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Mon Aug 7 08:39:04 2023 UTC (8 months, 3 weeks ago) by bertrand
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CVS tags: rpl-4_1_35, rpl-4_1_34, HEAD

Première mise à jour de lapack et blas.

1: *> \brief <b> DPOSV computes the solution to system of linear equations A * X = B for PO matrices</b> 2: * 3: * =========== DOCUMENTATION =========== 4: * 5: * Online html documentation available at 6: * http://www.netlib.org/lapack/explore-html/ 7: * 8: *> \htmlonly 9: *> Download DPOSV + dependencies 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dposv.f"> 11: *> [TGZ]</a> 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dposv.f"> 13: *> [ZIP]</a> 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dposv.f"> 15: *> [TXT]</a> 16: *> \endhtmlonly 17: * 18: * Definition: 19: * =========== 20: * 21: * SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) 22: * 23: * .. Scalar Arguments .. 24: * CHARACTER UPLO 25: * INTEGER INFO, LDA, LDB, N, NRHS 26: * .. 27: * .. Array Arguments .. 28: * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) 29: * .. 30: * 31: * 32: *> \par Purpose: 33: * ============= 34: *> 35: *> \verbatim 36: *> 37: *> DPOSV computes the solution to a real system of linear equations 38: *> A * X = B, 39: *> where A is an N-by-N symmetric positive definite matrix and X and B 40: *> are N-by-NRHS matrices. 41: *> 42: *> The Cholesky decomposition is used to factor A as 43: *> A = U**T* U, if UPLO = 'U', or 44: *> A = L * L**T, if UPLO = 'L', 45: *> where U is an upper triangular matrix and L is a lower triangular 46: *> matrix. The factored form of A is then used to solve the system of 47: *> equations A * X = B. 48: *> \endverbatim 49: * 50: * Arguments: 51: * ========== 52: * 53: *> \param[in] UPLO 54: *> \verbatim 55: *> UPLO is CHARACTER*1 56: *> = 'U': Upper triangle of A is stored; 57: *> = 'L': Lower triangle of A is stored. 58: *> \endverbatim 59: *> 60: *> \param[in] N 61: *> \verbatim 62: *> N is INTEGER 63: *> The number of linear equations, i.e., the order of the 64: *> matrix A. N >= 0. 65: *> \endverbatim 66: *> 67: *> \param[in] NRHS 68: *> \verbatim 69: *> NRHS is INTEGER 70: *> The number of right hand sides, i.e., the number of columns 71: *> of the matrix B. NRHS >= 0. 72: *> \endverbatim 73: *> 74: *> \param[in,out] A 75: *> \verbatim 76: *> A is DOUBLE PRECISION array, dimension (LDA,N) 77: *> On entry, the symmetric matrix A. If UPLO = 'U', the leading 78: *> N-by-N upper triangular part of A contains the upper 79: *> triangular part of the matrix A, and the strictly lower 80: *> triangular part of A is not referenced. If UPLO = 'L', the 81: *> leading N-by-N lower triangular part of A contains the lower 82: *> triangular part of the matrix A, and the strictly upper 83: *> triangular part of A is not referenced. 84: *> 85: *> On exit, if INFO = 0, the factor U or L from the Cholesky 86: *> factorization A = U**T*U or A = L*L**T. 87: *> \endverbatim 88: *> 89: *> \param[in] LDA 90: *> \verbatim 91: *> LDA is INTEGER 92: *> The leading dimension of the array A. LDA >= max(1,N). 93: *> \endverbatim 94: *> 95: *> \param[in,out] B 96: *> \verbatim 97: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) 98: *> On entry, the N-by-NRHS right hand side matrix B. 99: *> On exit, if INFO = 0, the N-by-NRHS solution matrix X. 100: *> \endverbatim 101: *> 102: *> \param[in] LDB 103: *> \verbatim 104: *> LDB is INTEGER 105: *> The leading dimension of the array B. LDB >= max(1,N). 106: *> \endverbatim 107: *> 108: *> \param[out] INFO 109: *> \verbatim 110: *> INFO is INTEGER 111: *> = 0: successful exit 112: *> < 0: if INFO = -i, the i-th argument had an illegal value 113: *> > 0: if INFO = i, the leading minor of order i of A is not 114: *> positive definite, so the factorization could not be 115: *> completed, and the solution has not been computed. 116: *> \endverbatim 117: * 118: * Authors: 119: * ======== 120: * 121: *> \author Univ. of Tennessee 122: *> \author Univ. of California Berkeley 123: *> \author Univ. of Colorado Denver 124: *> \author NAG Ltd. 125: * 126: *> \ingroup doublePOsolve 127: * 128: * ===================================================================== 129: SUBROUTINE DPOSV( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) 130: * 131: * -- LAPACK driver routine -- 132: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 134: * 135: * .. Scalar Arguments .. 136: CHARACTER UPLO 137: INTEGER INFO, LDA, LDB, N, NRHS 138: * .. 139: * .. Array Arguments .. 140: DOUBLE PRECISION A( LDA, * ), B( LDB, * ) 141: * .. 142: * 143: * ===================================================================== 144: * 145: * .. External Functions .. 146: LOGICAL LSAME 147: EXTERNAL LSAME 148: * .. 149: * .. External Subroutines .. 150: EXTERNAL DPOTRF, DPOTRS, XERBLA 151: * .. 152: * .. Intrinsic Functions .. 153: INTRINSIC MAX 154: * .. 155: * .. Executable Statements .. 156: * 157: * Test the input parameters. 158: * 159: INFO = 0 160: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 161: INFO = -1 162: ELSE IF( N.LT.0 ) THEN 163: INFO = -2 164: ELSE IF( NRHS.LT.0 ) THEN 165: INFO = -3 166: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN 167: INFO = -5 168: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN 169: INFO = -7 170: END IF 171: IF( INFO.NE.0 ) THEN 172: CALL XERBLA( 'DPOSV ', -INFO ) 173: RETURN 174: END IF 175: * 176: * Compute the Cholesky factorization A = U**T*U or A = L*L**T. 177: * 178: CALL DPOTRF( UPLO, N, A, LDA, INFO ) 179: IF( INFO.EQ.0 ) THEN 180: * 181: * Solve the system A*X = B, overwriting B with X. 182: * 183: CALL DPOTRS( UPLO, N, NRHS, A, LDA, B, LDB, INFO ) 184: * 185: END IF 186: RETURN 187: * 188: * End of DPOSV 189: * 190: END