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Refactor ?GEBAL (Reference-LAPACK PR 808)

tags/v0.3.24
Martin Kroeker GitHub 2 years ago
parent
5f1fb27c40
commit
d175b8f56f
No known key found for this signature in database GPG Key ID: 4AEE18F83AFDEB23
4 changed files with 654 additions and 574 deletions
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  1. +167
    -145
      lapack-netlib/SRC/cgebal.f
  2. +159
    -141
      lapack-netlib/SRC/dgebal.f
  3. +163
    -144
      lapack-netlib/SRC/sgebal.f
  4. +165
    -144
      lapack-netlib/SRC/zgebal.f

+ 167
- 145
lapack-netlib/SRC/cgebal.f View File

@@ -85,6 +85,7 @@
*> \verbatim
*> ILO is INTEGER
*> \endverbatim
*>
*> \param[out] IHI
*> \verbatim
*> IHI is INTEGER
@@ -154,6 +155,9 @@
*>
*> Modified by Tzu-Yi Chen, Computer Science Division, University of
*> California at Berkeley, USA
*>
*> Refactored by Evert Provoost, Department of Computer Science,
*> KU Leuven, Belgium
*> \endverbatim
*>
* =====================================================================
@@ -183,8 +187,8 @@
PARAMETER ( FACTOR = 0.95E+0 )
* ..
* .. Local Scalars ..
LOGICAL NOCONV
INTEGER I, ICA, IEXC, IRA, J, K, L, M
LOGICAL NOCONV, CANSWAP
INTEGER I, ICA, IRA, J, K, L
REAL C, CA, F, G, R, RA, S, SFMAX1, SFMAX2, SFMIN1,
$ SFMIN2
* ..
@@ -195,10 +199,10 @@
EXTERNAL SISNAN, LSAME, ICAMAX, SLAMCH, SCNRM2
* ..
* .. External Subroutines ..
EXTERNAL CSSCAL, CSWAP, XERBLA
EXTERNAL XERBLA, CSSCAL, CSWAP
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, AIMAG, MAX, MIN, REAL
INTRINSIC ABS, REAL, AIMAG, MAX, MIN
*
* Test the input parameters
*
@@ -216,176 +220,194 @@
RETURN
END IF
*
K = 1
L = N
* Quick returns.
*
IF( N.EQ.0 )
$ GO TO 210
IF( N.EQ.0 ) THEN
ILO = 1
IHI = 0
RETURN
END IF
*
IF( LSAME( JOB, 'N' ) ) THEN
DO 10 I = 1, N
DO I = 1, N
SCALE( I ) = ONE
10 CONTINUE
GO TO 210
END DO
ILO = 1
IHI = N
RETURN
END IF
*
IF( LSAME( JOB, 'S' ) )
$ GO TO 120
*
* Permutation to isolate eigenvalues if possible
*
GO TO 50
*
* Row and column exchange.
*
20 CONTINUE
SCALE( M ) = J
IF( J.EQ.M )
$ GO TO 30
*
CALL CSWAP( L, A( 1, J ), 1, A( 1, M ), 1 )
CALL CSWAP( N-K+1, A( J, K ), LDA, A( M, K ), LDA )
*
30 CONTINUE
GO TO ( 40, 80 )IEXC
*
* Search for rows isolating an eigenvalue and push them down.
*
40 CONTINUE
IF( L.EQ.1 )
$ GO TO 210
L = L - 1
*
50 CONTINUE
DO 70 J = L, 1, -1
* Permutation to isolate eigenvalues if possible.
*
DO 60 I = 1, L
IF( I.EQ.J )
$ GO TO 60
IF( REAL( A( J, I ) ).NE.ZERO .OR. AIMAG( A( J, I ) ).NE.
$ ZERO )GO TO 70
60 CONTINUE
*
M = L
IEXC = 1
GO TO 20
70 CONTINUE
*
GO TO 90
K = 1
L = N
*
* Search for columns isolating an eigenvalue and push them left.
IF( .NOT.LSAME( JOB, 'S' ) ) THEN
*
80 CONTINUE
K = K + 1
* Row and column exchange.
*
90 CONTINUE
DO 110 J = K, L
NOCONV = .TRUE.
DO WHILE( NOCONV )
*
* Search for rows isolating an eigenvalue and push them down.
*
NOCONV = .FALSE.
DO I = L, 1, -1
CANSWAP = .TRUE.
DO J = 1, L
IF( I.NE.J .AND. ( REAL( A( I, J ) ).NE.ZERO .OR.
$ AIMAG( A( I, J ) ).NE.ZERO ) ) THEN
CANSWAP = .FALSE.
EXIT
END IF
END DO
*
IF( CANSWAP ) THEN
SCALE( L ) = I
IF( I.NE.L ) THEN
CALL CSWAP( L, A( 1, I ), 1, A( 1, L ), 1 )
CALL CSWAP( N-K+1, A( I, K ), LDA, A( L, K ), LDA )
END IF
NOCONV = .TRUE.
*
IF( L.EQ.1 ) THEN
ILO = 1
IHI = 1
RETURN
END IF
*
L = L - 1
END IF
END DO
*
END DO

NOCONV = .TRUE.
DO WHILE( NOCONV )
*
* Search for columns isolating an eigenvalue and push them left.
*
NOCONV = .FALSE.
DO J = K, L
CANSWAP = .TRUE.
