SUBROUTINE CGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, \$ WORK, LWORK, RWORK, INFO ) * * -- LAPACK driver routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK REAL RCOND * .. * .. Array Arguments .. REAL RWORK( * ), S( * ) COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * Purpose * ======= * * CGELSS computes the minimum norm solution to a complex linear * least squares problem: * * Minimize 2-norm(| b - A*x |). * * using the singular value decomposition (SVD) 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 effective rank of A is determined by treating as zero those * singular values which are less than RCOND times the largest singular * value. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix A. M >= 0. * * N (input) INTEGER * The number of columns of the matrix A. N >= 0. * * NRHS (input) INTEGER * The number of right hand sides, i.e., the number of columns * of the matrices B and X. NRHS >= 0. * * A (input/output) COMPLEX array, dimension (LDA,N) * On entry, the M-by-N matrix A. * On exit, the first min(m,n) rows of A are overwritten with * its right singular vectors, stored rowwise. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M). * * B (input/output) COMPLEX array, dimension (LDB,NRHS) * On entry, the M-by-NRHS right hand side matrix B. * On exit, B is overwritten by 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 the modulus of elements n+1:m in that column. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,M,N). * * S (output) REAL array, dimension (min(M,N)) * The singular values of A in decreasing order. * The condition number of A in the 2-norm = S(1)/S(min(m,n)). * * RCOND (input) REAL * RCOND is used to determine the effective rank of A. * Singular values S(i) <= RCOND*S(1) are treated as zero. * If RCOND < 0, machine precision is used instead. * * RANK (output) INTEGER * The effective rank of A, i.e., the number of singular values * which are greater than RCOND*S(1). * * WORK (workspace/output) COMPLEX 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. LWORK >= 1, and also: * LWORK >= 2*min(M,N) + max(M,N,NRHS) * For good performance, LWORK should generally be larger. * * 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. * * RWORK (workspace) REAL array, dimension (5*min(M,N)) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value. * > 0: the algorithm for computing the SVD failed to converge; * if INFO = i, i off-diagonal elements of an intermediate * bidiagonal form did not converge to zero. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), \$ CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER BL, CHUNK, I, IASCL, IBSCL, IE, IL, IRWORK, \$ ITAU, ITAUP, ITAUQ, IWORK, LDWORK, MAXMN, \$ MAXWRK, MINMN, MINWRK, MM, MNTHR REAL ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM, THR * .. * .. Local Arrays .. COMPLEX VDUM( 1 ) * .. * .. External Subroutines .. EXTERNAL CBDSQR, CCOPY, CGEBRD, CGELQF, CGEMM, CGEMV, \$ CGEQRF, CLACPY, CLASCL, CLASET, CSRSCL, CUNGBR, \$ CUNMBR, CUNMLQ, CUNMQR, SLABAD, SLASCL, SLASET, \$ XERBLA * .. * .. External Functions .. INTEGER ILAENV REAL CLANGE, SLAMCH EXTERNAL ILAENV, CLANGE, SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 MINMN = MIN( M, N ) MAXMN = MAX( M, N ) LQUERY = ( LWORK.EQ.