LAPACK: TESTING/LIN/zlattp.f Source File

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00001       SUBROUTINE ZLATTP( IMAT, UPLO, TRANS, DIAG, ISEED, N, AP, B, WORK,
00002      $                   RWORK, 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          DIAG, TRANS, UPLO
00010       INTEGER            IMAT, INFO, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       INTEGER            ISEED( 4 )
00014       DOUBLE PRECISION   RWORK( * )
00015       COMPLEX*16         AP( * ), B( * ), WORK( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  ZLATTP generates a triangular test matrix in packed storage.
00022 *  IMAT and UPLO uniquely specify the properties of the test matrix,
00023 *  which is returned in the array AP.
00024 *
00025 *  Arguments
00026 *  =========
00027 *
00028 *  IMAT    (input) INTEGER
00029 *          An integer key describing which matrix to generate for this
00030 *          path.
00031 *
00032 *  UPLO    (input) CHARACTER*1
00033 *          Specifies whether the matrix A will be upper or lower
00034 *          triangular.
00035 *          = 'U':  Upper triangular
00036 *          = 'L':  Lower triangular
00037 *
00038 *  TRANS   (input) CHARACTER*1
00039 *          Specifies whether the matrix or its transpose will be used.
00040 *          = 'N':  No transpose
00041 *          = 'T':  Transpose
00042 *          = 'C':  Conjugate transpose
00043 *
00044 *  DIAG    (output) CHARACTER*1
00045 *          Specifies whether or not the matrix A is unit triangular.
00046 *          = 'N':  Non-unit triangular
00047 *          = 'U':  Unit triangular
00048 *
00049 *  ISEED   (input/output) INTEGER array, dimension (4)
00050 *          The seed vector for the random number generator (used in
00051 *          ZLATMS).  Modified on exit.
00052 *
00053 *  N       (input) INTEGER
00054 *          The order of the matrix to be generated.
00055 *
00056 *  AP      (output) COMPLEX*16 array, dimension (N*(N+1)/2)
00057 *          The upper or lower triangular matrix A, packed columnwise in
00058 *          a linear array.  The j-th column of A is stored in the array
00059 *          AP as follows:
00060 *          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
00061 *          if UPLO = 'L',
00062 *             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
00063 *
00064 *  B       (output) COMPLEX*16 array, dimension (N)
00065 *          The right hand side vector, if IMAT > 10.
00066 *
00067 *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
00068 *
00069 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
00070 *
00071 *  INFO    (output) INTEGER
00072 *          = 0:  successful exit
00073 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00074 *
00075 *  =====================================================================
00076 *
00077 *     .. Parameters ..
00078       DOUBLE PRECISION   ONE, TWO, ZERO
00079       PARAMETER          ( ONE = 1.0D+0, TWO = 2.0D+0, ZERO = 0.0D+0 )
00080 *     ..
00081 *     .. Local Scalars ..
00082       LOGICAL            UPPER
00083       CHARACTER          DIST, PACKIT, TYPE
00084       CHARACTER*3        PATH
00085       INTEGER            I, IY, J, JC, JCNEXT, JCOUNT, JJ, JL, JR, JX,
00086      $                   KL, KU, MODE
00087       DOUBLE PRECISION   ANORM, BIGNUM, BNORM, BSCAL, C, CNDNUM, REXP,
00088      $                   SFAC, SMLNUM, T, TEXP, TLEFT, TSCAL, ULP, UNFL,
00089      $                   X, Y, Z
00090       COMPLEX*16         CTEMP, PLUS1, PLUS2, RA, RB, S, STAR1
00091 *     ..
00092 *     .. External Functions ..
00093       LOGICAL            LSAME
00094       INTEGER            IZAMAX
00095       DOUBLE PRECISION   DLAMCH
00096       COMPLEX*16         ZLARND
00097       EXTERNAL           LSAME, IZAMAX, DLAMCH, ZLARND
00098 *     ..
00099 *     .. External Subroutines ..
00100       EXTERNAL           DLABAD, DLARNV, ZDSCAL, ZLARNV, ZLATB4, ZLATMS,
00101      $                   ZROT, ZROTG
00102 *     ..