DO I = K, L
IF( I.NE.J .AND. ( REAL( A( I, J ) ).NE.ZERO .OR.
$ AIMAG( A( I, J ) ).NE.ZERO ) ) THEN
CANSWAP = .FALSE.
EXIT
END IF
END DO
*
IF( CANSWAP ) THEN
SCALE( K ) = J
IF( J.NE.K ) THEN
CALL CSWAP( L, A( 1, J ), 1, A( 1, K ), 1 )
CALL CSWAP( N-K+1, A( J, K ), LDA, A( K, K ), LDA )
END IF
NOCONV = .TRUE.
*
K = K + 1
END IF
END DO
*
END DO
*
DO 100 I = K, L
IF( I.EQ.J )
$ GO TO 100
IF( REAL( A( I, J ) ).NE.ZERO .OR. AIMAG( A( I, J ) ).NE.
$ ZERO )GO TO 110
100 CONTINUE
END IF
*
M = K
IEXC = 2
GO TO 20
110 CONTINUE
* Initialize SCALE for non-permuted submatrix.
*
120 CONTINUE
DO 130 I = K, L
DO I = K, L
SCALE( I ) = ONE
130 CONTINUE
END DO
*
IF( LSAME( JOB, 'P' ) )
$ GO TO 210
* If we only had to permute, we are done.
*
IF( LSAME( JOB, 'P' ) ) THEN
ILO = K
IHI = L
RETURN
END IF
*
* Balance the submatrix in rows K to L.
*
* Iterative loop for norm reduction
* Iterative loop for norm reduction.
*
SFMIN1 = SLAMCH( 'S' ) / SLAMCH( 'P' )
SFMAX1 = ONE / SFMIN1
SFMIN2 = SFMIN1*SCLFAC
SFMAX2 = ONE / SFMIN2
140 CONTINUE
NOCONV = .FALSE.
*
DO 200 I = K, L
*
C = SCNRM2( L-K+1, A( K, I ), 1 )
R = SCNRM2( L-K+1, A( I , K ), LDA )
ICA = ICAMAX( L, A( 1, I ), 1 )
CA = ABS( A( ICA, I ) )
IRA = ICAMAX( N-K+1, A( I, K ), LDA )
RA = ABS( A( I, IRA+K-1 ) )
*
* Guard against zero C or R due to underflow.
*
IF( C.EQ.ZERO .OR. R.EQ.ZERO )
$ GO TO 200
G = R / SCLFAC
F = ONE
S = C + R
160 CONTINUE
IF( C.GE.G .OR. MAX( F, C, CA ).GE.SFMAX2 .OR.
$ MIN( R, G, RA ).LE.SFMIN2 )GO TO 170
IF( SISNAN( C+F+CA+R+G+RA ) ) THEN
*
* Exit if NaN to avoid infinite loop
NOCONV = .TRUE.
DO WHILE( NOCONV )
NOCONV = .FALSE.
*
INFO = -3
CALL XERBLA( 'CGEBAL', -INFO )
RETURN
END IF
F = F*SCLFAC
C = C*SCLFAC
CA = CA*SCLFAC
R = R / SCLFAC
G = G / SCLFAC
RA = RA / SCLFAC
GO TO 160
*
170 CONTINUE
G = C / SCLFAC
180 CONTINUE
IF( G.LT.R .OR. MAX( R, RA ).GE.SFMAX2 .OR.
$ MIN( F, C, G, CA ).LE.SFMIN2 )GO TO 190
F = F / SCLFAC
C = C / SCLFAC
G = G / SCLFAC
CA = CA / SCLFAC
R = R*SCLFAC
RA = RA*SCLFAC
GO TO 180
*
* Now balance.
*
190 CONTINUE
IF( ( C+R ).GE.FACTOR*S )
$ GO TO 200
IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN
IF( F*SCALE( I ).LE.SFMIN1 )
$ GO TO 200
END IF
IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN
IF( SCALE( I ).GE.SFMAX1 / F )
$ GO TO 200
END IF
G = ONE / F
SCALE( I ) = SCALE( I )*F
NOCONV = .TRUE.
DO I = K, L
*
CALL CSSCAL( N-K+1, G, A( I, K ), LDA )
CALL CSSCAL( L, F, A( 1, I ), 1 )
C = SCNRM2( L-K+1, A( K, I ), 1 )
R = SCNRM2( L-K+1, A( I, K ), LDA )
ICA = ICAMAX( L, A( 1, I ), 1 )
CA = ABS( A( ICA, I ) )
IRA = ICAMAX( N-K+1, A( I, K ), LDA )
RA = ABS( A( I, IRA+K-1 ) )
*
200 CONTINUE
* Guard against zero C or R due to underflow.
*
IF( C.EQ.ZERO .OR. R.EQ.ZERO ) CYCLE
*
* Exit if NaN to avoid infinite loop
*
IF( NOCONV )
$ GO TO 140
IF( SISNAN( C+CA+R+RA ) ) THEN
INFO = -3
CALL XERBLA( 'CGEBAL', -INFO )
RETURN
END IF
*
G = R / SCLFAC
F = ONE
S = C + R
*
DO WHILE( C.LT.G .AND. MAX( F, C, CA ).LT.SFMAX2 .AND.
$ MIN( R, G, RA ).GT.SFMIN2 )
F = F*SCLFAC
C = C*SCLFAC
CA = CA*SCLFAC
R = R / SCLFAC
G = G / SCLFAC
RA = RA / SCLFAC
END DO
*
G = C / SCLFAC
*
DO WHILE( G.GE.R .AND. MAX( R, RA ).LT.SFMAX2 .AND.
