'U', M <= N. When M = 0, <a name="CLANTR.62"></a><a href="clantr.f.html#CLANTR.1">CLANTR</a> is set to zero.
</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 number of columns of the matrix A. N >= 0, and if
</span><span class="comment">*</span><span class="comment"> UPLO = 'L', N <= M. When N = 0, <a name="CLANTR.66"></a><a href="clantr.f.html#CLANTR.1">CLANTR</a> is set to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input) COMPLEX array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> The trapezoidal matrix A (A is triangular if M = N).
</span><span class="comment">*</span><span class="comment"> If UPLO = 'U', the leading m by n upper trapezoidal part of
</span><span class="comment">*</span><span class="comment"> the array A contains the upper trapezoidal matrix, and the
</span><span class="comment">*</span><span class="comment"> strictly lower triangular part of A is not referenced.
</span><span class="comment">*</span><span class="comment"> If UPLO = 'L', the leading m by n lower trapezoidal part of
</span><span class="comment">*</span><span class="comment"> the array A contains the lower trapezoidal matrix, and the
</span><span class="comment">*</span><span class="comment"> strictly upper triangular part of A is not referenced. Note
</span><span class="comment">*</span><span class="comment"> that when DIAG = 'U', the diagonal elements of A are not
</span><span class="comment">*</span><span class="comment"> referenced and are assumed to be one.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(M,1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) REAL array, dimension (MAX(1,LWORK)),
</span><span class="comment">*</span><span class="comment"> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
</span><span class="comment">*</span><span class="comment"> referenced.
</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> REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UDIAG
INTEGER I, J
REAL SCALE, SUM, VALUE
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.98"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.99"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="CLASSQ.102"></a><a href="classq.f.html#CLASSQ.1">CLASSQ</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, MAX, MIN, SQRT
<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> IF( MIN( M, N ).EQ.0 ) THEN
VALUE = ZERO
ELSE IF( <a name="LSAME.111"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'M'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Find max(abs(A(i,j))).
</span><span class="comment">*</span><span class="comment">
</span> IF( <a name="LSAME.115"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'U'</span> ) ) THEN
VALUE = ONE
IF( <a name="LSAME.117"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
DO 20 J = 1, N
DO 10 I = 1, MIN( M, J-1 )
VALUE = MAX( VALUE, ABS( A( I, J ) ) )
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = J + 1, M
VALUE = MAX( VALUE, ABS( A( I, J ) ) )
30 CONTINUE
40 CONTINUE
END IF
ELSE
VALUE = ZERO
IF( <a name="LSAME.132"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
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