-1 ) 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, MAXMN ) ) THEN INFO = -7 END IF * * Compute workspace * (Note: Comments in the code beginning "Workspace:" describe the * minimal amount of workspace needed at that point in the code, * as well as the preferred amount for good performance. * CWorkspace refers to complex workspace, and RWorkspace refers * to real workspace. NB refers to the optimal block size for the * immediately following subroutine, as returned by ILAENV.) * IF( INFO.EQ.0 ) THEN MINWRK = 1 MAXWRK = 1 IF( MINMN.GT.0 ) THEN MM = M MNTHR = ILAENV( 6, 'CGELSS', ' ', M, N, NRHS, -1 ) IF( M.GE.N .AND. M.GE.MNTHR ) THEN * * Path 1a - overdetermined, with many more rows than * columns * MM = N MAXWRK = MAX( MAXWRK, N + N*ILAENV( 1, 'CGEQRF', ' ', M, \$ N, -1, -1 ) ) MAXWRK = MAX( MAXWRK, N + NRHS*ILAENV( 1, 'CUNMQR', 'LC', \$ M, NRHS, N, -1 ) ) END IF IF( M.GE.N ) THEN * * Path 1 - overdetermined or exactly determined * MAXWRK = MAX( MAXWRK, 2*N + ( MM + N )*ILAENV( 1, \$ 'CGEBRD', ' ', MM, N, -1, -1 ) ) MAXWRK = MAX( MAXWRK, 2*N + NRHS*ILAENV( 1, 'CUNMBR', \$ 'QLC', MM, NRHS, N, -1 ) ) MAXWRK = MAX( MAXWRK, 2*N + ( N - 1 )*ILAENV( 1, \$ 'CUNGBR', 'P', N, N, N, -1 ) ) MAXWRK = MAX( MAXWRK, N*NRHS ) MINWRK = 2*N + MAX( NRHS, M ) END IF IF( N.GT.M ) THEN MINWRK = 2*M + MAX( NRHS, N ) IF( N.GE.MNTHR ) THEN * * Path 2a - underdetermined, with many more columns * than rows * MAXWRK = M + M*ILAENV( 1, 'CGELQF', ' ', M, N, -1, \$ -1 ) MAXWRK = MAX( MAXWRK, 3*M + M*M + 2*M*ILAENV( 1, \$ 'CGEBRD', ' ', M, M, -1, -1 ) ) MAXWRK = MAX( MAXWRK, 3*M + M*M + NRHS*ILAENV( 1, \$ 'CUNMBR', 'QLC', M, NRHS, M, -1 ) ) MAXWRK = MAX( MAXWRK, 3*M + M*M + ( M - 1 )*ILAENV( 1, \$ 'CUNGBR', 'P', M, M, M, -1 ) ) IF( NRHS.GT.1 ) THEN MAXWRK = MAX( MAXWRK, M*M + M + M*NRHS ) ELSE MAXWRK = MAX( MAXWRK, M*M + 2*M ) END IF MAXWRK = MAX( MAXWRK, M + NRHS*ILAENV( 1, 'CUNMLQ', \$ 'LC', N, NRHS, M, -1 ) ) ELSE * * Path 2 - underdetermined * MAXWRK = 2*M + ( N + M )*ILAENV( 1, 'CGEBRD', ' ', M, \$ N, -1, -1 ) MAXWRK = MAX( MAXWRK, 2*M + NRHS*ILAENV( 1, 'CUNMBR', \$ 'QLC', M, NRHS, M, -1 ) ) MAXWRK = MAX( MAXWRK, 2*M + M*ILAENV( 1, 'CUNGBR', \$ 'P', M, N, M, -1 ) ) MAXWRK = MAX( MAXWRK, N*NRHS ) END IF END IF MAXWRK = MAX( MINWRK, MAXWRK ) END IF WORK( 1 ) = MAXWRK * IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) \$ INFO = -12 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CGELSS', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) THEN RANK = 0 RETURN END IF * * Get machine parameters * EPS = SLAMCH( 'P' ) SFMIN = SLAMCH( 'S' ) SMLNUM = SFMIN / EPS BIGNUM = ONE / SMLNUM CALL SLABAD( SMLNUM, BIGNUM ) * * Scale A if max element 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 ) CALL SLASET( 'F', MINMN, 1, ZERO, ZERO, S, MINMN ) RANK = 0 GO TO 70 END IF * * Scale B if max element outside range [SMLNUM,BIGNUM] * 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 * * Overdetermined case * IF( M.GE.N ) THEN * * Path 1 - overdetermined or exactly determined * MM = M IF( M.GE.MNTHR ) THEN * * Path 1a - overdetermined, with many more rows than columns * MM = N ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: none) * CALL CGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), \$ LWORK-IWORK+1, INFO ) * * Multiply B by transpose(Q) * (CWorkspace: need N+NRHS, prefer N+NRHS*NB) * (RWorkspace: none) * CALL CUNMQR( 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAU ), B, \$ LDB, WORK( IWORK ), LWORK-IWORK+1, INFO ) * * Zero out below R * IF( N.GT.1 ) \$ CALL CLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ), \$ LDA ) END IF * IE = 1 ITAUQ = 1 ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in A * (CWorkspace: need 2*N+MM, prefer 2*N+(MM+N)*NB) * (RWorkspace: need N) * CALL CGEBRD( MM, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), \$ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, \$ INFO ) * * Multiply B by transpose of left bidiagonalizing vectors of R * (CWorkspace: need 2*N+NRHS, prefer 2*N+NRHS*NB) * (RWorkspace: none) * CALL CUNMBR( 'Q', 'L', 'C', MM, NRHS, N, A, LDA, WORK( ITAUQ ), \$ B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO ) * * Generate right bidiagonalizing vectors of R in A * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: none) * CALL CUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), \$ WORK( IWORK ), LWORK-IWORK+1, INFO ) IRWORK = IE + N * * Perform bidiagonal QR iteration * multiply B by transpose of left singular vectors * compute right singular vectors in A * (CWorkspace: none) * (RWorkspace: need BDSPAC) * CALL CBDSQR( 'U', N, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM, \$ 1, B, LDB, RWORK( IRWORK ), INFO ) IF( INFO.NE.0 ) \$ GO TO 70 * * Multiply B by reciprocals of singular values * THR = MAX( RCOND*S( 1 ), SFMIN ) IF( RCOND.LT.ZERO ) \$ THR = MAX( EPS*S( 1 ), SFMIN ) RANK = 0 DO 10 I = 1, N IF( S( I ).GT.THR ) THEN CALL CSRSCL( NRHS, S( I ), B( I, 1 ), LDB ) RANK = RANK + 1 ELSE CALL CLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB ) END IF 10 CONTINUE * * Multiply B by right singular vectors * (CWorkspace: need N, prefer N*NRHS) * (RWorkspace: none) * IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN CALL CGEMM( 'C', 'N', N, NRHS, N, CONE, A, LDA, B, LDB, \$ CZERO, WORK, LDB ) CALL CLACPY( 'G', N, NRHS, WORK, LDB, B, LDB ) ELSE IF( NRHS.GT.1 ) THEN CHUNK = LWORK / N DO 20 I = 1, NRHS, CHUNK BL = MIN( NRHS-I+1, CHUNK ) CALL CGEMM( 'C', 'N', N, BL, N, CONE, A, LDA, B( 1, I ), \$ LDB, CZERO, WORK, N ) CALL CLACPY( 'G', N, BL, WORK, N, B( 1, I ), LDB ) 20 CONTINUE ELSE CALL CGEMV( 'C', N, N, CONE, A, LDA, B, 1, CZERO, WORK, 1 ) CALL CCOPY( N, WORK, 1, B, 1 ) END IF * ELSE IF( N.GE.MNTHR .AND. LWORK.GE.3*M+M*M+MAX( M, NRHS, N-2*M ) ) \$ THEN * * Underdetermined case, M much less than N * * Path 2a - underdetermined, with many more columns than rows * and sufficient workspace for an efficient algorithm * LDWORK = M IF( LWORK.GE.3*M+M*LDA+MAX( M, NRHS, N-2*M ) ) \$ LDWORK = LDA ITAU = 1 IWORK = M + 1 * * Compute A=L*Q * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: none) * CALL CGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), \$ LWORK-IWORK+1, INFO ) IL = IWORK * * Copy L to WORK(IL), zeroing out above it * CALL CLACPY( 'L', M, M, A, LDA, WORK( IL ), LDWORK ) CALL CLASET( 'U', M-1, M-1, CZERO, CZERO, WORK( IL+LDWORK ), \$ LDWORK ) IE = 1 ITAUQ = IL + LDWORK*M ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in WORK(IL) * (CWorkspace: need M*M+4*M, prefer M*M+3*M+2*M*NB) * (RWorkspace: need M) * CALL CGEBRD( M, M, WORK( IL ), LDWORK, S, RWORK( IE ), \$ WORK( ITAUQ ), WORK( ITAUP ), WORK( IWORK ), \$ LWORK-IWORK+1, INFO ) * * Multiply B by transpose of left bidiagonalizing vectors of L * (CWorkspace: need M*M+3*M+NRHS, prefer M*M+3*M+NRHS*NB) * (RWorkspace: none) * CALL CUNMBR( 'Q', 'L', 'C', M, NRHS, M, WORK( IL ), LDWORK, \$ WORK( ITAUQ ), B, LDB, WORK( IWORK ), \$ LWORK-IWORK+1, INFO ) * * Generate right bidiagonalizing vectors of R in WORK(IL) * (CWorkspace: need M*M+4*M-1, prefer M*M+3*M+(M-1)*NB) * (RWorkspace: none) * CALL CUNGBR( 'P', M, M, M, WORK( IL ), LDWORK, WORK( ITAUP ), \$ WORK( IWORK ), LWORK-IWORK+1, INFO ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing right singular * vectors of L in WORK(IL) and multiplying B by transpose of * left singular vectors * (CWorkspace: need M*M) * (RWorkspace: need BDSPAC) * CALL CBDSQR( 'U', M, M, 0, NRHS, S, RWORK( IE ), WORK( IL ), \$ LDWORK, A, LDA, B, LDB, RWORK( IRWORK ), INFO ) IF( INFO.NE.0 ) \$ GO TO 70 * * Multiply B by reciprocals of singular values * THR = MAX( RCOND*S( 1 ), SFMIN ) IF( RCOND.LT.ZERO ) \$ THR = MAX( EPS*S( 1 ), SFMIN ) RANK = 0 DO 30 I = 1, M IF( S( I ).GT.THR ) THEN CALL CSRSCL( NRHS, S( I ), B( I, 1 ), LDB ) RANK = RANK + 1 ELSE CALL CLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB ) END IF 30 CONTINUE IWORK = IL + M*LDWORK * * Multiply B by right singular vectors of L in WORK(IL) * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NRHS) * (RWorkspace: none) * IF( LWORK.GE.LDB*NRHS+IWORK-1 .AND. NRHS.GT.1 ) THEN CALL CGEMM( 'C', 'N', M, NRHS, M, CONE, WORK( IL ), LDWORK, \$ B, LDB, CZERO, WORK( IWORK ), LDB ) CALL CLACPY( 'G', M, NRHS, WORK( IWORK ), LDB, B, LDB ) ELSE IF( NRHS.GT.1 ) THEN CHUNK = ( LWORK-IWORK+1 ) / M DO 40 I = 1, NRHS, CHUNK BL = MIN( NRHS-I+1, CHUNK ) CALL CGEMM( 'C', 'N', M, BL, M, CONE, WORK( IL ), LDWORK, \$ B( 1, I ), LDB, CZERO, WORK( IWORK ), M ) CALL CLACPY( 'G', M, BL, WORK( IWORK ), M, B( 1, I ), \$ LDB ) 40 CONTINUE ELSE CALL CGEMV( 'C', M, M, CONE, WORK( IL ), LDWORK, B( 1, 1 ), \$ 1, CZERO, WORK( IWORK ), 1 ) CALL CCOPY( M, WORK( IWORK ), 1, B( 1, 1 ), 1 ) END IF * * Zero out below first M rows of B * CALL CLASET( 'F', N-M, NRHS, CZERO, CZERO, B( M+1, 1 ), LDB ) IWORK = ITAU + M * * Multiply transpose(Q) by B * (CWorkspace: need M+NRHS, prefer M+NHRS*NB) * (RWorkspace: none) * CALL CUNMLQ( 'L', 'C', N, NRHS, M, A, LDA, WORK( ITAU ), B, \$ LDB, WORK( IWORK ), LWORK-IWORK+1, INFO ) * ELSE * * Path 2 - remaining underdetermined cases * IE = 1 ITAUQ = 1 ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize A * (CWorkspace: need 3*M, prefer 2*M+(M+N)*NB) * (RWorkspace: need N) * CALL CGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), \$ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, \$ INFO ) * * Multiply B by transpose of left bidiagonalizing vectors * (CWorkspace: need 2*M+NRHS, prefer 2*M+NRHS*NB) * (RWorkspace: none) * CALL CUNMBR( 'Q', 'L', 'C', M, NRHS, N, A, LDA, WORK( ITAUQ ), \$ B, LDB, WORK( IWORK ), LWORK-IWORK+1, INFO ) * * Generate right bidiagonalizing vectors in A * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: none) * CALL CUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ), \$ WORK( IWORK ), LWORK-IWORK+1, INFO ) IRWORK = IE + M * * Perform bidiagonal QR iteration, * computing right singular vectors of A in A and * multiplying B by transpose of left singular vectors * (CWorkspace: none) * (RWorkspace: need BDSPAC) * CALL CBDSQR( 'L', M, N, 0, NRHS, S, RWORK( IE ), A, LDA, VDUM, \$ 1, B, LDB, RWORK( IRWORK ), INFO ) IF( INFO.NE.0 ) \$ GO TO 70 * * Multiply B by reciprocals of singular values * THR = MAX( RCOND*S( 1 ), SFMIN ) IF( RCOND.LT.ZERO ) \$ THR = MAX( EPS*S( 1 ), SFMIN ) RANK = 0 DO 50 I = 1, M IF( S( I ).GT.THR ) THEN CALL CSRSCL( NRHS, S( I ), B( I, 1 ), LDB ) RANK = RANK + 1 ELSE CALL CLASET( 'F', 1, NRHS, CZERO, CZERO, B( I, 1 ), LDB ) END IF 50 CONTINUE * * Multiply B by right singular vectors of A * (CWorkspace: need N, prefer N*NRHS) * (RWorkspace: none) * IF( LWORK.GE.LDB*NRHS .AND. NRHS.GT.1 ) THEN CALL CGEMM( 'C', 'N', N, NRHS, M, CONE, A, LDA, B, LDB, \$ CZERO, WORK, LDB ) CALL CLACPY( 'G', N, NRHS, WORK, LDB, B, LDB ) ELSE IF( NRHS.GT.1 ) THEN CHUNK = LWORK / N DO 60 I = 1, NRHS, CHUNK BL = MIN( NRHS-I+1, CHUNK ) CALL CGEMM( 'C', 'N', N, BL, M, CONE, A, LDA, B( 1, I ), \$ LDB, CZERO, WORK, N ) CALL CLACPY( 'F', N, BL, WORK, N, B( 1, I ), LDB ) 60 CONTINUE ELSE CALL CGEMV( 'C', M, N, CONE, A, LDA, B, 1, CZERO, WORK, 1 ) CALL CCOPY( N, WORK, 1, B, 1 ) END IF END IF * * Undo scaling * IF( IASCL.EQ.1 ) THEN CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO ) CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN, \$ INFO ) ELSE IF( IASCL.EQ.2 ) THEN CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO ) CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN, \$ 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 70 CONTINUE WORK( 1 ) = MAXWRK RETURN * * End of CGELSS * END