*> \brief \b DSBGST * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSBGST + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, * LDX, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO, VECT * INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N * .. * .. Array Arguments .. * DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ), * \$ X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSBGST reduces a real symmetric-definite banded generalized *> eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, *> such that C has the same bandwidth as A. *> *> B must have been previously factorized as S**T*S by DPBSTF, using a *> split Cholesky factorization. A is overwritten by C = X**T*A*X, where *> X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the *> bandwidth of A. *> \endverbatim * * Arguments: * ========== * *> \param[in] VECT *> \verbatim *> VECT is CHARACTER*1 *> = 'N': do not form the transformation matrix X; *> = 'V': form X. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in] KA *> \verbatim *> KA is INTEGER *> The number of superdiagonals of the matrix A if UPLO = 'U', *> or the number of subdiagonals if UPLO = 'L'. KA >= 0. *> \endverbatim *> *> \param[in] KB *> \verbatim *> KB is INTEGER *> The number of superdiagonals of the matrix B if UPLO = 'U', *> or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. *> \endverbatim *> *> \param[in,out] AB *> \verbatim *> AB is DOUBLE PRECISION array, dimension (LDAB,N) *> On entry, the upper or lower triangle of the symmetric band *> matrix A, stored in the first ka+1 rows of the array. The *> j-th column of A is stored in the j-th column of the array AB *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). *> *> On exit, the transformed matrix X**T*A*X, stored in the same *> format as A. *> \endverbatim *> *> \param[in] LDAB *> \verbatim *> LDAB is INTEGER *> The leading dimension of the array AB. LDAB >= KA+1. *> \endverbatim *> *> \param[in] BB *> \verbatim *> BB is DOUBLE PRECISION array, dimension (LDBB,N) *> The banded factor S from the split Cholesky factorization of *> B, as returned by DPBSTF, stored in the first KB+1 rows of *> the array. *> \endverbatim *> *> \param[in] LDBB *> \verbatim *> LDBB is INTEGER *> The leading dimension of the array BB. LDBB >= KB+1. *> \endverbatim *> *> \param[out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (LDX,N) *> If VECT = 'V', the n-by-n matrix X. *> If VECT = 'N', the array X is not referenced. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. *> LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (2*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, \$ LDX, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO, VECT INTEGER INFO, KA, KB, LDAB, LDBB, LDX, N * .. * .. Array Arguments .. DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ), \$ X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPDATE, UPPER, WANTX INTEGER I, I0, I1, I2, INCA, J, J1, J1T, J2, J2T, K, \$ KA1, KB1, KBT, L, M, NR, NRT, NX DOUBLE PRECISION BII, RA, RA1, T * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DGER, DLAR2V, DLARGV, DLARTG, DLARTV, DLASET, \$ DROT, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters * WANTX = LSAME( VECT, 'V' ) UPPER = LSAME( UPLO, 'U' ) KA1 = KA + 1 KB1 = KB + 1 INFO = 0 IF( .NOT.WANTX .AND. .NOT.LSAME( VECT, 'N' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( KA.LT.0 ) THEN INFO = -4 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN INFO = -5 ELSE IF( LDAB.LT.KA+1 ) THEN INFO = -7 ELSE IF( LDBB.LT.KB+1 ) THEN INFO = -9 ELSE IF( LDX.LT.1 .OR. WANTX .AND. LDX.LT.MAX( 1, N ) ) THEN INFO = -11 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSBGST', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * INCA = LDAB*KA1 * * Initialize X to the unit matrix, if needed * IF( WANTX ) \$ CALL DLASET( 'Full', N, N, ZERO, ONE, X, LDX ) * * Set M to the splitting point m. It must be the same value as is * used in DPBSTF. The chosen value allows the arrays WORK and RWORK * to be of dimension (N). * M = ( N+KB ) / 2 * * The routine works in two phases, corresponding to the two halves * of the split Cholesky factorization of B as S**T*S where * * S = ( U ) * ( M L ) * * with U upper triangular of order m, and L lower triangular of * order n-m. S has the same bandwidth as B. * * S is treated as a product of elementary matrices: * * S = S(m)*S(m-1)*...