--- rpl/lapack/lapack/dlantr.f 2010/08/06 15:28:41 1.3 +++ rpl/lapack/lapack/dlantr.f 2017/06/17 11:06:23 1.16 @@ -1,10 +1,150 @@ +*> \brief \b DLANTR 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 DLANTR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA, +* WORK ) +* +* .. Scalar Arguments .. +* CHARACTER DIAG, NORM, UPLO +* INTEGER LDA, M, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANTR 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 DLANTR +*> \verbatim +*> +*> DLANTR = ( 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 DLANTR 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, DLANTR 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, DLANTR is set to zero. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION 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 doubleOTHERauxiliary +* +* ===================================================================== DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA, $ WORK ) * -* -- LAPACK auxiliary routine (version 3.2) -- +* -- 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..-- -* November 2006 +* December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, NORM, UPLO @@ -14,75 +154,6 @@ DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DLANTR 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. -* -* Description -* =========== -* -* DLANTR returns the value -* -* DLANTR = ( 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. -* -* Arguments -* ========= -* -* NORM (input) CHARACTER*1 -* Specifies the value to be returned in DLANTR as described -* above. -* -* UPLO (input) 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. -* -* DIAG (input) CHARACTER*1 -* Specifies whether or not the matrix A has unit diagonal. -* = 'N': Non-unit diagonal -* = 'U': Unit diagonal -* -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0, and if -* UPLO = 'U', M <= N. When M = 0, DLANTR is set to zero. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= 0, and if -* UPLO = 'L', N <= M. When N = 0, DLANTR is set to zero. -* -* A (input) DOUBLE PRECISION 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. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(M,1). -* -* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), -* where LWORK >= M when NORM = 'I'; otherwise, WORK is not -* referenced. -* * ===================================================================== * * .. Parameters .. @@ -98,11 +169,11 @@ EXTERNAL DLASSQ * .. * .. External Functions .. - LOGICAL LSAME - EXTERNAL LSAME + LOGICAL LSAME, DISNAN + EXTERNAL LSAME, DISNAN * .. * .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN, SQRT + INTRINSIC ABS, MIN, SQRT * .. * .. Executable Statements .. * @@ -117,13 +188,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, MIN( M, J-1 ) - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + 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 - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + SUM = ABS( A( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE 40 CONTINUE END IF @@ -132,13 +205,15 @@ IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N DO 50 I = 1, MIN( M, J ) - VALUE = MAX( VALUE, ABS( A( I, 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 - VALUE = MAX( VALUE, ABS( A( I, J ) ) ) + SUM = ABS( A( I, J ) ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE 80 CONTINUE END IF @@ -162,7 +237,7 @@ SUM = SUM + ABS( A( I, J ) ) 100 CONTINUE END IF - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 110 CONTINUE ELSE DO 140 J = 1, N @@ -177,7 +252,7 @@ SUM = SUM + ABS( A( I, J ) ) 130 CONTINUE END IF - VALUE = MAX( VALUE, SUM ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 140 CONTINUE END IF ELSE IF( LSAME( NORM, 'I' ) ) THEN @@ -230,7 +305,8 @@ END IF VALUE = ZERO DO 280 I = 1, M - VALUE = MAX( VALUE, WORK( I ) ) + SUM = WORK( I ) + IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 280 CONTINUE ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN *