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