--- rpl/lapack/lapack/dlantr.f 2010/08/07 13:22:18 1.5
+++ rpl/lapack/lapack/dlantr.f 2020/05/21 21:45:59 1.18
@@ -1,11 +1,152 @@
+*> \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
*
+ IMPLICIT NONE
* .. Scalar Arguments ..
CHARACTER DIAG, NORM, UPLO
INTEGER LDA, M, N
@@ -14,75 +155,6 @@
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 ..
@@ -92,17 +164,20 @@
* .. Local Scalars ..
LOGICAL UDIAG
INTEGER I, J
- DOUBLE PRECISION SCALE, SUM, VALUE
+ DOUBLE PRECISION SUM, VALUE
* ..
-* .. External Subroutines ..
- EXTERNAL DLASSQ
+* .. Local Arrays ..
+ DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Functions ..
- LOGICAL LSAME
- EXTERNAL LSAME
+ LOGICAL LSAME, DISNAN
+ EXTERNAL LSAME, DISNAN
+* ..
+* .. External Subroutines ..
+ EXTERNAL DLASSQ, DCOMBSSQ
* ..
* .. Intrinsic Functions ..
- INTRINSIC ABS, MAX, MIN, SQRT
+ INTRINSIC ABS, MIN, SQRT
* ..
* .. Executable Statements ..
*
@@ -117,13 +192,15 @@
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 +209,15 @@
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 +241,7 @@
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 +256,7 @@
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
@@ -230,43 +309,62 @@
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
*
* 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
- SCALE = ONE
- SUM = MIN( M, N )
+ SSQ( 1 ) = ONE
+ SSQ( 2 ) = MIN( M, N )
DO 290 J = 2, N
- CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( MIN( M, J-1 ), A( 1, J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
290 CONTINUE
ELSE
- SCALE = ZERO
- SUM = ONE
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
DO 300 J = 1, N
- CALL DLASSQ( MIN( M, J ), A( 1, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( MIN( M, J ), A( 1, J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
300 CONTINUE
END IF
ELSE
IF( LSAME( DIAG, 'U' ) ) THEN
- SCALE = ONE
- SUM = MIN( M, N )
+ SSQ( 1 ) = ONE
+ SSQ( 2 ) = MIN( M, N )
DO 310 J = 1, N
- CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1, SCALE,
- $ SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( M-J, A( MIN( M, J+1 ), J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
310 CONTINUE
ELSE
- SCALE = ZERO
- SUM = ONE
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
DO 320 J = 1, N
- CALL DLASSQ( M-J+1, A( J, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( M-J+1, A( J, J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
320 CONTINUE
END IF
END IF
- VALUE = SCALE*SQRT( SUM )
+ VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
DLANTR = VALUE