*> \brief \b ZTRTRS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZTRTRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, * INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, TRANS, UPLO * INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTRTRS solves a triangular system of the form *> *> A * X = B, A**T * X = B, or A**H * X = B, *> *> where A is a triangular matrix of order N, and B is an N-by-NRHS *> matrix. A check is made to verify that A is nonsingular. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': A is upper triangular; *> = 'L': A is lower triangular. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the form of the system of equations: *> = 'N': A * X = B (No transpose) *> = 'T': A**T * X = B (Transpose) *> = 'C': A**H * X = B (Conjugate transpose) *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> = 'N': A is non-unit triangular; *> = 'U': A is unit triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order 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 the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The triangular matrix A. If UPLO = 'U', the leading N-by-N *> upper triangular part of the array A contains the upper *> triangular matrix, and the strictly lower triangular part of *> A is not referenced. If UPLO = 'L', the leading N-by-N lower *> triangular part of the array A contains the lower triangular *> matrix, and the strictly upper triangular part of A is not *> referenced. If DIAG = 'U', the diagonal elements of A are *> also not referenced and are assumed to be 1. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,NRHS) *> On entry, the right hand side matrix B. *> On exit, if INFO = 0, the solution matrix X. *> \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 = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the i-th diagonal element of A is zero, *> indicating that the matrix is singular and the solutions *> X have not been computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, \$ INFO ) * * -- LAPACK computational 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 .. COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), \$ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZTRSM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 NOUNIT = LSAME( DIAG, 'N' ) IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT. \$ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( NRHS.LT.0 ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZTRTRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Check for singularity. * IF( NOUNIT ) THEN DO 10 INFO = 1, N IF( A( INFO, INFO ).EQ.ZERO ) \$ RETURN 10 CONTINUE END IF INFO = 0 * * Solve A * x = b, A**T * x = b, or A**H * x = b. * CALL ZTRSM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B, \$ LDB ) * RETURN * * End of ZTRTRS * END