--- rpl/lapack/lapack/zlangb.f 2010/01/26 15:22:46 1.1.1.1
+++ rpl/lapack/lapack/zlangb.f 2020/05/21 21:46:07 1.18
@@ -1,11 +1,136 @@
+*> \brief \b ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLANGB + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
+* WORK )
+*
+* .. Scalar Arguments ..
+* CHARACTER NORM
+* INTEGER KL, KU, LDAB, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION WORK( * )
+* COMPLEX*16 AB( LDAB, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZLANGB returns the value of the one norm, or the Frobenius norm, or
+*> the infinity norm, or the element of largest absolute value of an
+*> n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
+*> \endverbatim
+*>
+*> \return ZLANGB
+*> \verbatim
+*>
+*> ZLANGB = ( 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 ZLANGB as described
+*> above.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0. When N = 0, ZLANGB is
+*> set to zero.
+*> \endverbatim
+*>
+*> \param[in] KL
+*> \verbatim
+*> KL is INTEGER
+*> The number of sub-diagonals of the matrix A. KL >= 0.
+*> \endverbatim
+*>
+*> \param[in] KU
+*> \verbatim
+*> KU is INTEGER
+*> The number of super-diagonals of the matrix A. KU >= 0.
+*> \endverbatim
+*>
+*> \param[in] AB
+*> \verbatim
+*> AB is COMPLEX*16 array, dimension (LDAB,N)
+*> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
+*> column of A is stored in the j-th column of the array AB as
+*> follows:
+*> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array AB. LDAB >= KL+KU+1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
+*> where LWORK >= N 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 complex16GBauxiliary
+*
+* =====================================================================
DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
$ 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
INTEGER KL, KU, LDAB, N
@@ -15,61 +140,6 @@
COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
-*
-* ZLANGB returns the value of the one norm, or the Frobenius norm, or
-* the infinity norm, or the element of largest absolute value of an
-* n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
-*
-* Description
-* ===========
-*
-* ZLANGB returns the value
-*
-* ZLANGB = ( 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 ZLANGB as described
-* above.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0. When N = 0, ZLANGB is
-* set to zero.
-*
-* KL (input) INTEGER
-* The number of sub-diagonals of the matrix A. KL >= 0.
-*
-* KU (input) INTEGER
-* The number of super-diagonals of the matrix A. KU >= 0.
-*
-* AB (input) COMPLEX*16 array, dimension (LDAB,N)
-* The band matrix A, stored in rows 1 to KL+KU+1. The j-th
-* column of A is stored in the j-th column of the array AB as
-* follows:
-* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array AB. LDAB >= KL+KU+1.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
-* where LWORK >= N when NORM = 'I'; otherwise, WORK is not
-* referenced.
-*
* =====================================================================
*
* .. Parameters ..
@@ -78,14 +148,17 @@
* ..
* .. Local Scalars ..
INTEGER I, J, K, L
- DOUBLE PRECISION SCALE, SUM, VALUE
+ DOUBLE PRECISION SUM, VALUE, TEMP
+* ..
+* .. Local Arrays ..
+ DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
* ..
* .. External Functions ..
- LOGICAL LSAME
- EXTERNAL LSAME
+ LOGICAL LSAME, DISNAN
+ EXTERNAL LSAME, DISNAN
* ..
* .. External Subroutines ..
- EXTERNAL ZLASSQ
+ EXTERNAL ZLASSQ, DCOMBSSQ
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, SQRT
@@ -101,7 +174,8 @@
VALUE = ZERO
DO 20 J = 1, N
DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
- VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
+ TEMP = ABS( AB( I, J ) )
+ IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
10 CONTINUE
20 CONTINUE
ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
@@ -114,7 +188,7 @@
DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
SUM = SUM + ABS( AB( I, J ) )
30 CONTINUE
- VALUE = MAX( VALUE, SUM )
+ IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM
40 CONTINUE
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
@@ -131,20 +205,28 @@
70 CONTINUE
VALUE = ZERO
DO 80 I = 1, N
- VALUE = MAX( VALUE, WORK( I ) )
+ TEMP = WORK( I )
+ IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
80 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.
*
- SCALE = ZERO
- SUM = ONE
+ SSQ( 1 ) = ZERO
+ SSQ( 2 ) = ONE
DO 90 J = 1, N
L = MAX( 1, J-KU )
K = KU + 1 - J + L
- CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
+ COLSSQ( 1 ) = ZERO
+ COLSSQ( 2 ) = ONE
+ CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1,
+ $ COLSSQ( 1 ), COLSSQ( 2 ) )
+ CALL DCOMBSSQ( SSQ, COLSSQ )
90 CONTINUE
- VALUE = SCALE*SQRT( SUM )
+ VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
END IF
*
ZLANGB = VALUE