*> \brief \b ZLAVHP * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZLAVHP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, * INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, TRANS, UPLO * INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAVHP performs one of the matrix-vector operations *> x := A*x or x := A^H*x, *> where x is an N element vector and A is one of the factors *> from the symmetric factorization computed by ZHPTRF. *> ZHPTRF produces a factorization of the form *> U * D * U^H or L * D * L^H, *> where U (or L) is a product of permutation and unit upper (lower) *> triangular matrices, U^H (or L^H) is the conjugate transpose of *> U (or L), and D is Hermitian and block diagonal with 1 x 1 and *> 2 x 2 diagonal blocks. The multipliers for the transformations *> and the upper or lower triangular parts of the diagonal blocks *> are stored columnwise in packed format in the linear array A. *> *> If TRANS = 'N' or 'n', ZLAVHP multiplies either by U or U * D *> (or L or L * D). *> If TRANS = 'C' or 'c', ZLAVHP multiplies either by U^H or D * U^H *> (or L^H or D * L^H ). *> \endverbatim * * Arguments: * ========== * *> \verbatim *> UPLO - CHARACTER*1 *> On entry, UPLO specifies whether the triangular matrix *> stored in A is upper or lower triangular. *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. *> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'C' or 'c' x := A^H*x. *> Unchanged on exit. *> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices, as follows: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. *> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. *> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. *> *> A - COMPLEX*16 array, dimension( N*(N+1)/2 ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a packed triangular matrix. *> Unchanged on exit. *> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by ZSPTRF or ZHPTRF. *> If IPIV( K ) = K, no interchange was done. *> If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter- *> changed with row IPIV( K ) and a 1 x 1 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> *> B - 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. *> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. *> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. *> A negative value, say -K, indicates that the K-th argument *> has an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_lin * * ===================================================================== SUBROUTINE ZLAVHP( UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, $ INFO ) * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, TRANS, UPLO INTEGER INFO, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL NOUNIT INTEGER J, K, KC, KCNEXT, KP COMPLEX*16 D11, D12, D21, D22, T1, T2 * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMV, ZGERU, ZLACGV, ZSCAL, ZSWAP * .. * .. Intrinsic Functions .. INTRINSIC ABS, DCONJG, 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, 'C' ) ) $ 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( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLAVHP ', -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 KC = 1 10 CONTINUE IF( K.GT.N ) $ GO TO 30 * * 1 x 1 pivot block * IF( IPIV( K ).GT.0 ) THEN * * Multiply by the diagonal element if forming U * D. * IF( NOUNIT ) $ CALL ZSCAL( NRHS, A( KC+K-1 ), 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, ONE, A( KC ), 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 KC = KC + K K = K + 1 ELSE * * 2 x 2 pivot block * KCNEXT = KC + K * * Multiply by the diagonal block if forming U * D. * IF( NOUNIT ) THEN D11 = A( KCNEXT-1 ) D22 = A( KCNEXT+K ) D12 = A( KCNEXT+K-1 ) D21 = DCONJG( 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, ONE, A( KC ), 1, B( K, 1 ), $ LDB, B( 1, 1 ), LDB ) CALL ZGERU( K-1, NRHS, ONE, A( KCNEXT ), 1, $ B( K+1, 1 ), LDB, B( 1, 1 ), LDB ) * * Interchange if P(K) != I. * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) END