SUBROUTINE SGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, \$ INFO ) * * -- LAPACK 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 * .. * .. Array Arguments .. REAL A( LDA, * ), B( LDB, * ), TAU( * ), \$ WORK( LWORK ) * .. * * Purpose * ======= * * Compute a minimum-norm solution * min || A*X - B || * using the RQ factorization * A = R*Q * computed by SGERQF. * * 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 >= M >= 0. * * NRHS (input) INTEGER * The number of columns of B. NRHS >= 0. * * A (input) REAL array, dimension (LDA,N) * Details of the RQ factorization of the original matrix A as * returned by SGERQF. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= M. * * TAU (input) REAL array, dimension (M) * Details of the orthogonal matrix Q. * * B (input/output) REAL array, dimension (LDB,NRHS) * On entry, the right hand side vectors for the linear system. * On exit, the solution vectors X. Each solution vector * is contained in rows 1:N of a column of B. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * WORK (workspace) REAL array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK must be at least NRHS, * and should be at least NRHS*NB, where NB is the block size * for this environment. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. External Subroutines .. EXTERNAL SLASET, SORMRQ, STRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. M.GT.N ) 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, N ) ) THEN INFO = -8 ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 ) \$ THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'SGERQS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 ) \$ RETURN * * Solve R*X = B(n-m+1:n,:) * CALL STRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS, \$ ONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB ) * * Set B(1:n-m,:) to zero * CALL SLASET( 'Full', N-M, NRHS, ZERO, ZERO, B, LDB ) * * B := Q' * B * CALL SORMRQ( 'Left', 'Transpose', N, NRHS, M, A, LDA, TAU, B, LDB, \$ WORK, LWORK, INFO ) * RETURN * * End of SGERQS * END