$ MIN( F, C, G, CA ).GT.SFMIN2 )
F = F / SCLFAC
C = C / SCLFAC
G = G / SCLFAC
CA = CA / SCLFAC
R = R*SCLFAC
RA = RA*SCLFAC
END DO
*
* Now balance.
*
IF( ( C+R ).GE.FACTOR*S ) CYCLE
IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN
IF( F*SCALE( I ).LE.SFMIN1 ) CYCLE
END IF
IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN
IF( SCALE( I ).GE.SFMAX1 / F ) CYCLE
END IF
G = ONE / F
SCALE( I ) = SCALE( I )*F
NOCONV = .TRUE.
*
CALL CSSCAL( N-K+1, G, A( I, K ), LDA )
CALL CSSCAL( L, F, A( 1, I ), 1 )
*
END DO
*
END DO
*
210 CONTINUE
ILO = K
IHI = L
*


+ 159
- 141
lapack-netlib/SRC/dgebal.f View File

@@ -153,6 +153,9 @@
*>
*> Modified by Tzu-Yi Chen, Computer Science Division, University of
*> California at Berkeley, USA
*>
*> Refactored by Evert Provoost, Department of Computer Science,
*> KU Leuven, Belgium
*> \endverbatim
*>
* =====================================================================
@@ -181,8 +184,8 @@
PARAMETER ( FACTOR = 0.95D+0 )
* ..
* .. Local Scalars ..
LOGICAL NOCONV
INTEGER I, ICA, IEXC, IRA, J, K, L, M
LOGICAL NOCONV, CANSWAP
INTEGER I, ICA, IRA, J, K, L
DOUBLE PRECISION C, CA, F, G, R, RA, S, SFMAX1, SFMAX2, SFMIN1,
$ SFMIN2
* ..
@@ -214,177 +217,192 @@
RETURN
END IF
*
K = 1
L = N
* Quick returns.
*
IF( N.EQ.0 )
$ GO TO 210
IF( N.EQ.0 ) THEN
ILO = 1
IHI = 0
RETURN
END IF
*
IF( LSAME( JOB, 'N' ) ) THEN
DO 10 I = 1, N
DO I = 1, N
SCALE( I ) = ONE
10 CONTINUE
GO TO 210
END DO
ILO = 1
IHI = N
RETURN
END IF
*
IF( LSAME( JOB, 'S' ) )
$ GO TO 120
*
* Permutation to isolate eigenvalues if possible
*
GO TO 50
*
* Row and column exchange.
*
20 CONTINUE
SCALE( M ) = J
IF( J.EQ.M )
$ GO TO 30
*
CALL DSWAP( L, A( 1, J ), 1, A( 1, M ), 1 )
CALL DSWAP( N-K+1, A( J, K ), LDA, A( M, K ), LDA )
*
30 CONTINUE
GO TO ( 40, 80 )IEXC
*
* Search for rows isolating an eigenvalue and push them down.
*
40 CONTINUE
IF( L.EQ.1 )
$ GO TO 210
L = L - 1
*
50 CONTINUE
DO 70 J = L, 1, -1
* Permutation to isolate eigenvalues if possible.
*
DO 60 I = 1, L
IF( I.EQ.J )
$ GO TO 60
IF( A( J, I ).NE.ZERO )
$ GO TO 70
60 CONTINUE
*
M = L
IEXC = 1
GO TO 20
70 CONTINUE
*
GO TO 90
K = 1
L = N
*
* Search for columns isolating an eigenvalue and push them left.
IF( .NOT.LSAME( JOB, 'S' ) ) THEN
*
80 CONTINUE
K = K + 1
* Row and column exchange.
*
90 CONTINUE
DO 110 J = K, L
NOCONV = .TRUE.
DO WHILE( NOCONV )
*
* Search for rows isolating an eigenvalue and push them down.
*
NOCONV = .FALSE.
DO I = L, 1, -1
CANSWAP = .TRUE.
DO J = 1, L
IF( I.NE.J .AND. A( I, J ).NE.ZERO ) THEN
CANSWAP = .FALSE.
EXIT
END IF
END DO
*
IF( CANSWAP ) THEN
SCALE( L ) = I
IF( I.NE.L ) THEN
CALL DSWAP( L, A( 1, I ), 1, A( 1, L ), 1 )
CALL DSWAP( N-K+1, A( I, K ), LDA, A( L, K ), LDA )
END IF
NOCONV = .TRUE.
*
IF( L.EQ.1 ) THEN
ILO = 1
IHI = 1
RETURN
END IF
*
L = L - 1
END IF
END DO
*
END DO

NOCONV = .TRUE.
DO WHILE( NOCONV )
*
* Search for columns isolating an eigenvalue and push them left.
*
NOCONV = .FALSE.
DO J = K, L
CANSWAP = .TRUE.
DO I = K, L
IF( I.NE.J .AND. A( I, J ).NE.ZERO ) THEN
CANSWAP = .FALSE.
EXIT
END IF
END DO
*
IF( CANSWAP ) THEN
SCALE( K ) = J
IF( J.NE.K ) THEN
CALL DSWAP( L, A( 1, J ), 1, A( 1, K ), 1 )
CALL DSWAP( N-K+1, A( J, K ), LDA, A( K, K ), LDA )
END IF
NOCONV = .TRUE.