00103 *     .. Intrinsic Functions ..
00104       INTRINSIC          ABS, DBLE, DCMPLX, DCONJG, MAX, SQRT
00105 *     ..
00106 *     .. Executable Statements ..
00107 *
00108       PATH( 1: 1 ) = 'Zomplex precision'
00109       PATH( 2: 3 ) = 'TP'
00110       UNFL = DLAMCH( 'Safe minimum' )
00111       ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
00112       SMLNUM = UNFL
00113       BIGNUM = ( ONE-ULP ) / SMLNUM
00114       CALL DLABAD( SMLNUM, BIGNUM )
00115       IF( ( IMAT.GE.7 .AND. IMAT.LE.10 ) .OR. IMAT.EQ.18 ) THEN
00116          DIAG = 'U'
00117       ELSE
00118          DIAG = 'N'
00119       END IF
00120       INFO = 0
00121 *
00122 *     Quick return if N.LE.0.
00123 *
00124       IF( N.LE.0 )
00125      $   RETURN
00126 *
00127 *     Call ZLATB4 to set parameters for CLATMS.
00128 *
00129       UPPER = LSAME( UPLO, 'U' )
00130       IF( UPPER ) THEN
00131          CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00132      $                CNDNUM, DIST )
00133          PACKIT = 'C'
00134       ELSE
00135          CALL ZLATB4( PATH, -IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
00136      $                CNDNUM, DIST )
00137          PACKIT = 'R'
00138       END IF
00139 *
00140 *     IMAT <= 6:  Non-unit triangular matrix
00141 *
00142       IF( IMAT.LE.6 ) THEN
00143          CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, CNDNUM,
00144      $                ANORM, KL, KU, PACKIT, AP, N, WORK, INFO )
00145 *
00146 *     IMAT > 6:  Unit triangular matrix
00147 *     The diagonal is deliberately set to something other than 1.
00148 *
00149 *     IMAT = 7:  Matrix is the identity
00150 *
00151       ELSE IF( IMAT.EQ.7 ) THEN
00152          IF( UPPER ) THEN
00153             JC = 1
00154             DO 20 J = 1, N
00155                DO 10 I = 1, J - 1
00156                   AP( JC+I-1 ) = ZERO
00157    10          CONTINUE
00158                AP( JC+J-1 ) = J
00159                JC = JC + J
00160    20       CONTINUE
00161          ELSE
00162             JC = 1
00163             DO 40 J = 1, N
00164                AP( JC ) = J
00165                DO 30 I = J + 1, N
00166                   AP( JC+I-J ) = ZERO
00167    30          CONTINUE
00168                JC = JC + N - J + 1
00169    40       CONTINUE
00170          END IF
00171 *
00172 *     IMAT > 7:  Non-trivial unit triangular matrix
00173 *
00174 *     Generate a unit triangular matrix T with condition CNDNUM by
00175 *     forming a triangular matrix with known singular values and
00176 *     filling in the zero entries with Givens rotations.
00177 *
00178       ELSE IF( IMAT.LE.10 ) THEN
00179          IF( UPPER ) THEN
00180             JC = 0
00181             DO 60 J = 1, N
00182                DO 50 I = 1, J - 1
00183                   AP( JC+I ) = ZERO
00184    50          CONTINUE
00185                AP( JC+J ) = J
00186                JC = JC + J
00187    60       CONTINUE
00188          ELSE
00189             JC = 1
00190             DO 80 J = 1, N
00191                AP( JC ) = J
00192                DO 70 I = J + 1, N
00193                   AP( JC+I-J ) = ZERO
00194    70          CONTINUE
00195                JC = JC + N - J + 1
00196    80       CONTINUE
00197          END IF
00198 *
00199 *        Since the trace of a unit triangular matrix is 1, the product
00200 *        of its singular values must be 1.  Let s = sqrt(CNDNUM),
00201 *        x = sqrt(s) - 1/sqrt(s), y = sqrt(2/(n-2))*x, and z = x**2.
