Annotation of rpl/lapack/lapack/zppsv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
! 2: *
! 3: * -- LAPACK driver routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER UPLO
! 10: INTEGER INFO, LDB, N, NRHS
! 11: * ..
! 12: * .. Array Arguments ..
! 13: COMPLEX*16 AP( * ), B( LDB, * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * ZPPSV computes the solution to a complex system of linear equations
! 20: * A * X = B,
! 21: * where A is an N-by-N Hermitian positive definite matrix stored in
! 22: * packed format and X and B are N-by-NRHS matrices.
! 23: *
! 24: * The Cholesky decomposition is used to factor A as
! 25: * A = U**H* U, if UPLO = 'U', or
! 26: * A = L * L**H, if UPLO = 'L',
! 27: * where U is an upper triangular matrix and L is a lower triangular
! 28: * matrix. The factored form of A is then used to solve the system of
! 29: * equations A * X = B.
! 30: *
! 31: * Arguments
! 32: * =========
! 33: *
! 34: * UPLO (input) CHARACTER*1
! 35: * = 'U': Upper triangle of A is stored;
! 36: * = 'L': Lower triangle of A is stored.
! 37: *
! 38: * N (input) INTEGER
! 39: * The number of linear equations, i.e., the order of the
! 40: * matrix A. N >= 0.
! 41: *
! 42: * NRHS (input) INTEGER
! 43: * The number of right hand sides, i.e., the number of columns
! 44: * of the matrix B. NRHS >= 0.
! 45: *
! 46: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
! 47: * On entry, the upper or lower triangle of the Hermitian matrix
! 48: * A, packed columnwise in a linear array. The j-th column of A
! 49: * is stored in the array AP as follows:
! 50: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 51: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
! 52: * See below for further details.
! 53: *
! 54: * On exit, if INFO = 0, the factor U or L from the Cholesky
! 55: * factorization A = U**H*U or A = L*L**H, in the same storage
! 56: * format as A.
! 57: *
! 58: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
! 59: * On entry, the N-by-NRHS right hand side matrix B.
! 60: * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
! 61: *
! 62: * LDB (input) INTEGER
! 63: * The leading dimension of the array B. LDB >= max(1,N).
! 64: *
! 65: * INFO (output) INTEGER
! 66: * = 0: successful exit
! 67: * < 0: if INFO = -i, the i-th argument had an illegal value
! 68: * > 0: if INFO = i, the leading minor of order i of A is not
! 69: * positive definite, so the factorization could not be
! 70: * completed, and the solution has not been computed.
! 71: *
! 72: * Further Details
! 73: * ===============
! 74: *
! 75: * The packed storage scheme is illustrated by the following example
! 76: * when N = 4, UPLO = 'U':
! 77: *
! 78: * Two-dimensional storage of the Hermitian matrix A:
! 79: *
! 80: * a11 a12 a13 a14
! 81: * a22 a23 a24
! 82: * a33 a34 (aij = conjg(aji))
! 83: * a44
! 84: *
! 85: * Packed storage of the upper triangle of A:
! 86: *
! 87: * AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
! 88: *
! 89: * =====================================================================
! 90: *
! 91: * .. External Functions ..
! 92: LOGICAL LSAME
! 93: EXTERNAL LSAME
! 94: * ..
! 95: * .. External Subroutines ..
! 96: EXTERNAL XERBLA, ZPPTRF, ZPPTRS
! 97: * ..
! 98: * .. Intrinsic Functions ..
! 99: INTRINSIC MAX
! 100: * ..
! 101: * .. Executable Statements ..
! 102: *
! 103: * Test the input parameters.
! 104: *
! 105: INFO = 0
! 106: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 107: INFO = -1
! 108: ELSE IF( N.LT.0 ) THEN
! 109: INFO = -2
! 110: ELSE IF( NRHS.LT.0 ) THEN
! 111: INFO = -3
! 112: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
! 113: INFO = -6
! 114: END IF
! 115: IF( INFO.NE.0 ) THEN
! 116: CALL XERBLA( 'ZPPSV ', -INFO )
! 117: RETURN
! 118: END IF
! 119: *
! 120: * Compute the Cholesky factorization A = U'*U or A = L*L'.
! 121: *
! 122: CALL ZPPTRF( UPLO, N, AP, INFO )
! 123: IF( INFO.EQ.0 ) THEN
! 124: *
! 125: * Solve the system A*X = B, overwriting B with X.
! 126: *
! 127: CALL ZPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
! 128: *
! 129: END IF
! 130: RETURN
! 131: *
! 132: * End of ZPPSV
! 133: *
! 134: END
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