*
K = K + 1
END IF
END DO
*
END DO
*
DO 100 I = K, L
IF( I.EQ.J )
$ GO TO 100
IF( A( I, J ).NE.ZERO )
$ GO TO 110
100 CONTINUE
END IF
*
M = K
IEXC = 2
GO TO 20
110 CONTINUE
* Initialize SCALE for non-permuted submatrix.
*
120 CONTINUE
DO 130 I = K, L
DO I = K, L
SCALE( I ) = ONE
130 CONTINUE
END DO
*
IF( LSAME( JOB, 'P' ) )
$ GO TO 210
* If we only had to permute, we are done.
*
IF( LSAME( JOB, 'P' ) ) THEN
ILO = K
IHI = L
RETURN
END IF
*
* Balance the submatrix in rows K to L.
*
* Iterative loop for norm reduction
* Iterative loop for norm reduction.
*
SFMIN1 = DLAMCH( 'S' ) / DLAMCH( 'P' )
SFMAX1 = ONE / SFMIN1
SFMIN2 = SFMIN1*SCLFAC
SFMAX2 = ONE / SFMIN2
*
140 CONTINUE
NOCONV = .FALSE.
NOCONV = .TRUE.
DO WHILE( NOCONV )
NOCONV = .FALSE.
*
DO 200 I = K, L
DO I = K, L
*
C = DNRM2( L-K+1, A( K, I ), 1 )
R = DNRM2( L-K+1, A( I, K ), LDA )
ICA = IDAMAX( L, A( 1, I ), 1 )
CA = ABS( A( ICA, I ) )
IRA = IDAMAX( N-K+1, A( I, K ), LDA )
RA = ABS( A( I, IRA+K-1 ) )
C = DNRM2( L-K+1, A( K, I ), 1 )
R = DNRM2( L-K+1, A( I, K ), LDA )
ICA = IDAMAX( L, A( 1, I ), 1 )
CA = ABS( A( ICA, I ) )
IRA = IDAMAX( N-K+1, A( I, K ), LDA )
RA = ABS( A( I, IRA+K-1 ) )
*
* Guard against zero C or R due to underflow.
* Guard against zero C or R due to underflow.
*
IF( C.EQ.ZERO .OR. R.EQ.ZERO )
$ GO TO 200
G = R / SCLFAC
F = ONE
S = C + R
160 CONTINUE
IF( C.GE.G .OR. MAX( F, C, CA ).GE.SFMAX2 .OR.
$ MIN( R, G, RA ).LE.SFMIN2 )GO TO 170
IF( DISNAN( C+F+CA+R+G+RA ) ) THEN
IF( C.EQ.ZERO .OR. R.EQ.ZERO ) CYCLE
*
* Exit if NaN to avoid infinite loop
*
INFO = -3
CALL XERBLA( 'DGEBAL', -INFO )
RETURN
END IF
F = F*SCLFAC
C = C*SCLFAC
CA = CA*SCLFAC
R = R / SCLFAC
G = G / SCLFAC
RA = RA / SCLFAC
GO TO 160
*
170 CONTINUE
G = C / SCLFAC
180 CONTINUE
IF( G.LT.R .OR. MAX( R, RA ).GE.SFMAX2 .OR.
$ MIN( F, C, G, CA ).LE.SFMIN2 )GO TO 190
F = F / SCLFAC
C = C / SCLFAC
G = G / SCLFAC
CA = CA / SCLFAC
R = R*SCLFAC
RA = RA*SCLFAC
GO TO 180
*
* Now balance.
*
190 CONTINUE
IF( ( C+R ).GE.FACTOR*S )
$ GO TO 200
IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN
IF( F*SCALE( I ).LE.SFMIN1 )
$ GO TO 200
END IF
IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN
IF( SCALE( I ).GE.SFMAX1 / F )
$ GO TO 200
END IF
G = ONE / F
SCALE( I ) = SCALE( I )*F
NOCONV = .TRUE.
*
CALL DSCAL( N-K+1, G, A( I, K ), LDA )
CALL DSCAL( L, F, A( 1, I ), 1 )
*
200 CONTINUE
*
IF( NOCONV )
$ GO TO 140
IF( DISNAN( C+CA+R+RA ) ) THEN
INFO = -3
CALL XERBLA( 'DGEBAL', -INFO )
RETURN
END IF
*
G = R / SCLFAC
F = ONE
S = C + R
*
DO WHILE( C.LT.G .AND. MAX( F, C, CA ).LT.SFMAX2 .AND.
$ MIN( R, G, RA ).GT.SFMIN2 )
F = F*SCLFAC
C = C*SCLFAC
CA = CA*SCLFAC
R = R / SCLFAC
G = G / SCLFAC
RA = RA / SCLFAC
END DO
*
G = C / SCLFAC
*
DO WHILE( G.GE.R .AND. MAX( R, RA ).LT.SFMAX2 .AND.
$ MIN( F, C, G, CA ).GT.SFMIN2 )
F = F / SCLFAC
C = C / SCLFAC
G = G / SCLFAC
CA = CA / SCLFAC
R = R*SCLFAC
RA = RA*SCLFAC
END DO
*
* Now balance.
*
IF( ( C+R ).GE.FACTOR*S ) CYCLE
IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN
IF( F*SCALE( I ).LE.SFMIN1 ) CYCLE
END IF
IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN
IF( SCALE( I ).GE.SFMAX1 / F ) CYCLE
END IF
G = ONE / F
SCALE( I ) = SCALE( I )*F
NOCONV = .TRUE.
