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*> \brief \b SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SLANTP + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slantp.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slantp.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slantp.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* REAL FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, NORM, UPLO
* INTEGER N
* ..
* .. Array Arguments ..
* REAL AP( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLANTP returns the value of the one norm, or the Frobenius norm, or
*> the infinity norm, or the element of largest absolute value of a
*> triangular matrix A, supplied in packed form.
*> \endverbatim
*>
*> \return SLANTP
*> \verbatim
*>
*> SLANTP = ( 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NORM
*> \verbatim
*> NORM is CHARACTER*1
*> Specifies the value to be returned in SLANTP as described
*> above.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the matrix A is upper or lower triangular.
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> Specifies whether or not the matrix A is unit triangular.
*> = 'N': Non-unit triangular
*> = 'U': Unit triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0. When N = 0, SLANTP is
*> set to zero.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is REAL array, dimension (N*(N+1)/2)
*> The upper or lower triangular matrix A, packed columnwise in
*> a linear array. The j-th column of A is stored in the array
*> AP as follows:
*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
*> Note that when DIAG = 'U', the elements of the array AP
*> corresponding to the diagonal elements of the matrix A are
*> not referenced, but are assumed to be one.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (MAX(1,LWORK)),
*> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
*> referenced.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup realOTHERauxiliary
*
* =====================================================================
REAL FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER DIAG, NORM, UPLO
INTEGER N
* ..
* .. Array Arguments ..
REAL AP( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UDIAG
INTEGER I, J, K
REAL SCALE, SUM, VALUE
* ..
* .. External Subroutines ..
EXTERNAL SLASSQ
* ..
* .. External Functions ..
LOGICAL LSAME, SISNAN
EXTERNAL LSAME, SISNAN
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, SQRT
* ..
* .. Executable Statements ..
*
IF( N.EQ.0 ) THEN
VALUE = ZERO
ELSE IF( LSAME( NORM, 'M' ) ) THEN
*
* Find max(abs(A(i,j))).
*
K = 1
IF( LSAME( DIAG, 'U' ) ) THEN
VALUE = ONE
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
DO 10 I = K, K + J - 2
SUM = ABS( AP( I ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
10 CONTINUE
K = K + J
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = K + 1, K + N - J
SUM = ABS( AP( I ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
30 CONTINUE
K = K + N - J + 1
40 CONTINUE
END IF
ELSE
VALUE = ZERO
IF( LSAME( UPLO, 'U' ) ) THEN
DO 60 J = 1, N
DO 50 I = K, K + J - 1
SUM = ABS( AP( I ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
50 CONTINUE
K = K + J
60 CONTINUE
ELSE
DO 80 J = 1, N
DO 70 I = K, K + N - J
SUM = ABS( AP( I ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
70 CONTINUE
K = K + N - J + 1
80 CONTINUE
END IF
END IF
ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
*
* Find norm1(A).
*
VALUE = ZERO
K = 1
UDIAG = LSAME( DIAG, 'U' )
IF( LSAME( UPLO, 'U' ) ) THEN
DO 110 J = 1, N
IF( UDIAG ) THEN
SUM = ONE
DO 90 I = K, K + J - 2
SUM = SUM + ABS( AP( I ) )
90 CONTINUE
ELSE
SUM = ZERO
DO 100 I = K, K + J - 1
SUM = SUM + ABS( AP( I ) )
100 CONTINUE
END IF
K = K + J
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
110 CONTINUE
ELSE
DO 140 J = 1, N
IF( UDIAG ) THEN
SUM = ONE
DO 120 I = K + 1, K + N - J
SUM = SUM + ABS( AP( I ) )
120 CONTINUE
ELSE
SUM = ZERO
DO 130 I = K, K + N - J
SUM = SUM + ABS( AP( I ) )
130 CONTINUE
END IF
K = K + N - J + 1
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
140 CONTINUE
END IF
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
* Find normI(A).
*
K = 1
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
DO 160 I = 1, J - 1
WORK( I ) = WORK( I ) + ABS( AP( K ) )
K = K + 1
160 CONTINUE
K = K + 1
170 CONTINUE
ELSE
DO 180 I = 1, N
WORK( I ) = ZERO
180 CONTINUE
DO 200 J = 1, N
DO 190 I = 1, J
WORK( I ) = WORK( I ) + ABS( AP( K ) )
K = K + 1
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
K = K + 1
DO 220 I = J + 1, N
WORK( I ) = WORK( I ) + ABS( AP( K ) )
K = K + 1
220 CONTINUE
230 CONTINUE
ELSE
DO 240 I = 1, N
WORK( I ) = ZERO
240 CONTINUE
DO 260 J = 1, N
DO 250 I = J, N
WORK( I ) = WORK( I ) + ABS( AP( K ) )
K = K + 1
250 CONTINUE
260 CONTINUE
END IF
END IF
VALUE = ZERO
DO 270 I = 1, N
SUM = WORK( I )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
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
K = 2
DO 280 J = 2, N
CALL SLASSQ( J-1, AP( K ), 1, SCALE, SUM )
K = K + J
280 CONTINUE
ELSE
SCALE = ZERO
SUM = ONE
K = 1
DO 290 J = 1, N
CALL SLASSQ( J, AP( K ), 1, SCALE, SUM )
K = K + J
290 CONTINUE
END IF
ELSE
IF( LSAME( DIAG, 'U' ) ) THEN
SCALE = ONE
SUM = N
K = 2
DO 300 J = 1, N - 1
CALL SLASSQ( N-J, AP( K ), 1, SCALE, SUM )
K = K + N - J + 1
300 CONTINUE
ELSE
SCALE = ZERO
SUM = ONE
K = 1
DO 310 J = 1, N
CALL SLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
K = K + N - J + 1
310 CONTINUE
END IF
END IF
VALUE = SCALE*SQRT( SUM )
END IF
*
SLANTP = VALUE
RETURN
*
* End of SLANTP
*
END
|
