clanhp.f.html
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REAL FUNCTION <a name="CLANHP.1"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a>( NORM, UPLO, N, AP, 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 NORM, UPLO
INTEGER N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL WORK( * )
COMPLEX AP( * )
<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="CLANHP.19"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</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"> complex hermitian matrix A, supplied in packed form.
</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="CLANHP.26"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a> returns the value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CLANHP.28"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</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="CLANHP.45"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</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 upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment"> hermitian matrix A is supplied.
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular part of A is supplied
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular part of A is supplied
</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="CLANHP.55"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</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"> AP (input) COMPLEX array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment"> The upper or lower triangle of the hermitian matrix A, packed
</span><span class="comment">*</span><span class="comment"> columnwise in a linear array. The j-th column of A is stored
</span><span class="comment">*</span><span class="comment"> in the array AP as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
</span><span class="comment">*</span><span class="comment"> Note that the imaginary parts of the diagonal elements need
</span><span class="comment">*</span><span class="comment"> not be set and are assumed to be zero.
</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 >= N when NORM = 'I' or '1' or 'O'; otherwise,
</span><span class="comment">*</span><span class="comment"> WORK is not 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> INTEGER I, J, K
REAL ABSA, 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.82"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.83"></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.86"></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, REAL, 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.95"></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> VALUE = ZERO
IF( <a name="LSAME.100"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
K = 0
DO 20 J = 1, N
DO 10 I = K + 1, K + J - 1
VALUE = MAX( VALUE, ABS( AP( I ) ) )
10 CONTINUE
K = K + J
VALUE = MAX( VALUE, ABS( REAL( AP( K ) ) ) )
20 CONTINUE
ELSE
K = 1
DO 40 J = 1, N
VALUE = MAX( VALUE, ABS( REAL( AP( K ) ) ) )
DO 30 I = K + 1, K + N - J
VALUE = MAX( VALUE, ABS( AP( I ) ) )
30 CONTINUE
K = K + N - J + 1
40 CONTINUE
END IF
ELSE IF( ( <a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'I'</span> ) ) .OR. ( <a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'O'</span> ) ) .OR.
$ ( NORM.EQ.<span class="string">'1'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Find normI(A) ( = norm1(A), since A is hermitian).
</span><span class="comment">*</span><span class="comment">
</span> VALUE = ZERO
K = 1
IF( <a name="LSAME.126"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
DO 60 J = 1, N
SUM = ZERO
DO 50 I = 1, J - 1
ABSA = ABS( AP( K ) )
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
K = K + 1
50 CONTINUE
WORK( J ) = SUM + ABS( REAL( AP( K ) ) )
K = K + 1
60 CONTINUE
DO 70 I = 1, N
VALUE = MAX( VALUE, WORK( I ) )
70 CONTINUE
ELSE
DO 80 I = 1, N
WORK( I ) = ZERO
80 CONTINUE
DO 100 J = 1, N
SUM = WORK( J ) + ABS( REAL( AP( K ) ) )
K = K + 1
DO 90 I = J + 1, N
ABSA = ABS( AP( K ) )
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
K = K + 1
90 CONTINUE
VALUE = MAX( VALUE, SUM )
100 CONTINUE
END IF
ELSE IF( ( <a name="LSAME.157"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'F'</span> ) ) .OR. ( <a name="LSAME.157"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'E'</span> ) ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Find normF(A).
</span><span class="comment">*</span><span class="comment">
</span> SCALE = ZERO
SUM = ONE
K = 2
IF( <a name="LSAME.164"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
DO 110 J = 2, N
CALL <a name="CLASSQ.166"></a><a href="classq.f.html#CLASSQ.1">CLASSQ</a>( J-1, AP( K ), 1, SCALE, SUM )
K = K + J
110 CONTINUE
ELSE
DO 120 J = 1, N - 1
CALL <a name="CLASSQ.171"></a><a href="classq.f.html#CLASSQ.1">CLASSQ</a>( N-J, AP( K ), 1, SCALE, SUM )
K = K + N - J + 1
120 CONTINUE
END IF
SUM = 2*SUM
K = 1
DO 130 I = 1, N
IF( REAL( AP( K ) ).NE.ZERO ) THEN
ABSA = ABS( REAL( AP( K ) ) )
IF( SCALE.LT.ABSA ) THEN
SUM = ONE + SUM*( SCALE / ABSA )**2
SCALE = ABSA
ELSE
SUM = SUM + ( ABSA / SCALE )**2
END IF
END IF
IF( <a name="LSAME.187"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
K = K + I + 1
ELSE
K = K + N - I + 1
END IF
130 CONTINUE
VALUE = SCALE*SQRT( SUM )
END IF
<span class="comment">*</span><span class="comment">
</span> <a name="CLANHP.196"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a> = VALUE
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="CLANHP.199"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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