SUBROUTINE SLATM4( ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND, \$ TRIANG, IDIST, ISEED, A, LDA ) * * -- LAPACK auxiliary test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER IDIST, ISIGN, ITYPE, LDA, N, NZ1, NZ2 REAL AMAGN, RCOND, TRIANG * .. * .. Array Arguments .. INTEGER ISEED( 4 ) REAL A( LDA, * ) * .. * * Purpose * ======= * * SLATM4 generates basic square matrices, which may later be * multiplied by others in order to produce test matrices. It is * intended mainly to be used to test the generalized eigenvalue * routines. * * It first generates the diagonal and (possibly) subdiagonal, * according to the value of ITYPE, NZ1, NZ2, ISIGN, AMAGN, and RCOND. * It then fills in the upper triangle with random numbers, if TRIANG is * non-zero. * * Arguments * ========= * * ITYPE (input) INTEGER * The "type" of matrix on the diagonal and sub-diagonal. * If ITYPE < 0, then type abs(ITYPE) is generated and then * swapped end for end (A(I,J) := A'(N-J,N-I).) See also * the description of AMAGN and ISIGN. * * Special types: * = 0: the zero matrix. * = 1: the identity. * = 2: a transposed Jordan block. * = 3: If N is odd, then a k+1 x k+1 transposed Jordan block * followed by a k x k identity block, where k=(N-1)/2. * If N is even, then k=(N-2)/2, and a zero diagonal entry * is tacked onto the end. * * Diagonal types. The diagonal consists of NZ1 zeros, then * k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE * specifies the nonzero diagonal entries as follows: * = 4: 1, ..., k * = 5: 1, RCOND, ..., RCOND * = 6: 1, ..., 1, RCOND * = 7: 1, a, a^2, ..., a^(k-1)=RCOND * = 8: 1, 1-d, 1-2*d, ..., 1-(k-1)*d=RCOND * = 9: random numbers chosen from (RCOND,1) * = 10: random numbers with distribution IDIST (see SLARND.) * * N (input) INTEGER * The order of the matrix. * * NZ1 (input) INTEGER * If abs(ITYPE) > 3, then the first NZ1 diagonal entries will * be zero. * * NZ2 (input) INTEGER * If abs(ITYPE) > 3, then the last NZ2 diagonal entries will * be zero. * * ISIGN (input) INTEGER * = 0: The sign of the diagonal and subdiagonal entries will * be left unchanged. * = 1: The diagonal and subdiagonal entries will have their * sign changed at random. * = 2: If ITYPE is 2 or 3, then the same as ISIGN=1. * Otherwise, with probability 0.5, odd-even pairs of * diagonal entries A(2*j-1,2*j-1), A(2*j,2*j) will be * converted to a 2x2 block by pre- and post-multiplying * by distinct random orthogonal rotations. The remaining * diagonal entries will have their sign changed at random. * * AMAGN (input) REAL * The diagonal and subdiagonal entries will be multiplied by * AMAGN. * * RCOND (input) REAL * If abs(ITYPE) > 4, then the smallest diagonal entry will be * entry will be RCOND. RCOND must be between 0 and 1. * * TRIANG (input) REAL * The entries above the diagonal will be random numbers with * magnitude bounded by TRIANG (i.e., random numbers multiplied * by TRIANG.) * * IDIST (input) INTEGER * Specifies the type of distribution to be used to generate a * random matrix. * = 1: UNIFORM( 0, 1 ) * = 2: UNIFORM( -1, 1 ) * = 3: NORMAL ( 0, 1 ) * * ISEED (input/output) INTEGER array, dimension (4) * On entry ISEED specifies the seed of the random number * generator. The values of ISEED are changed on exit, and can * be used in the next call to SLATM4 to continue the same * random number sequence. * Note: ISEED(4) should be odd, for the random number generator * used at present. * * A (output) REAL array, dimension (LDA, N) * Array to be computed. * * LDA (input) INTEGER * Leading dimension of A. Must be at least 1 and at least N. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE, TWO PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 ) REAL HALF PARAMETER ( HALF = ONE / TWO ) * .. * .. Local Scalars .. INTEGER I, IOFF, ISDB, ISDE, JC, JD, JR, K, KBEG, KEND, \$ KLEN REAL ALPHA, CL, CR, SAFMIN, SL, SR, SV1, SV2, TEMP * .. * .. External Functions .. REAL SLAMCH, SLARAN, SLARND EXTERNAL SLAMCH, SLARAN, SLARND * .. * .. External Subroutines .. EXTERNAL SLASET * .. * .. Intrinsic Functions .. INTRINSIC ABS, EXP, LOG, MAX, MIN, MOD, REAL, SQRT * .. * .. Executable Statements .. * IF( N.LE.0 ) \$ RETURN CALL SLASET( 'Full', N, N, ZERO, ZERO, A, LDA ) * * Insure a correct ISEED * IF( MOD( ISEED( 4 ), 2 ).NE.1 ) \$ ISEED( 4 ) = ISEED( 4 ) + 1 * * Compute diagonal and subdiagonal according to ITYPE, NZ1, NZ2, * and RCOND * IF( ITYPE.NE.0 ) THEN IF( ABS( ITYPE ).GE.4 ) THEN KBEG = MAX( 1, MIN( N, NZ1+1 ) ) KEND = MAX( KBEG, MIN( N, N-NZ2 ) ) KLEN = KEND + 1 - KBEG ELSE KBEG = 1 KEND = N KLEN = N END IF ISDB = 1 ISDE = 0 GO TO ( 10, 30, 50, 80, 100, 120, 140, 160, \$ 180, 200 )ABS( ITYPE ) * * abs(ITYPE) = 1: Identity * 10 CONTINUE DO 20 JD = 1, N A( JD, JD ) = ONE 20 CONTINUE GO TO 220 * * abs(ITYPE) = 2: Transposed Jordan block * 30 CONTINUE DO 40 JD = 1, N - 1 A( JD+1, JD ) = ONE 40 CONTINUE ISDB = 1 ISDE = N - 1 GO TO 220 * * abs(ITYPE) = 3: Transposed Jordan block, followed by the * identity. * 50 CONTINUE K = ( N-1 ) / 2 DO 60 JD = 1, K A( JD+1, JD ) = ONE 60 CONTINUE ISDB = 1 ISDE = K DO 70 JD = K + 2, 2*K + 1 A( JD, JD ) = ONE 70 CONTINUE GO TO 220 * * abs(ITYPE) = 4: 1,...,k * 80 CONTINUE DO 90 JD = KBEG, KEND A( JD, JD ) = REAL( JD-NZ1 ) 90 CONTINUE GO TO 220 * * abs(ITYPE) = 5: One large D value: * 100 CONTINUE DO 110 JD = KBEG + 1, KEND A( JD, JD ) = RCOND 110 CONTINUE A( KBEG, KBEG ) = ONE GO TO 220 * * abs(ITYPE) = 6: One small D value: * 120 CONTINUE DO 130 JD = KBEG, KEND - 1 A( JD, JD ) = ONE 130 CONTINUE A( KEND, KEND ) = RCOND GO TO 220 * * abs(ITYPE) = 7: Exponentially distributed D values: * 140 CONTINUE A( KBEG, KBEG ) = ONE IF( KLEN.GT.1 ) THEN ALPHA = RCOND**( ONE / REAL( KLEN-1 ) ) DO 150 I = 2, KLEN A( NZ1+I, NZ1+I ) = ALPHA**REAL( I-1 ) 150 CONTINUE END IF GO TO 220 * * abs(ITYPE) = 8: Arithmetically distributed D values: * 160 CONTINUE A( KBEG, KBEG ) = ONE IF( KLEN.GT.1 ) THEN ALPHA = ( ONE-RCOND ) / REAL( KLEN-1 ) DO 170 I = 2, KLEN A( NZ1+I, NZ1+I ) = REAL( KLEN-I )*ALPHA + RCOND 170 CONTINUE END IF GO TO 220 * * abs(ITYPE) = 9: Randomly distributed D values on ( RCOND, 1): * 180 CONTINUE ALPHA = LOG( RCOND ) DO 190 JD = KBEG, KEND A( JD, JD ) = EXP( ALPHA*SLARAN( ISEED ) ) 190 CONTINUE GO TO 220 * * abs(ITYPE) = 10: Randomly distributed D values from DIST * 200 CONTINUE DO 210 JD = KBEG, KEND A( JD, JD ) = SLARND( IDIST, ISEED ) 210 CONTINUE * 220 CONTINUE * * Scale by AMAGN * DO 230 JD = KBEG, KEND A( JD, JD ) = AMAGN*REAL( A( JD, JD ) ) 230 CONTINUE DO 240 JD = ISDB, ISDE A( JD+1, JD ) = AMAGN*REAL( A( JD+1, JD ) ) 240 CONTINUE * * If ISIGN = 1 or 2, assign random signs to diagonal and * subdiagonal * IF( ISIGN.GT.0 ) THEN DO 250 JD = KBEG, KEND IF( REAL( A( JD, JD ) ).NE.ZERO ) THEN IF( SLARAN( ISEED ).GT.HALF ) \$ A( JD, JD ) = -A( JD, JD ) END IF 250 CONTINUE DO 260 JD = ISDB, ISDE IF( REAL( A( JD+1, JD ) ).NE.ZERO ) THEN IF( SLARAN( ISEED ).GT.HALF ) \$ A( JD+1, JD ) = -A( JD+1, JD ) END IF 260 CONTINUE END IF * * Reverse if ITYPE < 0 * IF( ITYPE.LT.0 ) THEN DO 270 JD = KBEG, ( KBEG+KEND-1 ) / 2 TEMP = A( JD, JD ) A( JD, JD ) = A( KBEG+KEND-JD, KBEG+KEND-JD ) A( KBEG+KEND-JD, KBEG+KEND-JD ) = TEMP 270 CONTINUE DO 280 JD = 1, ( N-1 ) / 2 TEMP = A( JD+1, JD ) A( JD+1, JD ) = A( N+1-JD, N-JD ) A( N+1-JD, N-JD ) = TEMP 280 CONTINUE END IF * * If ISIGN = 2, and no subdiagonals already, then apply * random rotations to make 2x2 blocks. * IF( ISIGN.EQ.2 .AND. ITYPE.NE.2 .AND. ITYPE.NE.3 ) THEN SAFMIN = SLAMCH( 'S' ) DO 290 JD = KBEG, KEND - 1, 2 IF( SLARAN( ISEED ).GT.HALF ) THEN * * Rotation on left. * CL = TWO*SLARAN( ISEED ) - ONE SL = TWO*SLARAN( ISEED ) - ONE TEMP = ONE / MAX( SAFMIN, SQRT( CL**2+SL**2 ) ) CL = CL*TEMP SL = SL*TEMP * * Rotation on right. * CR = TWO*SLARAN( ISEED ) - ONE SR = TWO*SLARAN( ISEED ) - ONE TEMP = ONE / MAX( SAFMIN, SQRT( CR**2+SR**2 ) ) CR = CR*TEMP SR = SR*TEMP * * Apply * SV1 = A( JD, JD ) SV2 = A( JD+1, JD+1 ) A( JD, JD ) = CL*CR*SV1 + SL*SR*SV2 A( JD+1, JD ) = -SL*CR*SV1 + CL*SR*SV2 A( JD, JD+1 ) = -CL*SR*SV1 + SL*CR*SV2 A( JD+1, JD+1 ) = SL*SR*SV1 + CL*CR*SV2 END IF 290 CONTINUE END IF * END IF * * Fill in upper triangle (except for 2x2 blocks) * IF( TRIANG.NE.ZERO ) THEN IF( ISIGN.NE.2 .OR. ITYPE.EQ.2 .OR. ITYPE.EQ.3 ) THEN IOFF = 1 ELSE IOFF = 2 DO 300 JR = 1, N - 1 IF( A( JR+1, JR ).EQ.ZERO ) \$ A( JR, JR+1 ) = TRIANG*SLARND( IDIST, ISEED ) 300 CONTINUE END IF * DO 320 JC = 2, N DO 310 JR = 1, JC - IOFF A( JR, JC ) = TRIANG*SLARND( IDIST, ISEED ) 310 CONTINUE 320 CONTINUE END IF * RETURN * * End of SLATM4 * END