--- rpl/lapack/lapack/dlansf.f 2010/12/21 13:53:30 1.5
+++ rpl/lapack/lapack/dlansf.f 2016/08/27 15:34:28 1.14
@@ -1,12 +1,218 @@
- DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
+*> \brief \b DLANSF 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 in RFP format.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLANSF + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
*
-* -- LAPACK routine (version 3.3.0) --
+* DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
+*
+* .. Scalar Arguments ..
+* CHARACTER NORM, TRANSR, UPLO
+* INTEGER N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( 0: * ), WORK( 0: * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLANSF 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 in RFP format.
+*> \endverbatim
+*>
+*> \return DLANSF
+*> \verbatim
+*>
+*> DLANSF = ( 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 matrix norm.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] NORM
+*> \verbatim
+*> NORM is CHARACTER*1
+*> Specifies the value to be returned in DLANSF as described
+*> above.
+*> \endverbatim
+*>
+*> \param[in] TRANSR
+*> \verbatim
+*> TRANSR is CHARACTER*1
+*> Specifies whether the RFP format of A is normal or
+*> transposed format.
+*> = 'N': RFP format is Normal;
+*> = 'T': RFP format is Transpose.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> On entry, UPLO specifies whether the RFP matrix A came from
+*> an upper or lower triangular matrix as follows:
+*> = 'U': RFP A came from an upper triangular matrix;
+*> = 'L': RFP A came from a lower triangular matrix.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0. When N = 0, DLANSF is
+*> set to zero.
+*> \endverbatim
+*>
+*> \param[in] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 );
+*> On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
+*> part of the symmetric matrix A stored in RFP format. See the
+*> "Notes" below for more details.
+*> Unchanged on exit.
+*> \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 September 2012
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> We first consider Rectangular Full Packed (RFP) Format when N is
+*> even. We give an example where N = 6.
+*>
+*> AP is Upper AP is Lower
+*>
+*> 00 01 02 03 04 05 00
+*> 11 12 13 14 15 10 11
+*> 22 23 24 25 20 21 22
+*> 33 34 35 30 31 32 33
+*> 44 45 40 41 42 43 44
+*> 55 50 51 52 53 54 55
+*>
+*>
+*> Let TRANSR = 'N'. RFP holds AP as follows:
+*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
+*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
+*> the transpose of the first three columns of AP upper.
+*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
+*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
+*> the transpose of the last three columns of AP lower.
+*> This covers the case N even and TRANSR = 'N'.
+*>
+*> RFP A RFP A
+*>
+*> 03 04 05 33 43 53
+*> 13 14 15 00 44 54
+*> 23 24 25 10 11 55
+*> 33 34 35 20 21 22
+*> 00 44 45 30 31 32
+*> 01 11 55 40 41 42
+*> 02 12 22 50 51 52
+*>
+*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
+*> transpose of RFP A above. One therefore gets:
+*>
+*>
+*> RFP A RFP A
+*>
+*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
+*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
+*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
+*>
+*>
+*> We then consider Rectangular Full Packed (RFP) Format when N is
+*> odd. We give an example where N = 5.
+*>
+*> AP is Upper AP is Lower
+*>
+*> 00 01 02 03 04 00
+*> 11 12 13 14 10 11
+*> 22 23 24 20 21 22
+*> 33 34 30 31 32 33
+*> 44 40 41 42 43 44
+*>
+*>
+*> Let TRANSR = 'N'. RFP holds AP as follows:
+*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
+*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
+*> the transpose of the first two columns of AP upper.
+*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
+*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
+*> the transpose of the last two columns of AP lower.
+*> This covers the case N odd and TRANSR = 'N'.
+*>
+*> RFP A RFP A
+*>
+*> 02 03 04 00 33 43
+*> 12 13 14 10 11 44
+*> 22 23 24 20 21 22
+*> 00 33 34 30 31 32
+*> 01 11 44 40 41 42
+*>
+*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
+*> transpose of RFP A above. One therefore gets:
+*>
+*> RFP A RFP A
+*>
+*> 02 12 22 00 01 00 10 20 30 40 50
+*> 03 13 23 33 11 33 11 21 31 41 51
+*> 04 14 24 34 44 43 44 22 32 42 52
+*> \endverbatim
*
-* -- Contributed by Fred Gustavson of the IBM Watson Research Center --
-* November 2010
+* =====================================================================
+ DOUBLE PRECISION FUNCTION DLANSF( NORM, TRANSR, UPLO, N, A, WORK )
*
+* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* September 2012
*
* .. Scalar Arguments ..
