```      REAL             FUNCTION CLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
\$                 WORK )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          DIAG, NORM, UPLO
INTEGER            LDA, M, N
*     ..
*     .. Array Arguments ..
REAL               WORK( * )
COMPLEX            A( LDA, * )
*     ..
*
*  Purpose
*  =======
*
*  CLANTR  returns the value of the one norm,  or the Frobenius norm, or
*  the  infinity norm,  or the  element of  largest absolute value  of a
*  trapezoidal or triangular matrix A.
*
*  Description
*  ===========
*
*  CLANTR returns the value
*
*     CLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
*              (
*              ( norm1(A),         NORM = '1', 'O' or 'o'
*              (
*              ( normI(A),         NORM = 'I' or 'i'
*              (
*              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
*
*  where  norm1  denotes the  one norm of a matrix (maximum column sum),
*  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
*  normF  denotes the  Frobenius norm of a matrix (square root of sum of
*  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
*
*  Arguments
*  =========
*
*  NORM    (input) CHARACTER*1
*          Specifies the value to be returned in CLANTR as described
*          above.
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the matrix A is upper or lower trapezoidal.
*          = 'U':  Upper trapezoidal
*          = 'L':  Lower trapezoidal
*          Note that A is triangular instead of trapezoidal if M = N.
*
*  DIAG    (input) CHARACTER*1
*          Specifies whether or not the matrix A has unit diagonal.
*          = 'N':  Non-unit diagonal
*          = 'U':  Unit diagonal
*
*  M       (input) INTEGER
*          The number of rows of the matrix A.  M >= 0, and if
*          UPLO = 'U', M <= N.  When M = 0, CLANTR is set to zero.
*
*  N       (input) INTEGER
*          The number of columns of the matrix A.  N >= 0, and if
*          UPLO = 'L', N <= M.  When N = 0, CLANTR is set to zero.
*
*  A       (input) COMPLEX array, dimension (LDA,N)
*          The trapezoidal matrix A (A is triangular if M = N).
*          If UPLO = 'U', the leading m by n upper trapezoidal part of
*          the array A contains the upper trapezoidal matrix, and the
*          strictly lower triangular part of A is not referenced.
*          If UPLO = 'L', the leading m by n lower trapezoidal part of
*          the array A contains the lower trapezoidal matrix, and the
*          strictly upper triangular part of A is not referenced.  Note
*          that when DIAG = 'U', the diagonal elements of A are not
*          referenced and are assumed to be one.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(M,1).
*
*  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
*          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
*          referenced.
*
* =====================================================================
*
*     .. Parameters ..
REAL               ONE, ZERO
PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
*     ..
*     .. Local Scalars ..
LOGICAL            UDIAG
INTEGER            I, J
REAL               SCALE, SUM, VALUE
*     ..
*     .. External Functions ..
LOGICAL            LSAME
EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL           CLASSQ
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, MAX, MIN, SQRT
*     ..
*     .. Executable Statements ..
*
IF( MIN( M, N ).EQ.0 ) THEN
VALUE = ZERO
ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
*        Find max(abs(A(i,j))).
*
IF( LSAME( DIAG, 'U' ) ) THEN
VALUE = ONE
IF( LSAME( UPLO, 'U' ) ) 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( LSAME( UPLO, 'U' ) ) THEN
DO 60 J = 1, N
DO 50 I = 1, MIN( M, J )
VALUE = MAX( VALUE, ABS( A( I, J ) ) )
50             CONTINUE
60          CONTINUE
ELSE
DO 80 J = 1, N
DO 70 I = J, M
VALUE = MAX( VALUE, ABS( A( I, J ) ) )
70             CONTINUE
80          CONTINUE
END IF
END IF
ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
*
*        Find norm1(A).
*
VALUE = ZERO
UDIAG = LSAME( DIAG, 'U' )
IF( LSAME( UPLO, 'U' ) ) THEN
DO 110 J = 1, N
IF( ( UDIAG ) .AND. ( J.LE.M ) ) THEN
SUM = ONE
DO 90 I = 1, J - 1
SUM = SUM + ABS( A( I, J ) )
90             CONTINUE
ELSE
SUM = ZERO
DO 100 I = 1, MIN( M, J )
SUM = SUM + ABS( A( I, J ) )
100             CONTINUE
END IF
VALUE = MAX( VALUE, SUM )
110       CONTINUE
ELSE
DO 140 J = 1, N
IF( UDIAG ) THEN
SUM = ONE
DO 120 I = J + 1, M
SUM = SUM + ABS( A( I, J ) )
120             CONTINUE
ELSE
SUM = ZERO
DO 130 I = J, M
SUM = SUM + ABS( A( I, J ) )
130             CONTINUE
END IF
VALUE = MAX( VALUE, SUM )
140       CONTINUE
END IF
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
*        Find normI(A).
*
IF( LSAME( UPLO, 'U' ) ) THEN
IF( LSAME( DIAG, 'U' ) ) THEN
DO 150 I = 1, M
WORK( I ) = ONE
150          CONTINUE
DO 170 J = 1, N
DO 160 I = 1, MIN( M, J-1 )
WORK( I ) = WORK( I ) + ABS( A( I, J ) )
160             CONTINUE
170          CONTINUE
ELSE
DO 180 I = 1, M
WORK( I ) = ZERO
180          CONTINUE
DO 200 J = 1, N
DO 190 I = 1, MIN( M, J )
WORK( I ) = WORK( I ) + ABS( A( I, J ) )
190             CONTINUE
200          CONTINUE
END IF
ELSE
IF( LSAME( DIAG, 'U' ) ) THEN
DO 210 I = 1, N
WORK( I ) = ONE
210          CONTINUE
DO 220 I = N + 1, M
WORK( I ) = ZERO
220          CONTINUE
DO 240 J = 1, N
DO 230 I = J + 1, M
WORK( I ) = WORK( I ) + ABS( A( I, J ) )
230             CONTINUE
240          CONTINUE
ELSE
DO 250 I = 1, M
WORK( I ) = ZERO
250          CONTINUE
DO 270 J = 1, N
DO 260 I = J, M
WORK( I ) = WORK( I ) + ABS( A( I, J ) )
260             CONTINUE
270          CONTINUE
END IF
END IF
VALUE = ZERO
DO 280 I = 1, M
VALUE = MAX( VALUE, WORK( I ) )
280    CONTINUE
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
*
*        Find normF(A).
*
IF( LSAME( UPLO, 'U' ) ) THEN
IF( LSAME( DIAG, 'U' ) ) THEN
SCALE = ONE
SUM = MIN( M, N )
DO 290 J = 2, N
CALL CLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
290          CONTINUE
ELSE
SCALE = ZERO
SUM = ONE
DO 300 J = 1, N
CALL CLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
300          CONTINUE
END IF
ELSE
IF( LSAME( DIAG, 'U' ) ) THEN
SCALE = ONE
SUM = MIN( M, N )
DO 310 J = 1, N
CALL CLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
\$                         SUM )
310          CONTINUE
ELSE
SCALE = ZERO
SUM = ONE
DO 320 J = 1, N
CALL CLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
320          CONTINUE
END IF
END IF
VALUE = SCALE*SQRT( SUM )
END IF
*
CLANTR = VALUE
RETURN
*
*     End of CLANTR
*
END

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