00202 *        The following triangular matrix has singular values s, 1, 1,
00203 *        ..., 1, 1/s:
00204 *
00205 *        1  y  y  y  ...  y  y  z
00206 *           1  0  0  ...  0  0  y
00207 *              1  0  ...  0  0  y
00208 *                 .  ...  .  .  .
00209 *                     .   .  .  .
00210 *                         1  0  y
00211 *                            1  y
00212 *                               1
00213 *
00214 *        To fill in the zeros, we first multiply by a matrix with small
00215 *        condition number of the form
00216 *
00217 *        1  0  0  0  0  ...
00218 *           1  +  *  0  0  ...
00219 *              1  +  0  0  0
00220 *                 1  +  *  0  0
00221 *                    1  +  0  0
00222 *                       ...
00223 *                          1  +  0
00224 *                             1  0
00225 *                                1
00226 *
00227 *        Each element marked with a '*' is formed by taking the product
00228 *        of the adjacent elements marked with '+'.  The '*'s can be
00229 *        chosen freely, and the '+'s are chosen so that the inverse of
00230 *        T will have elements of the same magnitude as T.  If the *'s in
00231 *        both T and inv(T) have small magnitude, T is well conditioned.
00232 *        The two offdiagonals of T are stored in WORK.
00233 *
00234 *        The product of these two matrices has the form
00235 *
00236 *        1  y  y  y  y  y  .  y  y  z
00237 *           1  +  *  0  0  .  0  0  y
00238 *              1  +  0  0  .  0  0  y
00239 *                 1  +  *  .  .  .  .
00240 *                    1  +  .  .  .  .
00241 *                       .  .  .  .  .
00242 *                          .  .  .  .
00243 *                             1  +  y
00244 *                                1  y
00245 *                                   1
00246 *
00247 *        Now we multiply by Givens rotations, using the fact that
00248 *
00249 *              [  c   s ] [  1   w ] [ -c  -s ] =  [  1  -w ]
00250 *              [ -s   c ] [  0   1 ] [  s  -c ]    [  0   1 ]
00251 *        and
00252 *              [ -c  -s ] [  1   0 ] [  c   s ] =  [  1   0 ]
00253 *              [  s  -c ] [  w   1 ] [ -s   c ]    [ -w   1 ]
00254 *
00255 *        where c = w / sqrt(w**2+4) and s = 2 / sqrt(w**2+4).
00256 *
00257          STAR1 = 0.25D0*ZLARND( 5, ISEED )
00258          SFAC = 0.5D0
00259          PLUS1 = SFAC*ZLARND( 5, ISEED )
00260          DO 90 J = 1, N, 2
00261             PLUS2 = STAR1 / PLUS1
00262             WORK( J ) = PLUS1
00263             WORK( N+J ) = STAR1
00264             IF( J+1.LE.N ) THEN
00265                WORK( J+1 ) = PLUS2
00266                WORK( N+J+1 ) = ZERO
00267                PLUS1 = STAR1 / PLUS2
00268                REXP = ZLARND( 2, ISEED )
00269                IF( REXP.LT.ZERO ) THEN
00270                   STAR1 = -SFAC**( ONE-REXP )*ZLARND( 5, ISEED )
00271                ELSE
00272                   STAR1 = SFAC**( ONE+REXP )*ZLARND( 5, ISEED )
00273                END IF
00274             END IF
00275    90    CONTINUE
00276 *
00277          X = SQRT( CNDNUM ) - ONE / SQRT( CNDNUM )
00278          IF( N.GT.2 ) THEN
00279             Y = SQRT( TWO / DBLE( N-2 ) )*X
00280          ELSE
00281             Y = ZERO
00282          END IF
00283          Z = X*X
00284 *
00285          IF( UPPER ) THEN
00286 *
00287 *           Set the upper triangle of A with a unit triangular matrix
00288 *           of known condition number.