IF KC = KCNEXT + K + 1 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 KC = N*( N+1 ) / 2 + 1 40 CONTINUE IF( K.LT.1 ) $ GO TO 60 KC = KC - ( N-K+1 ) * * 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( KC ), 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, ONE, A( KC+1 ), 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: * KCNEXT = KC - ( N-K+2 ) * * Multiply by the diagonal block if forming L * D. * IF( NOUNIT ) THEN D11 = A( KCNEXT ) D22 = A( KC ) D21 = A( KCNEXT+1 ) D12 = DCONJG( 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, ONE, A( KC+1 ), 1, B( K, 1 ), $ LDB, B( K+1, 1 ), LDB ) CALL ZGERU( N-K, NRHS, ONE, A( KCNEXT+2 ), 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. * KP = ABS( IPIV( K ) ) IF( KP.NE.K ) $ CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) END IF KC = KCNEXT K = K - 2 END IF GO TO 40 60 CONTINUE END IF *------------------------------------------------- * * Compute B := A^H * B (conjugate transpose) * *------------------------------------------------- ELSE * * Form B := U^H*B * where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1)) * and U^H = inv(U^H(1))*P(1)* ... *inv(U^H(m))*P(m) * IF( LSAME( UPLO, 'U' ) ) THEN * * Loop backward applying the transformations. * K = N KC = N*( N+1 ) / 2 + 1 70 CONTINUE IF( K.LT.1 ) $ GO TO 90 KC = KC - K * * 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: * y := y - B' * conjg(x) * where x is a column of A and y is a row of B. * CALL ZLACGV( NRHS, B( K, 1 ), LDB ) CALL ZGEMV( 'Conjugate', K-1, NRHS, ONE, B, LDB, $ A( KC ), 1, ONE, B( K, 1 ), LDB ) CALL ZLACGV( NRHS, B( K, 1 ), LDB ) END IF IF( NOUNIT ) $ CALL ZSCAL( NRHS, A( KC+K-1 ), B( K, 1 ), LDB ) K = K - 1 * * 2 x 2 pivot block. * ELSE KCNEXT = KC - ( K-1 ) IF( K.GT.2 ) THEN * * Interchange if P(K) != I. * KP = ABS( IPIV( K ) ) IF( KP.NE.K-1 ) $ CALL ZSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), $ LDB ) * * Apply the transformations. * CALL ZLACGV( NRHS, B( K, 1 ), LDB ) CALL ZGEMV( 'Conjugate', K-2, NRHS, ONE, B, LDB, $ A( KC ), 1, ONE, B( K, 1 ), LDB ) CALL ZLACGV( NRHS, B( K, 1 ), LDB ) * CALL ZLACGV( NRHS, B( K-1, 1 ), LDB ) CALL ZGEMV( 'Conjugate', K-2, NRHS, ONE, B, LDB, $ A( KCNEXT ), 1, ONE, B( K-1, 1 ), LDB ) CALL ZLACGV( NRHS, B( K-1, 1 ), LDB ) END IF * * Multiply by the diagonal block if non-unit. * IF( NOUNIT ) THEN D11 = A( KC-1 ) D22 = A( KC+K-1 ) D12 = A( KC+K-2 ) D21 = DCONJG( 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 KC = KCNEXT K = K - 2 END IF GO TO 70 90 CONTINUE * * Form B := L^H*B * where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) * and L^H = inv(L(m))*P(m)* ... *inv(L(1))*P(1) * ELSE * * Loop forward applying the L-transformations. * K = 1 KC = 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 ZLACGV( NRHS, B( K, 1 ), LDB ) CALL ZGEMV( 'Conjugate', N-K, NRHS, ONE, B( K+1, 1 ), $ LDB, A( KC+1 ), 1, ONE, B( K, 1 ), LDB ) CALL ZLACGV( NRHS, B( K, 1 ), LDB ) END IF IF( NOUNIT ) $ CALL ZSCAL( NRHS, A( KC ), B( K, 1 ), LDB ) KC = KC + N - K + 1 K = K + 1 * * 2 x 2 pivot block. * ELSE KCNEXT = KC + N - K + 1 IF( K.LT.N-1 ) THEN * * Interchange if P(K) != I. * KP = ABS( IPIV( K ) ) IF( KP.NE.K+1 ) $ CALL ZSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), $ LDB ) * * Apply the transformation * CALL ZLACGV( NRHS, B( K+1, 1 ), LDB ) CALL ZGEMV( 'Conjugate', N-K-1, NRHS, ONE, $ B( K+2, 1 ), LDB, A( KCNEXT+1 ), 1, ONE, $ B( K+1, 1 ), LDB ) CALL ZLACGV( NRHS, B( K+1, 1 ), LDB ) * CALL ZLACGV( NRHS, B( K, 1 ), LDB ) CALL ZGEMV( 'Conjugate', N-K-1, NRHS, ONE, $ B( K+2, 1 ), LDB, A( KC+2 ), 1, ONE, $ B( K, 1 ), LDB ) CALL ZLACGV( NRHS, B( K, 1 ), LDB ) END IF * * Multiply by the diagonal block if non-unit. * IF( NOUNIT ) THEN D11 = A( KC ) D22 = A( KCNEXT ) D21 = A( KC+1 ) D12 = DCONJG( 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 KC = KCNEXT + ( N-K ) K = K + 2 END IF GO TO 100 120 CONTINUE END IF * END IF RETURN * * End of ZLAVHP * END