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Diffstat (limited to '2.3-1/src/fortran/lapack/dormlq.f')
| -rw-r--r-- | 2.3-1/src/fortran/lapack/dormlq.f | 267 |
1 files changed, 267 insertions, 0 deletions
diff --git a/2.3-1/src/fortran/lapack/dormlq.f b/2.3-1/src/fortran/lapack/dormlq.f new file mode 100644 index 00000000..f0c68ef2 --- /dev/null +++ b/2.3-1/src/fortran/lapack/dormlq.f @@ -0,0 +1,267 @@ + SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, + $ WORK, LWORK, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER SIDE, TRANS + INTEGER INFO, K, LDA, LDC, LWORK, M, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* DORMLQ overwrites the general real M-by-N matrix C with +* +* SIDE = 'L' SIDE = 'R' +* TRANS = 'N': Q * C C * Q +* TRANS = 'T': Q**T * C C * Q**T +* +* where Q is a real orthogonal matrix defined as the product of k +* elementary reflectors +* +* Q = H(k) . . . H(2) H(1) +* +* as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N +* if SIDE = 'R'. +* +* Arguments +* ========= +* +* SIDE (input) CHARACTER*1 +* = 'L': apply Q or Q**T from the Left; +* = 'R': apply Q or Q**T from the Right. +* +* TRANS (input) CHARACTER*1 +* = 'N': No transpose, apply Q; +* = 'T': Transpose, apply Q**T. +* +* M (input) INTEGER +* The number of rows of the matrix C. M >= 0. +* +* N (input) INTEGER +* The number of columns of the matrix C. N >= 0. +* +* K (input) INTEGER +* The number of elementary reflectors whose product defines +* the matrix Q. +* If SIDE = 'L', M >= K >= 0; +* if SIDE = 'R', N >= K >= 0. +* +* A (input) DOUBLE PRECISION array, dimension +* (LDA,M) if SIDE = 'L', +* (LDA,N) if SIDE = 'R' +* The i-th row must contain the vector which defines the +* elementary reflector H(i), for i = 1,2,...,k, as returned by +* DGELQF in the first k rows of its array argument A. +* A is modified by the routine but restored on exit. +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,K). +* +* TAU (input) DOUBLE PRECISION array, dimension (K) +* TAU(i) must contain the scalar factor of the elementary +* reflector H(i), as returned by DGELQF. +* +* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) +* On entry, the M-by-N matrix C. +* On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. +* +* LDC (input) INTEGER +* The leading dimension of the array C. LDC >= max(1,M). +* +* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The dimension of the array WORK. +* If SIDE = 'L', LWORK >= max(1,N); +* if SIDE = 'R', LWORK >= max(1,M). +* For optimum performance LWORK >= N*NB if SIDE = 'L', and +* LWORK >= M*NB if SIDE = 'R', where NB is the optimal +* blocksize. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* ===================================================================== +* +* .. Parameters .. + INTEGER NBMAX, LDT + PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) +* .. +* .. Local Scalars .. + LOGICAL LEFT, LQUERY, NOTRAN + CHARACTER TRANST + INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK, + $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW +* .. +* .. Local Arrays .. + DOUBLE PRECISION T( LDT, NBMAX ) +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + EXTERNAL LSAME, ILAENV +* .. +* .. External Subroutines .. + EXTERNAL DLARFB, DLARFT, DORML2, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input arguments +* + INFO = 0 + LEFT = LSAME( SIDE, 'L' ) + NOTRAN = LSAME( TRANS, 'N' ) + LQUERY = ( LWORK.EQ.-1 ) +* +* NQ is the order of Q and NW is the minimum dimension of WORK +* + IF( LEFT ) THEN + NQ = M + NW = N + ELSE + NQ = N + NW = M + END IF + IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN + INFO = -1 + ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN + INFO = -2 + ELSE IF( M.LT.0 ) THEN + INFO = -3 + ELSE IF( N.LT.0 ) THEN + INFO = -4 + ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN + INFO = -5 + ELSE IF( LDA.LT.MAX( 1, K ) ) THEN + INFO = -7 + ELSE IF( LDC.LT.MAX( 1, M ) ) THEN + INFO = -10 + ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN + INFO = -12 + END IF +* + IF( INFO.EQ.0 ) THEN +* +* Determine the block size. NB may be at most NBMAX, where NBMAX +* is used to define the local array T. +* + NB = MIN( NBMAX, ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N, K, + $ -1 ) ) + LWKOPT = MAX( 1, NW )*NB + WORK( 1 ) = LWKOPT + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DORMLQ', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* Quick return if possible +* + IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN + WORK( 1 ) = 1 + RETURN + END IF +* + NBMIN = 2 + LDWORK = NW + IF( NB.GT.1 .AND. NB.LT.K ) THEN + IWS = NW*NB + IF( LWORK.LT.IWS ) THEN + NB = LWORK / LDWORK + NBMIN = MAX( 2, ILAENV( 2, 'DORMLQ', SIDE // TRANS, M, N, K, + $ -1 ) ) + END IF + ELSE + IWS = NW + END IF +* + IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN +* +* Use unblocked code +* + CALL DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, + $ IINFO ) + ELSE +* +* Use blocked code +* + IF( ( LEFT .AND. NOTRAN ) .OR. + $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN + I1 = 1 + I2 = K + I3 = NB + ELSE + I1 = ( ( K-1 ) / NB )*NB + 1 + I2 = 1 + I3 = -NB + END IF +* + IF( LEFT ) THEN + NI = N + JC = 1 + ELSE + MI = M + IC = 1 + END IF +* + IF( NOTRAN ) THEN + TRANST = 'T' + ELSE + TRANST = 'N' + END IF +* + DO 10 I = I1, I2, I3 + IB = MIN( NB, K-I+1 ) +* +* Form the triangular factor of the block reflector +* H = H(i) H(i+1) . . . H(i+ib-1) +* + CALL DLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ), + $ LDA, TAU( I ), T, LDT ) + IF( LEFT ) THEN +* +* H or H' is applied to C(i:m,1:n) +* + MI = M - I + 1 + IC = I + ELSE +* +* H or H' is applied to C(1:m,i:n) +* + NI = N - I + 1 + JC = I + END IF +* +* Apply H or H' +* + CALL DLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB, + $ A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK, + $ LDWORK ) + 10 CONTINUE + END IF + WORK( 1 ) = LWKOPT + RETURN +* +* End of DORMLQ +* + END |