00289 *
00290             JC = 1
00291             DO 100 J = 2, N
00292                AP( JC+1 ) = Y
00293                IF( J.GT.2 )
00294      $            AP( JC+J-1 ) = WORK( J-2 )
00295                IF( J.GT.3 )
00296      $            AP( JC+J-2 ) = WORK( N+J-3 )
00297                JC = JC + J
00298   100       CONTINUE
00299             JC = JC - N
00300             AP( JC+1 ) = Z
00301             DO 110 J = 2, N - 1
00302                AP( JC+J ) = Y
00303   110       CONTINUE
00304          ELSE
00305 *
00306 *           Set the lower triangle of A with a unit triangular matrix
00307 *           of known condition number.
00308 *
00309             DO 120 I = 2, N - 1
00310                AP( I ) = Y
00311   120       CONTINUE
00312             AP( N ) = Z
00313             JC = N + 1
00314             DO 130 J = 2, N - 1
00315                AP( JC+1 ) = WORK( J-1 )
00316                IF( J.LT.N-1 )
00317      $            AP( JC+2 ) = WORK( N+J-1 )
00318                AP( JC+N-J ) = Y
00319                JC = JC + N - J + 1
00320   130       CONTINUE
00321          END IF
00322 *
00323 *        Fill in the zeros using Givens rotations
00324 *
00325          IF( UPPER ) THEN
00326             JC = 1
00327             DO 150 J = 1, N - 1
00328                JCNEXT = JC + J
00329                RA = AP( JCNEXT+J-1 )
00330                RB = TWO
00331                CALL ZROTG( RA, RB, C, S )
00332 *
00333 *              Multiply by [ c  s; -conjg(s)  c] on the left.
00334 *
00335                IF( N.GT.J+1 ) THEN
00336                   JX = JCNEXT + J
00337                   DO 140 I = J + 2, N
00338                      CTEMP = C*AP( JX+J ) + S*AP( JX+J+1 )
00339                      AP( JX+J+1 ) = -DCONJG( S )*AP( JX+J ) +
00340      $                              C*AP( JX+J+1 )
00341                      AP( JX+J ) = CTEMP
00342                      JX = JX + I
00343   140             CONTINUE
00344                END IF
00345 *
00346 *              Multiply by [-c -s;  conjg(s) -c] on the right.
00347 *
00348                IF( J.GT.1 )
00349      $            CALL ZROT( J-1, AP( JCNEXT ), 1, AP( JC ), 1, -C, -S )
00350 *
00351 *              Negate A(J,J+1).
00352 *
00353                AP( JCNEXT+J-1 ) = -AP( JCNEXT+J-1 )
00354                JC = JCNEXT
00355   150       CONTINUE
00356          ELSE
00357             JC = 1
00358             DO 170 J = 1, N - 1
00359                JCNEXT = JC + N - J + 1
00360                RA = AP( JC+1 )
00361                RB = TWO
00362                CALL ZROTG( RA, RB, C, S )
00363                S = DCONJG( S )
00364 *
00365 *              Multiply by [ c -s;  conjg(s) c] on the right.
00366 *
00367                IF( N.GT.J+1 )
00368      $            CALL ZROT( N-J-1, AP( JCNEXT+1 ), 1, AP( JC+2 ), 1, C,
00369      $                       -S )
00370 *
00371 *              Multiply by [-c  s; -conjg(s) -c] on the left.
00372 *
00373                IF( J.GT.1 ) THEN
00374                   JX = 1
00375                   DO 160 I = 1, J - 1
00376                      CTEMP = -C*AP( JX+J-I ) + S*AP( JX+J-I+1 )
00377                      AP( JX+J-I+1 ) = -DCONJG( S )*AP( JX+J-I ) -
00378      $                                C*AP( JX+J-I+1 )
00379                      AP( JX+J-I ) = CTEMP
00380                      JX = JX + N - I + 1
00381   160             CONTINUE
00382                END IF
00383 *
00384 *              Negate A(J+1,J).
00385 *
00386                AP( JC+1 ) = -AP( JC+1 )
00387                JC = JCNEXT
00388   170       CONTINUE
00389          END IF
00390 *
00391 *     IMAT > 10:  Pathological test cases.  These triangular matrices
00392 *     are badly scaled or badly conditioned, so when used in solving a
00393 *     triangular system they may cause overflow in the solution vector.
