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SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
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$ WORK, LWORK, INFO ) |
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* |
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* -- LAPACK 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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* January 2007 |
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* |
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* .. Scalar Arguments .. |
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CHARACTER SIDE, TRANS |
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INTEGER INFO, K, L, LDA, LDC, LWORK, M, N |
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* .. |
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* .. Array Arguments .. |
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DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
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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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* DORMRZ overwrites the general real M-by-N matrix C with |
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* |
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* SIDE = 'L' SIDE = 'R' |
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* TRANS = 'N': Q * C C * Q |
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* TRANS = 'T': Q**T * C C * Q**T |
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* |
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* where Q is a real orthogonal matrix defined as the product of k |
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* elementary reflectors |
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* |
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* Q = H(1) H(2) . . . H(k) |
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* |
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* as returned by DTZRZF. Q is of order M if SIDE = 'L' and of order N |
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* if SIDE = 'R'. |
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* |
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* Arguments |
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* ========= |
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* |
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* SIDE (input) CHARACTER*1 |
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* = 'L': apply Q or Q**T from the Left; |
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* = 'R': apply Q or Q**T from the Right. |
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* |
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* TRANS (input) CHARACTER*1 |
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* = 'N': No transpose, apply Q; |
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* = 'T': Transpose, apply Q**T. |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix C. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix C. N >= 0. |
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* |
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* K (input) INTEGER |
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* The number of elementary reflectors whose product defines |
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* the matrix Q. |
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* If SIDE = 'L', M >= K >= 0; |
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* if SIDE = 'R', N >= K >= 0. |
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* |
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* L (input) INTEGER |
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* The number of columns of the matrix A containing |
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* the meaningful part of the Householder reflectors. |
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* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. |
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* |
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* A (input) DOUBLE PRECISION array, dimension |
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* (LDA,M) if SIDE = 'L', |
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* (LDA,N) if SIDE = 'R' |
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* The i-th row must contain the vector which defines the |
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* elementary reflector H(i), for i = 1,2,...,k, as returned by |
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* DTZRZF in the last k rows of its array argument A. |
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* A is modified by the routine but restored on exit. |
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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,K). |
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* |
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* TAU (input) DOUBLE PRECISION array, dimension (K) |
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* TAU(i) must contain the scalar factor of the elementary |
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* reflector H(i), as returned by DTZRZF. |
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* |
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* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) |
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* On entry, the M-by-N matrix C. |
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* On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. |
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* |
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* LDC (input) INTEGER |
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* The leading dimension of the array C. LDC >= max(1,M). |
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* |
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* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The dimension of the array WORK. |
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* If SIDE = 'L', LWORK >= max(1,N); |
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* if SIDE = 'R', LWORK >= max(1,M). |
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* For optimum performance LWORK >= N*NB if SIDE = 'L', and |
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* LWORK >= M*NB if SIDE = 'R', where NB is the optimal |
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* blocksize. |
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* |
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* If LWORK = -1, then a workspace query is assumed; the routine |
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* only calculates the optimal size of the WORK array, returns |
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* this value as the first entry of the WORK array, and no error |
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* message related to LWORK is issued by XERBLA. |
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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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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA |
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* |
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* ===================================================================== |
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* |
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* .. Parameters .. |
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INTEGER NBMAX, LDT |
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PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) |
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* .. |
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* .. Local Scalars .. |
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LOGICAL LEFT, LQUERY, NOTRAN |
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CHARACTER TRANST |
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INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC, |
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$ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW |
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* .. |
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* .. Local Arrays .. |
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DOUBLE PRECISION T( LDT, NBMAX ) |
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* .. |
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* .. External Functions .. |
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LOGICAL LSAME |
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INTEGER ILAENV |
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EXTERNAL LSAME, ILAENV |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL DLARZB, DLARZT, DORMR3, XERBLA |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC MAX, MIN |
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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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LEFT = LSAME( SIDE, 'L' ) |
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NOTRAN = LSAME( TRANS, 'N' ) |
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LQUERY = ( LWORK.EQ.-1 ) |
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* |
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* NQ is the order of Q and NW is the minimum dimension of WORK |
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* |
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IF( LEFT ) THEN |
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NQ = M |
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NW = MAX( 1, N ) |