*
CALL DSCAL( N-K+1, G, A( I, K ), LDA )
CALL DSCAL( L, F, A( 1, I ), 1 )
*
END DO
*
END DO
*
210 CONTINUE
ILO = K
IHI = L
*


+ 163
- 144
lapack-netlib/SRC/sgebal.f View File

@@ -153,6 +153,9 @@
*>
*> Modified by Tzu-Yi Chen, Computer Science Division, University of
*> California at Berkeley, USA
*>
*> Refactored by Evert Provoost, Department of Computer Science,
*> KU Leuven, Belgium
*> \endverbatim
*>
* =====================================================================
@@ -181,8 +184,8 @@
PARAMETER ( FACTOR = 0.95E+0 )
* ..
* .. Local Scalars ..
LOGICAL NOCONV
INTEGER I, ICA, IEXC, IRA, J, K, L, M
LOGICAL NOCONV, CANSWAP
INTEGER I, ICA, IRA, J, K, L
REAL C, CA, F, G, R, RA, S, SFMAX1, SFMAX2, SFMIN1,
$ SFMIN2
* ..
@@ -197,7 +200,7 @@
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
*
* ..
* Test the input parameters
*
INFO = 0
@@ -214,176 +217,192 @@
RETURN
END IF
*
K = 1
L = N
* Quick returns.
*
IF( N.EQ.0 )
$ GO TO 210
IF( N.EQ.0 ) THEN
ILO = 1
IHI = 0
RETURN
END IF
*
IF( LSAME( JOB, 'N' ) ) THEN
DO 10 I = 1, N
DO I = 1, N
SCALE( I ) = ONE
10 CONTINUE
GO TO 210
END DO
ILO = 1
IHI = N
RETURN
END IF
*
IF( LSAME( JOB, 'S' ) )
$ GO TO 120
*
* Permutation to isolate eigenvalues if possible
*
GO TO 50
*
* Row and column exchange.
*
20 CONTINUE
SCALE( M ) = J
IF( J.EQ.M )
$ GO TO 30
*
CALL SSWAP( L, A( 1, J ), 1, A( 1, M ), 1 )
CALL SSWAP( N-K+1, A( J, K ), LDA, A( M, K ), LDA )
*
30 CONTINUE
GO TO ( 40, 80 )IEXC
*
* Search for rows isolating an eigenvalue and push them down.
*
40 CONTINUE
IF( L.EQ.1 )
$ GO TO 210
L = L - 1
* Permutation to isolate eigenvalues if possible.
*
50 CONTINUE
DO 70 J = L, 1, -1
*
DO 60 I = 1, L
IF( I.EQ.J )
$ GO TO 60
IF( A( J, I ).NE.ZERO )
$ GO TO 70
60 CONTINUE
*
M = L
IEXC = 1
GO TO 20
70 CONTINUE
*
GO TO 90
K = 1
L = N
*
* Search for columns isolating an eigenvalue and push them left.
IF( .NOT.LSAME( JOB, 'S' ) ) THEN
*
80 CONTINUE
K = K + 1
* Row and column exchange.
*
90 CONTINUE
DO 110 J = K, L
NOCONV = .TRUE.
DO WHILE( NOCONV )
*
* Search for rows isolating an eigenvalue and push them down.
*
NOCONV = .FALSE.
DO I = L, 1, -1
CANSWAP = .TRUE.
DO J = 1, L
IF( I.NE.J .AND. A( I, J ).NE.ZERO ) THEN
CANSWAP = .FALSE.
EXIT
END IF
END DO
*
IF( CANSWAP ) THEN
SCALE( L ) = I
IF( I.NE.L ) THEN
CALL SSWAP( L, A( 1, I ), 1, A( 1, L ), 1 )
CALL SSWAP( N-K+1, A( I, K ), LDA, A( L, K ), LDA )
END IF
NOCONV = .TRUE.
*
IF( L.EQ.1 ) THEN
ILO = 1
IHI = 1
RETURN
END IF
*
L = L - 1
END IF
END DO
*
END DO

NOCONV = .TRUE.
DO WHILE( NOCONV )
*
* Search for columns isolating an eigenvalue and push them left.
*
NOCONV = .FALSE.
DO J = K, L
CANSWAP = .TRUE.
DO I = K, L
IF( I.NE.J .AND. A( I, J ).NE.ZERO ) THEN
CANSWAP = .FALSE.
EXIT
END IF
END DO
*
IF( CANSWAP ) THEN
SCALE( K ) = J
IF( J.NE.K ) THEN
CALL SSWAP( L, A( 1, J ), 1, A( 1, K ), 1 )
CALL SSWAP( N-K+1, A( J, K ), LDA, A( K, K ), LDA )
END IF
NOCONV = .TRUE.
*
K = K + 1
END IF
END DO
*
END DO
*
DO 100 I = K, L
IF( I.EQ.J )
$ GO TO 100
IF( A( I, J ).NE.ZERO )
$ GO TO 110
100 CONTINUE
END IF
*
M = K
IEXC = 2
GO TO 20
110 CONTINUE
* Initialize SCALE for non-permuted submatrix.
*
120 CONTINUE
DO 130 I = K, L
DO I = K, L
SCALE( I ) = ONE
130 CONTINUE
END DO
*
IF( LSAME( JOB, 'P' ) )
$ GO TO 210
* If we only had to permute, we are done.