00394 *
00395       ELSE IF( IMAT.EQ.11 ) THEN
00396 *
00397 *        Type 11:  Generate a triangular matrix with elements between
00398 *        -1 and 1. Give the diagonal norm 2 to make it well-conditioned.
00399 *        Make the right hand side large so that it requires scaling.
00400 *
00401          IF( UPPER ) THEN
00402             JC = 1
00403             DO 180 J = 1, N
00404                CALL ZLARNV( 4, ISEED, J-1, AP( JC ) )
00405                AP( JC+J-1 ) = ZLARND( 5, ISEED )*TWO
00406                JC = JC + J
00407   180       CONTINUE
00408          ELSE
00409             JC = 1
00410             DO 190 J = 1, N
00411                IF( J.LT.N )
00412      $            CALL ZLARNV( 4, ISEED, N-J, AP( JC+1 ) )
00413                AP( JC ) = ZLARND( 5, ISEED )*TWO
00414                JC = JC + N - J + 1
00415   190       CONTINUE
00416          END IF
00417 *
00418 *        Set the right hand side so that the largest value is BIGNUM.
00419 *
00420          CALL ZLARNV( 2, ISEED, N, B )
00421          IY = IZAMAX( N, B, 1 )
00422          BNORM = ABS( B( IY ) )
00423          BSCAL = BIGNUM / MAX( ONE, BNORM )
00424          CALL ZDSCAL( N, BSCAL, B, 1 )
00425 *
00426       ELSE IF( IMAT.EQ.12 ) THEN
00427 *
00428 *        Type 12:  Make the first diagonal element in the solve small to
00429 *        cause immediate overflow when dividing by T(j,j).
00430 *        In type 12, the offdiagonal elements are small (CNORM(j) < 1).
00431 *
00432          CALL ZLARNV( 2, ISEED, N, B )
00433          TSCAL = ONE / MAX( ONE, DBLE( N-1 ) )
00434          IF( UPPER ) THEN
00435             JC = 1
00436             DO 200 J = 1, N
00437                CALL ZLARNV( 4, ISEED, J-1, AP( JC ) )
00438                CALL ZDSCAL( J-1, TSCAL, AP( JC ), 1 )
00439                AP( JC+J-1 ) = ZLARND( 5, ISEED )
00440                JC = JC + J
00441   200       CONTINUE
00442             AP( N*( N+1 ) / 2 ) = SMLNUM*AP( N*( N+1 ) / 2 )
00443          ELSE
00444             JC = 1
00445             DO 210 J = 1, N
00446                CALL ZLARNV( 2, ISEED, N-J, AP( JC+1 ) )
00447                CALL ZDSCAL( N-J, TSCAL, AP( JC+1 ), 1 )
00448                AP( JC ) = ZLARND( 5, ISEED )
00449                JC = JC + N - J + 1
00450   210       CONTINUE
00451             AP( 1 ) = SMLNUM*AP( 1 )
00452          END IF
00453 *
00454       ELSE IF( IMAT.EQ.13 ) THEN
00455 *
00456 *        Type 13:  Make the first diagonal element in the solve small to
00457 *        cause immediate overflow when dividing by T(j,j).
00458 *        In type 13, the offdiagonal elements are O(1) (CNORM(j) > 1).
00459 *
00460          CALL ZLARNV( 2, ISEED, N, B )
00461          IF( UPPER ) THEN
00462             JC = 1
00463             DO 220 J = 1, N
00464                CALL ZLARNV( 4, ISEED, J-1, AP( JC ) )
00465                AP( JC+J-1 ) = ZLARND( 5, ISEED )
00466                JC = JC + J
00467   220       CONTINUE
00468             AP( N*( N+1 ) / 2 ) = SMLNUM*AP( N*( N+1 ) / 2 )
00469          ELSE
00470             JC = 1
00471             DO 230 J = 1, N
00472                CALL ZLARNV( 4, ISEED, N-J, AP( JC+1 ) )
00473                AP( JC ) = ZLARND( 5, ISEED )
00474                JC = JC + N - J + 1
00475   230       CONTINUE
00476             AP( 1 ) = SMLNUM*AP( 1 )
00477          END IF
00478 *
00479       ELSE IF( IMAT.EQ.14 ) THEN
00480 *
00481 *        Type 14:  T is diagonal with small numbers on the diagonal to
00482 *        make the growth factor underflow, but a small right hand side
00483 *        chosen so that the solution does not overflow.
