Annotation of rpl/lapack/lapack/dspsv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, 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: 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' or A = L*D*L'.
! 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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