--- rpl/lapack/lapack/dlansp.f 2010/08/07 13:22:18 1.5
+++ rpl/lapack/lapack/dlansp.f 2020/05/21 21:45:59 1.18
@@ -1,10 +1,125 @@
+*> \brief \b DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLANSP + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )
+*
+* .. Scalar Arguments ..
+* CHARACTER NORM, UPLO
+* INTEGER N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION AP( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLANSP returns the value of the one norm, or the Frobenius norm, or
+*> the infinity norm, or the element of largest absolute value of a
+*> real symmetric matrix A, supplied in packed form.
+*> \endverbatim
+*>
+*> \return DLANSP
+*> \verbatim
+*>
+*> DLANSP = ( 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 DLANSP as described
+*> above.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> symmetric matrix A is supplied.
+*> = 'U': Upper triangular part of A is supplied
+*> = 'L': Lower triangular part of A is supplied
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0. When N = 0, DLANSP is
+*> set to zero.
+*> \endverbatim
+*>
+*> \param[in] AP
+*> \verbatim
+*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
+*> The upper or lower triangle of the symmetric matrix A, packed
+*> columnwise in a linear array. The j-th column of A is stored
+*> in the array AP as follows:
+*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
+*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
+*> where LWORK >= N when NORM = 'I' or '1' or 'O'; 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 DLANSP( NORM, UPLO, N, AP, 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 NORM, UPLO
INTEGER N
@@ -13,59 +128,6 @@
DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DLANSP returns the value of the one norm, or the Frobenius norm, or
-* the infinity norm, or the element of largest absolute value of a
-* real symmetric matrix A, supplied in packed form.
-*
-* Description
-* ===========
-*
-* DLANSP returns the value
-*
-* DLANSP = ( 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 DLANSP as described
-* above.
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the upper or lower triangular part of the
-* symmetric matrix A is supplied.
-* = 'U': Upper triangular part of A is supplied
-* = 'L': Lower triangular part of A is supplied
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0. When N = 0, DLANSP is
-* set to zero.
-*
-* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
-* The upper or lower triangle of the symmetric matrix A, packed
-* columnwise in a linear array. The j-th column of A is stored
-* in the array AP as follows:
-* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
-* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
-* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
-* WORK is not referenced.
-*
* =====================================================================
*
* .. Parameters ..
@@ -74,17 +136,20 @@
* ..
* .. Local Scalars ..
INTEGER I, J, K
- DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
+ DOUBLE PRECISION ABSA, 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, SQRT
+ INTRINSIC ABS, SQRT
* ..
* .. Executable Statements ..
*
@@ -99,7 +164,8 @@
K = 1
DO 20 J = 1, N
DO 10 I = K, K + J - 1
- VALUE = MAX( VALUE, ABS( AP( I ) ) )
+ SUM = ABS( AP( I ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
10 CONTINUE
K = K + J
20 CONTINUE
@@ -107,7 +173,8 @@
K = 1
DO 40 J = 1, N
DO 30 I = K, K + N - J
- VALUE = MAX( VALUE, ABS( AP( I ) ) )
+ SUM = ABS( AP( I ) )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
30 CONTINUE
K = K + N - J + 1
40 CONTINUE
@@ -132,7 +199,8 @@
K = K + 1
60 CONTINUE
DO 70 I = 1, N
- VALUE = MAX( VALUE, WORK( I ) )
+ SUM = WORK( I )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
70 CONTINUE
ELSE
DO 80 I = 1, N
@@ -147,37 +215,54 @@
WORK( I ) = WORK( I ) + ABSA
K = K + 1
90 CONTINUE
- VALUE = MAX( VALUE, SUM )
+ IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
100 CONTINUE
END IF
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.
+*
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
+*
+* Sum off-diagonals
*
- SCALE = ZERO
- SUM = ONE
K = 2
IF( LSAME( UPLO, 'U' ) ) THEN
DO 110 J = 2, N
- CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( J-1, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
K = K + J
110 CONTINUE
ELSE
DO 120 J = 1, N - 1
- CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL DLASSQ( N-J, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
K = K + N - J + 1
120 CONTINUE
END IF
- SUM = 2*SUM
+ SSQ( 2 ) = 2*SSQ( 2 )
+*
+* Sum diagonal
+*
K = 1
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
DO 130 I = 1, N
IF( AP( K ).NE.ZERO ) THEN
ABSA = ABS( AP( K ) )
- IF( SCALE.LT.ABSA ) THEN
- SUM = ONE + SUM*( SCALE / ABSA )**2
- SCALE = ABSA
+ IF( COLSSQ( 1 ).LT.ABSA ) THEN
+ COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2
+ COLSSQ( 1 ) = ABSA
ELSE
- SUM = SUM + ( ABSA / SCALE )**2
+ COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2
END IF
END IF
IF( LSAME( UPLO, 'U' ) ) THEN
@@ -186,7 +271,8 @@
K = K + N - I + 1
END IF
130 CONTINUE
- VALUE = SCALE*SQRT( SUM )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
+ VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
DLANSP = VALUE