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SUBROUTINE CLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT,
$ XRIGHT ) * * -- LAPACK auxiliary test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL LLEFT, LRIGHT, LROWS INTEGER LDA, NL COMPLEX C, S, XLEFT, XRIGHT * .. * .. Array Arguments .. COMPLEX A( * ) * .. * * Purpose * ======= * * CLAROT applies a (Givens) rotation to two adjacent rows or * columns, where one element of the first and/or last column/row * for use on matrices stored in some format other than GE, so * that elements of the matrix may be used or modified for which * no array element is provided. * * One example is a symmetric matrix in SB format (bandwidth=4), for * which UPLO='L': Two adjacent rows will have the format: * * row j: * * * * * . . . . * row j+1: * * * * * . . . . * * '*' indicates elements for which storage is provided, * '.' indicates elements for which no storage is provided, but * are not necessarily zero; their values are determined by * symmetry. ' ' indicates elements which are necessarily zero, * and have no storage provided. * * Those columns which have two '*'s can be handled by SROT. * Those columns which have no '*'s can be ignored, since as long * as the Givens rotations are carefully applied to preserve * symmetry, their values are determined. * Those columns which have one '*' have to be handled separately, * by using separate variables "p" and "q": * * row j: * * * * * p . . . * row j+1: q * * * * * . . . . * * The element p would have to be set correctly, then that column * is rotated, setting p to its new value. The next call to * CLAROT would rotate columns j and j+1, using p, and restore * symmetry. The element q would start out being zero, and be * made non-zero by the rotation. Later, rotations would presumably * be chosen to zero q out. * * Typical Calling Sequences: rotating the i-th and (i+1)-st rows. * ------- ------- --------- * * General dense matrix: * * CALL CLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S, * A(i,1),LDA, DUMMY, DUMMY) * * General banded matrix in GB format: * * j = MAX(1, i-KL ) * NL = MIN( N, i+KU+1 ) + 1-j * CALL CLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S, * A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT ) * * [ note that i+1-j is just MIN(i,KL+1) ] * * Symmetric banded matrix in SY format, bandwidth K, * lower triangle only: * * j = MAX(1, i-K ) * NL = MIN( K+1, i ) + 1 * CALL CLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S, * A(i,j), LDA, XLEFT, XRIGHT ) * * Same, but upper triangle only: * * NL = MIN( K+1, N-i ) + 1 * CALL CLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S, * A(i,i), LDA, XLEFT, XRIGHT ) * * Symmetric banded matrix in SB format, bandwidth K, * lower triangle only: * * [ same as for SY, except:] * . . . . * A(i+1-j,j), LDA-1, XLEFT, XRIGHT ) * * [ note that i+1-j is just MIN(i,K+1) ] * * Same, but upper triangle only: * . . . * A(K+1,i), LDA-1, XLEFT, XRIGHT ) * * Rotating columns is just the transpose of rotating rows, except * for GB and SB: (rotating columns i and i+1) * * GB: * j = MAX(1, i-KU ) * NL = MIN( N, i+KL+1 ) + 1-j * CALL CLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S, * A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM ) * * [note that KU+j+1-i is just MAX(1,KU+2-i)] * * SB: (upper triangle) * * . . . . . . * A(K+j+1-i,i),LDA-1, XTOP, XBOTTM ) * * SB: (lower triangle) * * . . . . . . * A(1,i),LDA-1, XTOP, XBOTTM ) * * Arguments * ========= * * LROWS - LOGICAL * If .TRUE., then CLAROT will rotate two rows. If .FALSE., * then it will rotate two columns. * Not modified. * * LLEFT - LOGICAL * If .TRUE., then XLEFT will be used instead of the * corresponding element of A for the first element in the * second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) * If .FALSE., then the corresponding element of A will be * used. * Not modified. * * LRIGHT - LOGICAL * If .TRUE., then XRIGHT will be used instead of the * corresponding element of A for the