373 lines
11 KiB
FortranFixed
373 lines
11 KiB
FortranFixed
SUBROUTINE DLATM4( ITYPE, N, NZ1, NZ2, ISIGN, AMAGN, RCOND,
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$ TRIANG, IDIST, ISEED, A, LDA )
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*
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* -- LAPACK auxiliary test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* October 2006
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*
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* .. Scalar Arguments ..
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INTEGER IDIST, ISIGN, ITYPE, LDA, N, NZ1, NZ2
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DOUBLE PRECISION AMAGN, RCOND, TRIANG
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( 4 )
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DOUBLE PRECISION A( LDA, * )
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* ..
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*
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* Purpose
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* =======
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*
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* DLATM4 generates basic square matrices, which may later be
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* multiplied by others in order to produce test matrices. It is
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* intended mainly to be used to test the generalized eigenvalue
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* routines.
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*
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* It first generates the diagonal and (possibly) subdiagonal,
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* according to the value of ITYPE, NZ1, NZ2, ISIGN, AMAGN, and RCOND.
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* It then fills in the upper triangle with random numbers, if TRIANG is
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* non-zero.
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*
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* Arguments
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* =========
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*
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* ITYPE (input) INTEGER
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* The "type" of matrix on the diagonal and sub-diagonal.
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* If ITYPE < 0, then type abs(ITYPE) is generated and then
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* swapped end for end (A(I,J) := A'(N-J,N-I).) See also
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* the description of AMAGN and ISIGN.
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*
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* Special types:
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* = 0: the zero matrix.
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* = 1: the identity.
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* = 2: a transposed Jordan block.
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* = 3: If N is odd, then a k+1 x k+1 transposed Jordan block
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* followed by a k x k identity block, where k=(N-1)/2.
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* If N is even, then k=(N-2)/2, and a zero diagonal entry
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* is tacked onto the end.
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*
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* Diagonal types. The diagonal consists of NZ1 zeros, then
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* k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE
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* specifies the nonzero diagonal entries as follows:
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* = 4: 1, ..., k
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* = 5: 1, RCOND, ..., RCOND
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* = 6: 1, ..., 1, RCOND
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* = 7: 1, a, a^2, ..., a^(k-1)=RCOND
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* = 8: 1, 1-d, 1-2*d, ..., 1-(k-1)*d=RCOND
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* = 9: random numbers chosen from (RCOND,1)
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* = 10: random numbers with distribution IDIST (see DLARND.)
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*
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* N (input) INTEGER
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* The order of the matrix.
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*
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* NZ1 (input) INTEGER
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* If abs(ITYPE) > 3, then the first NZ1 diagonal entries will
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* be zero.
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*
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* NZ2 (input) INTEGER
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* If abs(ITYPE) > 3, then the last NZ2 diagonal entries will
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* be zero.
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*
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* ISIGN (input) INTEGER
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* = 0: The sign of the diagonal and subdiagonal entries will
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* be left unchanged.
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* = 1: The diagonal and subdiagonal entries will have their
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* sign changed at random.
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* = 2: If ITYPE is 2 or 3, then the same as ISIGN=1.
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* Otherwise, with probability 0.5, odd-even pairs of
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* diagonal entries A(2*j-1,2*j-1), A(2*j,2*j) will be
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* converted to a 2x2 block by pre- and post-multiplying
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* by distinct random orthogonal rotations. The remaining
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* diagonal entries will have their sign changed at random.
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*
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* AMAGN (input) DOUBLE PRECISION
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* The diagonal and subdiagonal entries will be multiplied by
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* AMAGN.
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*
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* RCOND (input) DOUBLE PRECISION
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* If abs(ITYPE) > 4, then the smallest diagonal entry will be
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* entry will be RCOND. RCOND must be between 0 and 1.
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*
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* TRIANG (input) DOUBLE PRECISION
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* The entries above the diagonal will be random numbers with
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* magnitude bounded by TRIANG (i.e., random numbers multiplied
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* by TRIANG.)
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*
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* IDIST (input) INTEGER
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* Specifies the type of distribution to be used to generate a
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* random matrix.
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* = 1: UNIFORM( 0, 1 )
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* = 2: UNIFORM( -1, 1 )
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* = 3: NORMAL ( 0, 1 )
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*
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* ISEED (input/output) INTEGER array, dimension (4)
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* On entry ISEED specifies the seed of the random number
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* generator. The values of ISEED are changed on exit, and can
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* be used in the next call to DLATM4 to continue the same
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* random number sequence.
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* Note: ISEED(4) should be odd, for the random number generator
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* used at present.
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*
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* A (output) DOUBLE PRECISION array, dimension (LDA, N)
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* Array to be computed.
