added lapack 3.7.0 with latest patches from git
This commit is contained in:
Werner Saar
353
lapack-netlib/SRC/slantr.f
Normal file
353
lapack-netlib/SRC/slantr.f
Normal file
@@ -0,0 +1,353 @@
|
||||
*> \brief \b SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
*> \htmlonly
|
||||
*> Download SLANTR + dependencies
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slantr.f">
|
||||
*> [TGZ]</a>
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slantr.f">
|
||||
*> [ZIP]</a>
|
||||
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slantr.f">
|
||||
*> [TXT]</a>
|
||||
*> \endhtmlonly
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* REAL FUNCTION SLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
|
||||
* WORK )
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* CHARACTER DIAG, NORM, UPLO
|
||||
* INTEGER LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* REAL A( LDA, * ), WORK( * )
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> SLANTR returns the value of the one norm, or the Frobenius norm, or
|
||||
*> the infinity norm, or the element of largest absolute value of a
|
||||
*> trapezoidal or triangular matrix A.
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \return SLANTR
|
||||
*> \verbatim
|
||||
*>
|
||||
*> SLANTR = ( 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 SLANTR as described
|
||||
*> above.
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] UPLO
|
||||
*> \verbatim
|
||||
*> UPLO is CHARACTER*1
|
||||
*> Specifies whether the matrix A is upper or lower trapezoidal.
|
||||
*> = 'U': Upper trapezoidal
|
||||
*> = 'L': Lower trapezoidal
|
||||
*> Note that A is triangular instead of trapezoidal if M = N.
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] DIAG
|
||||
*> \verbatim
|
||||
*> DIAG is CHARACTER*1
|
||||
*> Specifies whether or not the matrix A has unit diagonal.
|
||||
*> = 'N': Non-unit diagonal
|
||||
*> = 'U': Unit diagonal
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] M
|
||||
*> \verbatim
|
||||
*> M is INTEGER
|
||||
*> The number of rows of the matrix A. M >= 0, and if
|
||||
*> UPLO = 'U', M <= N. When M = 0, SLANTR is set to zero.
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] N
|
||||
*> \verbatim
|
||||
*> N is INTEGER
|
||||
*> The number of columns of the matrix A. N >= 0, and if
|
||||
*> UPLO = 'L', N <= M. When N = 0, SLANTR is set to zero.
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] A
|
||||
*> \verbatim
|
||||
*> A is REAL array, dimension (LDA,N)
|
||||
*> The trapezoidal matrix A (A is triangular if M = N).
|
||||
*> If UPLO = 'U', the leading m by n upper trapezoidal part of
|
||||
*> the array A contains the upper trapezoidal matrix, and the
|
||||
*> strictly lower triangular part of A is not referenced.
|
||||
*> If UPLO = 'L', the leading m by n lower trapezoidal part of
|
||||
*> the array A contains the lower trapezoidal matrix, and the
|
||||
*> strictly upper triangular part of A is not referenced. Note
|
||||
*> that when DIAG = 'U', the diagonal elements of A are not
|
||||
*> referenced and are assumed to be one.
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] LDA
|
||||
*> \verbatim
|
||||
*> LDA is INTEGER
|
||||
*> The leading dimension of the array A. LDA >= max(M,1).
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] WORK
|
||||
*> \verbatim
|
||||
*> WORK is REAL array, dimension (MAX(1,LWORK)),
|
||||
*> where LWORK >= M 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 SLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
|
||||
$ 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 LDA, M, N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
REAL A( LDA, * ), WORK( * )
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
REAL ONE, ZERO
|
||||
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
LOGICAL UDIAG
|
||||
INTEGER I, J
|
||||
REAL SCALE, SUM, VALUE
|
||||
* ..
|
||||
* .. External Subroutines ..
|
||||
EXTERNAL SLASSQ
|
||||
* ..
|
||||
* .. External Functions ..
|
||||
LOGICAL LSAME, SISNAN
|
||||
EXTERNAL LSAME, SISNAN
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC ABS, MIN, SQRT
|
||||
* ..
|
||||
* .. Executable Statements ..
