numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/zlavsy_rook.f | 17420B | -rw-r--r-- |
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*> \brief \b ZLAVSY_ROOK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZLAVSY_ROOK( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, * LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, TRANS, UPLO * INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAVSY_ROOK performs one of the matrix-vector operations *> x := A*x or x := A'*x, *> where x is an N element vector and A is one of the factors *> from the block U*D*U' or L*D*L' factorization computed by ZSYTRF_ROOK. *> *> If TRANS = 'N', multiplies by U or U * D (or L or L * D) *> If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L') *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the factor stored in A is upper or lower *> triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation to be performed: *> = 'N': x := A*x *> = 'T': x := A'*x *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> Specifies whether or not the diagonal blocks are unit *> matrices. If the diagonal blocks are assumed to be unit, *> then A = U or A = L, otherwise A = U*D or A = L*D. *> = 'U': Diagonal blocks are assumed to be unit matrices. *> = 'N': Diagonal blocks are assumed to be non-unit matrices. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and 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 vectors *> x to be multiplied by A. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The block diagonal matrix D and the multipliers used to *> obtain the factor U or L as computed by ZSYTRF_ROOK. *> Stored as a 2-D triangular matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> Details of the interchanges and the block structure of D, *> as determined by ZSYTRF_ROOK. *> *> If UPLO = 'U': *> If IPIV(k) > 0, then rows and columns k and IPIV(k) *> were interchanged and D(k,k) is a 1-by-1 diagonal block. *> (If IPIV( k ) = k, no interchange was done). *> *> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and *> columns k and -IPIV(k) were interchanged and rows and *> columns k-1 and -IPIV(k-1) were inerchaged, *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. *> *> If UPLO = 'L': *> If IPIV(k) > 0, then rows and columns k and IPIV(k) *> were interchanged and D(k,k) is a 1-by-1 diagonal block. *> (If IPIV( k ) = k, no interchange was done). *> *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and *> columns k and -IPIV(k) were interchanged and rows and *> columns k+1 and -IPIV(k+1) were inerchaged, *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,NRHS) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-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. * *> \ingroup complex16_lin * * ===================================================================== SUBROUTINE ZLAVSY_ROOK( UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, $ B, LDB, INFO ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER DIAG, TRANS, UPLO INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL NOUNIT INTEGER J, K, KP COMPLEX*16 D11, D12, D21, D22, T1, T2 * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) $ THEN INFO = -2 ELSE IF( .NOT.LSAME( DIAG, 'U' ) .AND. .NOT.LSAME( DIAG, 'N' ) ) $ THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLAVSY_ROOK ', -INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) *------------------------------------------ * * Compute B := A * B (No transpose) * *------------------------------------------ IF( LSAME( TRANS, 'N' ) ) THEN * * Compute B := U*B * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) * IF( LSAME( UPLO, 'U' ) ) THEN * * Loop forward applying the transformations. * K = 1 10 CONTINUE IF( K.GT.N ) $ GO TO 30 IF( IPIV( K ).GT.0 ) THEN * * 1 x 1 pivot block * * Multiply by the diagonal element if forming U * D. * IF( NOUNIT ) $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) * * Multiply by P(K) * inv(U(K)) if K > 1. * IF( K.GT.1 ) THEN * * Apply the transformation. * CALL ZGERU( K-1, NRHS, CONE, A( 1, K ), 1, B( K, 1 ), $ LDB, B( 1, 1 ), LDB ) * * Interchange if P(K) != I. * KP = IPIV( K ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) END IF K = K + 1 ELSE * * 2 x 2 pivot block * * Multiply by the diagonal block if forming U * D. * IF( NOUNIT ) THEN D11 = A( K, K ) D22 = A( K+1, K+1 ) D12 = A( K, K+1 ) D21 = D12 DO 20 J = 1, NRHS T1 = B( K, J ) T2 = B( K+1, J ) B( K, J ) = D11*T1 + D12*T2 B( K+1, J ) = D21*T1 + D22*T2 20 CONTINUE END IF * * Multiply by P(K) * inv(U(K)) if K > 1. * IF( K.GT.1 ) THEN * * Apply the transformations. * CALL ZGERU( K-1, NRHS, CONE, A( 1, K ), 1, B( K, 1 ), $ LDB, B( 1, 1 ), LDB ) CALL ZGERU( K-1, NRHS, CONE, A( 1, K+1 ), 1, $ B( K+1, 1 ), LDB, B( 1, 1 ), LDB ) * * Interchange if a permutation was applied at the * K-th step of the factorization. * * Swap the first of pair with IMAXth * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * * NOW swap the first of pair with Pth * KP = ABS( IPIV( K+1 ) ) IF( KP.NE.K+1 ) $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), $ LDB ) END IF K = K + 2 END IF GO TO 10 30 CONTINUE * * Compute B := L*B * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) . * ELSE * * Loop backward applying the transformations to B. * K = N 40 CONTINUE IF( K.LT.1 ) $ GO TO 60 * * Test the pivot index. If greater than zero, a 1 x 1 * pivot was used, otherwise a 2 x 2 pivot was used. * IF( IPIV( K ).GT.0 ) THEN * * 1 x 1 pivot block: * * Multiply by the diagonal element if forming L * D. * IF( NOUNIT ) $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) * * Multiply by P(K) * inv(L(K)) if K < N. * IF( K.NE.N ) THEN KP = IPIV( K ) * * Apply the transformation. * CALL ZGERU( N-K, NRHS, CONE, A( K+1, K ), 1, $ B( K, 1 ), LDB, B( K+1, 1 ), LDB ) * * Interchange if a permutation was applied at the * K-th step of the factorization. * IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) END IF K = K - 1 * ELSE * * 2 x 2 pivot block: * * Multiply by the diagonal block if forming L * D. * IF( NOUNIT ) THEN D11 = A( K-1, K-1 ) D22 = A( K, K ) D21 = A( K, K-1 ) D12 = D21 DO 50 J = 1, NRHS T1 = B( K-1, J ) T2 = B( K, J ) B( K-1, J ) = D11*T1 + D12*T2 B( K, J ) = D21*T1 + D22*T2 50 CONTINUE END IF * * Multiply by P(K) * inv(L(K)) if K < N. * IF( K.NE.N ) THEN * * Apply the transformation. * CALL ZGERU( N-K, NRHS, CONE, A( K+1, K ), 1, $ B( K, 1 ), LDB, B( K+1, 1 ), LDB ) CALL ZGERU( N-K, NRHS, CONE, A( K+1, K-1 ), 1, $ B( K-1, 1 ), LDB, B( K+1, 1 ), LDB ) * * Interchange if a permutation was applied at the * K-th step of the factorization. * * Swap the second of pair with IMAXth * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * * NOW swap the first of pair with Pth * KP = ABS( IPIV( K-1 ) ) IF( KP.NE.K-1 ) $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), $ LDB ) END IF K = K - 2 END IF GO TO 40 60 CONTINUE END IF *---------------------------------------- * * Compute B := A' * B (transpose) * *---------------------------------------- ELSE IF( LSAME( TRANS, 'T' ) ) THEN * * Form B := U'*B * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) * and U' = inv(U'(1))*P(1)* ... *inv(U'(m))*P(m) * IF( LSAME( UPLO, 'U' ) ) THEN * * Loop backward applying the transformations. * K = N 70 CONTINUE IF( K.LT.1 ) $ GO TO 90 * * 1 x 1 pivot block. * IF( IPIV( K ).GT.0 ) THEN IF( K.GT.1 ) THEN * * Interchange if P(K) != I. * KP = IPIV( K ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * * Apply the transformation * CALL ZGEMV( 'Transpose', K-1, NRHS, CONE, B, LDB, $ A( 1, K ), 1, CONE, B( K, 1 ), LDB ) END IF IF( NOUNIT ) $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) K = K - 1 * * 2 x 2 pivot block. * ELSE IF( K.GT.2 ) THEN * * Swap the second of pair with Pth * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * * Now swap the first of pair with IMAX(r)th * KP = ABS( IPIV( K-1 ) ) IF( KP.NE.K-1 ) $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), $ LDB ) * * Apply the transformations * CALL ZGEMV( 'Transpose', K-2, NRHS, CONE, B, LDB, $ A( 1, K ), 1, CONE, B( K, 1 ), LDB ) CALL ZGEMV( 'Transpose', K-2, NRHS, CONE, B, LDB, $ A( 1, K-1 ), 1, CONE, B( K-1, 1 ), LDB ) END IF * * Multiply by the diagonal block if non-unit. * IF( NOUNIT ) THEN D11 = A( K-1, K-1 ) D22 = A( K, K ) D12 = A( K-1, K ) D21 = D12 DO 80 J = 1, NRHS T1 = B( K-1, J ) T2 = B( K, J ) B( K-1, J ) = D11*T1 + D12*T2 B( K, J ) = D21*T1 + D22*T2 80 CONTINUE END IF K = K - 2 END IF GO TO 70 90 CONTINUE * * Form B := L'*B * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) * and L' = inv(L'(m))*P(m)* ... *inv(L'(1))*P(1) * ELSE * * Loop forward applying the L-transformations. * K = 1 100 CONTINUE IF( K.GT.N ) $ GO TO 120 * * 1 x 1 pivot block * IF( IPIV( K ).GT.0 ) THEN IF( K.LT.N ) THEN * * Interchange if P(K) != I. * KP = IPIV( K ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * * Apply the transformation * CALL ZGEMV( 'Transpose', N-K, NRHS, CONE, B( K+1, 1 ), $ LDB, A( K+1, K ), 1, CONE, B( K, 1 ), LDB ) END IF IF( NOUNIT ) $ CALL ZSCAL( NRHS, A( K, K ), B( K, 1 ), LDB ) K = K + 1 * * 2 x 2 pivot block. * ELSE IF( K.LT.N-1 ) THEN * * Swap the first of pair with Pth * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) * * Now swap the second of pair with IMAX(r)th * KP = ABS( IPIV( K+1 ) ) IF( KP.NE.K+1 ) $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), $ LDB ) * * Apply the transformation * CALL ZGEMV( 'Transpose', N-K-1, NRHS, CONE, $ B( K+2, 1 ), LDB, A( K+2, K+1 ), 1, CONE, $ B( K+1, 1 ), LDB ) CALL ZGEMV( 'Transpose', N-K-1, NRHS, CONE, $ B( K+2, 1 ), LDB, A( K+2, K ), 1, CONE, $ B( K, 1 ), LDB ) END IF * * Multiply by the diagonal block if non-unit. * IF( NOUNIT ) THEN D11 = A( K, K ) D22 = A( K+1, K+1 ) D21 = A( K+1, K ) D12 = D21 DO 110 J = 1, NRHS T1 = B( K, J ) T2 = B( K+1, J ) B( K, J ) = D11*T1 + D12*T2 B( K+1, J ) = D21*T1 + D22*T2 110 CONTINUE END IF K = K + 2 END IF GO TO 100 120 CONTINUE END IF END IF RETURN * * End of ZLAVSY_ROOK * END