LAPACK 3.3.0

# stpt03.f

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```00001       SUBROUTINE STPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
00002      \$                   TSCAL, X, LDX, B, LDB, WORK, RESID )
00003 *
00004 *  -- LAPACK test routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          DIAG, TRANS, UPLO
00010       INTEGER            LDB, LDX, N, NRHS
00011       REAL               RESID, SCALE, TSCAL
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               AP( * ), B( LDB, * ), CNORM( * ), WORK( * ),
00015      \$                   X( LDX, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  STPT03 computes the residual for the solution to a scaled triangular
00022 *  system of equations A*x = s*b  or  A'*x = s*b  when the triangular
00023 *  matrix A is stored in packed format.  Here A' is the transpose of A,
00024 *  s is a scalar, and x and b are N by NRHS matrices.  The test ratio is
00025 *  the maximum over the number of right hand sides of
00026 *     norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
00027 *  where op(A) denotes A or A' and EPS is the machine epsilon.
00028 *
00029 *  Arguments
00030 *  =========
00031 *
00032 *  UPLO    (input) CHARACTER*1
00033 *          Specifies whether the matrix A is upper or lower triangular.
00034 *          = 'U':  Upper triangular
00035 *          = 'L':  Lower triangular
00036 *
00037 *  TRANS   (input) CHARACTER*1
00038 *          Specifies the operation applied to A.
00039 *          = 'N':  A *x = s*b  (No transpose)
00040 *          = 'T':  A'*x = s*b  (Transpose)
00041 *          = 'C':  A'*x = s*b  (Conjugate transpose = Transpose)
00042 *
00043 *  DIAG    (input) CHARACTER*1
00044 *          Specifies whether or not the matrix A is unit triangular.
00045 *          = 'N':  Non-unit triangular
00046 *          = 'U':  Unit triangular
00047 *
00048 *  N       (input) INTEGER
00049 *          The order of the matrix A.  N >= 0.
00050 *
00051 *  NRHS    (input) INTEGER
00052 *          The number of right hand sides, i.e., the number of columns
00053 *          of the matrices X and B.  NRHS >= 0.
00054 *
00055 *  AP      (input) REAL array, dimension (N*(N+1)/2)
00056 *          The upper or lower triangular matrix A, packed columnwise in
00057 *          a linear array.  The j-th column of A is stored in the array
00058 *          AP as follows:
00059 *          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
00060 *          if UPLO = 'L',
00061 *             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
00062 *
00063 *  SCALE   (input) REAL
00064 *          The scaling factor s used in solving the triangular system.
00065 *
00066 *  CNORM   (input) REAL array, dimension (N)
00067 *          The 1-norms of the columns of A, not counting the diagonal.
00068 *
00069 *  TSCAL   (input) REAL
00070 *          The scaling factor used in computing the 1-norms in CNORM.
00071 *          CNORM actually contains the column norms of TSCAL*A.
00072 *
00073 *  X       (input) REAL array, dimension (LDX,NRHS)
00074 *          The computed solution vectors for the system of linear
00075 *          equations.
00076 *
00077 *  LDX     (input) INTEGER
00078 *          The leading dimension of the array X.  LDX >= max(1,N).
00079 *
00080 *  B       (input) REAL array, dimension (LDB,NRHS)
00081 *          The right hand side vectors for the system of linear
00082 *          equations.
00083 *
00084 *  LDB     (input) INTEGER
00085 *          The leading dimension of the array B.  LDB >= max(1,N).
00086 *
00087 *  WORK    (workspace) REAL array, dimension (N)
00088 *
00089 *  RESID   (output) REAL
00090 *          The maximum over the number of right hand sides of
00091 *          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
00092 *
00093 *  =====================================================================
00094 *
00095 *     .. Parameters ..
00096       REAL               ONE, ZERO
00097       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00098 *     ..
00099 *     .. Local Scalars ..
00100       INTEGER            IX, J, JJ
00101       REAL               BIGNUM, EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
00102 *     ..
00103 *     .. External Functions ..
00104       LOGICAL            LSAME
00105       INTEGER            ISAMAX
00106       REAL               SLAMCH
00107       EXTERNAL           LSAME, ISAMAX, SLAMCH
00108 *     ..
00109 *     .. External Subroutines ..
00110       EXTERNAL           SAXPY, SCOPY, SLABAD, SSCAL, STPMV
00111 *     ..
00112 *     .. Intrinsic Functions ..
00113       INTRINSIC          ABS, MAX, REAL
00114 *     ..
00115 *     .. Executable Statements ..
00116 *
00117 *     Quick exit if N = 0.
00118 *
00119       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00120          RESID = ZERO
00121          RETURN
00122       END IF
00123       EPS = SLAMCH( 'Epsilon' )
00124       SMLNUM = SLAMCH( 'Safe minimum' )
00125       BIGNUM = ONE / SMLNUM
00126       CALL SLABAD( SMLNUM, BIGNUM )
00127 *
00128 *     Compute the norm of the triangular matrix A using the column
00129 *     norms already computed by SLATPS.
00130 *
00131       TNORM = ZERO
00132       IF( LSAME( DIAG, 'N' ) ) THEN
00133          IF( LSAME( UPLO, 'U' ) ) THEN
00134             JJ = 1
00135             DO 10 J = 1, N
00136                TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
00137                JJ = JJ + J + 1
00138    10       CONTINUE
00139          ELSE
00140             JJ = 1
00141             DO 20 J = 1, N
00142                TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
00143                JJ = JJ + N - J + 1
00144    20       CONTINUE
00145          END IF
00146       ELSE
00147          DO 30 J = 1, N
00148             TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
00149    30    CONTINUE
00150       END IF
00151 *
00152 *     Compute the maximum over the number of right hand sides of
00153 *        norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
00154 *
00155       RESID = ZERO
00156       DO 40 J = 1, NRHS
00157          CALL SCOPY( N, X( 1, J ), 1, WORK, 1 )
00158          IX = ISAMAX( N, WORK, 1 )
00159          XNORM = MAX( ONE, ABS( X( IX, J ) ) )
00160          XSCAL = ( ONE / XNORM ) / REAL( N )
00161          CALL SSCAL( N, XSCAL, WORK, 1 )
00162          CALL STPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 )
00163          CALL SAXPY( N, -SCALE*XSCAL, B( 1, J ), 1, WORK, 1 )
00164          IX = ISAMAX( N, WORK, 1 )
00165          ERR = TSCAL*ABS( WORK( IX ) )
00166          IX = ISAMAX( N, X( 1, J ), 1 )
00167          XNORM = ABS( X( IX, J ) )
00168          IF( ERR*SMLNUM.LE.XNORM ) THEN
00169             IF( XNORM.GT.ZERO )
00170      \$         ERR = ERR / XNORM
00171          ELSE
00172             IF( ERR.GT.ZERO )
00173      \$         ERR = ONE / EPS
00174          END IF
00175          IF( ERR*SMLNUM.LE.TNORM ) THEN
00176             IF( TNORM.GT.ZERO )
00177      \$         ERR = ERR / TNORM
00178          ELSE
00179             IF( ERR.GT.ZERO )
00180      \$         ERR = ONE / EPS
00181          END IF
00182          RESID = MAX( RESID, ERR )
00183    40 CONTINUE
00184 *
00185       RETURN
00186 *
00187 *     End of STPT03
00188 *
00189       END
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