00484 *
00485          IF( UPPER ) THEN
00486             JCOUNT = 1
00487             JC = ( N-1 )*N / 2 + 1
00488             DO 250 J = N, 1, -1
00489                DO 240 I = 1, J - 1
00490                   AP( JC+I-1 ) = ZERO
00491   240          CONTINUE
00492                IF( JCOUNT.LE.2 ) THEN
00493                   AP( JC+J-1 ) = SMLNUM*ZLARND( 5, ISEED )
00494                ELSE
00495                   AP( JC+J-1 ) = ZLARND( 5, ISEED )
00496                END IF
00497                JCOUNT = JCOUNT + 1
00498                IF( JCOUNT.GT.4 )
00499      $            JCOUNT = 1
00500                JC = JC - J + 1
00501   250       CONTINUE
00502          ELSE
00503             JCOUNT = 1
00504             JC = 1
00505             DO 270 J = 1, N
00506                DO 260 I = J + 1, N
00507                   AP( JC+I-J ) = ZERO
00508   260          CONTINUE
00509                IF( JCOUNT.LE.2 ) THEN
00510                   AP( JC ) = SMLNUM*ZLARND( 5, ISEED )
00511                ELSE
00512                   AP( JC ) = ZLARND( 5, ISEED )
00513                END IF
00514                JCOUNT = JCOUNT + 1
00515                IF( JCOUNT.GT.4 )
00516      $            JCOUNT = 1
00517                JC = JC + N - J + 1
00518   270       CONTINUE
00519          END IF
00520 *
00521 *        Set the right hand side alternately zero and small.
00522 *
00523          IF( UPPER ) THEN
00524             B( 1 ) = ZERO
00525             DO 280 I = N, 2, -2
00526                B( I ) = ZERO
00527                B( I-1 ) = SMLNUM*ZLARND( 5, ISEED )
00528   280       CONTINUE
00529          ELSE
00530             B( N ) = ZERO
00531             DO 290 I = 1, N - 1, 2
00532                B( I ) = ZERO
00533                B( I+1 ) = SMLNUM*ZLARND( 5, ISEED )
00534   290       CONTINUE
00535          END IF
00536 *
00537       ELSE IF( IMAT.EQ.15 ) THEN
00538 *
00539 *        Type 15:  Make the diagonal elements small to cause gradual
00540 *        overflow when dividing by T(j,j).  To control the amount of
00541 *        scaling needed, the matrix is bidiagonal.
00542 *
00543          TEXP = ONE / MAX( ONE, DBLE( N-1 ) )
00544          TSCAL = SMLNUM**TEXP
00545          CALL ZLARNV( 4, ISEED, N, B )
00546          IF( UPPER ) THEN
00547             JC = 1
00548             DO 310 J = 1, N
00549                DO 300 I = 1, J - 2
00550                   AP( JC+I-1 ) = ZERO
00551   300          CONTINUE
00552                IF( J.GT.1 )
00553      $            AP( JC+J-2 ) = DCMPLX( -ONE, -ONE )
00554                AP( JC+J-1 ) = TSCAL*ZLARND( 5, ISEED )
00555                JC = JC + J
00556   310       CONTINUE
00557             B( N ) = DCMPLX( ONE, ONE )
00558          ELSE
00559             JC = 1
00560             DO 330 J = 1, N
00561                DO 320 I = J + 2, N
00562                   AP( JC+I-J ) = ZERO
00563   320          CONTINUE
00564                IF( J.LT.N )
00565      $            AP( JC+1 ) = DCMPLX( -ONE, -ONE )
00566                AP( JC ) = TSCAL*ZLARND( 5, ISEED )
00567                JC = JC + N - J + 1
00568   330       CONTINUE
00569             B( 1 ) = DCMPLX( ONE, ONE )
00570          END IF
00571 *
00572       ELSE IF( IMAT.EQ.16 ) THEN
00573 *
00574 *        Type 16:  One zero diagonal element.
