numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/MATGEN/slatm7.f | 8486B | -rw-r--r-- |
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*> \brief \b SLATM7 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N, * RANK, INFO ) * * .. Scalar Arguments .. * REAL COND * INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK * .. * .. Array Arguments .. * REAL D( * ) * INTEGER ISEED( 4 ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLATM7 computes the entries of D as specified by MODE *> COND and IRSIGN. IDIST and ISEED determine the generation *> of random numbers. SLATM7 is called by SLATMT to generate *> random test matrices. *> \endverbatim * * Arguments: * ========== * *> \verbatim *> MODE - INTEGER *> On entry describes how D is to be computed: *> MODE = 0 means do not change D. *> *> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND *> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND *> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK *> *> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) *> MODE = 5 sets D to random numbers in the range *> ( 1/COND , 1 ) such that their logarithms *> are uniformly distributed. *> MODE = 6 set D to random numbers from same distribution *> as the rest of the matrix. *> MODE < 0 has the same meaning as ABS(MODE), except that *> the order of the elements of D is reversed. *> Thus if MODE is positive, D has entries ranging from *> 1 to 1/COND, if negative, from 1/COND to 1, *> Not modified. *> *> COND - REAL *> On entry, used as described under MODE above. *> If used, it must be >= 1. Not modified. *> *> IRSIGN - INTEGER *> On entry, if MODE neither -6, 0 nor 6, determines sign of *> entries of D *> 0 => leave entries of D unchanged *> 1 => multiply each entry of D by 1 or -1 with probability .5 *> *> IDIST - CHARACTER*1 *> On entry, IDIST 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 ) *> Not modified. *> *> ISEED - INTEGER array, dimension ( 4 ) *> On entry ISEED specifies the seed of the random number *> generator. The random number generator uses a *> linear congruential sequence limited to small *> integers, and so should produce machine independent *> random numbers. The values of ISEED are changed on *> exit, and can be used in the next call to SLATM7 *> to continue the same random number sequence. *> Changed on exit. *> *> D - REAL array, dimension ( MIN( M , N ) ) *> Array to be computed according to MODE, COND and IRSIGN. *> May be changed on exit if MODE is nonzero. *> *> N - INTEGER *> Number of entries of D. Not modified. *> *> RANK - INTEGER *> The rank of matrix to be generated for modes 1,2,3 only. *> D( RANK+1:N ) = 0. *> Not modified. *> *> INFO - INTEGER *> 0 => normal termination *> -1 => if MODE not in range -6 to 6 *> -2 => if MODE neither -6, 0 nor 6, and *> IRSIGN neither 0 nor 1 *> -3 => if MODE neither -6, 0 nor 6 and COND less than 1 *> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3 *> -7 => if N negative *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup real_matgen * * ===================================================================== SUBROUTINE SLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N, $ RANK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. REAL COND INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK * .. * .. Array Arguments .. REAL D( * ) INTEGER ISEED( 4 ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E0 ) REAL ZERO PARAMETER ( ZERO = 0.0E0 ) REAL HALF PARAMETER ( HALF = 0.5E0 ) * .. * .. Local Scalars .. REAL ALPHA, TEMP INTEGER I * .. * .. External Functions .. REAL SLARAN EXTERNAL SLARAN * .. * .. External Subroutines .. EXTERNAL SLARNV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, EXP, LOG, REAL * .. * .. Executable Statements .. * * Decode and Test the input parameters. Initialize flags & seed. * INFO = 0 * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Set INFO if an error * IF( MODE.LT.-6 .OR. MODE.GT.6 ) THEN INFO = -1 ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND. $ ( IRSIGN.NE.0 .AND. IRSIGN.NE.1 ) ) THEN INFO = -2 ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND. $ COND.LT.ONE ) THEN INFO = -3 ELSE IF( ( MODE.EQ.6 .OR. MODE.EQ.-6 ) .AND. $ ( IDIST.LT.1 .OR. IDIST.GT.3 ) ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -7 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SLATM7', -INFO ) RETURN END IF * * Compute D according to COND and MODE * IF( MODE.NE.0 ) THEN GO TO ( 100, 130, 160, 190, 210, 230 )ABS( MODE ) * * One large D value: * 100 CONTINUE DO 110 I = 2, RANK D( I ) = ONE / COND 110 CONTINUE DO 120 I = RANK + 1, N D( I ) = ZERO 120 CONTINUE D( 1 ) = ONE GO TO 240 * * One small D value: * 130 CONTINUE DO 140 I = 1, RANK - 1 D( I ) = ONE 140 CONTINUE DO 150 I = RANK + 1, N D( I ) = ZERO 150 CONTINUE D( RANK ) = ONE / COND GO TO 240 * * Exponentially distributed D values: * 160 CONTINUE D( 1 ) = ONE IF( N.GT.1 .AND. RANK.GT.1 ) THEN ALPHA = COND**( -ONE / REAL( RANK-1 ) ) DO 170 I = 2, RANK D( I ) = ALPHA**( I-1 ) 170 CONTINUE DO 180 I = RANK + 1, N D( I ) = ZERO 180 CONTINUE END IF GO TO 240 * * Arithmetically distributed D values: * 190 CONTINUE D( 1 ) = ONE IF( N.GT.1 ) THEN TEMP = ONE / COND ALPHA = ( ONE-TEMP ) / REAL( N-1 ) DO 200 I = 2, N D( I ) = REAL( N-I )*ALPHA + TEMP 200 CONTINUE END IF GO TO 240 * * Randomly distributed D values on ( 1/COND , 1): * 210 CONTINUE ALPHA = LOG( ONE / COND ) DO 220 I = 1, N D( I ) = EXP( ALPHA*SLARAN( ISEED ) ) 220 CONTINUE GO TO 240 * * Randomly distributed D values from IDIST * 230 CONTINUE CALL SLARNV( IDIST, ISEED, N, D ) * 240 CONTINUE * * If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign * random signs to D * IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND. $ IRSIGN.EQ.1 ) THEN DO 250 I = 1, N TEMP = SLARAN( ISEED ) IF( TEMP.GT.HALF ) $ D( I ) = -D( I ) 250 CONTINUE END IF * * Reverse if MODE < 0 * IF( MODE.LT.0 ) THEN DO 260 I = 1, N / 2 TEMP = D( I ) D( I ) = D( N+1-I ) D( N+1-I ) = TEMP 260 CONTINUE END IF * END IF * RETURN * * End of SLATM7 * END