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REAL FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB,
$ LDAB, WORK )
*
* -- LAPACK auxiliary routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* October 31, 1992
*
* .. Scalar Arguments ..
CHARACTER DIAG, NORM, UPLO
INTEGER K, LDAB, N
* ..
* .. Array Arguments ..
REAL WORK( * )
COMPLEX AB( LDAB, * )
* ..
*
* Purpose
* =======
*
* CLANTB returns the value of the one norm, or the Frobenius norm, or
* the infinity norm, or the element of largest absolute value of an
* n by n triangular band matrix A, with ( k + 1 ) diagonals.
*
* Description
* ===========
*
* CLANTB returns the value
*
* CLANTB = ( 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 matrix norm.
*
* Arguments
* =========
*
* NORM (input) CHARACTER*1
* Specifies the value to be returned in CLANTB as described
* above.
*
* UPLO (input) CHARACTER*1
* Specifies whether the matrix A is upper or lower triangular.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* DIAG (input) CHARACTER*1
* Specifies whether or not the matrix A is unit triangular.
* = 'N': Non-unit triangular
* = 'U': Unit triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0. When N = 0, CLANTB is
* set to zero.
*
* K (input) INTEGER
* The number of super-diagonals of the matrix A if UPLO = 'U',
* or the number of sub-diagonals of the matrix A if UPLO = 'L'.
* K >= 0.
*
* AB (input) COMPLEX array, dimension (LDAB,N)
* The upper or lower triangular band matrix A, stored in the
* first k+1 rows of AB. The j-th column of A is stored
* in the j-th column of the array AB as follows:
* if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
* Note that when DIAG = 'U', the elements of the array AB
* corresponding to the diagonal elements of the matrix A are
* not referenced, but are assumed to be one.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= K+1.
*
* WORK (workspace) REAL array, dimension (LWORK),
* where LWORK >= N 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, L
REAL SCALE, SUM, VALUE
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLASSQ
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, SQRT
* ..
* .. Executable Statements ..
*
IF( 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 = MAX( K+2-J, 1 ), K
VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = 2, MIN( N+1-J, K+1 )
VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
30 CONTINUE
40 CONTINUE
END IF
ELSE
VALUE = ZERO
IF( LSAME( UPLO, 'U' ) ) THEN
DO 60 J = 1, N
DO 50 I = MAX( K+2-J, 1 ), K + 1
VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
50 CONTINUE
60 CONTINUE
ELSE
DO 80 J = 1, N
DO 70 I = 1, MIN( N+1-J, K+1 )
VALUE = MAX( VALUE, ABS( AB( 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 ) THEN
SUM = ONE
DO 90 I = MAX( K+2-J, 1 ), K
SUM = SUM + ABS( AB( I, J ) )
90 CONTINUE
ELSE
SUM = ZERO
DO 100 I = MAX( K+2-J, 1 ), K + 1
SUM = SUM + ABS( AB( 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 = 2, MIN( N+1-J, K+1 )
SUM = SUM + ABS( AB( I, J ) )
120 CONTINUE
ELSE
SUM = ZERO
DO 130 I = 1, MIN( N+1-J, K+1 )
SUM = SUM + ABS( AB( I, J ) )
130 CONTINUE
END IF
VALUE = MAX( VALUE, SUM )
140 CONTINUE
END IF
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
* Find normI(A).
*
VALUE = ZERO
IF( LSAME( UPLO, 'U' ) ) THEN
IF( LSAME( DIAG, 'U' ) ) THEN
DO 150 I = 1, N
WORK( I ) = ONE
150 CONTINUE
DO 170 J = 1, N
L = K + 1 - J
DO 160 I = MAX( 1, J-K ), J - 1
WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
160 CONTINUE
170 CONTINUE
ELSE
DO 180 I = 1, N
WORK( I ) = ZERO
180 CONTINUE
DO 200 J = 1, N
L = K + 1 - J
DO 190 I = MAX( 1, J-K ), J
WORK( I ) = WORK( I ) + ABS( AB( L+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 230 J = 1, N
L = 1 - J
DO 220 I = J + 1, MIN( N, J+K )
WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
220 CONTINUE
230 CONTINUE
ELSE
DO 240 I = 1, N
WORK( I ) = ZERO
240 CONTINUE
DO 260 J = 1, N
L = 1 - J
DO 250 I = J, MIN( N, J+K )
WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
250 CONTINUE
260 CONTINUE
END IF
END IF
DO 270 I = 1, N
VALUE = MAX( VALUE, WORK( I ) )
270 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 = N
IF( K.GT.0 ) THEN
DO 280 J = 2, N
CALL CLASSQ( MIN( J-1, K ),
$ AB( MAX( K+2-J, 1 ), J ), 1, SCALE,
$ SUM )
280 CONTINUE
END IF
ELSE
SCALE = ZERO
SUM = ONE
DO 290 J = 1, N
CALL CLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
$ 1, SCALE, SUM )
290 CONTINUE
END IF
ELSE
IF( LSAME( DIAG, 'U' ) ) THEN
SCALE = ONE
SUM = N
IF( K.GT.0 ) THEN
DO 300 J = 1, N - 1
CALL CLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
$ SUM )
300 CONTINUE
END IF
ELSE
SCALE = ZERO
SUM = ONE
DO 310 J = 1, N
CALL CLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE,
$ SUM )
310 CONTINUE
END IF
END IF
VALUE = SCALE*SQRT( SUM )
END IF
*
CLANTB = VALUE
RETURN
*
* End of CLANTB
*
END
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