*
IF( LSAME( JOB, 'P' ) ) THEN
ILO = K
IHI = L
RETURN
END IF
*
* Balance the submatrix in rows K to L.
*
* Iterative loop for norm reduction
* Iterative loop for norm reduction.
*
SFMIN1 = SLAMCH( 'S' ) / SLAMCH( 'P' )
SFMAX1 = ONE / SFMIN1
SFMIN2 = SFMIN1*SCLFAC
SFMAX2 = ONE / SFMIN2
140 CONTINUE
NOCONV = .FALSE.
*
DO 200 I = K, L
*
C = SNRM2( L-K+1, A( K, I ), 1 )
R = SNRM2( L-K+1, A( I, K ), LDA )
ICA = ISAMAX( L, A( 1, I ), 1 )
CA = ABS( A( ICA, I ) )
IRA = ISAMAX( N-K+1, A( I, K ), LDA )
RA = ABS( A( I, IRA+K-1 ) )
*
* Guard against zero C or R due to underflow.
*
IF( C.EQ.ZERO .OR. R.EQ.ZERO )
$ GO TO 200
G = R / SCLFAC
F = ONE
S = C + R
160 CONTINUE
IF( C.GE.G .OR. MAX( F, C, CA ).GE.SFMAX2 .OR.
$ MIN( R, G, RA ).LE.SFMIN2 )GO TO 170
F = F*SCLFAC
C = C*SCLFAC
CA = CA*SCLFAC
R = R / SCLFAC
G = G / SCLFAC
RA = RA / SCLFAC
GO TO 160
*
170 CONTINUE
G = C / SCLFAC
180 CONTINUE
IF( G.LT.R .OR. MAX( R, RA ).GE.SFMAX2 .OR.
$ MIN( F, C, G, CA ).LE.SFMIN2 )GO TO 190
IF( SISNAN( C+F+CA+R+G+RA ) ) THEN
*
* Exit if NaN to avoid infinite loop
NOCONV = .TRUE.
DO WHILE( NOCONV )
NOCONV = .FALSE.
*
INFO = -3
CALL XERBLA( 'SGEBAL', -INFO )
RETURN
END IF
F = F / SCLFAC
C = C / SCLFAC
G = G / SCLFAC
CA = CA / SCLFAC
R = R*SCLFAC
RA = RA*SCLFAC
GO TO 180
*
* Now balance.
*
190 CONTINUE
IF( ( C+R ).GE.FACTOR*S )
$ GO TO 200
IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN
IF( F*SCALE( I ).LE.SFMIN1 )
$ GO TO 200
END IF
IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN
IF( SCALE( I ).GE.SFMAX1 / F )
$ GO TO 200
END IF
G = ONE / F
SCALE( I ) = SCALE( I )*F
NOCONV = .TRUE.
DO I = K, L
*
C = SNRM2( L-K+1, A( K, I ), 1 )
R = SNRM2( L-K+1, A( I, K ), LDA )
ICA = ISAMAX( L, A( 1, I ), 1 )
CA = ABS( A( ICA, I ) )
IRA = ISAMAX( N-K+1, A( I, K ), LDA )
RA = ABS( A( I, IRA+K-1 ) )
*
CALL SSCAL( N-K+1, G, A( I, K ), LDA )
CALL SSCAL( L, F, A( 1, I ), 1 )
* Guard against zero C or R due to underflow.
*
200 CONTINUE
IF( C.EQ.ZERO .OR. R.EQ.ZERO ) CYCLE
*
* Exit if NaN to avoid infinite loop
*
IF( NOCONV )
$ GO TO 140
IF( SISNAN( C+CA+R+RA ) ) THEN
INFO = -3
CALL XERBLA( 'SGEBAL', -INFO )
RETURN
END IF
*
G = R / SCLFAC
F = ONE
S = C + R
*
DO WHILE( C.LT.G .AND. MAX( F, C, CA ).LT.SFMAX2 .AND.
$ MIN( R, G, RA ).GT.SFMIN2 )
F = F*SCLFAC
C = C*SCLFAC
CA = CA*SCLFAC
R = R / SCLFAC
G = G / SCLFAC
RA = RA / SCLFAC
END DO
*
G = C / SCLFAC
*
DO WHILE( G.GE.R .AND. MAX( R, RA ).LT.SFMAX2 .AND.
$ MIN( F, C, G, CA ).GT.SFMIN2 )
F = F / SCLFAC
C = C / SCLFAC
G = G / SCLFAC
CA = CA / SCLFAC
R = R*SCLFAC
RA = RA*SCLFAC
END DO
*
* Now balance.
*
IF( ( C+R ).GE.FACTOR*S ) CYCLE
IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN
IF( F*SCALE( I ).LE.SFMIN1 ) CYCLE
END IF
IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN
IF( SCALE( I ).GE.SFMAX1 / F ) CYCLE
END IF
G = ONE / F
SCALE( I ) = SCALE( I )*F
NOCONV = .TRUE.
*
CALL SSCAL( N-K+1, G, A( I, K ), LDA )
CALL SSCAL( L, F, A( 1, I ), 1 )
*
END DO
*
END DO
*
210 CONTINUE
ILO = K
IHI = L
*


+ 165
- 144
lapack-netlib/SRC/zgebal.f View File

@@ -89,7 +89,7 @@
*> \param[out] IHI
*> \verbatim
*> IHI is INTEGER
*> ILO and IHI are set to INTEGER such that on exit
*> ILO and IHI are set to integers such that on exit
*> A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
*> If JOB = 'N' or 'S', ILO = 1 and IHI = N.