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*
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* LDA (input) INTEGER
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* Leading dimension of A. Must be at least 1 and at least N.
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE, TWO
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 )
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DOUBLE PRECISION HALF
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PARAMETER ( HALF = ONE / TWO )
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* ..
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* .. Local Scalars ..
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INTEGER I, IOFF, ISDB, ISDE, JC, JD, JR, K, KBEG, KEND,
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$ KLEN
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DOUBLE PRECISION ALPHA, CL, CR, SAFMIN, SL, SR, SV1, SV2, TEMP
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DLARAN, DLARND
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EXTERNAL DLAMCH, DLARAN, DLARND
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* ..
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* .. External Subroutines ..
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EXTERNAL DLASET
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, EXP, LOG, MAX, MIN, MOD, SQRT
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* ..
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* .. Executable Statements ..
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*
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IF( N.LE.0 )
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$ RETURN
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CALL DLASET( 'Full', N, N, ZERO, ZERO, A, LDA )
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*
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* Insure a correct ISEED
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*
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IF( MOD( ISEED( 4 ), 2 ).NE.1 )
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$ ISEED( 4 ) = ISEED( 4 ) + 1
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*
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* Compute diagonal and subdiagonal according to ITYPE, NZ1, NZ2,
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* and RCOND
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*
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IF( ITYPE.NE.0 ) THEN
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IF( ABS( ITYPE ).GE.4 ) THEN
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KBEG = MAX( 1, MIN( N, NZ1+1 ) )
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KEND = MAX( KBEG, MIN( N, N-NZ2 ) )
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KLEN = KEND + 1 - KBEG
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ELSE
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KBEG = 1
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KEND = N
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KLEN = N
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END IF
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ISDB = 1
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ISDE = 0
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GO TO ( 10, 30, 50, 80, 100, 120, 140, 160,
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$ 180, 200 )ABS( ITYPE )
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*
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* |ITYPE| = 1: Identity
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*
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10 CONTINUE
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DO 20 JD = 1, N
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A( JD, JD ) = ONE
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20 CONTINUE
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GO TO 220
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*
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* |ITYPE| = 2: Transposed Jordan block
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*
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30 CONTINUE
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DO 40 JD = 1, N - 1
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A( JD+1, JD ) = ONE
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40 CONTINUE
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ISDB = 1
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ISDE = N - 1
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GO TO 220
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*
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* |ITYPE| = 3: Transposed Jordan block, followed by the identity.
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*
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50 CONTINUE
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K = ( N-1 ) / 2
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DO 60 JD = 1, K
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A( JD+1, JD ) = ONE
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60 CONTINUE
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ISDB = 1
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ISDE = K
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DO 70 JD = K + 2, 2*K + 1
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A( JD, JD ) = ONE
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70 CONTINUE
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GO TO 220
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*
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* |ITYPE| = 4: 1,...,k
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*
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80 CONTINUE
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DO 90 JD = KBEG, KEND
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A( JD, JD ) = DBLE( JD-NZ1 )
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90 CONTINUE
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GO TO 220
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*
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* |ITYPE| = 5: One large D value:
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*
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100 CONTINUE
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DO 110 JD = KBEG + 1, KEND
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A( JD, JD ) = RCOND
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110 CONTINUE
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A( KBEG, KBEG ) = ONE
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GO TO 220
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*
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* |ITYPE| = 6: One small D value:
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*
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120 CONTINUE
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DO 130 JD = KBEG, KEND - 1
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A( JD, JD ) = ONE
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130 CONTINUE
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A( KEND, KEND ) = RCOND
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GO TO 220
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*
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* |ITYPE| = 7: Exponentially distributed D values:
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*
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140 CONTINUE
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A( KBEG, KBEG ) = ONE
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IF( KLEN.GT.1 ) THEN
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ALPHA = RCOND**( ONE / DBLE( KLEN-1 ) )
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DO 150 I = 2, KLEN
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A( NZ1+I, NZ1+I ) = ALPHA**( I-1 )
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150 CONTINUE
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END IF
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GO TO 220
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*
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* |ITYPE| = 8: Arithmetically distributed D values:
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*
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160 CONTINUE
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A( KBEG, KBEG ) = ONE
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IF( KLEN.GT.1 ) THEN
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ALPHA = ( ONE-RCOND ) / DBLE( KLEN-1 )
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DO 170 I = 2, KLEN
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A( NZ1+I, NZ1+I ) = DBLE( KLEN-I )*ALPHA + RCOND
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170 CONTINUE
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END IF
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GO TO 220