|
||||
*
|
||||
IF( MIN( M, 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 = 1, MIN( M, J-1 )
|
||||
SUM = ABS( A( I, J ) )
|
||||
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
|
||||
10 CONTINUE
|
||||
20 CONTINUE
|
||||
ELSE
|
||||
DO 40 J = 1, N
|
||||
DO 30 I = J + 1, M
|
||||
SUM = ABS( A( 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 = 1, MIN( M, J )
|
||||
SUM = ABS( A( I, J ) )
|
||||
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
|
||||
50 CONTINUE
|
||||
60 CONTINUE
|
||||
ELSE
|
||||
DO 80 J = 1, N
|
||||
DO 70 I = J, M
|
||||
SUM = ABS( A( 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 ) .AND. ( J.LE.M ) ) THEN
|
||||
SUM = ONE
|
||||
DO 90 I = 1, J - 1
|
||||
SUM = SUM + ABS( A( I, J ) )
|
||||
90 CONTINUE
|
||||
ELSE
|
||||
SUM = ZERO
|
||||
DO 100 I = 1, MIN( M, J )
|
||||
SUM = SUM + ABS( A( 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 = J + 1, M
|
||||
SUM = SUM + ABS( A( I, J ) )
|
||||
120 CONTINUE
|
||||
ELSE
|
||||
SUM = ZERO
|
||||
DO 130 I = J, M
|
||||
SUM = SUM + ABS( A( 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).
|
||||
*
|
||||
IF( LSAME( UPLO, 'U' ) ) THEN
|
||||
IF( LSAME( DIAG, 'U' ) ) THEN
|
||||
DO 150 I = 1, M
|
||||
WORK( I ) = ONE
|
||||
150 CONTINUE
|
||||
DO 170 J = 1, N
|
||||
DO 160 I = 1, MIN( M, J-1 )
|
||||
WORK( I ) = WORK( I ) + ABS( A( I, J ) )
|
||||
160 CONTINUE
|
||||
170 CONTINUE
|
||||
ELSE
|
||||
DO 180 I = 1, M
|
||||
WORK( I ) = ZERO
|
||||
180 CONTINUE
|
||||
DO 200 J = 1, N
|
||||
DO 190 I = 1, MIN( M, J )
|
||||
WORK( I ) = WORK( I ) + ABS( A( 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 220 I = N + 1, M
|
||||
WORK( I ) = ZERO
|
||||
220 CONTINUE
|
||||
DO 240 J = 1, N
|
||||
DO 230 I = J + 1, M
|
||||
WORK( I ) = WORK( I ) + ABS( A( I, J ) )
|
||||
230 CONTINUE
|
||||
240 CONTINUE
|
||||
ELSE
|
||||
DO 250 I = 1, M
|
||||
WORK( I ) = ZERO
|
||||
250 CONTINUE
|
||||
DO 270 J = 1, N
|
||||
DO 260 I = J, M
|
||||
WORK( I ) = WORK( I ) + ABS( A( I, J ) )
|
||||
260 CONTINUE
|
||||
270 CONTINUE
|
||||
END IF
|
||||
END IF
|
||||
VALUE = ZERO
|
||||
DO 280 I = 1, M
|
||||
SUM = WORK( I )
|
||||
IF( VALUE .LT. SUM .OR. SISNAN( SUM ) ) VALUE = SUM
|
||||
280 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 = MIN( M, N )
|
||||
DO 290 J = 2, N
|
||||
CALL SLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
|
||||
290 CONTINUE
|
||||
ELSE
|
||||
SCALE = ZERO
|
||||
SUM = ONE
|
||||
DO 300 J = 1, N
|
||||
CALL SLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
|
||||
300 CONTINUE
|
||||
END IF
|
||||
ELSE
|
||||
IF( LSAME( DIAG, 'U' ) ) THEN
|
||||
SCALE = ONE
|
||||
SUM = MIN( M, N )
|
||||
DO 310 J = 1, N
|
||||
CALL SLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
|
||||
$ SUM )
|
||||
310 CONTINUE
|
||||
ELSE
|
||||
SCALE = ZERO
|
||||
SUM = ONE
|
||||
DO 320 J = 1, N
|
||||
CALL SLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
|
||||
320 CONTINUE
|
||||
END IF
|
||||
END IF
|
||||
VALUE = SCALE*SQRT( SUM )
|
||||
END IF
|
||||
*
|
||||
SLANTR = VALUE
|
||||
RETURN
|
||||
*
|
||||
* End of SLANTR
|
||||
*
|
||||
END
|
||||
Reference in New Issue
Block a user