LAPACK 3.3.1 Linear Algebra PACKage

EIG/clarhs.f

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```00001       SUBROUTINE CLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
00002      \$                   A, LDA, X, LDX, B, LDB, ISEED, INFO )
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          TRANS, UPLO, XTYPE
00010       CHARACTER*3        PATH
00011       INTEGER            INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
00012 *     ..
00013 *     .. Array Arguments ..
00014       INTEGER            ISEED( 4 )
00015       COMPLEX            A( LDA, * ), B( LDB, * ), X( LDX, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  CLARHS chooses a set of NRHS random solution vectors and sets
00022 *  up the right hand sides for the linear system
00023 *     op( A ) * X = B,
00024 *  where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
00025 *  transpose of A).
00026 *
00027 *  Arguments
00028 *  =========
00029 *
00030 *  PATH    (input) CHARACTER*3
00031 *          The type of the complex matrix A.  PATH may be given in any
00032 *          combination of upper and lower case.  Valid paths include
00033 *             xGE:  General m x n matrix
00034 *             xGB:  General banded matrix
00035 *             xPO:  Hermitian positive definite, 2-D storage
00036 *             xPP:  Hermitian positive definite packed
00037 *             xPB:  Hermitian positive definite banded
00038 *             xHE:  Hermitian indefinite, 2-D storage
00039 *             xHP:  Hermitian indefinite packed
00040 *             xHB:  Hermitian indefinite banded
00041 *             xSY:  Symmetric indefinite, 2-D storage
00042 *             xSP:  Symmetric indefinite packed
00043 *             xSB:  Symmetric indefinite banded
00044 *             xTR:  Triangular
00045 *             xTP:  Triangular packed
00046 *             xTB:  Triangular banded
00047 *             xQR:  General m x n matrix
00048 *             xLQ:  General m x n matrix
00049 *             xQL:  General m x n matrix
00050 *             xRQ:  General m x n matrix
00051 *          where the leading character indicates the precision.
00052 *
00053 *  XTYPE   (input) CHARACTER*1
00054 *          Specifies how the exact solution X will be determined:
00055 *          = 'N':  New solution; generate a random X.
00056 *          = 'C':  Computed; use value of X on entry.
00057 *
00058 *  UPLO    (input) CHARACTER*1
00059 *          Used only if A is symmetric or triangular; specifies whether
00060 *          the upper or lower triangular part of the matrix A is stored.
00061 *          = 'U':  Upper triangular
00062 *          = 'L':  Lower triangular
00063 *
00064 *  TRANS   (input) CHARACTER*1
00065 *          Used only if A is nonsymmetric; specifies the operation
00066 *          applied to the matrix A.
00067 *          = 'N':  B := A    * X
00068 *          = 'T':  B := A**T * X
00069 *          = 'C':  B := A**H * X
00070 *
00071 *  M       (input) INTEGER
00072 *          The number of rows of the matrix A.  M >= 0.
00073 *
00074 *  N       (input) INTEGER
00075 *          The number of columns of the matrix A.  N >= 0.
00076 *
00077 *  KL      (input) INTEGER
00078 *          Used only if A is a band matrix; specifies the number of
00079 *          subdiagonals of A if A is a general band matrix or if A is
00080 *          symmetric or triangular and UPLO = 'L'; specifies the number
00081 *          of superdiagonals of A if A is symmetric or triangular and
00082 *          UPLO = 'U'.  0 <= KL <= M-1.
00083 *
00084 *  KU      (input) INTEGER
00085 *          Used only if A is a general band matrix or if A is
00086 *          triangular.
00087 *
00088 *          If PATH = xGB, specifies the number of superdiagonals of A,
00089 *          and 0 <= KU <= N-1.
00090 *
00091 *          If PATH = xTR, xTP, or xTB, specifies whether or not the
00092 *          matrix has unit diagonal:
00093 *          = 1:  matrix has non-unit diagonal (default)
00094 *          = 2:  matrix has unit diagonal
00095 *
00096 *  NRHS    (input) INTEGER
00097 *          The number of right hand side vectors in the system A*X = B.