last element in the * first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If * .FALSE., then the corresponding element of A will be used. * Not modified. * * NL - INTEGER * The length of the rows (if LROWS=.TRUE.) or columns (if * LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are * used, the columns/rows they are in should be included in * NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at * least 2. The number of rows/columns to be rotated * exclusive of those involving XLEFT and/or XRIGHT may * not be negative, i.e., NL minus how many of LLEFT and * LRIGHT are .TRUE. must be at least zero; if not, XERBLA * will be called. * Not modified. * * C, S - COMPLEX * Specify the Givens rotation to be applied. If LROWS is * true, then the matrix ( c s ) * ( _ _ ) * (-s c ) is applied from the left; * if false, then the transpose (not conjugated) thereof is * applied from the right. Note that in contrast to the * output of CROTG or to most versions of CROT, both C and S * are complex. For a Givens rotation, |C|**2 + |S|**2 should * be 1, but this is not checked. * Not modified. * * A - COMPLEX array. * The array containing the rows/columns to be rotated. The * first element of A should be the upper left element to * be rotated. * Read and modified. * * LDA - INTEGER * The "effective" leading dimension of A. If A contains * a matrix stored in GE, HE, or SY format, then this is just * the leading dimension of A as dimensioned in the calling * routine. If A contains a matrix stored in band (GB, HB, or * SB) format, then this should be *one less* than the leading * dimension used in the calling routine. Thus, if A were * dimensioned A(LDA,*) in CLAROT, then A(1,j) would be the * j-th element in the first of the two rows to be rotated, * and A(2,j) would be the j-th in the second, regardless of * how the array may be stored in the calling routine. [A * cannot, however, actually be dimensioned thus, since for * band format, the row number may exceed LDA, which is not * legal FORTRAN.] * If LROWS=.TRUE., then LDA must be at least 1, otherwise * it must be at least NL minus the number of .TRUE. values * in XLEFT and XRIGHT. * Not modified. * * XLEFT - COMPLEX * If LLEFT is .TRUE., then XLEFT will be used and modified * instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) * (if LROWS=.FALSE.). * Read and modified. * * XRIGHT - COMPLEX * If LRIGHT is .TRUE., then XRIGHT will be used and modified * instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) * (if LROWS=.FALSE.). * Read and modified. * * ===================================================================== * * .. Local Scalars .. INTEGER IINC, INEXT, IX, IY, IYT, J, NT COMPLEX TEMPX * .. * .. Local Arrays .. COMPLEX XT( 2 ), YT( 2 ) * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG * .. * .. Executable Statements .. * * Set up indices, arrays for ends * IF( LROWS ) THEN IINC = LDA INEXT = 1 ELSE IINC = 1 INEXT = LDA END IF * IF( LLEFT ) THEN NT = 1 IX = 1 + IINC IY = 2 + LDA XT( 1 ) = A( 1 ) YT( 1 ) = XLEFT ELSE NT = 0 IX = 1 IY = 1 + INEXT END IF * IF( LRIGHT ) THEN IYT = 1 + INEXT + ( NL-1 )*IINC NT = NT + 1 XT( NT ) = XRIGHT YT( NT ) = A( IYT ) END IF * * Check for errors * IF( NL.LT.NT ) THEN CALL XERBLA( 'CLAROT', 4 ) RETURN END IF IF( LDA.LE.0 .OR. ( .NOT.LROWS .AND. LDA.LT.NL-NT ) ) THEN CALL XERBLA( 'CLAROT', 8 ) RETURN END IF * * Rotate * * CROT( NL-NT, A(IX),IINC, A(IY),IINC, C, S ) with complex C, S * DO 10 J = 0, NL - NT - 1 TEMPX = C*A( IX+J*IINC ) + S*A( IY+J*IINC ) A( IY+J*IINC ) = -CONJG( S )*A( IX+J*IINC ) + $ CONJG( C )*A( IY+J*IINC ) A( IX+J*IINC ) = TEMPX 10 CONTINUE * * CROT( NT, XT,1, YT,1, C, S ) with complex C, S * DO 20 J = 1, NT TEMPX = C*XT( J ) + S*YT( J ) YT( J ) = -CONJG( S )*XT( J ) + CONJG( C )*YT( J ) XT( J ) = TEMPX 20 CONTINUE * * Stuff values back into XLEFT, XRIGHT, etc. * IF( LLEFT ) THEN A( 1 ) = XT( 1 ) XLEFT = YT( 1 ) END IF * IF( LRIGHT ) THEN XRIGHT = XT( NT ) A( IYT ) = YT( NT ) END IF * RETURN * * End of CLAROT * END |