*> \endverbatim
@@ -155,6 +155,9 @@
*>
*> Modified by Tzu-Yi Chen, Computer Science Division, University of
*> California at Berkeley, USA
*>
*> Refactored by Evert Provoost, Department of Computer Science,
*> KU Leuven, Belgium
*> \endverbatim
*>
* =====================================================================
@@ -184,8 +187,8 @@
PARAMETER ( FACTOR = 0.95D+0 )
* ..
* .. Local Scalars ..
LOGICAL NOCONV
INTEGER I, ICA, IEXC, IRA, J, K, L, M
LOGICAL NOCONV, CANSWAP
INTEGER I, ICA, IRA, J, K, L
DOUBLE PRECISION C, CA, F, G, R, RA, S, SFMAX1, SFMAX2, SFMIN1,
$ SFMIN2
* ..
@@ -217,176 +220,194 @@
RETURN
END IF
*
K = 1
L = N
* Quick returns.
*
IF( N.EQ.0 )
$ GO TO 210
IF( N.EQ.0 ) THEN
ILO = 1
IHI = 0
RETURN
END IF
*
IF( LSAME( JOB, 'N' ) ) THEN
DO 10 I = 1, N
DO I = 1, N
SCALE( I ) = ONE
10 CONTINUE
GO TO 210
END DO
ILO = 1
IHI = N
RETURN
END IF
*
IF( LSAME( JOB, 'S' ) )
$ GO TO 120
*
* Permutation to isolate eigenvalues if possible
*
GO TO 50
*
* Row and column exchange.
*
20 CONTINUE
SCALE( M ) = J
IF( J.EQ.M )
$ GO TO 30
*
CALL ZSWAP( L, A( 1, J ), 1, A( 1, M ), 1 )
CALL ZSWAP( N-K+1, A( J, K ), LDA, A( M, K ), LDA )
*
30 CONTINUE
GO TO ( 40, 80 )IEXC
*
* Search for rows isolating an eigenvalue and push them down.
*
40 CONTINUE
IF( L.EQ.1 )
$ GO TO 210
L = L - 1
*
50 CONTINUE
DO 70 J = L, 1, -1
* Permutation to isolate eigenvalues if possible.
*
DO 60 I = 1, L
IF( I.EQ.J )
$ GO TO 60
IF( DBLE( A( J, I ) ).NE.ZERO .OR. DIMAG( A( J, I ) ).NE.
$ ZERO )GO TO 70
60 CONTINUE
*
M = L
IEXC = 1
GO TO 20
70 CONTINUE
*
GO TO 90
K = 1
L = N
*
* Search for columns isolating an eigenvalue and push them left.
IF( .NOT.LSAME( JOB, 'S' ) ) THEN
*
80 CONTINUE
K = K + 1
* Row and column exchange.
*
90 CONTINUE
DO 110 J = K, L
NOCONV = .TRUE.
DO WHILE( NOCONV )
*
* Search for rows isolating an eigenvalue and push them down.
*
NOCONV = .FALSE.
DO I = L, 1, -1
CANSWAP = .TRUE.
DO J = 1, L
IF( I.NE.J .AND. ( DBLE( A( I, J ) ).NE.ZERO .OR.
$ DIMAG( A( I, J ) ).NE.ZERO ) ) THEN
CANSWAP = .FALSE.
EXIT
END IF
END DO
*
IF( CANSWAP ) THEN
SCALE( L ) = I
IF( I.NE.L ) THEN
CALL ZSWAP( L, A( 1, I ), 1, A( 1, L ), 1 )
CALL ZSWAP( N-K+1, A( I, K ), LDA, A( L, K ), LDA )
END IF
NOCONV = .TRUE.
*
IF( L.EQ.1 ) THEN
ILO = 1
IHI = 1
RETURN
END IF
*
L = L - 1
END IF
END DO
*
END DO

NOCONV = .TRUE.
DO WHILE( NOCONV )
*
* Search for columns isolating an eigenvalue and push them left.
*
NOCONV = .FALSE.
DO J = K, L
CANSWAP = .TRUE.
DO I = K, L
IF( I.NE.J .AND. ( DBLE( A( I, J ) ).NE.ZERO .OR.
$ DIMAG( A( I, J ) ).NE.ZERO ) ) THEN
CANSWAP = .FALSE.
EXIT
END IF
END DO
*
IF( CANSWAP ) THEN
SCALE( K ) = J
IF( J.NE.K ) THEN
CALL ZSWAP( L, A( 1, J ), 1, A( 1, K ), 1 )
CALL ZSWAP( N-K+1, A( J, K ), LDA, A( K, K ), LDA )
END IF
NOCONV = .TRUE.
*
K = K + 1
END IF
END DO
*
END DO
*
DO 100 I = K, L
IF( I.EQ.J )
$ GO TO 100
IF( DBLE( A( I, J ) ).NE.ZERO .OR. DIMAG( A( I, J ) ).NE.
$ ZERO )GO TO 110
100 CONTINUE
END IF
*
M = K
IEXC = 2
GO TO 20
110 CONTINUE
* Initialize SCALE for non-permuted submatrix.
