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SUBROUTINE CTRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
$ CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER DIAG, TRANS, UPLO
INTEGER LDA, LDB, LDX, N, NRHS
REAL RESID, SCALE, TSCAL
* ..
* .. Array Arguments ..
REAL CNORM( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
$ X( LDX, * )
* ..
*
* Purpose
* =======
*
* CTRT03 computes the residual for the solution to a scaled triangular
* system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b.
* Here A is a triangular matrix, A**T denotes the transpose of A, A**H
* denotes the conjugate transpose of A, s is a scalar, and x and b are
* N by NRHS matrices. The test ratio is the maximum over the number of
* right hand sides of
* norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
* where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the matrix A is upper or lower triangular.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* TRANS (input) CHARACTER*1
* Specifies the operation applied to A.
* = 'N': A *x = s*b (No transpose)
* = 'T': A**T *x = s*b (Transpose)
* = 'C': A**H *x = s*b (Conjugate transpose)
*
* DIAG (input) CHARACTER*1
* Specifies whether or not the matrix A is unit triangular.
* = 'N': Non-unit triangular
* = 'U': Unit triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrices X and B. NRHS >= 0.
*
* A (input) COMPLEX array, dimension (LDA,N)
* The triangular matrix A. If UPLO = 'U', the leading n by n
* upper triangular part of the array A contains the upper
* triangular matrix, and the strictly lower triangular part of
* A is not referenced. If UPLO = 'L', the leading n by n lower
* triangular part of the array A contains the lower triangular
* matrix, and the strictly upper triangular part of A is not
* referenced. If DIAG = 'U', the diagonal elements of A are
* also not referenced and are assumed to be 1.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* SCALE (input) REAL
* The scaling factor s used in solving the triangular system.
*
* CNORM (input) REAL array, dimension (N)
* The 1-norms of the columns of A, not counting the diagonal.
*
* TSCAL (input) REAL
* The scaling factor used in computing the 1-norms in CNORM.
* CNORM actually contains the column norms of TSCAL*A.
*
* X (input) COMPLEX array, dimension (LDX,NRHS)
* The computed solution vectors for the system of linear
* equations.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(1,N).
*
* B (input) COMPLEX array, dimension (LDB,NRHS)
* The right hand side vectors for the system of linear
* equations.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* WORK (workspace) COMPLEX array, dimension (N)
*
* RESID (output) REAL
* The maximum over the number of right hand sides of
* norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER IX, J
REAL EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICAMAX
REAL SLAMCH
EXTERNAL LSAME, ICAMAX, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CAXPY, CCOPY, CSSCAL, CTRMV
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, CMPLX, MAX, REAL
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0
*
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
EPS = SLAMCH( 'Epsilon' )
SMLNUM = SLAMCH( 'Safe minimum' )
*
* Compute the norm of the triangular matrix A using the column
* norms already computed by CLATRS.
*
TNORM = ZERO
IF( LSAME( DIAG, 'N' ) ) THEN
DO 10 J = 1, N
TNORM = MAX( TNORM, TSCAL*ABS( A( J, J ) )+CNORM( J ) )
10 CONTINUE
ELSE
DO 20 J = 1, N
TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
20 CONTINUE
END IF
*
* Compute the maximum over the number of right hand sides of
* norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*
RESID = ZERO
DO 30 J = 1, NRHS
CALL CCOPY( N, X( 1, J ), 1, WORK, 1 )
IX = ICAMAX( N, WORK, 1 )
XNORM = MAX( ONE, ABS( X( IX, J ) ) )
XSCAL = ( ONE / XNORM ) / REAL( N )
CALL CSSCAL( N, XSCAL, WORK, 1 )
CALL CTRMV( UPLO, TRANS, DIAG, N, A, LDA, WORK, 1 )
CALL CAXPY( N, CMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 )
IX = ICAMAX( N, WORK, 1 )
ERR = TSCAL*ABS( WORK( IX ) )
IX = ICAMAX( N, X( 1, J ), 1 )
XNORM = ABS( X( IX, J ) )
IF( ERR*SMLNUM.LE.XNORM ) THEN
IF( XNORM.GT.ZERO )
$ ERR = ERR / XNORM
ELSE
IF( ERR.GT.ZERO )
$ ERR = ONE / EPS
END IF
IF( ERR*SMLNUM.LE.TNORM ) THEN
IF( TNORM.GT.ZERO )
$ ERR = ERR / TNORM
ELSE
IF( ERR.GT.ZERO )
$ ERR = ONE / EPS
END IF
RESID = MAX( RESID, ERR )
30 CONTINUE
*
RETURN
*
* End of CTRT03
*
END
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