00098 *
00099 *  A       (input) COMPLEX array, dimension (LDA,N)
00100 *          The test matrix whose type is given by PATH.
00101 *
00102 *  LDA     (input) INTEGER
00103 *          The leading dimension of the array A.
00104 *          If PATH = xGB, LDA >= KL+KU+1.
00105 *          If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.
00106 *          Otherwise, LDA >= max(1,M).
00107 *
00108 *  X       (input or output) COMPLEX  array, dimension (LDX,NRHS)
00109 *          On entry, if XTYPE = 'C' (for 'Computed'), then X contains
00110 *          the exact solution to the system of linear equations.
00111 *          On exit, if XTYPE = 'N' (for 'New'), then X is initialized
00112 *          with random values.
00113 *
00114 *  LDX     (input) INTEGER
00115 *          The leading dimension of the array X.  If TRANS = 'N',
00116 *          LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).
00117 *
00118 *  B       (output) COMPLEX  array, dimension (LDB,NRHS)
00119 *          The right hand side vector(s) for the system of equations,
00120 *          computed from B = op(A) * X, where op(A) is determined by
00121 *          TRANS.
00122 *
00123 *  LDB     (input) INTEGER
00124 *          The leading dimension of the array B.  If TRANS = 'N',
00125 *          LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).
00126 *
00127 *  ISEED   (input/output) INTEGER array, dimension (4)
00128 *          The seed vector for the random number generator (used in
00129 *          CLATMS).  Modified on exit.
00130 *
00131 *  INFO    (output) INTEGER
00132 *          = 0:  successful exit
00133 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00134 *
00135 *  =====================================================================
00136 *
00137 *     .. Parameters ..
00138       COMPLEX            ONE, ZERO
00139       PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
00140      \$                   ZERO = ( 0.0E+0, 0.0E+0 ) )
00141 *     ..
00142 *     .. Local Scalars ..
00143       LOGICAL            BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI
00144       CHARACTER          C1, DIAG
00145       CHARACTER*2        C2
00146       INTEGER            J, MB, NX
00147 *     ..
00148 *     .. External Functions ..
00149       LOGICAL            LSAME, LSAMEN
00150       EXTERNAL           LSAME, LSAMEN
00151 *     ..
00152 *     .. External Subroutines ..
00153       EXTERNAL           CGBMV, CGEMM, CHBMV, CHEMM, CHPMV, CLACPY,
00154      \$                   CLARNV, CSBMV, CSPMV, CSYMM, CTBMV, CTPMV,
00155      \$                   CTRMM, XERBLA
00156 *     ..
00157 *     .. Intrinsic Functions ..
00158       INTRINSIC          MAX
00159 *     ..
00160 *     .. Executable Statements ..
00161 *
00162 *     Test the input parameters.
00163 *
00164       INFO = 0
00165       C1 = PATH( 1: 1 )
00166       C2 = PATH( 2: 3 )
00167       TRAN = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' )
00168       NOTRAN = .NOT.TRAN
00169       GEN = LSAME( PATH( 2: 2 ), 'G' )
00170       QRS = LSAME( PATH( 2: 2 ), 'Q' ) .OR. LSAME( PATH( 3: 3 ), 'Q' )
00171       SYM = LSAME( PATH( 2: 2 ), 'P' ) .OR.
00172      \$      LSAME( PATH( 2: 2 ), 'S' ) .OR. LSAME( PATH( 2: 2 ), 'H' )