CHARACTER NORM, TRANSR, UPLO
@@ -16,151 +222,6 @@
DOUBLE PRECISION A( 0: * ), WORK( 0: * )
* ..
*
-* Purpose
-* =======
-*
-* DLANSF 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 in RFP format.
-*
-* Description
-* ===========
-*
-* DLANSF returns the value
-*
-* DLANSF = ( 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 matrix norm.
-*
-* Arguments
-* =========
-*
-* NORM (input) CHARACTER*1
-* Specifies the value to be returned in DLANSF as described
-* above.
-*
-* TRANSR (input) CHARACTER*1
-* Specifies whether the RFP format of A is normal or
-* transposed format.
-* = 'N': RFP format is Normal;
-* = 'T': RFP format is Transpose.
-*
-* UPLO (input) CHARACTER*1
-* On entry, UPLO specifies whether the RFP matrix A came from
-* an upper or lower triangular matrix as follows:
-* = 'U': RFP A came from an upper triangular matrix;
-* = 'L': RFP A came from a lower triangular matrix.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0. When N = 0, DLANSF is
-* set to zero.
-*
-* A (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 );
-* On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
-* part of the symmetric matrix A stored in RFP format. See the
-* "Notes" below for more details.
-* Unchanged on exit.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
-* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
-* WORK is not referenced.
-*
-* Further Details
-* ===============
-*
-* We first consider Rectangular Full Packed (RFP) Format when N is
-* even. We give an example where N = 6.
-*
-* AP is Upper AP is Lower
-*
-* 00 01 02 03 04 05 00
-* 11 12 13 14 15 10 11
-* 22 23 24 25 20 21 22
-* 33 34 35 30 31 32 33
-* 44 45 40 41 42 43 44
-* 55 50 51 52 53 54 55
-*
-*
-* Let TRANSR = 'N'. RFP holds AP as follows:
-* For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
-* three columns of AP upper. The lower triangle A(4:6,0:2) consists of
-* the transpose of the first three columns of AP upper.
-* For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
-* three columns of AP lower. The upper triangle A(0:2,0:2) consists of
-* the transpose of the last three columns of AP lower.
-* This covers the case N even and TRANSR = 'N'.
-*
-* RFP A RFP A
-*
-* 03 04 05 33 43 53
-* 13 14 15 00 44 54
-* 23 24 25 10 11 55
-* 33 34 35 20 21 22
-* 00 44 45 30 31 32
-* 01 11 55 40 41 42
-* 02 12 22 50 51 52
-*
-* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
-* transpose of RFP A above. One therefore gets:
-*
-*
-* RFP A RFP A
-*
-* 03 13 23 33 00 01 02 33 00 10 20 30 40 50
-* 04 14 24 34 44 11 12 43 44 11 21 31 41 51
-* 05 15 25 35 45 55 22 53 54 55 22 32 42 52
-*
-*
-* We then consider Rectangular Full Packed (RFP) Format when N is
-* odd. We give an example where N = 5.
-*
-* AP is Upper AP is Lower
-*
-* 00 01 02 03 04 00
-* 11 12 13 14 10 11
-* 22 23 24 20 21 22
-* 33 34 30 31 32 33
-* 44 40 41 42 43 44
-*
-*
-* Let TRANSR = 'N'. RFP holds AP as follows:
-* For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
-* three columns of AP upper. The lower triangle A(3:4,0:1) consists of
-* the transpose of the first two columns of AP upper.
-* For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
-* three columns of AP lower. The upper triangle A(0:1,1:2) consists of
-* the transpose of the last two columns of AP lower.
-* This covers the case N odd and TRANSR = 'N'.