*S(2)*S(1)*S(m+1)*S(m+2)*...*S(n-1)*S(n) * * where S(i) is determined by the i-th row of S. * * In phase 1, the index i takes the values n, n-1, ... , m+1; * in phase 2, it takes the values 1, 2, ... , m. * * For each value of i, the current matrix A is updated by forming * inv(S(i))**T*A*inv(S(i)). This creates a triangular bulge outside * the band of A. The bulge is then pushed down toward the bottom of * A in phase 1, and up toward the top of A in phase 2, by applying * plane rotations. * * There are kb*(kb+1)/2 elements in the bulge, but at most 2*kb-1 * of them are linearly independent, so annihilating a bulge requires * only 2*kb-1 plane rotations. The rotations are divided into a 1st * set of kb-1 rotations, and a 2nd set of kb rotations. * * Wherever possible, rotations are generated and applied in vector * operations of length NR between the indices J1 and J2 (sometimes * replaced by modified values NRT, J1T or J2T). * * The cosines and sines of the rotations are stored in the array * WORK. The cosines of the 1st set of rotations are stored in * elements n+2:n+m-kb-1 and the sines of the 1st set in elements * 2:m-kb-1; the cosines of the 2nd set are stored in elements * n+m-kb+1:2*n and the sines of the second set in elements m-kb+1:n. * * The bulges are not formed explicitly; nonzero elements outside the * band are created only when they are required for generating new * rotations; they are stored in the array WORK, in positions where * they are later overwritten by the sines of the rotations which * annihilate them. * * **************************** Phase 1 ***************************** * * The logical structure of this phase is: * * UPDATE = .TRUE. * DO I = N, M + 1, -1 * use S(i) to update A and create a new bulge * apply rotations to push all bulges KA positions downward * END DO * UPDATE = .FALSE. * DO I = M + KA + 1, N - 1 * apply rotations to push all bulges KA positions downward * END DO * * To avoid duplicating code, the two loops are merged. * UPDATE = .TRUE. I = N + 1 10 CONTINUE IF( UPDATE ) THEN I = I - 1 KBT = MIN( KB, I-1 ) I0 = I - 1 I1 = MIN( N, I+KA ) I2 = I - KBT + KA1 IF( I.LT.M+1 ) THEN UPDATE = .FALSE. I = I + 1 I0 = M IF( KA.EQ.0 ) \$ GO TO 480 GO TO 10 END IF ELSE I = I + KA IF( I.GT.N-1 ) \$ GO TO 480 END IF * IF( UPPER ) THEN * * Transform A, working with the upper triangle * IF( UPDATE ) THEN * * Form inv(S(i))**T * A * inv(S(i)) * BII = BB( KB1, I ) DO 20 J = I, I1 AB( I-J+KA1, J ) = AB( I-J+KA1, J ) / BII 20 CONTINUE DO 30 J = MAX( 1, I-KA ), I AB( J-I+KA1, I ) = AB( J-I+KA1, I ) / BII 30 CONTINUE DO 60 K = I - KBT, I - 1 DO 40 J = I - KBT, K AB( J-K+KA1, K ) = AB( J-K+KA1, K ) - \$ BB( J-I+KB1, I )*AB( K-I+KA1, I ) - \$ BB( K-I+KB1, I )*AB( J-I+KA1, I ) + \$ AB( KA1, I )*BB( J-I+KB1, I )* \$ BB( K-I+KB1, I ) 40 CONTINUE DO 50 J = MAX( 1, I-KA ), I - KBT - 1 AB( J-K+KA1, K ) = AB( J-K+KA1, K ) - \$ BB( K-I+KB1, I )*AB( J-I+KA1, I ) 50 CONTINUE 60 CONTINUE DO 80 J = I, I1 DO 70 K = MAX( J-KA, I-KBT ), I - 1 AB( K-J+KA1, J ) = AB( K-J+KA1, J ) - \$ BB( K-I+KB1, I )*AB( I-J+KA1, J ) 70 CONTINUE 80 CONTINUE * IF( WANTX ) THEN * * post-multiply X by inv(S(i)) * CALL DSCAL( N-M, ONE / BII, X( M+1, I ), 1 ) IF( KBT.GT.0 ) \$ CALL DGER( N-M, KBT, -ONE, X( M+1, I ), 1, \$ BB( KB1-KBT, I ), 1, X( M+1, I-KBT ), LDX ) END IF * * store a(i,i1) in RA1 for use in next loop over K * RA1 = AB( I-I1+KA1, I1 ) END IF * * Generate and apply vectors of rotations to chase all the * existing bulges KA positions down toward the bottom of the * band * DO 130 K = 1, KB - 1 IF( UPDATE ) THEN * * Determine the rotations which would annihilate the bulge * which has in theory just been created * IF( I-K+KA.LT.N .AND. I-K.GT.1 ) THEN * * generate rotation to annihilate a(i,i-k+ka+1) * CALL DLARTG( AB( K+1, I-K+KA ), RA1, \$ WORK( N+I-K+KA-M ), WORK( I-K+KA-M ), \$ RA ) * * create nonzero element a(i-k,i-k+ka+1) outside the * band and store it in WORK(i-k) * T = -BB( KB1-K, I )*RA1 WORK( I-K ) = WORK( N+I-K+KA-M )*T - \$ WORK( I-K+KA-M )*AB( 1, I-K+KA ) AB( 1, I-K+KA ) = WORK( I-K+KA-M )*T + \$ WORK( N+I-K+KA-M )*AB( 1, I-K+KA ) RA1 = RA END IF END IF J2 = I - K - 1 + MAX( 1, K-I0+2 )*KA1 NR = ( N-J2+KA ) / KA1 J1 = J2 + ( NR-1 )*KA1 IF( UPDATE ) THEN J2T = MAX( J2, I+2*KA-K+1 ) ELSE J2T = J2 END IF NRT = ( N-J2T+KA ) / KA1 DO 90 J = J2T, J1, KA1 * * create nonzero element a(j-ka,j+1) outside the band * and store it in WORK(j-m) * WORK( J-M ) = WORK( J-M )*AB( 1, J+1 ) AB( 1, J+1 ) = WORK( N+J-M )*AB( 1, J+1 ) 90 CONTINUE * * generate rotations in 1st set to annihilate elements which * have been created outside the band * IF( NRT.GT.0 ) \$ CALL DLARGV( NRT, AB( 1, J2T ), INCA, WORK( J2T-M ), KA1, \$ WORK( N+J2T-M ), KA1 ) IF( NR.GT.0 ) THEN * * apply rotations in 1st set from the right * DO 100 L = 1, KA - 1 CALL DLARTV( NR, AB( KA1-L, J2 ), INCA, \$ AB( KA-L, J2+1 ), INCA, WORK( N+J2-M ), \$ WORK( J2-M ), KA1 ) 100 CONTINUE * * apply rotations in 1st set from both sides to diagonal * blocks * CALL DLAR2V( NR, AB( KA1, J2 ), AB( KA1, J2+1 ), \$ AB( KA, J2+1 ), INCA, WORK( N+J2-M ), \$ WORK( J2-M ), KA1 ) * END IF * * start applying rotations in 1st set from the left * DO 110 L = KA - 1, KB - K + 1, -1 NRT = ( N-J2+L ) / KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( L, J2+KA1-L ), INCA, \$ AB( L+1, J2+KA1-L ), INCA, \$ WORK( N+J2-M ), WORK( J2-M ), KA1 ) 110 CONTINUE * IF( WANTX ) THEN * * post-multiply X by product of rotations in 1st set * DO 120 J = J2, J1, KA1 CALL DROT( N-M, X( M+1, J ), 1, X( M+1, J+1 ), 1, \$ WORK( N+J-M ), WORK( J-M ) ) 120 CONTINUE END IF 130 CONTINUE * IF( UPDATE ) THEN IF( I2.LE.N .AND. KBT.GT.0 ) THEN * * create nonzero element a(i-kbt,i-kbt+ka+1) outside the * band and store it in WORK(i-kbt) * WORK( I-KBT ) = -BB( KB1-KBT, I )*RA1 END IF END IF * DO 170 K = KB, 1, -1 IF( UPDATE ) THEN J2 = I - K - 1 + MAX( 2, K-I0+1 )*KA1 ELSE J2 = I - K - 1 + MAX( 1, K-I0+1 )*KA1 END IF * * finish applying rotations in 2nd set from the left * DO 140 L = KB - K, 1, -1 NRT = ( N-J2+KA+L ) / KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( L, J2-L+1 ), INCA, \$ AB( L+1, J2-L+1 ), INCA, WORK( N+J2-KA ), \$ WORK( J2-KA ), KA1 ) 140 CONTINUE NR = ( N-J2+KA ) / KA1 J1 = J2 + ( NR-1 )*KA1 DO 150 J = J1, J2, -KA1 WORK( J ) = WORK( J-KA ) WORK( N+J ) = WORK( N+J-KA ) 150 CONTINUE DO 160 J = J2, J1, KA1 * * create nonzero element a(j-ka,j+1) outside the band * and store it in WORK(j) * WORK( J ) = WORK( J )*AB( 1, J+1 ) AB( 1, J+1 ) = WORK( N+J )*AB( 1, J+1 ) 160 CONTINUE IF( UPDATE ) THEN IF( I-K.LT.N-KA .AND. K.LE.KBT ) \$ WORK( I-K+KA ) = WORK( I-K ) END IF 170 CONTINUE * DO 210 K = KB, 1, -1 J2 = I - K - 1 + MAX( 1, K-I0+1 )*KA1 NR = ( N-J2+KA ) / KA1 J1 = J2 + ( NR-1 )*KA1 IF( NR.GT.0 ) THEN * * generate rotations in 2nd set to annihilate elements * which have been created outside the band * CALL DLARGV( NR, AB( 1, J2 ), INCA, WORK( J2 ), KA1, \$ WORK( N+J2 ), KA1 ) * * apply rotations in 2nd set from the right * DO 180 L = 1, KA - 1 CALL DLARTV( NR, AB( KA1-L, J2 ), INCA, \$ AB( KA-L, J2+1 ), INCA, WORK( N+J2 ), \$ WORK( J2 ), KA1 ) 180 CONTINUE * * apply rotations in 2nd set from both sides to diagonal * blocks * CALL DLAR2V( NR, AB( KA1, J2 ), AB( KA1, J2+1 ), \$ AB( KA, J2+1 ), INCA, WORK( N+J2 ), \$ WORK( J2 ), KA1 ) * END IF * * start applying rotations in 2nd set from the left * DO 190 L = KA - 1, KB - K + 1, -1 NRT = ( N-J2+L ) / KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( L, J2+KA1-L ), INCA, \$ AB( L+1, J2+KA1-L ), INCA, WORK( N+J2 ), \$ WORK( J2 ), KA1 ) 190 CONTINUE * IF( WANTX ) THEN * * post-multiply X by product of rotations in 2nd set * DO 200 J = J2, J1, KA1 CALL DROT( N-M, X( M+1, J ), 1, X( M+1, J+1 ), 1, \$ WORK( N+J ), WORK( J ) ) 200 CONTINUE END IF 210 CONTINUE * DO 230 K = 1, KB - 1 J2 = I - K - 1 + MAX( 1, K-I0+2 )*KA1 * * finish applying rotations in 1st set from the left * DO 220 L = KB - K, 1, -1 NRT = ( N-J2+L ) / KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( L, J2+KA1-L ), INCA, \$ AB( L+1, J2+KA1-L ), INCA, \$ WORK( N+J2-M ), WORK( J2-M ), KA1 ) 220 CONTINUE 230 CONTINUE * IF( KB.GT.1 ) THEN DO 240 J = N - 1, I - KB + 2*KA + 1, -1 WORK( N+J-M ) = WORK( N+J-KA-M ) WORK( J-M ) = WORK( J-KA-M ) 240 CONTINUE END IF * ELSE * * Transform A, working with the lower triangle * IF( UPDATE ) THEN * * Form inv(S(i))**T * A * inv(S(i)) * BII = BB( 1, I ) DO 250 J = I, I1 AB( J-I+1, I ) = AB( J-I+1, I ) / BII 250 CONTINUE DO 260 J = MAX( 1, I-KA ), I AB( I-J+1, J ) = AB( I-J+1, J ) / BII 260 CONTINUE DO 290 K = I - KBT, I - 1 DO 270 J = I - KBT, K AB( K-J+1, J ) = AB( K-J+1, J ) - \$ BB( I-J+1, J )*AB( I-K+1, K ) - \$ BB( I-K+1, K )*AB( I-J+1, J ) + \$ AB( 1, I )*BB( I-J+1, J )* \$ BB( I-K+1, K ) 270 CONTINUE DO 280 J = MAX( 1, I-KA ), I - KBT - 1 AB( K-J+1, J ) = AB( K-J+1, J ) - \$ BB( I-K+1, K )*AB( I-J+1, J ) 280 CONTINUE 290 CONTINUE DO 310 J = I, I1 DO 300 K = MAX( J-KA, I-KBT ), I - 1 AB( J-K+1, K ) = AB( J-K+1, K ) - \$ BB( I-K+1, K )*AB( J-I+1, I ) 300 CONTINUE 310 CONTINUE * IF( WANTX ) THEN * * post-multiply X by inv(S(i)) * CALL DSCAL( N-M, ONE / BII, X( M+1, I ), 1 ) IF( KBT.GT.0 ) \$ CALL DGER( N-M, KBT, -ONE, X( M+1, I ), 1, \$ BB( KBT+1, I-KBT ), LDBB-1, \$ X( M+1, I-KBT ), LDX ) END IF * * store a(i1,i) in RA1 for use in next loop over K * RA1 = AB( I1-I+1, I ) END IF * * Generate and apply vectors of rotations to chase all the * existing bulges KA positions down toward the bottom of the * band * DO 360 K = 1, KB - 1 IF( UPDATE ) THEN * * Determine the rotations which would annihilate the bulge * which has in theory just been created * IF( I-K+KA.LT.N .AND. I-K.GT.1 ) THEN * * generate rotation to annihilate a(i-k+ka+1,i) * CALL DLARTG( AB( KA1-K, I ), RA1, WORK( N+I-K+KA-M ), \$ WORK( I-K+KA-M ), RA ) * * create nonzero element a(i-k+ka+1,i-k) outside the * band and store it in WORK(i-k) * T = -BB( K+1, I-K )*RA1 WORK( I-K ) = WORK( N+I-K+KA-M )*T - \$ WORK( I-K+KA-M )*AB( KA1, I-K ) AB( KA1, I-K ) = WORK( I-K+KA-M )*T + \$ WORK( N+I-K+KA-M )*AB( KA1, I-K ) RA1 = RA END IF END IF J2 = I - K - 1 + MAX( 1, K-I0+2 )*KA1 NR = ( N-J2+KA ) / KA1 J1 = J2 + ( NR-1 )*KA1 IF( UPDATE ) THEN J2T = MAX( J2, I+2*KA-K+1 ) ELSE J2T = J2 END IF NRT = ( N-J2T+KA ) / KA1 DO 320 J = J2T, J1, KA1 * * create nonzero element a(j+1,j-ka) outside the band * and store it in WORK(j-m) * WORK( J-M ) = WORK( J-M )*AB( KA1, J-KA+1 ) AB( KA1, J-KA+1 ) = WORK( N+J-M )*AB( KA1, J-KA+1 ) 320 CONTINUE * * generate rotations in 1st set to annihilate elements which * have been created outside the band * IF( NRT.GT.0 ) \$ CALL DLARGV( NRT, AB( KA1, J2T-KA ), INCA, WORK( J2T-M ), \$ KA1, WORK( N+J2T-M ), KA1 ) IF( NR.GT.0 ) THEN * * apply rotations in 1st set from the left * DO 330 L = 1, KA - 1 CALL DLARTV( NR, AB( L+1, J2-L ), INCA, \$ AB( L+2, J2-L ), INCA, WORK( N+J2-M ), \$ WORK( J2-M ), KA1 ) 330 CONTINUE * * apply rotations in 1st set from both sides to diagonal * blocks * CALL DLAR2V( NR, AB( 1, J2 ), AB( 1, J2+1 ), AB( 2, J2 ), \$ INCA, WORK( N+J2-M ), WORK( J2-M ), KA1 ) * END IF * * start applying rotations in 1st set from the right * DO 340 L = KA - 1, KB - K + 1, -1 NRT = ( N-J2+L ) / KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( KA1-L+1, J2 ), INCA, \$ AB( KA1-L, J2+1 ), INCA, WORK( N+J2-M ), \$ WORK( J2-M ), KA1 ) 340 CONTINUE * IF( WANTX ) THEN * * post-multiply X by product of rotations in 1st set * DO 350 J = J2, J1, KA1 CALL DROT( N-M, X( M+1, J ), 