218 lines
6.4 KiB
FortranFixed
218 lines
6.4 KiB
FortranFixed
SUBROUTINE CSPT03( UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND,
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$ RESID )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDW, N
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REAL RCOND, RESID
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* ..
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* .. Array Arguments ..
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REAL RWORK( * )
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COMPLEX A( * ), AINV( * ), WORK( LDW, * )
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* ..
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*
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* Purpose
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* =======
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*
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* CSPT03 computes the residual for a complex symmetric packed matrix
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* times its inverse:
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* norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
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* where EPS is the machine epsilon.
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*
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* Arguments
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* ==========
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*
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* UPLO (input) CHARACTER*1
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* Specifies whether the upper or lower triangular part of the
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* complex symmetric matrix A is stored:
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* = 'U': Upper triangular
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* = 'L': Lower triangular
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*
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* N (input) INTEGER
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* The number of rows and columns of the matrix A. N >= 0.
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*
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* A (input) COMPLEX array, dimension (N*(N+1)/2)
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* The original complex symmetric matrix A, stored as a packed
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* triangular matrix.
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*
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* AINV (input) COMPLEX array, dimension (N*(N+1)/2)
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* The (symmetric) inverse of the matrix A, stored as a packed
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* triangular matrix.
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*
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* WORK (workspace) COMPLEX array, dimension (LDWORK,N)
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*
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* LDWORK (input) INTEGER
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* The leading dimension of the array WORK. LDWORK >= max(1,N).
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*
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* RWORK (workspace) REAL array, dimension (N)
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*
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* RCOND (output) REAL
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* The reciprocal of the condition number of A, computed as
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* ( 1/norm(A) ) / norm(AINV).
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*
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* RESID (output) REAL
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* norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, ICOL, J, JCOL, K, KCOL, NALL
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REAL AINVNM, ANORM, EPS
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COMPLEX T
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL CLANGE, CLANSP, SLAMCH
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COMPLEX CDOTU
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EXTERNAL LSAME, CLANGE, CLANSP, SLAMCH, CDOTU
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC REAL
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0.
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*
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IF( N.LE.0 ) THEN
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RCOND = ONE
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
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*
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EPS = SLAMCH( 'Epsilon' )
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ANORM = CLANSP( '1', UPLO, N, A, RWORK )
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AINVNM = CLANSP( '1', UPLO, N, AINV, RWORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCOND = ZERO
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RESID = ONE / EPS
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RETURN
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END IF
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RCOND = ( ONE/ANORM ) / AINVNM
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*
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* Case where both A and AINV are upper triangular:
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* Each element of - A * AINV is computed by taking the dot product
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* of a row of A with a column of AINV.
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 70 I = 1, N
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ICOL = ( ( I-1 )*I ) / 2 + 1
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*
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* Code when J <= I
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*
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DO 30 J = 1, I
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JCOL = ( ( J-1 )*J ) / 2 + 1
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T = CDOTU( J, A( ICOL ), 1, AINV( JCOL ), 1 )
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JCOL = JCOL + 2*J - 1
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KCOL = ICOL - 1
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DO 10 K = J + 1, I
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T = T + A( KCOL+K )*AINV( JCOL )
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JCOL = JCOL + K
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10 CONTINUE
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KCOL = KCOL + 2*I
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DO 20 K = I + 1, N
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T = T + A( KCOL )*AINV( JCOL )
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KCOL = KCOL + K
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JCOL = JCOL + K
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20 CONTINUE
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WORK( I, J ) = -T
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30 CONTINUE
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*
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* Code when J > I
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*
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DO 60 J = I + 1, N
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JCOL = ( ( J-1 )*J ) / 2 + 1
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T = CDOTU( I, A( ICOL ), 1, AINV( JCOL ), 1 )
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JCOL = JCOL - 1
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KCOL = ICOL + 2*I - 1
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DO 40 K = I + 1, J
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T = T + A( KCOL )*AINV( JCOL+K )
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KCOL = KCOL + K
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40 CONTINUE
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JCOL = JCOL + 2*J
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DO 50 K = J + 1, N
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T = T + A( KCOL )*AINV( JCOL )
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KCOL = KCOL + K
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JCOL = JCOL + K
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50 CONTINUE
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WORK( I, J ) = -T
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60 CONTINUE
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70 CONTINUE
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ELSE
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*
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* Case where both A and AINV are lower triangular
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*
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NALL = ( N*( N+1 ) ) / 2
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DO 140 I = 1, N
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*
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* Code when J <= I
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*
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ICOL = NALL - ( ( N-I+1 )*( N-I+2 ) ) / 2 + 1
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DO 100 J = 1, I
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JCOL = NALL - ( ( N-J )*( N-J+1 ) ) / 2 - ( N-I )
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T = CDOTU( N-I+1, A( ICOL ), 1, AINV( JCOL ), 1 )
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KCOL = I
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JCOL = J
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DO 80 K = 1, J - 1
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T = T + A( KCOL )*AINV( JCOL )
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JCOL = JCOL + N - K
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KCOL = KCOL + N - K
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80 CONTINUE
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JCOL = JCOL - J
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DO 90 K = J, I - 1
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T = T + A( KCOL )*AINV( JCOL+K )
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KCOL = KCOL + N - K
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90 CONTINUE
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WORK( I, J ) = -T
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100 CONTINUE
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*
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* Code when J > I
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*
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ICOL = NALL - ( ( N-I )*( N-I+1 ) ) / 2
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DO 130 J = I + 1, N
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JCOL = NALL - ( ( N-J+1 )*( N-J+2 ) ) / 2 + 1
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T = CDOTU( N-J+1, A( ICOL-N+J ), 1, AINV( JCOL ), 1 )
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KCOL = I
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JCOL = J
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DO 110 K = 1, I - 1
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T = T + A( KCOL )*AINV( JCOL )
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JCOL = JCOL + N - K
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KCOL = KCOL + N - K
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110 CONTINUE
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KCOL = KCOL - I
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DO 120 K = I, J - 1
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T = T + A( KCOL+K )*AINV( JCOL )
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JCOL = JCOL + N - K
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120 CONTINUE
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WORK( I, J ) = -T
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130 CONTINUE
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140 CONTINUE
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END IF
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*
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* Add the identity matrix to WORK .
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*
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DO 150 I = 1, N
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WORK( I, I ) = WORK( I, I ) + ONE
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150 CONTINUE
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*
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* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
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*
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RESID = CLANGE( '1', N, N, WORK, LDW, RWORK )
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*
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RESID = ( ( RESID*RCOND )/EPS ) / REAL( N )
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*
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RETURN
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*
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* End of CSPT03
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*
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END
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