1 SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, 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 INTEGER IPIV( * )
14 DOUBLE PRECISION AP( * ), B( LDB, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DSPSV computes the solution to a real system of linear equations
21 * A * X = B,
22 * where A is an N-by-N symmetric matrix stored in packed format and X
23 * and B are N-by-NRHS matrices.
24 *
25 * The diagonal pivoting method is used to factor A as
26 * A = U * D * U**T, if UPLO = 'U', or
27 * A = L * D * L**T, if UPLO = 'L',
28 * where U (or L) is a product of permutation and unit upper (lower)
29 * triangular matrices, D is symmetric and block diagonal with 1-by-1
30 * and 2-by-2 diagonal blocks. The factored form of A is then used to
31 * solve the system of equations A * X = B.
32 *
33 * Arguments
34 * =========
35 *
36 * UPLO (input) CHARACTER*1
37 * = 'U': Upper triangle of A is stored;
38 * = 'L': Lower triangle of A is stored.
39 *
40 * N (input) INTEGER
41 * The number of linear equations, i.e., the order of the
42 * matrix A. N >= 0.
43 *
44 * NRHS (input) INTEGER
45 * The number of right hand sides, i.e., the number of columns
46 * of the matrix B. NRHS >= 0.
47 *
48 * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
49 * On entry, the upper or lower triangle of the symmetric matrix
50 * A, packed columnwise in a linear array. The j-th column of A
51 * is stored in the array AP as follows:
52 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
53 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
54 * See below for further details.
55 *
56 * On exit, the block diagonal matrix D and the multipliers used
57 * to obtain the factor U or L from the factorization
58 * A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
59 * a packed triangular matrix in the same storage format as A.
60 *
61 * IPIV (output) INTEGER array, dimension (N)
62 * Details of the interchanges and the block structure of D, as
63 * determined by DSPTRF. If IPIV(k) > 0, then rows and columns
64 * k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
65 * diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
66 * then rows and columns k-1 and -IPIV(k) were interchanged and
67 * D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
68 * IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
69 * -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
70 * diagonal block.
71 *
72 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
73 * On entry, the N-by-NRHS right hand side matrix B.
74 * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
75 *
76 * LDB (input) INTEGER
77 * The leading dimension of the array B. LDB >= max(1,N).
78 *
79 * INFO (output) INTEGER
80 * = 0: successful exit
81 * < 0: if INFO = -i, the i-th argument had an illegal value
82 * > 0: if INFO = i, D(i,i) is exactly zero. The factorization
83 * has been completed, but the block diagonal matrix D is
84 * exactly singular, so the solution could not be
85 * computed.
86 *
87 * Further Details
88 * ===============
89 *
90 * The packed storage scheme is illustrated by the following example
91 * when N = 4, UPLO = 'U':
92 *
93 * Two-dimensional storage of the symmetric matrix A:
94 *
95 * a11 a12 a13 a14
96 * a22 a23 a24
97 * a33 a34 (aij = aji)
98 * a44
99 *
100 * Packed storage of the upper triangle of A:
101 *
102 * AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
103 *
104 * =====================================================================
105 *
106 * .. External Functions ..
107 LOGICAL LSAME
108 EXTERNAL LSAME
109 * ..
110 * .. External Subroutines ..
111 EXTERNAL DSPTRF, DSPTRS, XERBLA
112 * ..
113 * .. Intrinsic Functions ..
114 INTRINSIC MAX
115 * ..
116 * .. Executable Statements ..
117 *
118 * Test the input parameters.
119 *
120 INFO = 0
121 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
122 INFO = -1
123 ELSE IF( N.LT.0 ) THEN
124 INFO = -2
125 ELSE IF( NRHS.LT.0 ) THEN
126 INFO = -3
127 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
128 INFO = -7
129 END IF
130 IF( INFO.NE.0 ) THEN
131 CALL XERBLA( 'DSPSV ', -INFO )
132 RETURN
133 END IF
134 *
135 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
136 *
137 CALL DSPTRF( UPLO, N, AP, IPIV, INFO )
138 IF( INFO.EQ.0 ) THEN
139 *
140 * Solve the system A*X = B, overwriting B with X.
