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OpenBLAS/lapack-netlib/SRC/slantb.f

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*> \brief \b SLANTB 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 band matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SLANTB + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slantb.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slantb.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slantb.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* REAL FUNCTION SLANTB( NORM, UPLO, DIAG, N, K, AB,
* LDAB, WORK )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, NORM, UPLO
* INTEGER K, LDAB, N
* ..
* .. Array Arguments ..
* REAL AB( LDAB, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLANTB 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.
*> \endverbatim
*>
*> \return SLANTB
*> \verbatim
*>
*> SLANTB = ( 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 SLANTB 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, SLANTB is
*> set to zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is 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.
*> \endverbatim
*>
*> \param[in] AB
*> \verbatim
*> AB is REAL 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.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= K+1.
*> \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 SLANTB( NORM, UPLO, DIAG, N, K, AB,
$ LDAB, 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
*
IMPLICIT NONE
* .. Scalar Arguments ..
CHARACTER DIAG, NORM, UPLO
INTEGER K, LDAB, N
* ..
* .. Array Arguments ..
REAL AB( LDAB, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UDIAG
INTEGER I, J, L
REAL SUM, VALUE
* ..
* .. Local Arrays ..
REAL SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Functions ..
LOGICAL LSAME, SISNAN
EXTERNAL LSAME, SISNAN
* ..
* .. External Subroutines ..
EXTERNAL SLASSQ, SCOMBSSQ
* ..
* .. 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
SUM = ABS( AB( I, J ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = 2, MIN( N+1-J, K+1 )
SUM = ABS( AB( I, J ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
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
SUM = ABS( AB( I, J ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
50 CONTINUE
60 CONTINUE
ELSE
DO 80 J = 1, N
DO 70 I = 1, MIN( N+1-J, K+1 )
SUM = ABS( AB( I, J ) )
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
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
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 = 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
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) 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
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).
* SSQ(1) is scale
* SSQ(2) is sum-of-squares
* For better accuracy, sum each column separately.
*
IF( LSAME( UPLO, 'U' ) ) THEN
IF( LSAME( DIAG, 'U' ) ) THEN
SSQ( 1 ) = ONE
SSQ( 2 ) = N
IF( K.GT.0 ) THEN
DO 280 J = 2, N
COLSSQ( 1 ) = ZERO
COLSSQ( 2 ) = ONE
CALL SLASSQ( MIN( J-1, K ),
$ AB( MAX( K+2-J, 1 ), J ), 1,
$ COLSSQ( 1 ), COLSSQ( 2 ) )
CALL SCOMBSSQ( SSQ, COLSSQ )
280 CONTINUE
END IF
ELSE
SSQ( 1 ) = ZERO
SSQ( 2 ) = ONE
DO 290 J = 1, N
COLSSQ( 1 ) = ZERO
COLSSQ( 2 ) = ONE
CALL SLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
$ 1, COLSSQ( 1 ), COLSSQ( 2 ) )
CALL SCOMBSSQ( SSQ, COLSSQ )
290 CONTINUE
END IF
ELSE
IF( LSAME( DIAG, 'U' ) ) THEN
SSQ( 1 ) = ONE
SSQ( 2 ) = N
IF( K.GT.0 ) THEN
DO 300 J = 1, N - 1
COLSSQ( 1 ) = ZERO
COLSSQ( 2 ) = ONE
CALL SLASSQ( MIN( N-J, K ), AB( 2, J ), 1,
$ COLSSQ( 1 ), COLSSQ( 2 ) )
CALL SCOMBSSQ( SSQ, COLSSQ )
300 CONTINUE
END IF
ELSE
SSQ( 1 ) = ZERO
SSQ( 2 ) = ONE
DO 310 J = 1, N
COLSSQ( 1 ) = ZERO
COLSSQ( 2 ) = ONE
CALL SLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1,
$ COLSSQ( 1 ), COLSSQ( 2 ) )
CALL SCOMBSSQ( SSQ, COLSSQ )
310 CONTINUE
END IF
END IF
VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
SLANTB = VALUE
RETURN
*
* End of SLANTB
*
END
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