*> \brief \b ZLANTR 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 ZLANTR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION ZLANTR( NORM, UPLO, DIAG, M, N, A, LDA, * WORK ) * * .. Scalar Arguments .. * CHARACTER DIAG, NORM, UPLO * INTEGER LDA, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION WORK( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLANTR 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 ZLANTR *> \verbatim *> *> ZLANTR = ( 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 ZLANTR 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, ZLANTR 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, ZLANTR is set to zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 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 DOUBLE PRECISION 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 complex16OTHERauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION ZLANTR( 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 .. DOUBLE PRECISION WORK( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL UDIAG INTEGER I, J DOUBLE PRECISION SCALE, SUM, VALUE * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZLASSQ * .. * .. 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. DISNAN( 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. DISNAN( 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. DISNAN( 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. DISNAN( 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. DISNAN( 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. DISNAN( 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. DISNAN( 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 ZLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM ) 290 CONTINUE ELSE SCALE = ZERO SUM = ONE DO 300 J = 1, N CALL ZLASSQ( 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 ZLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE, \$ SUM ) 310 CONTINUE ELSE SCALE = ZERO SUM = ONE DO 320 J = 1, N CALL ZLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM ) 320 CONTINUE END IF END IF VALUE = SCALE*SQRT( SUM ) END IF * ZLANTR = VALUE RETURN * * End of ZLANTR * END