diff --git a/lib/linalg/dposv.f b/lib/linalg/dposv.f new file mode 100644 index 0000000000..ee2988e6fd --- /dev/null +++ b/lib/linalg/dposv.f @@ -0,0 +1,190 @@ +*> \brief DPOSV computes the solution to system of linear equations A * X = B for PO matrices +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DPOSV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DPOSV computes the solution to a real system of linear equations +*> A * X = B, +*> where A is an N-by-N symmetric positive definite matrix and X and B +*> are N-by-NRHS matrices. +*> +*> The Cholesky decomposition is used to factor A as +*> A = U**T* U, if UPLO = 'U', or +*> A = L * L**T, if UPLO = 'L', +*> where U is an upper triangular matrix and L is a lower triangular +*> matrix. The factored form of A is then used to solve the system of +*> equations A * X = B. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of linear equations, i.e., 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,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the symmetric matrix A. If UPLO = 'U', the leading +*> N-by-N upper triangular part of A contains the upper +*> triangular part of the matrix A, and the strictly lower +*> triangular part of A is not referenced. If UPLO = 'L', the +*> leading N-by-N lower triangular part of A contains the lower +*> triangular part of the matrix A, and the strictly upper +*> triangular part of A is not referenced. +*> +*> On exit, if INFO = 0, the factor U or L from the Cholesky +*> factorization A = U**T*U or A = L*L**T. +*> \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 DOUBLE PRECISION array, dimension (LDB,NRHS) +*> On entry, the N-by-NRHS right hand side matrix B. +*> On exit, if INFO = 0, the N-by-NRHS 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 leading minor of order i of A is not +*> positive definite, so the factorization could not be +*> completed, and the solution has not been computed. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup doublePOsolve +* +* ===================================================================== + SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) +* +* -- LAPACK driver 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 UPLO + INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* ===================================================================== +* +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL DPOTRF, DPOTRS, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) 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, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DPOSV ', -INFO ) + RETURN + END IF +* +* Compute the Cholesky factorization A = U**T*U or A = L*L**T. +* + CALL DPOTRF( UPLO, N, A, LDA, INFO ) + IF( INFO.EQ.0 ) THEN +* +* Solve the system A*X = B, overwriting B with X. +* + CALL DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) +* + END IF + RETURN +* +* End of DPOSV +* + END diff --git a/lib/linalg/dpotrs.f b/lib/linalg/dpotrs.f new file mode 100644 index 0000000000..862ee078fd --- /dev/null +++ b/lib/linalg/dpotrs.f @@ -0,0 +1,201 @@ +*> \brief \b DPOTRS +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DPOTRS + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DPOTRS solves a system of linear equations A*X = B with a symmetric +*> positive definite matrix A using the Cholesky factorization +*> A = U**T*U or A = L*L**T computed by DPOTRF. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \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 DOUBLE PRECISION array, dimension (LDA,N) +*> The triangular factor U or L from the Cholesky factorization +*> A = U**T*U or A = L*L**T, as computed by DPOTRF. +*> \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 DOUBLE PRECISION array, dimension (LDB,NRHS) +*> On entry, the right hand side matrix B. +*> On exit, 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 +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \ingroup doublePOcomputational +* +* ===================================================================== + SUBROUTINE DPOTRS( UPLO, 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 UPLO + INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL UPPER +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL DTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + UPPER = LSAME( UPLO, 'U' ) + IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) 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, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DPOTRS', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 .OR. NRHS.EQ.0 ) + $ RETURN +* + IF( UPPER ) THEN +* +* Solve A*X = B where A = U**T *U. +* +* Solve U**T *X = B, overwriting B with X. +* + CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS, + $ ONE, A, LDA, B, LDB ) +* +* Solve U*X = B, overwriting B with X. +* + CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, + $ NRHS, ONE, A, LDA, B, LDB ) + ELSE +* +* Solve A*X = B where A = L*L**T. +* +* Solve L*X = B, overwriting B with X. +* + CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N, + $ NRHS, ONE, A, LDA, B, LDB ) +* +* Solve L**T *X = B, overwriting B with X. +* + CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', N, NRHS, + $ ONE, A, LDA, B, LDB ) + END IF +* + RETURN +* +* End of DPOTRS +* + END