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ELSE |
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NQ = N |
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NW = MAX( 1, M ) |
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END IF |
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IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN |
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INFO = -1 |
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ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN |
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INFO = -2 |
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ELSE IF( M.LT.0 ) THEN |
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INFO = -3 |
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ELSE IF( N.LT.0 ) THEN |
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INFO = -4 |
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ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN |
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INFO = -5 |
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ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR. |
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$ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN |
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INFO = -6 |
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ELSE IF( LDA.LT.MAX( 1, K ) ) THEN |
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INFO = -8 |
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
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INFO = -11 |
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END IF |
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* |
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IF( INFO.EQ.0 ) THEN |
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IF( M.EQ.0 .OR. N.EQ.0 ) THEN |
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LWKOPT = 1 |
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ELSE |
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* |
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* Determine the block size. NB may be at most NBMAX, where |
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* NBMAX is used to define the local array T. |
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* |
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NB = MIN( NBMAX, ILAENV( 1, 'DORMRQ', SIDE // TRANS, M, N, |
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$ K, -1 ) ) |
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LWKOPT = NW*NB |
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END IF |
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WORK( 1 ) = LWKOPT |
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* |
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IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN |
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INFO = -13 |
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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( 'DORMRZ', -INFO ) |
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RETURN |
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ELSE IF( LQUERY ) THEN |
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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( M.EQ.0 .OR. N.EQ.0 ) THEN |
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WORK( 1 ) = 1 |
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RETURN |
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END IF |
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* |
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NBMIN = 2 |
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LDWORK = NW |
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IF( NB.GT.1 .AND. NB.LT.K ) THEN |
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IWS = NW*NB |
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IF( LWORK.LT.IWS ) THEN |
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NB = LWORK / LDWORK |
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NBMIN = MAX( 2, ILAENV( 2, 'DORMRQ', SIDE // TRANS, M, N, K, |
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$ -1 ) ) |
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END IF |
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ELSE |
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IWS = NW |
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END IF |
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* |
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IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN |
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* |
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* Use unblocked code |
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* |
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CALL DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, |
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$ WORK, IINFO ) |
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ELSE |
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* |
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* Use blocked code |
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* |
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IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. |
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$ ( .NOT.LEFT .AND. NOTRAN ) ) THEN |
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I1 = 1 |
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I2 = K |
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I3 = NB |
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ELSE |
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I1 = ( ( K-1 ) / NB )*NB + 1 |
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I2 = 1 |
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I3 = -NB |
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END IF |
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* |
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IF( LEFT ) THEN |
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NI = N |
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JC = 1 |
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JA = M - L + 1 |
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ELSE |
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MI = M |
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IC = 1 |
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JA = N - L + 1 |
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END IF |
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* |
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IF( NOTRAN ) THEN |
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TRANST = 'T' |
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ELSE |
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TRANST = 'N' |
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END IF |
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* |
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DO 10 I = I1, I2, I3 |
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IB = MIN( NB, K-I+1 ) |
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* |
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* Form the triangular factor of the block reflector |
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* H = H(i+ib-1) . . . H(i+1) H(i) |
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* |
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CALL DLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA, |
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$ TAU( I ), T, LDT ) |
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* |
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IF( LEFT ) THEN |
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* |
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* H or H' is applied to C(i:m,1:n) |
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* |
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MI = M - I + 1 |
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IC = I |
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ELSE |
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* |
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* H or H' is applied to C(1:m,i:n) |
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* |
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NI = N - I + 1 |
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JC = I |
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END IF |
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* |
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* Apply H or H' |
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* |
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CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, |
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$ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ), |
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$ LDC, WORK, LDWORK ) |
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10 CONTINUE |
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* |
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END IF |
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* |
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WORK( 1 ) = LWKOPT |
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* |
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RETURN |
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* |
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* End of DORMRZ |
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* |
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END |