1 SUBROUTINE ZPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
2 *
3 * -- LAPACK driver routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
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**H *U or A = L*L**H.
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
2 *
3 * -- LAPACK driver routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
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**H *U or A = L*L**H.
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