00173       TRI = LSAME( PATH( 2: 2 ), 'T' )
00174       BAND = LSAME( PATH( 3: 3 ), 'B' )
00175       IF( .NOT.LSAME( C1, 'Complex precision' ) ) THEN
00176          INFO = -1
00177       ELSE IF( .NOT.( LSAME( XTYPE, 'N' ) .OR. LSAME( XTYPE, 'C' ) ) )
00178      \$          THEN
00179          INFO = -2
00180       ELSE IF( ( SYM .OR. TRI ) .AND. .NOT.
00181      \$         ( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) ) THEN
00182          INFO = -3
00183       ELSE IF( ( GEN.OR.QRS ) .AND.
00184      \$   .NOT.( TRAN .OR. LSAME( TRANS, 'N' ) ) ) THEN
00185          INFO = -4
00186       ELSE IF( M.LT.0 ) THEN
00187          INFO = -5
00188       ELSE IF( N.LT.0 ) THEN
00189          INFO = -6
00190       ELSE IF( BAND .AND. KL.LT.0 ) THEN
00191          INFO = -7
00192       ELSE IF( BAND .AND. KU.LT.0 ) THEN
00193          INFO = -8
00194       ELSE IF( NRHS.LT.0 ) THEN
00195          INFO = -9
00196       ELSE IF( ( .NOT.BAND .AND. LDA.LT.MAX( 1, M ) ) .OR.
00197      \$         ( BAND .AND. ( SYM .OR. TRI ) .AND. LDA.LT.KL+1 ) .OR.
00198      \$         ( BAND .AND. GEN .AND. LDA.LT.KL+KU+1 ) ) THEN
00199          INFO = -11
00200       ELSE IF( ( NOTRAN .AND. LDX.LT.MAX( 1, N ) ) .OR.
00201      \$         ( TRAN .AND. LDX.LT.MAX( 1, M ) ) ) THEN
00202          INFO = -13
00203       ELSE IF( ( NOTRAN .AND. LDB.LT.MAX( 1, M ) ) .OR.
00204      \$         ( TRAN .AND. LDB.LT.MAX( 1, N ) ) ) THEN
00205          INFO = -15
00206       END IF
00207       IF( INFO.NE.0 ) THEN
00208          CALL XERBLA( 'CLARHS', -INFO )
00209          RETURN
00210       END IF
00211 *
00212 *     Initialize X to NRHS random vectors unless XTYPE = 'C'.
00213 *
00214       IF( TRAN ) THEN
00215          NX = M
00216          MB = N
00217       ELSE
00218          NX = N
00219          MB = M
00220       END IF
00221       IF( .NOT.LSAME( XTYPE, 'C' ) ) THEN
00222          DO 10 J = 1, NRHS
00223             CALL CLARNV( 2, ISEED, N, X( 1, J ) )
00224    10    CONTINUE
00225       END IF
00226 *
00227 *     Multiply X by op( A ) using an appropriate
00228 *     matrix multiply routine.
00229 *
00230       IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
00231      \$    LSAMEN( 2, C2, 'LQ' ) .OR. LSAMEN( 2, C2, 'QL' ) .OR.
