Annotation of rpl/lapack/lapack/zhesv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
! 2: $ LWORK, INFO )
! 3: *
! 4: * -- LAPACK driver routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER UPLO
! 11: INTEGER INFO, LDA, LDB, LWORK, N, NRHS
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IPIV( * )
! 15: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * ZHESV computes the solution to a complex system of linear equations
! 22: * A * X = B,
! 23: * where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
! 24: * matrices.
! 25: *
! 26: * The diagonal pivoting method is used to factor A as
! 27: * A = U * D * U**H, if UPLO = 'U', or
! 28: * A = L * D * L**H, if UPLO = 'L',
! 29: * where U (or L) is a product of permutation and unit upper (lower)
! 30: * triangular matrices, and D is Hermitian and block diagonal with
! 31: * 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then
! 32: * used to solve the system of equations A * X = B.
! 33: *
! 34: * Arguments
! 35: * =========
! 36: *
! 37: * UPLO (input) CHARACTER*1
! 38: * = 'U': Upper triangle of A is stored;
! 39: * = 'L': Lower triangle of A is stored.
! 40: *
! 41: * N (input) INTEGER
! 42: * The number of linear equations, i.e., the order of the
! 43: * matrix A. N >= 0.
! 44: *
! 45: * NRHS (input) INTEGER
! 46: * The number of right hand sides, i.e., the number of columns
! 47: * of the matrix B. NRHS >= 0.
! 48: *
! 49: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
! 50: * On entry, the Hermitian matrix A. If UPLO = 'U', the leading
! 51: * N-by-N upper triangular part of A contains the upper
! 52: * triangular part of the matrix A, and the strictly lower
! 53: * triangular part of A is not referenced. If UPLO = 'L', the
! 54: * leading N-by-N lower triangular part of A contains the lower
! 55: * triangular part of the matrix A, and the strictly upper
! 56: * triangular part of A is not referenced.
! 57: *
! 58: * On exit, if INFO = 0, the block diagonal matrix D and the
! 59: * multipliers used to obtain the factor U or L from the
! 60: * factorization A = U*D*U**H or A = L*D*L**H as computed by
! 61: * ZHETRF.
! 62: *
! 63: * LDA (input) INTEGER
! 64: * The leading dimension of the array A. LDA >= max(1,N).
! 65: *
! 66: * IPIV (output) INTEGER array, dimension (N)
! 67: * Details of the interchanges and the block structure of D, as
! 68: * determined by ZHETRF. If IPIV(k) > 0, then rows and columns
! 69: * k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
! 70: * diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
! 71: * then rows and columns k-1 and -IPIV(k) were interchanged and
! 72: * D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
! 73: * IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
! 74: * -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
! 75: * diagonal block.
! 76: *
! 77: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 78: * On entry, the N-by-NRHS right hand side matrix B.
! 79: * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 80: *
! 81: * LDB (input) INTEGER
! 82: * The leading dimension of the array B. LDB >= max(1,N).
! 83: *
! 84: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 85: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 86: *
! 87: * LWORK (input) INTEGER
! 88: * The length of WORK. LWORK >= 1, and for best performance
! 89: * LWORK >= max(1,N*NB), where NB is the optimal blocksize for
! 90: * ZHETRF.
! 91: *
! 92: * If LWORK = -1, then a workspace query is assumed; the routine
! 93: * only calculates the optimal size of the WORK array, returns
! 94: * this value as the first entry of the WORK array, and no error
! 95: * message related to LWORK is issued by XERBLA.
! 96: *
! 97: * INFO (output) INTEGER
! 98: * = 0: successful exit
! 99: * < 0: if INFO = -i, the i-th argument had an illegal value
! 100: * > 0: if INFO = i, D(i,i) is exactly zero. The factorization
! 101: * has been completed, but the block diagonal matrix D is
! 102: * exactly singular, so the solution could not be computed.
! 103: *
! 104: * =====================================================================
! 105: *
! 106: * .. Local Scalars ..
! 107: LOGICAL LQUERY
! 108: INTEGER LWKOPT, NB
! 109: * ..
! 110: * .. External Functions ..
! 111: LOGICAL LSAME
! 112: INTEGER ILAENV
! 113: EXTERNAL LSAME, ILAENV
! 114: * ..
! 115: * .. External Subroutines ..
! 116: EXTERNAL XERBLA, ZHETRF, ZHETRS
! 117: * ..
! 118: * .. Intrinsic Functions ..
! 119: INTRINSIC MAX
! 120: * ..
! 121: * .. Executable Statements ..
! 122: *
! 123: * Test the input parameters.
! 124: *
! 125: INFO = 0
! 126: LQUERY = ( LWORK.EQ.-1 )
! 127: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 128: INFO = -1
! 129: ELSE IF( N.LT.0 ) THEN
! 130: INFO = -2
! 131: ELSE IF( NRHS.LT.0 ) THEN
! 132: INFO = -3
! 133: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 134: INFO = -5
! 135: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 136: INFO = -8
! 137: ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
! 138: INFO = -10
! 139: END IF
! 140: *
! 141: IF( INFO.EQ.0 ) THEN
! 142: IF( N.EQ.0 ) THEN
! 143: LWKOPT = 1
! 144: ELSE
! 145: NB = ILAENV( 1, 'ZHETRF', UPLO, N, -1, -1, -1 )
! 146: LWKOPT = N*NB
! 147: END IF
! 148: WORK( 1 ) = LWKOPT
! 149: END IF
! 150: *
! 151: IF( INFO.NE.0 ) THEN
! 152: CALL XERBLA( 'ZHESV ', -INFO )
! 153: RETURN
! 154: ELSE IF( LQUERY ) THEN
! 155: RETURN
! 156: END IF
! 157: *
! 158: * Compute the factorization A = U*D*U' or A = L*D*L'.
! 159: *
! 160: CALL ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
! 161: IF( INFO.EQ.0 ) THEN
! 162: *
! 163: * Solve the system A*X = B, overwriting B with X.
! 164: *
! 165: CALL ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
! 166: *
! 167: END IF
! 168: *
! 169: WORK( 1 ) = LWKOPT
! 170: *
! 171: RETURN
! 172: *
! 173: * End of ZHESV
! 174: *
! 175: END
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