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SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) |
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* |
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* -- LAPACK auxiliary routine (version 3.2) -- |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2006 |
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* |
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* .. Scalar Arguments .. |
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CHARACTER TYPE |
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INTEGER INFO, KL, KU, LDA, M, N |
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DOUBLE PRECISION CFROM, CTO |
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* .. |
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* .. Array Arguments .. |
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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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* DLASCL multiplies the M by N real matrix A by the real scalar |
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* CTO/CFROM. This is done without over/underflow as long as the final |
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* result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that |
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* A may be full, upper triangular, lower triangular, upper Hessenberg, |
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* or banded. |
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* |
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* Arguments |
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* ========= |
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* |
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* TYPE (input) CHARACTER*1 |
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* TYPE indices the storage type of the input matrix. |
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* = 'G': A is a full matrix. |
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* = 'L': A is a lower triangular matrix. |
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* = 'U': A is an upper triangular matrix. |
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* = 'H': A is an upper Hessenberg matrix. |
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* = 'B': A is a symmetric band matrix with lower bandwidth KL |
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* and upper bandwidth KU and with the only the lower |
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* half stored. |
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* = 'Q': A is a symmetric band matrix with lower bandwidth KL |
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* and upper bandwidth KU and with the only the upper |
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* half stored. |
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* = 'Z': A is a band matrix with lower bandwidth KL and upper |
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* bandwidth KU. |
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* |
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* KL (input) INTEGER |
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* The lower bandwidth of A. Referenced only if TYPE = 'B', |
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* 'Q' or 'Z'. |
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* |
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* KU (input) INTEGER |
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* The upper bandwidth of A. Referenced only if TYPE = 'B', |
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* 'Q' or 'Z'. |
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* |
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* CFROM (input) DOUBLE PRECISION |
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* CTO (input) DOUBLE PRECISION |
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* The matrix A is multiplied by CTO/CFROM. A(I,J) is computed |
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* without over/underflow if the final result CTO*A(I,J)/CFROM |
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* can be represented without over/underflow. CFROM must be |
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* nonzero. |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix A. N >= 0. |
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* |
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* The matrix to be multiplied by CTO/CFROM. See TYPE for the |
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* storage type. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,M). |
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* |
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* INFO (output) INTEGER |
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* 0 - successful exit |
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* <0 - if INFO = -i, the i-th argument had an illegal value. |
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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 |
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) |
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* .. |
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* .. Local Scalars .. |
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LOGICAL DONE |
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INTEGER I, ITYPE, J, K1, K2, K3, K4 |
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DOUBLE PRECISION BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM |
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* .. |
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* .. External Functions .. |
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LOGICAL LSAME, DISNAN |
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DOUBLE PRECISION DLAMCH |
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EXTERNAL LSAME, DLAMCH, DISNAN |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC ABS, MAX, MIN |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL XERBLA |
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* .. |
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* .. Executable Statements .. |
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* |
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* Test the input arguments |
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* |
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INFO = 0 |
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* |
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IF( LSAME( TYPE, 'G' ) ) THEN |
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ITYPE = 0 |
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ELSE IF( LSAME( TYPE, 'L' ) ) THEN |
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ITYPE = 1 |
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ELSE IF( LSAME( TYPE, 'U' ) ) THEN |
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ITYPE = 2 |
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ELSE IF( LSAME( TYPE, 'H' ) ) THEN |
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ITYPE = 3 |
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ELSE IF( LSAME( TYPE, 'B' ) ) THEN |
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ITYPE = 4 |
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ELSE IF( LSAME( TYPE, 'Q' ) ) THEN |
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ITYPE = 5 |
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ELSE IF( LSAME( TYPE, 'Z' ) ) THEN |
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ITYPE = 6 |
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ELSE |
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ITYPE = -1 |
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END IF |
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* |
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IF( ITYPE.EQ.-1 ) THEN |
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INFO = -1 |
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ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN |
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INFO = -4 |
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ELSE IF( DISNAN(CTO) ) THEN |
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INFO = -5 |
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ELSE IF( M.LT.0 ) THEN |
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INFO = -6 |
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ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR. |
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$ ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN |
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INFO = -7 |
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ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN |
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INFO = -9 |
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ELSE IF( ITYPE.GE.4 ) THEN |
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IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN |
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INFO = -2 |
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ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR. |
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$ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) ) |
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$ THEN |
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INFO = -3 |
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ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR. |
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$ ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR. |
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$ ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN |
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INFO = -9 |
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END IF |
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END IF |
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* |
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IF( INFO.NE.0 ) THEN |
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CALL XERBLA( 'DLASCL', -INFO ) |
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RETURN |
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END IF |
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* |
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* Quick return if possible |
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* |
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IF( N.EQ.0 .OR. M.EQ.0 ) |
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$ RETURN |
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* |
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* Get machine parameters |
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* |
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SMLNUM = DLAMCH( 'S' ) |
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BIGNUM = ONE / SMLNUM |
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* |
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CFROMC = CFROM |
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CTOC = CTO |
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* |
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10 CONTINUE |
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CFROM1 = CFROMC*SMLNUM |
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IF( CFROM1.EQ.CFROMC ) THEN |
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! CFROMC is an inf. Multiply by a correctly signed zero for |
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! finite CTOC, or a NaN if CTOC is infinite. |
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MUL = CTOC / CFROMC |
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DONE = .TRUE. |
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CTO1 = CTOC |
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ELSE |
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CTO1 = CTOC / BIGNUM |
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IF( CTO1.EQ.CTOC ) THEN |
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! CTOC is either 0 or an inf. In both cases, CTOC itself |
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! serves as the correct multiplication factor. |
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MUL = CTOC |
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DONE = .TRUE. |
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CFROMC = ONE |
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ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN |
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MUL = SMLNUM |
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DONE = .FALSE. |
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CFROMC = CFROM1 |
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ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN |
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MUL = BIGNUM |
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DONE = .FALSE. |
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CTOC = CTO1 |
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ELSE |
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MUL = CTOC / CFROMC |
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DONE = .TRUE. |
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END IF |
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END IF |
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* |
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IF( ITYPE.EQ.0 ) THEN |
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* |
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* Full matrix |
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* |
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DO 30 J = 1, N |
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DO 20 I = 1, M |
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A( I, J ) = A( I, J )*MUL |
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20 CONTINUE |
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30 CONTINUE |
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* |
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ELSE IF( ITYPE.EQ.1 ) THEN |
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* |
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* Lower triangular matrix |
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* |
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DO 50 J = 1, N |
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DO 40 I = J, M |
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A( I, J ) = A( I, J )*MUL |
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40 CONTINUE |
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50 CONTINUE |
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* |
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ELSE IF( ITYPE.EQ.2 ) THEN |
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* |
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* Upper triangular matrix |
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* |
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DO 70 J = 1, N |
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DO 60 I = 1, MIN( J, M ) |
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A( I, J ) = A( I, J )*MUL |
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60 CONTINUE |
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70 CONTINUE |
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* |
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ELSE IF( ITYPE.EQ.3 ) THEN |
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* |
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* Upper Hessenberg matrix |
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* |
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DO 90 J = 1, N |
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DO 80 I = 1, MIN( J+1, M ) |
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A( I, J ) = A( I, J )*MUL |
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80 CONTINUE |
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90 CONTINUE |
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* |
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ELSE IF( ITYPE.EQ.4 ) THEN |
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* |
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* Lower half of a symmetric band matrix |
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* |
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K3 = KL + 1 |
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K4 = N + 1 |
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DO 110 J = 1, N |
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DO 100 I = 1, MIN( K3, K4-J ) |
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A( I, J ) = A( I, J )*MUL |
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100 CONTINUE |
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110 CONTINUE |
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* |
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ELSE IF( ITYPE.EQ.5 ) THEN |
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* |
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* Upper half of a symmetric band matrix |
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* |
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K1 = KU + 2 |
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K3 = KU + 1 |
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DO 130 J = 1, N |
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DO 120 I = MAX( K1-J, 1 ), K3 |
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A( I, J ) = A( I, J )*MUL |
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120 CONTINUE |
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130 CONTINUE |
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* |
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ELSE IF( ITYPE.EQ.6 ) THEN |
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* |
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* Band matrix |
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* |
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K1 = KL + KU + 2 |
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K2 = KL + 1 |
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K3 = 2*KL + KU + 1 |
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K4 = KL + KU + 1 + M |
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DO 150 J = 1, N |
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DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J ) |
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A( I, J ) = A( I, J )*MUL |
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140 CONTINUE |
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150 CONTINUE |
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* |
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END IF |
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* |
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IF( .NOT.DONE ) |
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$ GO TO 10 |
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* |
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RETURN |
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* |
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* End of DLASCL |
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* |
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END |