1: SUBROUTINE DPPSV( 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: DOUBLE PRECISION AP( * ), B( LDB, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DPPSV computes the solution to a real system of linear equations
20: * A * X = B,
21: * where A is an N-by-N symmetric 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**T* U, if UPLO = 'U', or
26: * A = L * L**T, 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) DOUBLE PRECISION array, dimension (N*(N+1)/2)
47: * On entry, the upper or lower triangle of the symmetric 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**T*U or A = L*L**T, in the same storage
56: * format as A.
57: *
58: * B (input/output) DOUBLE PRECISION 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 symmetric 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 DPPTRF, DPPTRS, XERBLA
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( 'DPPSV ', -INFO )
117: RETURN
118: END IF
119: *
120: * Compute the Cholesky factorization A = U'*U or A = L*L'.
121: *
122: CALL DPPTRF( 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 DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
128: *
129: END IF
130: RETURN
131: *
132: * End of DPPSV
133: *
134: END
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