00232      \$    LSAMEN( 2, C2, 'RQ' ) ) THEN
00233 *
00234 *        General matrix
00235 *
00236          CALL CGEMM( TRANS, 'N', MB, NRHS, NX, ONE, A, LDA, X, LDX,
00237      \$               ZERO, B, LDB )
00238 *
00239       ELSE IF( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'HE' ) ) THEN
00240 *
00241 *        Hermitian matrix, 2-D storage
00242 *
00243          CALL CHEMM( 'Left', UPLO, N, NRHS, ONE, A, LDA, X, LDX, ZERO,
00244      \$               B, LDB )
00245 *
00246       ELSE IF( LSAMEN( 2, C2, 'SY' ) ) THEN
00247 *
00248 *        Symmetric matrix, 2-D storage
00249 *
00250          CALL CSYMM( 'Left', UPLO, N, NRHS, ONE, A, LDA, X, LDX, ZERO,
00251      \$               B, LDB )
00252 *
00253       ELSE IF( LSAMEN( 2, C2, 'GB' ) ) THEN
00254 *
00255 *        General matrix, band storage
00256 *
00257          DO 20 J = 1, NRHS
00258             CALL CGBMV( TRANS, M, N, KL, KU, ONE, A, LDA, X( 1, J ), 1,
00259      \$                  ZERO, B( 1, J ), 1 )
00260    20    CONTINUE
00261 *
00262       ELSE IF( LSAMEN( 2, C2, 'PB' ) .OR. LSAMEN( 2, C2, 'HB' ) ) THEN
00263 *
00264 *        Hermitian matrix, band storage
00265 *
00266          DO 30 J = 1, NRHS
00267             CALL CHBMV( UPLO, N, KL, ONE, A, LDA, X( 1, J ), 1, ZERO,
00268      \$                  B( 1, J ), 1 )
00269    30    CONTINUE
00270 *
00271       ELSE IF( LSAMEN( 2, C2, 'SB' ) ) THEN
00272 *
00273 *        Symmetric matrix, band storage
00274 *
00275          DO 40 J = 1, NRHS
00276             CALL CSBMV( UPLO, N, KL, ONE, A, LDA, X( 1, J ), 1, ZERO,
00277      \$                  B( 1, J ), 1 )
00278    40    CONTINUE
00279 *
00280       ELSE IF( LSAMEN( 2, C2, 'PP' ) .OR. LSAMEN( 2, C2, 'HP' ) ) THEN
00281 *
00282 *        Hermitian matrix, packed storage
00283 *
00284          DO 50 J = 1, NRHS
00285             CALL CHPMV( UPLO, N, ONE, A, X( 1, J ), 1, ZERO, B( 1, J ),
00286      \$                  1 )
00287    50    CONTINUE
00288 *
00289       ELSE IF( LSAMEN( 2, C2, 'SP' ) ) THEN
00290 *
00291 *        Symmetric matrix, packed storage
00292 *
00293          DO 60 J = 1, NRHS
00294             CALL CSPMV( UPLO, N, ONE, A, X( 1, J ), 1, ZERO, B( 1, J ),
00295      \$                  1 )
00296    60    CONTINUE
00297 *
00298       ELSE IF( LSAMEN( 2, C2, 'TR' ) ) THEN
00299 *
00300 *        Triangular matrix.  Note that for triangular matrices,
00301 *           KU = 1 => non-unit triangular
00302 *           KU = 2 => unit triangular
00303 *
00304          CALL CLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
00305          IF( KU.EQ.2 ) THEN
00306             DIAG = 'U'
00307          ELSE
00308             DIAG = 'N'
00309          END IF
00310          CALL CTRMM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
00311      \$               LDB )
00312 *
00313       ELSE IF( LSAMEN( 2, C2, 'TP' ) ) THEN
00314 *
00315 *        Triangular matrix, packed storage
00316 *
00317          CALL CLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
00318          IF( KU.EQ.2 ) THEN
00319             DIAG = 'U'
00320          ELSE
00321             DIAG = 'N'
00322          END IF
00323          DO 70 J = 1, NRHS
00324             CALL CTPMV( UPLO, TRANS, DIAG, N, A, B( 1, J ), 1 )
00325    70    CONTINUE
00326 *
00327       ELSE IF( LSAMEN( 2, C2, 'TB' ) ) THEN
00328 *
00329 *        Triangular matrix, banded storage
00330 *
00331          CALL CLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
00332          IF( KU.EQ.2 ) THEN
00333             DIAG = 'U'
00334          ELSE
00335             DIAG = 'N'
00336          END IF
00337          DO 80 J = 1, NRHS
00338             CALL CTBMV( UPLO, TRANS, DIAG, N, KL, A, LDA, B( 1, J ), 1 )
00339    80    CONTINUE
00340 *
00341       ELSE
00342 *
00343 *        If none of the above, set INFO = -1 and return
00344 *
00345          INFO = -1
00346          CALL XERBLA( 'CLARHS', -INFO )
00347       END IF
00348 *
00349       RETURN
00350 *
00351 *     End of CLARHS
00352 *
00353       END
```