Annotation of rpl/lapack/lapack/dspsv.f, revision 1.8
1.1 bertrand 1: SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
2: *
1.8 ! bertrand 3: * -- LAPACK driver routine (version 3.3.1) --
1.1 bertrand 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 6: * -- April 2011 --
1.1 bertrand 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: *
1.8 ! bertrand 135: * Compute the factorization A = U*D*U**T or A = L*D*L**T.
1.1 bertrand 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
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