-*
-* RFP A RFP A
-*
-* 02 03 04 00 33 43
-* 12 13 14 10 11 44
-* 22 23 24 20 21 22
-* 00 33 34 30 31 32
-* 01 11 44 40 41 42
-*
-* Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
-* transpose of RFP A above. One therefore gets:
-*
-* RFP A RFP A
-*
-* 02 12 22 00 01 00 10 20 30 40 50
-* 03 13 23 33 11 33 11 21 31 41 51
-* 04 14 24 34 44 43 44 22 32 42 52
-*
-* Reference
-* =========
-*
* =====================================================================
*
* .. Parameters ..
@@ -169,12 +230,11 @@
* ..
* .. Local Scalars ..
INTEGER I, J, IFM, ILU, NOE, N1, K, L, LDA
- DOUBLE PRECISION SCALE, S, VALUE, AA
+ DOUBLE PRECISION SCALE, S, VALUE, AA, TEMP
* ..
* .. External Functions ..
- LOGICAL LSAME
- INTEGER IDAMAX
- EXTERNAL LSAME, IDAMAX
+ LOGICAL LSAME, DISNAN
+ EXTERNAL LSAME, DISNAN
* ..
* .. External Subroutines ..
EXTERNAL DLASSQ
@@ -187,25 +247,28 @@
IF( N.EQ.0 ) THEN
DLANSF = ZERO
RETURN
+ ELSE IF( N.EQ.1 ) THEN
+ DLANSF = ABS( A(0) )
+ RETURN
END IF
*
* set noe = 1 if n is odd. if n is even set noe=0
*
NOE = 1
IF( MOD( N, 2 ).EQ.0 )
- + NOE = 0
+ $ NOE = 0
*
* set ifm = 0 when form='T or 't' and 1 otherwise
*
IFM = 1
IF( LSAME( TRANSR, 'T' ) )
- + IFM = 0
+ $ IFM = 0
*
* set ilu = 0 when uplo='U or 'u' and 1 otherwise
*
ILU = 1
IF( LSAME( UPLO, 'U' ) )
- + ILU = 0
+ $ ILU = 0
*
* set lda = (n+1)/2 when ifm = 0
* set lda = n when ifm = 1 and noe = 1
@@ -235,14 +298,18 @@
* A is n by k
DO J = 0, K - 1
DO I = 0, N - 1
- VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ TEMP = ABS( A( I+J*LDA ) )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
END DO
END DO
ELSE
* xpose case; A is k by n
DO J = 0, N - 1
DO I = 0, K - 1
- VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ TEMP = ABS( A( I+J*LDA ) )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
END DO
END DO
END IF
@@ -252,20 +319,24 @@
* A is n+1 by k
DO J = 0, K - 1
DO I = 0, N
- VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ TEMP = ABS( A( I+J*LDA ) )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
END DO
END DO
ELSE
* xpose case; A is k by n+1
DO J = 0, N
DO I = 0, K - 1
- VALUE = MAX( VALUE, ABS( A( I+J*LDA ) ) )
+ TEMP = ABS( A( I+J*LDA ) )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
END DO
END DO
END IF
END IF
ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
- + ( NORM.EQ.'1' ) ) THEN
+ $ ( NORM.EQ.'1' ) ) THEN
*
* Find normI(A) ( = norm1(A), since A is symmetric).
