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Diffstat (limited to 'SRC/zspsv.f')
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diff --git a/SRC/zspsv.f b/SRC/zspsv.f new file mode 100644 index 00000000..46f73786 --- /dev/null +++ b/SRC/zspsv.f @@ -0,0 +1,148 @@ + SUBROUTINE ZSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) +* +* -- LAPACK driver routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, LDB, N, NRHS +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + COMPLEX*16 AP( * ), B( LDB, * ) +* .. +* +* Purpose +* ======= +* +* ZSPSV computes the solution to a complex system of linear equations +* A * X = B, +* where A is an N-by-N symmetric matrix stored in packed format and X +* and B are N-by-NRHS matrices. +* +* The diagonal pivoting method is used to factor A as +* A = U * D * U**T, if UPLO = 'U', or +* A = L * D * L**T, if UPLO = 'L', +* where U (or L) is a product of permutation and unit upper (lower) +* triangular matrices, D is symmetric and block diagonal with 1-by-1 +* and 2-by-2 diagonal blocks. The factored form of A is then used to +* solve the system of equations A * X = B. +* +* Arguments +* ========= +* +* UPLO (input) CHARACTER*1 +* = 'U': Upper triangle of A is stored; +* = 'L': Lower triangle of A is stored. +* +* N (input) INTEGER +* The number of linear equations, i.e., the order of the +* matrix A. N >= 0. +* +* NRHS (input) INTEGER +* The number of right hand sides, i.e., the number of columns +* of the matrix B. NRHS >= 0. +* +* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) +* On entry, the upper or lower triangle of the symmetric matrix +* A, packed columnwise in a linear array. The j-th column of A +* is stored in the array AP as follows: +* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; +* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. +* See below for further details. +* +* On exit, the block diagonal matrix D and the multipliers used +* to obtain the factor U or L from the factorization +* A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as +* a packed triangular matrix in the same storage format as A. +* +* IPIV (output) INTEGER array, dimension (N) +* Details of the interchanges and the block structure of D, as +* determined by ZSPTRF. If IPIV(k) > 0, then rows and columns +* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 +* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, +* then rows and columns k-1 and -IPIV(k) were interchanged and +* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and +* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and +* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 +* diagonal block. +* +* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) +* On entry, the N-by-NRHS right hand side matrix B. +* On exit, if INFO = 0, the N-by-NRHS solution matrix X. +* +* LDB (input) INTEGER +* The leading dimension of the array B. LDB >= max(1,N). +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* > 0: if INFO = i, D(i,i) is exactly zero. The factorization +* has been completed, but the block diagonal matrix D is +* exactly singular, so the solution could not be +* computed. +* +* Further Details +* =============== +* +* The packed storage scheme is illustrated by the following example +* when N = 4, UPLO = 'U': +* +* Two-dimensional storage of the symmetric matrix A: +* +* a11 a12 a13 a14 +* a22 a23 a24 +* a33 a34 (aij = aji) +* a44 +* +* Packed storage of the upper triangle of A: +* +* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] +* +* ===================================================================== +* +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA, ZSPTRF, ZSPTRS +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -3 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'ZSPSV ', -INFO ) + RETURN + END IF +* +* Compute the factorization A = U*D*U' or A = L*D*L'. +* + CALL ZSPTRF( UPLO, N, AP, IPIV, INFO ) + IF( INFO.EQ.0 ) THEN +* +* Solve the system A*X = B, overwriting B with X. +* + CALL ZSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO ) +* + END IF + RETURN +* +* End of ZSPSV +* + END |