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DOUBLE PRECISION FUNCTION <a name="ZLANTB.1"></a><a href="zlantb.f.html#ZLANTB.1">ZLANTB</a>( NORM, UPLO, DIAG, N, K, AB,
$ LDAB, 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 K, LDAB, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION WORK( * )
COMPLEX*16 AB( LDAB, * )
<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="ZLANTB.20"></a><a href="zlantb.f.html#ZLANTB.1">ZLANTB</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 an
</span><span class="comment">*</span><span class="comment"> n by n triangular band matrix A, with ( k + 1 ) diagonals.
</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="ZLANTB.27"></a><a href="zlantb.f.html#ZLANTB.1">ZLANTB</a> returns the value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="ZLANTB.29"></a><a href="zlantb.f.html#ZLANTB.1">ZLANTB</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="ZLANTB.46"></a><a href="zlantb.f.html#ZLANTB.1">ZLANTB</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 triangular.
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular
</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 is unit triangular.
</span><span class="comment">*</span><span class="comment"> = 'N': Non-unit triangular
</span><span class="comment">*</span><span class="comment"> = 'U': Unit triangular
</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 A. N >= 0. When N = 0, <a name="ZLANTB.60"></a><a href="zlantb.f.html#ZLANTB.1">ZLANTB</a> is
</span><span class="comment">*</span><span class="comment"> set to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> K (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of super-diagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of sub-diagonals of the matrix A if UPLO = 'L'.
</span><span class="comment">*</span><span class="comment"> K >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input) COMPLEX*16 array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> The upper or lower triangular band matrix A, stored in the
</span><span class="comment">*</span><span class="comment"> first k+1 rows of AB. The j-th column of A is stored
</span><span class="comment">*</span><span class="comment"> in the j-th column of the array AB as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
</span><span class="comment">*</span><span class="comment"> Note that when DIAG = 'U', the elements of the array AB
</span><span class="comment">*</span><span class="comment"> corresponding to the diagonal elements of the matrix A are
</span><span class="comment">*</span><span class="comment"> not referenced, but are assumed to be one.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= K+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
</span><span class="comment">*</span><span class="comment"> where LWORK >= N 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> DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UDIAG
INTEGER I, J, L
DOUBLE PRECISION 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.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.98"></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="ZLASSQ.101"></a><a href="zlassq.f.html#ZLASSQ.1">ZLASSQ</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( N.EQ.0 ) THEN
VALUE = ZERO
ELSE IF( <a name="LSAME.110"></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.114"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( DIAG, <span class="string">'U'</span> ) ) THEN
VALUE = ONE
IF( <a name="LSAME.116"></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 = 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( <a name="LSAME.131"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) 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
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