*
@@ -289,7 +360,7 @@
* -> A(j+k,j+k)
WORK( J+K ) = S + AA
IF( I.EQ.K+K )
- + GO TO 10
+ $ GO TO 10
I = I + 1
AA = ABS( A( I+J*LDA ) )
* -> A(j,j)
@@ -305,8 +376,12 @@
WORK( J ) = WORK( J ) + S
END DO
10 CONTINUE
- I = IDAMAX( N, WORK, 1 )
- VALUE = WORK( I-1 )
+ VALUE = WORK( 0 )
+ DO I = 1, N-1
+ TEMP = WORK( I )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
+ END DO
ELSE
* ilu = 1
K = K + 1
@@ -343,8 +418,12 @@
END DO
WORK( J ) = WORK( J ) + S
END DO
- I = IDAMAX( N, WORK, 1 )
- VALUE = WORK( I-1 )
+ VALUE = WORK( 0 )
+ DO I = 1, N-1
+ TEMP = WORK( I )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
+ END DO
END IF
ELSE
* n is even
@@ -377,8 +456,12 @@
END DO
WORK( J ) = WORK( J ) + S
END DO
- I = IDAMAX( N, WORK, 1 )
- VALUE = WORK( I-1 )
+ VALUE = WORK( 0 )
+ DO I = 1, N-1
+ TEMP = WORK( I )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
+ END DO
ELSE
* ilu = 1
DO I = K, N - 1
@@ -411,8 +494,12 @@
END DO
WORK( J ) = WORK( J ) + S
END DO
- I = IDAMAX( N, WORK, 1 )
- VALUE = WORK( I-1 )
+ VALUE = WORK( 0 )
+ DO I = 1, N-1
+ TEMP = WORK( I )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
+ END DO
END IF
END IF
ELSE
@@ -473,8 +560,12 @@
END DO
WORK( J ) = WORK( J ) + S
END DO
- I = IDAMAX( N, WORK, 1 )
- VALUE = WORK( I-1 )
+ VALUE = WORK( 0 )
+ DO I = 1, N-1
+ TEMP = WORK( I )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
+ END DO
ELSE
* ilu=1
K = K + 1
@@ -534,8 +625,12 @@
END DO
WORK( J ) = WORK( J ) + S
END DO
- I = IDAMAX( N, WORK, 1 )
- VALUE = WORK( I-1 )
+ VALUE = WORK( 0 )
+ DO I = 1, N-1
+ TEMP = WORK( I )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
+ END DO
END IF
ELSE
* n is even
@@ -603,8 +698,12 @@
* A(k-1,k-1)
S = S + AA
WORK( I ) = WORK( I ) + S
- I = IDAMAX( N, WORK, 1 )
- VALUE = WORK( I-1 )
+ VALUE = WORK( 0 )
+ DO I = 1, N-1
+ TEMP = WORK( I )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
+ END DO
ELSE
* ilu=1
DO I = K, N - 1
@@ -672,8 +771,12 @@
END DO
WORK( J-1 ) = WORK( J-1 ) + S
END DO
- I = IDAMAX( N, WORK, 1 )
- VALUE = WORK( I-1 )
+ VALUE = WORK( 0 )
+ DO I = 1, N-1
+ TEMP = WORK( I )
+ IF( VALUE .LT. TEMP .OR. DISNAN( TEMP ) )
+ $ VALUE = TEMP
+ END DO
END IF
END IF
END IF
@@ -724,7 +827,7 @@
ELSE
* A is xpose
IF( ILU.EQ.0 ) THEN
-* A' is upper
+* A**T is upper
DO J = 1, K - 2
CALL DLASSQ( J, A( 0+( K+J )*LDA ), 1, SCALE, S )
* U at A(0,k)
@@ -735,7 +838,7 @@
END DO
DO J = 0, K - 2
CALL DLASSQ( K-J-1, A( J+1+( J+K-1 )*LDA ), 1,
- + SCALE, S )
+ $ SCALE, S )
* L at A(0,k-1)
END DO
S = S + S
@@ -745,7 +848,7 @@
CALL DLASSQ( K, A( 0+( K-1 )*LDA ), LDA+1, SCALE, S )
* tri L at A(0,k-1)
ELSE
-* A' is lower
+* A**T is lower
DO J = 1, K - 1
CALL DLASSQ( J, A( 0+J*LDA ), 1, SCALE, S )
* U at A(0,0)
@@ -806,7 +909,7 @@
ELSE
* A is xpose
IF( ILU.EQ.0 ) THEN
-* A' is upper
+* A**T is upper
DO J = 1, K - 1
CALL DLASSQ( J, A( 0+( K+1+J )*LDA ), 1, SCALE, S )
* U at A(0,k+1)
@@ -817,7 +920,7 @@
END DO
DO J = 0, K - 2
CALL DLASSQ( K-J-1, A( J+1+( J+K )*LDA ), 1, SCALE,
- + S )
+ $ S )
* L at A(0,k)
END DO
S = S + S
@@ -827,7 +930,7 @@
CALL DLASSQ( K, A( 0+K*LDA ), LDA+1, SCALE, S )
* tri L at A(0,k)
ELSE
-* A' is lower
+* A**T is lower
DO J = 1, K - 1
CALL DLASSQ( J, A( 0+( J+1 )*LDA ), 1, SCALE, S )
* U at A(0,1)