00575 *
00576          IY = N / 2 + 1
00577          IF( UPPER ) THEN
00578             JC = 1
00579             DO 340 J = 1, N
00580                CALL ZLARNV( 4, ISEED, J, AP( JC ) )
00581                IF( J.NE.IY ) THEN
00582                   AP( JC+J-1 ) = ZLARND( 5, ISEED )*TWO
00583                ELSE
00584                   AP( JC+J-1 ) = ZERO
00585                END IF
00586                JC = JC + J
00587   340       CONTINUE
00588          ELSE
00589             JC = 1
00590             DO 350 J = 1, N
00591                CALL ZLARNV( 4, ISEED, N-J+1, AP( JC ) )
00592                IF( J.NE.IY ) THEN
00593                   AP( JC ) = ZLARND( 5, ISEED )*TWO
00594                ELSE
00595                   AP( JC ) = ZERO
00596                END IF
00597                JC = JC + N - J + 1
00598   350       CONTINUE
00599          END IF
00600          CALL ZLARNV( 2, ISEED, N, B )
00601          CALL ZDSCAL( N, TWO, B, 1 )
00602 *
00603       ELSE IF( IMAT.EQ.17 ) THEN
00604 *
00605 *        Type 17:  Make the offdiagonal elements large to cause overflow
00606 *        when adding a column of T.  In the non-transposed case, the
00607 *        matrix is constructed to cause overflow when adding a column in
00608 *        every other step.
00609 *
00610          TSCAL = UNFL / ULP
00611          TSCAL = ( ONE-ULP ) / TSCAL
00612          DO 360 J = 1, N*( N+1 ) / 2
00613             AP( J ) = ZERO
00614   360    CONTINUE
00615          TEXP = ONE
00616          IF( UPPER ) THEN
00617             JC = ( N-1 )*N / 2 + 1
00618             DO 370 J = N, 2, -2
00619                AP( JC ) = -TSCAL / DBLE( N+1 )
00620                AP( JC+J-1 ) = ONE
00621                B( J ) = TEXP*( ONE-ULP )
00622                JC = JC - J + 1
00623                AP( JC ) = -( TSCAL / DBLE( N+1 ) ) / DBLE( N+2 )
00624                AP( JC+J-2 ) = ONE
00625                B( J-1 ) = TEXP*DBLE( N*N+N-1 )
00626                TEXP = TEXP*TWO
00627                JC = JC - J + 2
00628   370       CONTINUE
00629             B( 1 ) = ( DBLE( N+1 ) / DBLE( N+2 ) )*TSCAL
00630          ELSE
00631             JC = 1
00632             DO 380 J = 1, N - 1, 2
00633                AP( JC+N-J ) = -TSCAL / DBLE( N+1 )
00634                AP( JC ) = ONE
00635                B( J ) = TEXP*( ONE-ULP )
00636                JC = JC + N - J + 1
00637                AP( JC+N-J-1 ) = -( TSCAL / DBLE( N+1 ) ) / DBLE( N+2 )
00638                AP( JC ) = ONE
00639                B( J+1 ) = TEXP*DBLE( N*N+N-1 )
00640                TEXP = TEXP*TWO
00641                JC = JC + N - J
00642   380       CONTINUE
00643             B( N ) = ( DBLE( N+1 ) / DBLE( N+2 ) )*TSCAL
00644          END IF
00645 *
00646       ELSE IF( IMAT.EQ.18 ) THEN
00647 *
00648 *        Type 18:  Generate a unit triangular matrix with elements
00649 *        between -1 and 1, and make the right hand side large so that it
00650 *        requires scaling.