1, X( M+1, J+1 ), 1, \$ WORK( N+J-M ), WORK( J-M ) ) 350 CONTINUE END IF 360 CONTINUE * IF( UPDATE ) THEN IF( I2.LE.N .AND. KBT.GT.0 ) THEN * * create nonzero element a(i-kbt+ka+1,i-kbt) outside the * band and store it in WORK(i-kbt) * WORK( I-KBT ) = -BB( KBT+1, I-KBT )*RA1 END IF END IF * DO 400 K = KB, 1, -1 IF( UPDATE ) THEN J2 = I - K - 1 + MAX( 2, K-I0+1 )*KA1 ELSE J2 = I - K - 1 + MAX( 1, K-I0+1 )*KA1 END IF * * finish applying rotations in 2nd set from the right * DO 370 L = KB - K, 1, -1 NRT = ( N-J2+KA+L ) / KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( KA1-L+1, J2-KA ), INCA, \$ AB( KA1-L, J2-KA+1 ), INCA, \$ WORK( N+J2-KA ), WORK( J2-KA ), KA1 ) 370 CONTINUE NR = ( N-J2+KA ) / KA1 J1 = J2 + ( NR-1 )*KA1 DO 380 J = J1, J2, -KA1 WORK( J ) = WORK( J-KA ) WORK( N+J ) = WORK( N+J-KA ) 380 CONTINUE DO 390 J = J2, J1, KA1 * * create nonzero element a(j+1,j-ka) outside the band * and store it in WORK(j) * WORK( J ) = WORK( J )*AB( KA1, J-KA+1 ) AB( KA1, J-KA+1 ) = WORK( N+J )*AB( KA1, J-KA+1 ) 390 CONTINUE IF( UPDATE ) THEN IF( I-K.LT.N-KA .AND. K.LE.KBT ) \$ WORK( I-K+KA ) = WORK( I-K ) END IF 400 CONTINUE * DO 440 K = KB, 1, -1 J2 = I - K - 1 + MAX( 1, K-I0+1 )*KA1 NR = ( N-J2+KA ) / KA1 J1 = J2 + ( NR-1 )*KA1 IF( NR.GT.0 ) THEN * * generate rotations in 2nd set to annihilate elements * which have been created outside the band * CALL DLARGV( NR, AB( KA1, J2-KA ), INCA, WORK( J2 ), KA1, \$ WORK( N+J2 ), KA1 ) * * apply rotations in 2nd set from the left * DO 410 L = 1, KA - 1 CALL DLARTV( NR, AB( L+1, J2-L ), INCA, \$ AB( L+2, J2-L ), INCA, WORK( N+J2 ), \$ WORK( J2 ), KA1 ) 410 CONTINUE * * apply rotations in 2nd set from both sides to diagonal * blocks * CALL DLAR2V( NR, AB( 1, J2 ), AB( 1, J2+1 ), AB( 2, J2 ), \$ INCA, WORK( N+J2 ), WORK( J2 ), KA1 ) * END IF * * start applying rotations in 2nd set from the right * DO 420 L = KA - 1, KB - K + 1, -1 NRT = ( N-J2+L ) / KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( KA1-L+1, J2 ), INCA, \$ AB( KA1-L, J2+1 ), INCA, WORK( N+J2 ), \$ WORK( J2 ), KA1 ) 420 CONTINUE * IF( WANTX ) THEN * * post-multiply X by product of rotations in 2nd set * DO 430 J = J2, J1, KA1 CALL DROT( N-M, X( M+1, J ), 1, X( M+1, J+1 ), 1, \$ WORK( N+J ), WORK( J ) ) 430 CONTINUE END IF 440 CONTINUE * DO 460 K = 1, KB - 1 J2 = I - K - 1 + MAX( 1, K-I0+2 )*KA1 * * finish applying rotations in 1st set from the right * DO 450 L = KB - K, 1, -1 NRT = ( N-J2+L ) / KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( KA1-L+1, J2 ), INCA, \$ AB( KA1-L, J2+1 ), INCA, WORK( N+J2-M ), \$ WORK( J2-M ), KA1 ) 450 CONTINUE 460 CONTINUE * IF( KB.GT.1 ) THEN DO 470 J = N - 1, I - KB + 2*KA + 1, -1 WORK( N+J-M ) = WORK( N+J-KA-M ) WORK( J-M ) = WORK( J-KA-M ) 470 CONTINUE END IF * END IF * GO TO 10 * 480 CONTINUE * * **************************** Phase 2 ***************************** * * The logical structure of this phase is: * * UPDATE = .TRUE. * DO I = 1, M * use S(i) to update A and create a new bulge * apply rotations to push all bulges KA positions upward * END DO * UPDATE = .FALSE. * DO I = M - KA - 1, 2, -1 * apply rotations to push all bulges KA positions upward * END DO * * To avoid duplicating code, the two loops are merged. * UPDATE = .TRUE. I = 0 490 CONTINUE IF( UPDATE ) THEN I = I + 1 KBT = MIN( KB, M-I ) I0 = I + 1 I1 = MAX( 1, I-KA ) I2 = I + KBT - KA1 IF( I.GT.M ) THEN UPDATE = .FALSE. I = I - 1 I0 = M + 1 IF( KA.EQ.0 ) \$ RETURN GO TO 490 END IF ELSE I = I - KA IF( I.LT.2 ) \$ RETURN END IF * IF( I.LT.M-KBT ) THEN NX = M ELSE NX = N END IF * IF( UPPER ) THEN * * Transform A, working with the upper triangle * IF( UPDATE ) THEN * * Form inv(S(i))**T * A * inv(S(i)) * BII = BB( KB1, I ) DO 500 J = I1, I AB( J-I+KA1, I ) = AB( J-I+KA1, I ) / BII 500 CONTINUE DO 510 J = I, MIN( N, I+KA ) AB( I-J+KA1, J ) = AB( I-J+KA1, J ) / BII 510 CONTINUE DO 540 K = I + 1, I + KBT DO 520 J = K, I + KBT AB( K-J+KA1, J ) = AB( K-J+KA1, J ) - \$ BB( I-J+KB1, J )*AB( I-K+KA1, K ) - \$ BB( I-K+KB1, K )*AB( I-J+KA1, J ) + \$ AB( KA1, I )*BB( I-J+KB1, J )* \$ BB( I-K+KB1, K ) 520 CONTINUE DO 530 J = I + KBT + 1, MIN( N, I+KA ) AB( K-J+KA1, J ) = AB( K-J+KA1, J ) - \$ BB( I-K+KB1, K )*AB( I-J+KA1, J ) 530 CONTINUE 540 CONTINUE DO 560 J = I1, I DO 550 K = I + 1, MIN( J+KA, I+KBT ) AB( J-K+KA1, K ) = AB( J-K+KA1, K ) - \$ BB( I-K+KB1, K )*AB( J-I+KA1, I ) 550 CONTINUE 560 CONTINUE * IF( WANTX ) THEN * * post-multiply X by inv(S(i)) * CALL DSCAL( NX, ONE / BII, X( 1, I ), 1 ) IF( KBT.GT.0 ) \$ CALL DGER( NX, KBT, -ONE, X( 1, I ), 1, BB( KB, I+1 ), \$ LDBB-1, X( 1, I+1 ), LDX ) END IF * * store a(i1,i) in RA1 for use in next loop over K * RA1 = AB( I1-I+KA1, I ) END IF * * Generate and apply vectors of rotations to chase all the * existing bulges KA positions up toward the top of the band * DO 610 K = 1, KB - 1 IF( UPDATE ) THEN * * Determine the rotations which would annihilate the bulge * which has in theory just been created * IF( I+K-KA1.GT.0 .AND. I+K.LT.M ) THEN * * generate rotation to annihilate a(i+k-ka-1,i) * CALL DLARTG( AB( K+1, I ), RA1, WORK( N+I+K-KA ), \$ WORK( I+K-KA ), RA ) * * create nonzero element a(i+k-ka-1,i+k) outside the * band and store it in WORK(m-kb+i+k) * T = -BB( KB1-K, I+K )*RA1 WORK( M-KB+I+K ) = WORK( N+I+K-KA )*T - \$ WORK( I+K-KA )*AB( 1, I+K ) AB( 1, I+K ) = WORK( I+K-KA )*T + \$ WORK( N+I+K-KA )*AB( 1, I+K ) RA1 = RA END IF END IF J2 = I + K + 1 - MAX( 1, K+I0-M+1 )*KA1 NR = ( J2+KA-1 ) / KA1 J1 = J2 - ( NR-1 )*KA1 IF( UPDATE ) THEN J2T = MIN( J2, I-2*KA+K-1 ) ELSE J2T = J2 END IF NRT = ( J2T+KA-1 ) / KA1 DO 570 J = J1, J2T, KA1 * * create nonzero element a(j-1,j+ka) outside the band * and store it in WORK(j) * WORK( J ) = WORK( J )*AB( 1, J+KA-1 ) AB( 1, J+KA-1 ) = WORK( N+J )*AB( 1, J+KA-1 ) 570 CONTINUE * * generate rotations in 1st set to annihilate elements which * have been created outside the band * IF( NRT.GT.0 ) \$ CALL DLARGV( NRT, AB( 1, J1+KA ), INCA, WORK( J1 ), KA1, \$ WORK( N+J1 ), KA1 ) IF( NR.GT.0 ) THEN * * apply rotations in 1st set from the left * DO 580 L = 1, KA - 1 CALL DLARTV( NR, AB( KA1-L, J1+L ), INCA, \$ AB( KA-L, J1+L ), INCA, WORK( N+J1 ), \$ WORK( J1 ), KA1 ) 580 CONTINUE * * apply rotations in 1st set from both sides to diagonal * blocks * CALL DLAR2V( NR, AB( KA1, J1 ), AB( KA1, J1-1 ), \$ AB( KA, J1 ), INCA, WORK( N+J1 ), \$ WORK( J1 ), KA1 ) * END IF * * start applying rotations in 1st set from the right * DO 590 L = KA - 1, KB - K + 1, -1 NRT = ( J2+L-1 ) / KA1 J1T = J2 - ( NRT-1 )*KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( L, J1T ), INCA, \$ AB( L+1, J1T-1 ), INCA, WORK( N+J1T ), \$ WORK( J1T ), KA1 ) 590 CONTINUE * IF( WANTX ) THEN * * post-multiply X by product of rotations in 1st set * DO 600 J = J1, J2, KA1 CALL DROT( NX, X( 1, J ), 1, X( 1, J-1 ), 1, \$ WORK( N+J ), WORK( J ) ) 600 CONTINUE END IF 610 CONTINUE * IF( UPDATE ) THEN IF( I2.GT.0 .AND. KBT.GT.0 ) THEN * * create nonzero element a(i+kbt-ka-1,i+kbt) outside the * band and store it in WORK(m-kb+i+kbt) * WORK( M-KB+I+KBT ) = -BB( KB1-KBT, I+KBT )*RA1 END IF END IF * DO 650 K = KB, 1, -1 IF( UPDATE ) THEN J2 = I + K + 1 - MAX( 2, K+I0-M )*KA1 ELSE J2 = I + K + 1 - MAX( 1, K+I0-M )*KA1 END IF * * finish applying rotations in 2nd set from the right * DO 620 L = KB - K, 1, -1 NRT = ( J2+KA+L-1 ) / KA1 J1T = J2 - ( NRT-1 )*KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( L, J1T+KA ), INCA, \$ AB( L+1, J1T+KA-1 ), INCA, \$ WORK( N+M-KB+J1T+KA ), \$ WORK( M-KB+J1T+KA ), KA1 ) 620 CONTINUE NR = ( J2+KA-1 ) / KA1 J1 = J2 - ( NR-1 )*KA1 DO 630 J = J1, J2, KA1 WORK( M-KB+J ) = WORK( M-KB+J+KA ) WORK( N+M-KB+J ) = WORK( N+M-KB+J+KA ) 630 CONTINUE DO 640 J = J1, J2, KA1 * * create nonzero element a(j-1,j+ka) outside the band * and store it in WORK(m-kb+j) * WORK( M-KB+J ) = WORK( M-KB+J )*AB( 1, J+KA-1 ) AB( 1, J+KA-1 ) = WORK( N+M-KB+J )*AB( 1, J+KA-1 ) 640 CONTINUE IF( UPDATE ) THEN IF( I+K.GT.KA1 .AND. K.LE.KBT ) \$ WORK( M-KB+I+K-KA ) = WORK( M-KB+I+K ) END IF 650 CONTINUE * DO 690 K = KB, 1, -1 J2 = I + K + 1 - MAX( 1, K+I0-M )*KA1 NR = ( J2+KA-1 ) / KA1 J1 = J2 - ( NR-1 )*KA1 IF( NR.GT.0 ) THEN * * generate rotations in 2nd set to annihilate elements * which have been created outside the band * CALL DLARGV( NR, AB( 1, J1+KA ), INCA, WORK( M-KB+J1 ), \$ KA1, WORK( N+M-KB+J1 ), KA1 ) * * apply rotations in 2nd set from the left * DO 660 L = 1, KA - 1 CALL DLARTV( NR, AB( KA1-L, J1+L ), INCA, \$ AB( KA-L, J1+L ), INCA, \$ WORK( N+M-KB+J1 ), WORK( M-KB+J1 ), KA1 ) 660 CONTINUE * * apply rotations in 2nd set from both sides to diagonal * blocks * CALL DLAR2V( NR, AB( KA1, J1 ), AB( KA1, J1-1 ), \$ AB( KA, J1 ), INCA, WORK( N+M-KB+J1 ), \$ WORK( M-KB+J1 ), KA1 ) * END IF * * start applying rotations in 2nd set from the right * DO 670 L = KA - 1, KB - K + 1, -1 NRT = ( J2+L-1 ) / KA1 J1T = J2 - ( NRT-1 )*KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( L, J1T ), INCA, \$ AB( L+1, J1T-1 ), INCA, \$ WORK( N+M-KB+J1T ), WORK( M-KB+J1T ), \$ KA1 ) 670 CONTINUE * IF( WANTX ) THEN * * post-multiply X by product of rotations in 2nd set * DO 680 J = J1, J2, KA1 CALL DROT( NX, X( 1, J ), 1, X( 1, J-1 ), 1, \$ WORK( N+M-KB+J ), WORK( M-KB+J ) ) 680 CONTINUE END IF 690 CONTINUE * DO 710 K = 1, KB - 1 J2 = I + K + 1 - MAX( 1, K+I0-M+1 )*KA1 * * finish applying rotations in 1st set from the right * DO 700 L = KB - K, 1, -1 NRT = ( J2+L-1 ) / KA1 J1T = J2 - ( NRT-1 )*KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( L, J1T ), INCA, \$ AB( L+1, J1T-1 ), INCA, WORK( N+J1T ), \$ WORK( J1T ), KA1 ) 700 CONTINUE 710 CONTINUE * IF( KB.GT.1 ) THEN DO 720 J = 2, MIN( I+KB, M ) - 2*KA - 1 WORK( N+J ) = WORK( N+J+KA ) WORK( J ) = WORK( J+KA ) 720 CONTINUE END IF * ELSE * * Transform A, working with the lower triangle * IF( UPDATE ) THEN * * Form inv(S(i))**T * A * inv(S(i)) * BII = BB( 1, I ) DO 730 J = I1, I AB( I-J+1, J ) = AB( I-J+1, J ) / BII 730 CONTINUE DO 740 J = I, MIN( N, I+KA ) AB( J-I+1, I ) = AB( J-I+1, I ) / BII 740 CONTINUE DO 770 K = I + 1, I + KBT DO 750 J = K, I + KBT AB( J-K+1, K ) = AB( J-K+1, K ) - \$ BB( J-I+1, I )*AB( K-I+1, I ) - \$ BB( K-I+1, I )*AB( J-I+1, I ) + \$ AB( 1, I )*BB( J-I+1, I )* \$ BB( K-I+1, I ) 750 CONTINUE DO 760 J = I + KBT + 1, MIN( N, I+KA ) AB( J-K+1, K ) = AB( J-K+1, K ) - \$ BB( K-I+1, I )*AB( J-I+1, I ) 760 CONTINUE 770 CONTINUE DO 790 J = I1, I DO 780 K = I + 1, MIN( J+KA, I+KBT ) AB( K-J+1, J ) = AB( K-J+1, J ) - \$ BB( K-I+1, I )*AB( I-J+1, J ) 780 CONTINUE 790 CONTINUE * IF( WANTX ) THEN * * post-multiply X by inv(S(i)) * CALL DSCAL( NX, ONE / BII, X( 1, I ), 1 ) IF( KBT.GT.0 ) \$ CALL DGER( NX, KBT, -ONE, X( 1, I ), 1, BB( 2, I ), 1, \$ X( 1, I+1 ), LDX ) END IF * * store a(i,i1) in RA1 for use in next loop over K * RA1 = AB( I-I1+1, I1 ) END IF * * Generate and apply vectors of rotations to chase all the * existing bulges KA positions up toward the top of the band * DO 840 K = 1, KB - 1 IF( UPDATE ) THEN * * Determine the rotations which would annihilate the bulge * which has in theory just been created * IF( I+K-KA1.GT.0 .AND. I+K.LT.M ) THEN * * generate rotation to annihilate a(i,i+k-ka-1) * CALL DLARTG( AB( KA1-K, I+K-KA ), RA1, \$ WORK( N+I+K-KA ), WORK( I+K-KA ), RA ) * * create nonzero element a(i+k,i+k-ka-1) outside the * band and store it in WORK(m-kb+i+k) * T = -BB( K+1, I )*RA1 WORK( M-KB+I+K ) = WORK( N+I+K-KA )*T - \$ WORK( I+K-KA )*AB( KA1, I+K-KA ) AB( KA1, I+K-KA ) = WORK( I+K-KA )*T + \$ WORK( N+I+K-KA )*AB( KA1, I+K-KA ) RA1 = RA END IF END IF J2 = I + K + 1 - MAX( 1, K+I0-M+1 )*KA1 NR = ( J2+KA-1 ) / KA1 J1 = J2 - ( NR-1 )*KA1 IF( UPDATE ) THEN J2T = MIN( J2, I-2*KA+K-1 ) ELSE J2T = J2 END IF NRT = ( J2T+KA-1 ) / KA1 DO 800 J = J1, J2T, KA1 * * create nonzero element a(j+ka,j-1) outside the band * and store it in WORK(j) * WORK( J ) = WORK( J )*AB( KA1, J-1 ) AB( KA1, J-1 ) = WORK( N+J )*AB( KA1, J-1 ) 800 CONTINUE * * generate rotations in 