141 *
142 CALL DSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
143 *
144 END IF
145 RETURN
146 *
147 * End of DSPSV
148 *
149 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 INTEGER IPIV( * )
14 DOUBLE PRECISION AP( * ), B( LDB, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DSPSV computes the solution to a real system of linear equations
21 * A * X = B,
22 * where A is an N-by-N symmetric matrix stored in packed format and X
23 * and B are N-by-NRHS matrices.
24 *
25 * The diagonal pivoting method is used to factor A as
26 * A = U * D * U**T, if UPLO = 'U', or
27 * A = L * D * L**T, if UPLO = 'L',
28 * where U (or L) is a product of permutation and unit upper (lower)
29 * triangular matrices, D is symmetric and block diagonal with 1-by-1
30 * and 2-by-2 diagonal blocks. The factored form of A is then used to
31 * solve the system of equations A * X = B.
32 *
33 * Arguments
34 * =========
35 *
36 * UPLO (input) CHARACTER*1
37 * = 'U': Upper triangle of A is stored;
38 * = 'L': Lower triangle of A is stored.
39 *
40 * N (input) INTEGER
41 * The number of linear equations, i.e., the order of the
42 * matrix A. N >= 0.
43 *
44 * NRHS (input) INTEGER
45 * The number of right hand sides, i.e., the number of columns
46 * of the matrix B. NRHS >= 0.
47 *
48 * AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
49 * On entry, the upper or lower triangle of the symmetric matrix
50 * A, packed columnwise in a linear array. The j-th column of A
51 * is stored in the array AP as follows:
52 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
53 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
54 * See below for further details.
55 *
56 * On exit, the block diagonal matrix D and the multipliers used
57 * to obtain the factor U or L from the factorization
58 * A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
59 * a packed triangular matrix in the same storage format as A.
60 *
61 * IPIV (output) INTEGER array, dimension (N)
62 * Details of the interchanges and the block structure of D, as
63 * determined by DSPTRF. If IPIV(k) > 0, then rows and columns
64 * k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
65 * diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
66 * then rows and columns k-1 and -IPIV(k) were interchanged and
67 * D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
68 * IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
69 * -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
70 * diagonal block.
71 *
72 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
73 * On entry, the N-by-NRHS right hand side matrix B.
74 * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
75 *
76 * LDB (input) INTEGER
77 * The leading dimension of the array B. LDB >= max(1,N).
78 *
79 * INFO (output) INTEGER
80 * = 0: successful exit
81 * < 0: if INFO = -i, the i-th argument had an illegal value
82 * > 0: if INFO = i, D(i,i) is exactly zero. The factorization
83 * has been completed, but the block diagonal matrix D is
84 * exactly singular, so the solution could not be
85 * computed.
86 *
87 * Further Details
88 * ===============
89 *
90 * The packed storage scheme is illustrated by the following example
91 * when N = 4, UPLO = 'U':
92 *
93 * Two-dimensional storage of the symmetric matrix A:
94 *
95 * a11 a12 a13 a14
96 * a22 a23 a24
97 * a33 a34 (aij = aji)
98 * a44
99 *
100 * Packed storage of the upper triangle of A:
101 *
102 * AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
103 *
104 * =====================================================================
105 *
106 * .. External Functions ..
107 LOGICAL LSAME
108 EXTERNAL LSAME
109 * ..
110 * .. External Subroutines ..
111 EXTERNAL DSPTRF, DSPTRS, XERBLA
112 * ..
113 * .. Intrinsic Functions ..
114 INTRINSIC MAX
115 * ..
116 * .. Executable Statements ..
117 *
118 * Test the input parameters.
119 *
120 INFO = 0
121 IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
122 INFO = -1
123 ELSE IF( N.LT.0 ) THEN
124 INFO = -2
125 ELSE IF( NRHS.LT.0 ) THEN
126 INFO = -3
127 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
128 INFO = -7
129 END IF
130 IF( INFO.NE.0 ) THEN
131 CALL XERBLA( 'DSPSV ', -INFO )
132 RETURN
133 END IF
134 *
135 * Compute the factorization A = U*D*U**T or A = L*D*L**T.
136 *
137 CALL DSPTRF( UPLO, N, AP, IPIV, INFO )
138 IF( INFO.EQ.0 ) THEN
139 *
140 * Solve the system A*X = B, overwriting B with X.
141 *
142 CALL DSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
143 *
144 END IF
145 RETURN
146 *
147 * End of DSPSV
148 *
149 END