00651 *
00652          IF( UPPER ) THEN
00653             JC = 1
00654             DO 390 J = 1, N
00655                CALL ZLARNV( 4, ISEED, J-1, AP( JC ) )
00656                AP( JC+J-1 ) = ZERO
00657                JC = JC + J
00658   390       CONTINUE
00659          ELSE
00660             JC = 1
00661             DO 400 J = 1, N
00662                IF( J.LT.N )
00663      $            CALL ZLARNV( 4, ISEED, N-J, AP( JC+1 ) )
00664                AP( JC ) = ZERO
00665                JC = JC + N - J + 1
00666   400       CONTINUE
00667          END IF
00668 *
00669 *        Set the right hand side so that the largest value is BIGNUM.
00670 *
00671          CALL ZLARNV( 2, ISEED, N, B )
00672          IY = IZAMAX( N, B, 1 )
00673          BNORM = ABS( B( IY ) )
00674          BSCAL = BIGNUM / MAX( ONE, BNORM )
00675          CALL ZDSCAL( N, BSCAL, B, 1 )
00676 *
00677       ELSE IF( IMAT.EQ.19 ) THEN
00678 *
00679 *        Type 19:  Generate a triangular matrix with elements between
00680 *        BIGNUM/(n-1) and BIGNUM so that at least one of the column
00681 *        norms will exceed BIGNUM.
00682 *        1/3/91:  ZLATPS no longer can handle this case
00683 *
00684          TLEFT = BIGNUM / MAX( ONE, DBLE( N-1 ) )
00685          TSCAL = BIGNUM*( DBLE( N-1 ) / MAX( ONE, DBLE( N ) ) )
00686          IF( UPPER ) THEN
00687             JC = 1
00688             DO 420 J = 1, N
00689                CALL ZLARNV( 5, ISEED, J, AP( JC ) )
00690                CALL DLARNV( 1, ISEED, J, RWORK )
00691                DO 410 I = 1, J
00692                   AP( JC+I-1 ) = AP( JC+I-1 )*( TLEFT+RWORK( I )*TSCAL )
00693   410          CONTINUE
00694                JC = JC + J
00695   420       CONTINUE
00696          ELSE
00697             JC = 1
00698             DO 440 J = 1, N
00699                CALL ZLARNV( 5, ISEED, N-J+1, AP( JC ) )
00700                CALL DLARNV( 1, ISEED, N-J+1, RWORK )
00701                DO 430 I = J, N
00702                   AP( JC+I-J ) = AP( JC+I-J )*
00703      $                           ( TLEFT+RWORK( I-J+1 )*TSCAL )
00704   430          CONTINUE
00705                JC = JC + N - J + 1
00706   440       CONTINUE
00707          END IF
00708          CALL ZLARNV( 2, ISEED, N, B )
00709          CALL ZDSCAL( N, TWO, B, 1 )
00710       END IF
00711 *
00712 *     Flip the matrix across its counter-diagonal if the transpose will
00713 *     be used.
00714 *
00715       IF( .NOT.LSAME( TRANS, 'N' ) ) THEN
00716          IF( UPPER ) THEN
00717             JJ = 1
00718             JR = N*( N+1 ) / 2
00719             DO 460 J = 1, N / 2
00720                JL = JJ
00721                DO 450 I = J, N - J
00722                   T = AP( JR-I+J )
00723                   AP( JR-I+J ) = AP( JL )
00724                   AP( JL ) = T
00725                   JL = JL + I
00726   450          CONTINUE
00727                JJ = JJ + J + 1
00728                JR = JR - ( N-J+1 )
00729   460       CONTINUE
00730          ELSE
00731             JL = 1
00732             JJ = N*( N+1 ) / 2
00733             DO 480 J = 1, N / 2
00734                JR = JJ
00735                DO 470 I = J, N - J
00736                   T = AP( JL+I-J )
00737                   AP( JL+I-J ) = AP( JR )
00738                   AP( JR ) = T
00739                   JR = JR - I
00740   470          CONTINUE
00741                JL = JL + N - J + 1
00742                JJ = JJ - J - 1
00743   480       CONTINUE
00744          END IF
00745       END IF
00746 *
00747       RETURN
00748 *
00749 *     End of ZLATTP
00750 *
00751       END