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diff --git a/SRC/DEPRECATED/cgelsx.f b/SRC/DEPRECATED/cgelsx.f new file mode 100644 index 00000000..39380e6a --- /dev/null +++ b/SRC/DEPRECATED/cgelsx.f @@ -0,0 +1,447 @@ +*> \brief <b> CGELSX solves overdetermined or underdetermined systems for GE matrices</b> +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CGELSX + dependencies +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgelsx.f"> +*> [TGZ]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgelsx.f"> +*> [ZIP]</a> +*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgelsx.f"> +*> [TXT]</a> +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, +* WORK, RWORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, LDB, M, N, NRHS, RANK +* REAL RCOND +* .. +* .. Array Arguments .. +* INTEGER JPVT( * ) +* REAL RWORK( * ) +* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> This routine is deprecated and has been replaced by routine CGELSY. +*> +*> CGELSX computes the minimum-norm solution to a complex linear least +*> squares problem: +*> minimize || A * X - B || +*> using a complete orthogonal factorization of A. A is an M-by-N +*> matrix which may be rank-deficient. +*> +*> Several right hand side vectors b and solution vectors x can be +*> handled in a single call; they are stored as the columns of the +*> M-by-NRHS right hand side matrix B and the N-by-NRHS solution +*> matrix X. +*> +*> The routine first computes a QR factorization with column pivoting: +*> A * P = Q * [ R11 R12 ] +*> [ 0 R22 ] +*> with R11 defined as the largest leading submatrix whose estimated +*> condition number is less than 1/RCOND. The order of R11, RANK, +*> is the effective rank of A. +*> +*> Then, R22 is considered to be negligible, and R12 is annihilated +*> by unitary transformations from the right, arriving at the +*> complete orthogonal factorization: +*> A * P = Q * [ T11 0 ] * Z +*> [ 0 0 ] +*> The minimum-norm solution is then +*> X = P * Z**H [ inv(T11)*Q1**H*B ] +*> [ 0 ] +*> where Q1 consists of the first RANK columns of Q. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of right hand sides, i.e., the number of +*> columns of matrices B and X. NRHS >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> On entry, the M-by-N matrix A. +*> On exit, A has been overwritten by details of its +*> complete orthogonal factorization. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is COMPLEX array, dimension (LDB,NRHS) +*> On entry, the M-by-NRHS right hand side matrix B. +*> On exit, the N-by-NRHS solution matrix X. +*> If m >= n and RANK = n, the residual sum-of-squares for +*> the solution in the i-th column is given by the sum of +*> squares of elements N+1:M in that column. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,M,N). +*> \endverbatim +*> +*> \param[in,out] JPVT +*> \verbatim +*> JPVT is INTEGER array, dimension (N) +*> On entry, if JPVT(i) .ne. 0, the i-th column of A is an +*> initial column, otherwise it is a free column. Before +*> the QR factorization of A, all initial columns are +*> permuted to the leading positions; only the remaining +*> free columns are moved as a result of column pivoting +*> during the factorization. +*> On exit, if JPVT(i) = k, then the i-th column of A*P +*> was the k-th column of A. +*> \endverbatim +*> +*> \param[in] RCOND +*> \verbatim +*> RCOND is REAL +*> RCOND is used to determine the effective rank of A, which +*> is defined as the order of the largest leading triangular +*> submatrix R11 in the QR factorization with pivoting of A, +*> whose estimated condition number < 1/RCOND. +*> \endverbatim +*> +*> \param[out] RANK +*> \verbatim +*> RANK is INTEGER +*> The effective rank of A, i.e., the order of the submatrix +*> R11. This is the same as the order of the submatrix T11 +*> in the complete orthogonal factorization of A. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX array, dimension +*> (min(M,N) + max( N, 2*min(M,N)+NRHS )), +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is REAL 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 November 2011 +* +*> \ingroup complexGEsolve +* +* ===================================================================== + SUBROUTINE CGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, + $ WORK, RWORK, INFO ) +* +* -- LAPACK driver routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, LDB, M, N, NRHS, RANK + REAL RCOND +* .. +* .. Array Arguments .. + INTEGER JPVT( * ) + REAL RWORK( * ) + COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + INTEGER IMAX, IMIN + PARAMETER ( IMAX = 1, IMIN = 2 ) + REAL ZERO, ONE, DONE, NTDONE + PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, DONE = ZERO, + $ NTDONE = ONE ) + COMPLEX CZERO, CONE + PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), + $ CONE = ( 1.0E+0, 0.0E+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I, IASCL, IBSCL, ISMAX, ISMIN, J, K, MN + REAL ANRM, BIGNUM, BNRM, SMAX, SMAXPR, SMIN, SMINPR, + $ SMLNUM + COMPLEX C1, C2, S1, S2, T1, T2 +* .. +* .. External Subroutines .. + EXTERNAL CGEQPF, CLAIC1, CLASCL, CLASET, CLATZM, CTRSM, + $ CTZRQF, CUNM2R, SLABAD, XERBLA +* .. +* .. External Functions .. + REAL CLANGE, SLAMCH + EXTERNAL CLANGE, SLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, CONJG, MAX, MIN +* .. +* .. Executable Statements .. +* + MN = MIN( M, N ) + ISMIN = MN + 1 + ISMAX = 2*MN + 1 +* +* Test the input arguments. +* + INFO = 0 + IF( M.LT.0 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, M, N ) ) THEN + INFO = -7 + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'CGELSX', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( MIN( M, N, NRHS ).EQ.0 ) THEN + RANK = 0 + RETURN + END IF +* +* Get machine parameters +* + SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' ) + BIGNUM = ONE / SMLNUM + CALL SLABAD( SMLNUM, BIGNUM ) +* +* Scale A, B if max elements outside range [SMLNUM,BIGNUM] +* + ANRM = CLANGE( 'M', M, N, A, LDA, RWORK ) + IASCL = 0 + IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN +* +* Scale matrix norm up to SMLNUM +* + CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO ) + IASCL = 1 + ELSE IF( ANRM.GT.BIGNUM ) THEN +* +* Scale matrix norm down to BIGNUM +* + CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO ) + IASCL = 2 + ELSE IF( ANRM.EQ.ZERO ) THEN +* +* Matrix all zero. Return zero solution. +* + CALL CLASET( 'F', MAX( M, N ), NRHS, CZERO, CZERO, B, LDB ) + RANK = 0 + GO TO 100 + END IF +* + BNRM = CLANGE( 'M', M, NRHS, B, LDB, RWORK ) + IBSCL = 0 + IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN +* +* Scale matrix norm up to SMLNUM +* + CALL CLASCL( 'G', 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO ) + IBSCL = 1 + ELSE IF( BNRM.GT.BIGNUM ) THEN +* +* Scale matrix norm down to BIGNUM +* + CALL CLASCL( 'G', 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO ) + IBSCL = 2 + END IF +* +* Compute QR factorization with column pivoting of A: +* A * P = Q * R +* + CALL CGEQPF( M, N, A, LDA, JPVT, WORK( 1 ), WORK( MN+1 ), RWORK, + $ INFO ) +* +* complex workspace MN+N. Real workspace 2*N. Details of Householder +* rotations stored in WORK(1:MN). +* +* Determine RANK using incremental condition estimation +* + WORK( ISMIN ) = CONE + WORK( ISMAX ) = CONE + SMAX = ABS( A( 1, 1 ) ) + SMIN = SMAX + IF( ABS( A( 1, 1 ) ).EQ.ZERO ) THEN + RANK = 0 + CALL CLASET( 'F', MAX( M, N ), NRHS, CZERO, CZERO, B, LDB ) + GO TO 100 + ELSE + RANK = 1 + END IF +* + 10 CONTINUE + IF( RANK.LT.MN ) THEN + I = RANK + 1 + CALL CLAIC1( IMIN, RANK, WORK( ISMIN ), SMIN, A( 1, I ), + $ A( I, I ), SMINPR, S1, C1 ) + CALL CLAIC1( IMAX, RANK, WORK( ISMAX ), SMAX, A( 1, I ), + $ A( I, I ), SMAXPR, S2, C2 ) +* + IF( SMAXPR*RCOND.LE.SMINPR ) THEN + DO 20 I = 1, RANK + WORK( ISMIN+I-1 ) = S1*WORK( ISMIN+I-1 ) + WORK( ISMAX+I-1 ) = S2*WORK( ISMAX+I-1 ) + 20 CONTINUE + WORK( ISMIN+RANK ) = C1 + WORK( ISMAX+RANK ) = C2 + SMIN = SMINPR + SMAX = SMAXPR + RANK = RANK + 1 + GO TO 10 + END IF + END IF +* +* Logically partition R = [ R11 R12 ] +* [ 0 R22 ] +* where R11 = R(1:RANK,1:RANK) +* +* [R11,R12] = [ T11, 0 ] * Y +* + IF( RANK.LT.N ) + $ CALL CTZRQF( RANK, N, A, LDA, WORK( MN+1 ), INFO ) +* +* Details of Householder rotations stored in WORK(MN+1:2*MN) +* +* B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS) +* + CALL CUNM2R( 'Left', 'Conjugate transpose', M, NRHS, MN, A, LDA, + $ WORK( 1 ), B, LDB, WORK( 2*MN+1 ), INFO ) +* +* workspace NRHS +* +* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) +* + CALL CTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', RANK, + $ NRHS, CONE, A, LDA, B, LDB ) +* + DO 40 I = RANK + 1, N + DO 30 J = 1, NRHS + B( I, J ) = CZERO + 30 CONTINUE + 40 CONTINUE +* +* B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS) +* + IF( RANK.LT.N ) THEN + DO 50 I = 1, RANK + CALL CLATZM( 'Left', N-RANK+1, NRHS, A( I, RANK+1 ), LDA, + $ CONJG( WORK( MN+I ) ), B( I, 1 ), + $ B( RANK+1, 1 ), LDB, WORK( 2*MN+1 ) ) + 50 CONTINUE + END IF +* +* workspace NRHS +* +* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) +* + DO 90 J = 1, NRHS + DO 60 I = 1, N + WORK( 2*MN+I ) = NTDONE + 60 CONTINUE + DO 80 I = 1, N + IF( WORK( 2*MN+I ).EQ.NTDONE ) THEN + IF( JPVT( I ).NE.I ) THEN + K = I + T1 = B( K, J ) + T2 = B( JPVT( K ), J ) + 70 CONTINUE + B( JPVT( K ), J ) = T1 + WORK( 2*MN+K ) = DONE + T1 = T2 + K = JPVT( K ) + T2 = B( JPVT( K ), J ) + IF( JPVT( K ).NE.I ) + $ GO TO 70 + B( I, J ) = T1 + WORK( 2*MN+K ) = DONE + END IF + END IF + 80 CONTINUE + 90 CONTINUE +* +* Undo scaling +* + IF( IASCL.EQ.1 ) THEN + CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO ) + CALL CLASCL( 'U', 0, 0, SMLNUM, ANRM, RANK, RANK, A, LDA, + $ INFO ) + ELSE IF( IASCL.EQ.2 ) THEN + CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO ) + CALL CLASCL( 'U', 0, 0, BIGNUM, ANRM, RANK, RANK, A, LDA, + $ INFO ) + END IF + IF( IBSCL.EQ.1 ) THEN + CALL CLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO ) + ELSE IF( IBSCL.EQ.2 ) THEN + CALL CLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO ) + END IF +* + 100 CONTINUE +* + RETURN +* +* End of CGELSX +* + END |