1st set to annihilate elements which * have been created outside the band * IF( NRT.GT.0 ) \$ CALL DLARGV( NRT, AB( KA1, J1 ), INCA, WORK( J1 ), KA1, \$ WORK( N+J1 ), KA1 ) IF( NR.GT.0 ) THEN * * apply rotations in 1st set from the right * DO 810 L = 1, KA - 1 CALL DLARTV( NR, AB( L+1, J1 ), INCA, AB( L+2, J1-1 ), \$ INCA, WORK( N+J1 ), WORK( J1 ), KA1 ) 810 CONTINUE * * apply rotations in 1st set from both sides to diagonal * blocks * CALL DLAR2V( NR, AB( 1, J1 ), AB( 1, J1-1 ), \$ AB( 2, J1-1 ), INCA, WORK( N+J1 ), \$ WORK( J1 ), KA1 ) * END IF * * start applying rotations in 1st set from the left * DO 820 L = KA - 1, KB - K + 1, -1 NRT = ( J2+L-1 ) / KA1 J1T = J2 - ( NRT-1 )*KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( KA1-L+1, J1T-KA1+L ), INCA, \$ AB( KA1-L, J1T-KA1+L ), INCA, \$ WORK( N+J1T ), WORK( J1T ), KA1 ) 820 CONTINUE * IF( WANTX ) THEN * * post-multiply X by product of rotations in 1st set * DO 830 J = J1, J2, KA1 CALL DROT( NX, X( 1, J ), 1, X( 1, J-1 ), 1, \$ WORK( N+J ), WORK( J ) ) 830 CONTINUE END IF 840 CONTINUE * IF( UPDATE ) THEN IF( I2.GT.0 .AND. KBT.GT.0 ) THEN * * create nonzero element a(i+kbt,i+kbt-ka-1) outside the * band and store it in WORK(m-kb+i+kbt) * WORK( M-KB+I+KBT ) = -BB( KBT+1, I )*RA1 END IF END IF * DO 880 K = KB, 1, -1 IF( UPDATE ) THEN J2 = I + K + 1 - MAX( 2, K+I0-M )*KA1 ELSE J2 = I + K + 1 - MAX( 1, K+I0-M )*KA1 END IF * * finish applying rotations in 2nd set from the left * DO 850 L = KB - K, 1, -1 NRT = ( J2+KA+L-1 ) / KA1 J1T = J2 - ( NRT-1 )*KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( KA1-L+1, J1T+L-1 ), INCA, \$ AB( KA1-L, J1T+L-1 ), INCA, \$ WORK( N+M-KB+J1T+KA ), \$ WORK( M-KB+J1T+KA ), KA1 ) 850 CONTINUE NR = ( J2+KA-1 ) / KA1 J1 = J2 - ( NR-1 )*KA1 DO 860 J = J1, J2, KA1 WORK( M-KB+J ) = WORK( M-KB+J+KA ) WORK( N+M-KB+J ) = WORK( N+M-KB+J+KA ) 860 CONTINUE DO 870 J = J1, J2, KA1 * * create nonzero element a(j+ka,j-1) outside the band * and store it in WORK(m-kb+j) * WORK( M-KB+J ) = WORK( M-KB+J )*AB( KA1, J-1 ) AB( KA1, J-1 ) = WORK( N+M-KB+J )*AB( KA1, J-1 ) 870 CONTINUE IF( UPDATE ) THEN IF( I+K.GT.KA1 .AND. K.LE.KBT ) \$ WORK( M-KB+I+K-KA ) = WORK( M-KB+I+K ) END IF 880 CONTINUE * DO 920 K = KB, 1, -1 J2 = I + K + 1 - MAX( 1, K+I0-M )*KA1 NR = ( J2+KA-1 ) / KA1 J1 = J2 - ( NR-1 )*KA1 IF( NR.GT.0 ) THEN * * generate rotations in 2nd set to annihilate elements * which have been created outside the band * CALL DLARGV( NR, AB( KA1, J1 ), INCA, WORK( M-KB+J1 ), \$ KA1, WORK( N+M-KB+J1 ), KA1 ) * * apply rotations in 2nd set from the right * DO 890 L = 1, KA - 1 CALL DLARTV( NR, AB( L+1, J1 ), INCA, AB( L+2, J1-1 ), \$ INCA, WORK( N+M-KB+J1 ), WORK( M-KB+J1 ), \$ KA1 ) 890 CONTINUE * * apply rotations in 2nd set from both sides to diagonal * blocks * CALL DLAR2V( NR, AB( 1, J1 ), AB( 1, J1-1 ), \$ AB( 2, J1-1 ), INCA, WORK( N+M-KB+J1 ), \$ WORK( M-KB+J1 ), KA1 ) * END IF * * start applying rotations in 2nd set from the left * DO 900 L = KA - 1, KB - K + 1, -1 NRT = ( J2+L-1 ) / KA1 J1T = J2 - ( NRT-1 )*KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( KA1-L+1, J1T-KA1+L ), INCA, \$ AB( KA1-L, J1T-KA1+L ), INCA, \$ WORK( N+M-KB+J1T ), WORK( M-KB+J1T ), \$ KA1 ) 900 CONTINUE * IF( WANTX ) THEN * * post-multiply X by product of rotations in 2nd set * DO 910 J = J1, J2, KA1 CALL DROT( NX, X( 1, J ), 1, X( 1, J-1 ), 1, \$ WORK( N+M-KB+J ), WORK( M-KB+J ) ) 910 CONTINUE END IF 920 CONTINUE * DO 940 K = 1, KB - 1 J2 = I + K + 1 - MAX( 1, K+I0-M+1 )*KA1 * * finish applying rotations in 1st set from the left * DO 930 L = KB - K, 1, -1 NRT = ( J2+L-1 ) / KA1 J1T = J2 - ( NRT-1 )*KA1 IF( NRT.GT.0 ) \$ CALL DLARTV( NRT, AB( KA1-L+1, J1T-KA1+L ), INCA, \$ AB( KA1-L, J1T-KA1+L ), INCA, \$ WORK( N+J1T ), WORK( J1T ), KA1 ) 930 CONTINUE 940 CONTINUE * IF( KB.GT.1 ) THEN DO 950 J = 2, MIN( I+KB, M ) - 2*KA - 1 WORK( N+J ) = WORK( N+J+KA ) WORK( J ) = WORK( J+KA ) 950 CONTINUE END IF * END IF * GO TO 490 * * End of DSBGST * END