*
120 CONTINUE
DO 130 I = K, L
DO I = K, L
SCALE( I ) = ONE
130 CONTINUE
END DO
*
IF( LSAME( JOB, 'P' ) )
$ GO TO 210
* If we only had to permute, we are done.
*
IF( LSAME( JOB, 'P' ) ) THEN
ILO = K
IHI = L
RETURN
END IF
*
* Balance the submatrix in rows K to L.
*
* Iterative loop for norm reduction
* Iterative loop for norm reduction.
*
SFMIN1 = DLAMCH( 'S' ) / DLAMCH( 'P' )
SFMAX1 = ONE / SFMIN1
SFMIN2 = SFMIN1*SCLFAC
SFMAX2 = ONE / SFMIN2
140 CONTINUE
NOCONV = .FALSE.
*
DO 200 I = K, L
*
C = DZNRM2( L-K+1, A( K, I ), 1 )
R = DZNRM2( L-K+1, A( I, K ), LDA )
ICA = IZAMAX( L, A( 1, I ), 1 )
CA = ABS( A( ICA, I ) )
IRA = IZAMAX( N-K+1, A( I, K ), LDA )
RA = ABS( A( I, IRA+K-1 ) )
*
* Guard against zero C or R due to underflow.
*
IF( C.EQ.ZERO .OR. R.EQ.ZERO )
$ GO TO 200
G = R / SCLFAC
F = ONE
S = C + R
160 CONTINUE
IF( C.GE.G .OR. MAX( F, C, CA ).GE.SFMAX2 .OR.
$ MIN( R, G, RA ).LE.SFMIN2 )GO TO 170
IF( DISNAN( C+F+CA+R+G+RA ) ) THEN
*
* Exit if NaN to avoid infinite loop
NOCONV = .TRUE.
DO WHILE( NOCONV )
NOCONV = .FALSE.
*
INFO = -3
CALL XERBLA( 'ZGEBAL', -INFO )
RETURN
END IF
F = F*SCLFAC
C = C*SCLFAC
CA = CA*SCLFAC
R = R / SCLFAC
G = G / SCLFAC
RA = RA / SCLFAC
GO TO 160
*
170 CONTINUE
G = C / SCLFAC
180 CONTINUE
IF( G.LT.R .OR. MAX( R, RA ).GE.SFMAX2 .OR.
$ MIN( F, C, G, CA ).LE.SFMIN2 )GO TO 190
F = F / SCLFAC
C = C / SCLFAC
G = G / SCLFAC
CA = CA / SCLFAC
R = R*SCLFAC
RA = RA*SCLFAC
GO TO 180
*
* Now balance.
*
190 CONTINUE
IF( ( C+R ).GE.FACTOR*S )
$ GO TO 200
IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN
IF( F*SCALE( I ).LE.SFMIN1 )
$ GO TO 200
END IF
IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN
IF( SCALE( I ).GE.SFMAX1 / F )
$ GO TO 200
END IF
G = ONE / F
SCALE( I ) = SCALE( I )*F
NOCONV = .TRUE.
DO I = K, L
*
CALL ZDSCAL( N-K+1, G, A( I, K ), LDA )
CALL ZDSCAL( L, F, A( 1, I ), 1 )
C = DZNRM2( L-K+1, A( K, I ), 1 )
R = DZNRM2( L-K+1, A( I, K ), LDA )
ICA = IZAMAX( L, A( 1, I ), 1 )
CA = ABS( A( ICA, I ) )
IRA = IZAMAX( N-K+1, A( I, K ), LDA )
RA = ABS( A( I, IRA+K-1 ) )
*
200 CONTINUE
* Guard against zero C or R due to underflow.
*
IF( C.EQ.ZERO .OR. R.EQ.ZERO ) CYCLE
*
* Exit if NaN to avoid infinite loop
*
IF( NOCONV )
$ GO TO 140
IF( DISNAN( C+CA+R+RA ) ) THEN
INFO = -3
CALL XERBLA( 'ZGEBAL', -INFO )
RETURN
END IF
*
G = R / SCLFAC
F = ONE
S = C + R
*
DO WHILE( C.LT.G .AND. MAX( F, C, CA ).LT.SFMAX2 .AND.
$ MIN( R, G, RA ).GT.SFMIN2 )
F = F*SCLFAC
C = C*SCLFAC
CA = CA*SCLFAC
R = R / SCLFAC
G = G / SCLFAC
RA = RA / SCLFAC
END DO
*
G = C / SCLFAC
*
DO WHILE( G.GE.R .AND. MAX( R, RA ).LT.SFMAX2 .AND.
$ MIN( F, C, G, CA ).GT.SFMIN2 )
F = F / SCLFAC
C = C / SCLFAC
G = G / SCLFAC
CA = CA / SCLFAC
R = R*SCLFAC
RA = RA*SCLFAC
END DO
*
* Now balance.
*
IF( ( C+R ).GE.FACTOR*S ) CYCLE
IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN
IF( F*SCALE( I ).LE.SFMIN1 ) CYCLE
END IF
IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN
IF( SCALE( I ).GE.SFMAX1 / F ) CYCLE
END IF
G = ONE / F
SCALE( I ) = SCALE( I )*F
NOCONV = .TRUE.
*
CALL ZDSCAL( N-K+1, G, A( I, K ), LDA )
CALL ZDSCAL( L, F, A( 1, I ), 1 )
*
END DO
*
END DO
*
210 CONTINUE
ILO = K
IHI = L
*


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