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*
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* |ITYPE| = 9: Randomly distributed D values on ( RCOND, 1):
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*
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180 CONTINUE
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ALPHA = LOG( RCOND )
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DO 190 JD = KBEG, KEND
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A( JD, JD ) = EXP( ALPHA*DLARAN( ISEED ) )
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190 CONTINUE
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GO TO 220
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*
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* |ITYPE| = 10: Randomly distributed D values from DIST
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*
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200 CONTINUE
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DO 210 JD = KBEG, KEND
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A( JD, JD ) = DLARND( IDIST, ISEED )
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210 CONTINUE
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*
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220 CONTINUE
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*
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* Scale by AMAGN
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*
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DO 230 JD = KBEG, KEND
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A( JD, JD ) = AMAGN*DBLE( A( JD, JD ) )
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230 CONTINUE
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DO 240 JD = ISDB, ISDE
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A( JD+1, JD ) = AMAGN*DBLE( A( JD+1, JD ) )
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240 CONTINUE
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*
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* If ISIGN = 1 or 2, assign random signs to diagonal and
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* subdiagonal
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*
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IF( ISIGN.GT.0 ) THEN
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DO 250 JD = KBEG, KEND
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IF( DBLE( A( JD, JD ) ).NE.ZERO ) THEN
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IF( DLARAN( ISEED ).GT.HALF )
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$ A( JD, JD ) = -A( JD, JD )
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END IF
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250 CONTINUE
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DO 260 JD = ISDB, ISDE
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IF( DBLE( A( JD+1, JD ) ).NE.ZERO ) THEN
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IF( DLARAN( ISEED ).GT.HALF )
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$ A( JD+1, JD ) = -A( JD+1, JD )
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END IF
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260 CONTINUE
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END IF
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*
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* Reverse if ITYPE < 0
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*
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IF( ITYPE.LT.0 ) THEN
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DO 270 JD = KBEG, ( KBEG+KEND-1 ) / 2
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TEMP = A( JD, JD )
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A( JD, JD ) = A( KBEG+KEND-JD, KBEG+KEND-JD )
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A( KBEG+KEND-JD, KBEG+KEND-JD ) = TEMP
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270 CONTINUE
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DO 280 JD = 1, ( N-1 ) / 2
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TEMP = A( JD+1, JD )
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A( JD+1, JD ) = A( N+1-JD, N-JD )
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A( N+1-JD, N-JD ) = TEMP
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280 CONTINUE
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END IF
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*
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* If ISIGN = 2, and no subdiagonals already, then apply
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* random rotations to make 2x2 blocks.
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*
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IF( ISIGN.EQ.2 .AND. ITYPE.NE.2 .AND. ITYPE.NE.3 ) THEN
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SAFMIN = DLAMCH( 'S' )
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DO 290 JD = KBEG, KEND - 1, 2
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IF( DLARAN( ISEED ).GT.HALF ) THEN
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*
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* Rotation on left.
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*
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CL = TWO*DLARAN( ISEED ) - ONE
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SL = TWO*DLARAN( ISEED ) - ONE
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TEMP = ONE / MAX( SAFMIN, SQRT( CL**2+SL**2 ) )
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CL = CL*TEMP
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SL = SL*TEMP
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*
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* Rotation on right.
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*
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CR = TWO*DLARAN( ISEED ) - ONE
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SR = TWO*DLARAN( ISEED ) - ONE
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TEMP = ONE / MAX( SAFMIN, SQRT( CR**2+SR**2 ) )
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CR = CR*TEMP
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SR = SR*TEMP
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*
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* Apply
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*
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SV1 = A( JD, JD )
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SV2 = A( JD+1, JD+1 )
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A( JD, JD ) = CL*CR*SV1 + SL*SR*SV2
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A( JD+1, JD ) = -SL*CR*SV1 + CL*SR*SV2
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A( JD, JD+1 ) = -CL*SR*SV1 + SL*CR*SV2
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A( JD+1, JD+1 ) = SL*SR*SV1 + CL*CR*SV2
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END IF
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290 CONTINUE
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END IF
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*
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END IF
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*
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* Fill in upper triangle (except for 2x2 blocks)
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*
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IF( TRIANG.NE.ZERO ) THEN
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IF( ISIGN.NE.2 .OR. ITYPE.EQ.2 .OR. ITYPE.EQ.3 ) THEN
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IOFF = 1
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ELSE
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IOFF = 2
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DO 300 JR = 1, N - 1
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IF( A( JR+1, JR ).EQ.ZERO )
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$ A( JR, JR+1 ) = TRIANG*DLARND( IDIST, ISEED )
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300 CONTINUE
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END IF
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*
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DO 320 JC = 2, N
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DO 310 JR = 1, JC - IOFF
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A( JR, JC ) = TRIANG*DLARND( IDIST, ISEED )
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310 CONTINUE
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320 CONTINUE
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END IF
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*
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RETURN
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*
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* End of DLATM4
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*
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END
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